<!DOCTYPE article PUBLIC "-//NLM//DTD JATS (Z39.96) Journal Archiving and Interchange DTD v1.1 20151215//EN" "JATS-archivearticle1.dtd"> <article xmlns:ali="http://www.niso.org/schemas/ali/1.0/" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" article-type="research-article" dtd-version="1.1"><front><journal-meta><journal-id journal-id-type="nlm-ta">elife</journal-id><journal-id journal-id-type="publisher-id">eLife</journal-id><journal-title-group><journal-title>eLife</journal-title></journal-title-group><issn pub-type="epub" publication-format="electronic">2050-084X</issn><publisher><publisher-name>eLife Sciences Publications, Ltd</publisher-name></publisher></journal-meta><article-meta><article-id pub-id-type="publisher-id">52258</article-id><article-id pub-id-type="doi">10.7554/eLife.52258</article-id><article-categories><subj-group subj-group-type="display-channel"><subject>Research Article</subject></subj-group><subj-group subj-group-type="heading"><subject>Neuroscience</subject></subj-group></article-categories><title-group><article-title>Inter- and intra-animal variation in the integrative properties of stellate cells in the medial entorhinal cortex</article-title></title-group><contrib-group><contrib contrib-type="author" id="author-159263"><name><surname>Pastoll</surname><given-names>Hugh</given-names></name><xref ref-type="aff" rid="aff1">1</xref><xref ref-type="fn" rid="con1"/><xref ref-type="fn" rid="conf1"/></contrib><contrib contrib-type="author" id="author-131674"><name><surname>Garden</surname><given-names>Derek L</given-names></name><contrib-id authenticated="true" contrib-id-type="orcid">https://orcid.org/0000-0003-3336-3791</contrib-id><xref ref-type="aff" rid="aff1">1</xref><xref ref-type="fn" rid="con2"/><xref ref-type="fn" rid="conf1"/></contrib><contrib contrib-type="author" id="author-159264"><name><surname>Papastathopoulos</surname><given-names>Ioannis</given-names></name><xref ref-type="aff" rid="aff2">2</xref><xref ref-type="aff" rid="aff3">3</xref><xref ref-type="fn" rid="con3"/><xref ref-type="fn" rid="conf1"/></contrib><contrib contrib-type="author" id="author-159265"><name><surname>Sürmeli</surname><given-names>Gülşen</given-names></name><xref ref-type="aff" rid="aff1">1</xref><xref ref-type="fn" rid="con4"/><xref ref-type="fn" rid="conf1"/></contrib><contrib contrib-type="author" corresp="yes" id="author-149081"><name><surname>Nolan</surname><given-names>Matthew F</given-names></name><contrib-id authenticated="true" contrib-id-type="orcid">https://orcid.org/0000-0003-1062-6501</contrib-id><email>mattnolan@ed.ac.uk</email><xref ref-type="aff" rid="aff1">1</xref><xref ref-type="other" rid="fund1"/><xref ref-type="other" rid="fund2"/><xref ref-type="other" rid="fund3"/><xref ref-type="other" rid="fund4"/><xref ref-type="fn" rid="con5"/><xref ref-type="fn" rid="conf1"/></contrib><aff id="aff1"><label>1</label><institution>Centre for Discovery Brain Sciences, University of Edinburgh</institution><addr-line><named-content content-type="city">Edinburgh</named-content></addr-line><country>United Kingdom</country></aff><aff id="aff2"><label>2</label><institution>The Alan Turing Institute</institution><addr-line><named-content content-type="city">London</named-content></addr-line><country>United States</country></aff><aff id="aff3"><label>3</label><institution>School of Mathematics, Maxwell Institute and Centre for Statistics, University of Edinburgh</institution><addr-line><named-content content-type="city">Edinburgh</named-content></addr-line><country>United Kingdom</country></aff></contrib-group><contrib-group content-type="section"><contrib contrib-type="senior_editor"><name><surname>Colgin</surname><given-names>Laura L</given-names></name><role>Senior Editor</role><aff><institution>University of Texas at Austin</institution><country>United States</country></aff></contrib><contrib contrib-type="editor"><name><surname>Giocomo</surname><given-names>Lisa</given-names></name><role>Reviewing Editor</role><aff><institution>Stanford School of Medicine</institution><country>United States</country></aff></contrib></contrib-group><pub-date date-type="publication" publication-format="electronic"><day>13</day><month>02</month><year>2020</year></pub-date><pub-date pub-type="collection"><year>2020</year></pub-date><volume>9</volume><elocation-id>e52258</elocation-id><history><date date-type="received" iso-8601-date="2019-09-26"><day>26</day><month>09</month><year>2019</year></date><date date-type="accepted" iso-8601-date="2020-02-04"><day>04</day><month>02</month><year>2020</year></date></history><permissions><copyright-statement>© 2020, Pastoll et al</copyright-statement><copyright-year>2020</copyright-year><copyright-holder>Pastoll et al</copyright-holder><ali:free_to_read/><license xlink:href="http://creativecommons.org/licenses/by/4.0/"><ali:license_ref>http://creativecommons.org/licenses/by/4.0/</ali:license_ref><license-p>This article is distributed under the terms of the <ext-link ext-link-type="uri" xlink:href="http://creativecommons.org/licenses/by/4.0/">Creative Commons Attribution License</ext-link>, which permits unrestricted use and redistribution provided that the original author and source are credited.</license-p></license></permissions><self-uri content-type="pdf" xlink:href="elife-52258-v4.pdf"/><abstract><p>Distinctions between cell types underpin organizational principles for nervous system function. Functional variation also exists between neurons of the same type. This is exemplified by correspondence between grid cell spatial scales and the synaptic integrative properties of stellate cells (SCs) in the medial entorhinal cortex. However, we know little about how functional variability is structured either within or between individuals. Using ex-vivo patch-clamp recordings from up to 55 SCs per mouse, we found that integrative properties vary between mice and, in contrast to the modularity of grid cell spatial scales, have a continuous dorsoventral organization. Our results constrain mechanisms for modular grid firing and provide evidence for inter-animal phenotypic variability among neurons of the same type. We suggest that neuron type properties are tuned to circuit-level set points that vary within and between animals.</p></abstract><abstract abstract-type="executive-summary"><title>eLife digest</title><p>The brain consists of many types of cells that are specialised to perform different tasks. This is similar to how different groups of people will have different responsibilities in a large company. But within each group with the same role, individual employees will also do their jobs in different ways. Does the same apply to the brain? In other words, do individual neurons of the same type – with the same role – process information differently?</p><p>To find out, Pastoll et al. studied stellate cells in the mouse brain: these neurons take their name from their distinctive star-shaped arrays of projections, and they work together in groups known as modules to help animals navigate their environment. To determine whether stellate cells differ between mice, and how they might differ within a single animal, Pastoll et al. measured the activity of more than 800 stellate cells in more than two dozen individuals.</p><p>The results revealed that stellate cells process the same information differently between mice, which may contribute to variations in behaviour across the species. But even within an individual, stellate cells also showed differences in information processing. In fact, the properties of the stellate cells within each mouse varied along a continuum. This discovery rules out several previous theories on how stellate cells form the modules that support navigation.</p><p>The work by Pastoll et al. helps to understand how the brain supports thinking and memory. In the long term, these findings could also have implications for treating brain disorders, as they suggest that variations between people in the properties of their neurons could lead to variations in drug response. Researchers may need to take inter-individual differences into account when planning experiments, and ultimately when designing drugs.</p></abstract><kwd-group kwd-group-type="author-keywords"><kwd>entorhinal cortex</kwd><kwd>synaptic integration</kwd><kwd>presynaptic function</kwd><kwd>multi-vesicular release</kwd><kwd>synaptic vesicle</kwd></kwd-group><kwd-group kwd-group-type="research-organism"><title>Research organism</title><kwd>Mouse</kwd></kwd-group><funding-group><award-group id="fund1"><funding-source><institution-wrap><institution-id institution-id-type="FundRef">http://dx.doi.org/10.13039/100010269</institution-id><institution>Biotechnology and Biological Sciences Research Council (BBSRC)</institution></institution-wrap></funding-source><award-id>200855/Z/16/Z</award-id><principal-award-recipient><name><surname>Nolan</surname><given-names>Matthew F</given-names></name></principal-award-recipient></award-group><award-group id="fund2"><funding-source><institution-wrap><institution-id institution-id-type="FundRef">http://dx.doi.org/10.13039/100010269</institution-id><institution>Biotechnology and Biological Sciences Research Council (BBSRC)</institution></institution-wrap></funding-source><award-id>BB/1022147/1</award-id><principal-award-recipient><name><surname>Nolan</surname><given-names>Matthew F</given-names></name></principal-award-recipient></award-group><award-group id="fund3"><funding-source><institution-wrap><institution-id institution-id-type="FundRef">http://dx.doi.org/10.13039/501100000268</institution-id><institution>Biotechnology and Biological Sciences Research Council</institution></institution-wrap></funding-source><award-id>BB/H020284/1</award-id><principal-award-recipient><name><surname>Nolan</surname><given-names>Matthew F</given-names></name></principal-award-recipient></award-group><award-group id="fund4"><funding-source><institution-wrap><institution-id institution-id-type="FundRef">http://dx.doi.org/10.13039/100004440</institution-id><institution>Wellcome</institution></institution-wrap></funding-source><award-id>200855/Z/16/Z</award-id><principal-award-recipient><name><surname>Nolan</surname><given-names>Matthew F</given-names></name></principal-award-recipient></award-group><funding-statement>The funders had no role in study design, data collection and interpretation, or the decision to submit the work for publication.</funding-statement></funding-group><custom-meta-group><custom-meta specific-use="meta-only"><meta-name>Author impact statement</meta-name><meta-value>Setpoints that determine the integrative properties of neurons in the medial entorhinal cortex are established at a population level and differ between animals.</meta-value></custom-meta></custom-meta-group></article-meta></front><body><sec id="s1" sec-type="intro"><title>Introduction</title><p>The concept of cell types provides a general organizing principle for understanding biological structures including the brain (<xref ref-type="bibr" rid="bib65">Regev et al., 2017</xref>; <xref ref-type="bibr" rid="bib84">Zeng and Sanes, 2017</xref>). The simplest conceptualization of a neuronal cell type, as a population of phenotypically similar neurons with features that cluster around a single set point (<xref ref-type="bibr" rid="bib79">Wang et al., 2011b</xref>), is extended by observations of variability in cell type features, suggesting that some neuronal cell types may be conceived as clustering along a line rather than around a point in a feature space (<xref ref-type="bibr" rid="bib19">Cembrowski and Menon, 2018</xref>; <xref ref-type="bibr" rid="bib55">O'Donnell and Nolan, 2011</xref>; <xref ref-type="fig" rid="fig1">Figure 1A</xref>). Correlations between the functional organization of sensory, motor and cognitive circuits and the electrophysiological properties of individual neuronal cell types suggest that this feature variability underlies key neural computations (<xref ref-type="bibr" rid="bib1">Adamson et al., 2002</xref>; <xref ref-type="bibr" rid="bib3">Angelo et al., 2012</xref>; <xref ref-type="bibr" rid="bib24">Fletcher and Williams, 2019</xref>; <xref ref-type="bibr" rid="bib28">Garden et al., 2008</xref>; <xref ref-type="bibr" rid="bib30">Giocomo et al., 2007</xref>; <xref ref-type="bibr" rid="bib46">Kuba et al., 2005</xref>; <xref ref-type="bibr" rid="bib55">O'Donnell and Nolan, 2011</xref>). However, within-cell type variability has typically been deduced by combining data obtained from multiple animals. By contrast, the structure of variation within individual animals or between different animals has received little attention. For example, apparent clustering of properties along lines in feature space could reflect a continuum of set points, or could result from a small number of discrete set points that are obscured by inter-animal variation (<xref ref-type="fig" rid="fig1">Figure 1B</xref>). Moreover, although investigations of invertebrate nervous systems show that set points may differ between animals (<xref ref-type="bibr" rid="bib36">Goaillard et al., 2009</xref>), it is not clear whether mammalian neurons exhibit similar phenotypic diversity (<xref ref-type="fig" rid="fig1">Figure 1B</xref>). Distinguishing these possibilities requires many more electrophysiological observations for each animal than are obtained in typical studies.</p><fig-group><fig id="fig1" position="float"><label>Figure 1.</label><caption><title>Classification and variability of neuronal cell types.</title><p>(<bold>A</bold>) Neuronal cell types are identifiable by features clustering around a distinct point (blue, green and yellow) or a line (orange) in feature space. The clustering implies that neuron types are defined by either a single set point (blue, green and yellow) or by multiple set points spread along a line (orange). (<bold>B</bold>) Phenotypic variability of a single neuron type could result from distinct set points that subdivide the neuron type but appear continuous when data from multiple animals are combined (modular), from differences in components of a set point that do not extend along a continuum but that in different animals cluster at different locations in feature space (orthogonal), or from differences between animals in the range covered by a continuum of set points (offset). These distinct forms of variability can only be made apparent by measuring the features of many neurons from multiple animals.</p></caption><graphic mime-subtype="jpeg" mimetype="image" xlink:href="elife-52258.xml.media/fig1.jpg"/></fig><fig id="fig1s1" position="float" specific-use="child-fig"><label>Figure 1—figure supplement 1.</label><caption><title>A quantitative adaptation of the gap statistic clustering algorithm.</title><p>(<bold>A–C</bold>) Logic of the gap statistic. (<bold>A</bold>) Simulated clustered dataset with three modes (k = 3) (open gray circles) (upper) and the corresponding simulated reference dataset drawn from a uniform distribution with lower and upper limits set by the minimum and maximum values from the corresponding clustered dataset (open gray diamonds). Data were allocated to clusters by running a K-means algorithm 20 times on each set of data and selecting the partition with the lowest average intracluster dispersion. Red, green, blue and yellow dashed ovals show a realization of the data subsets allocated to each cluster when k<sub>Eval</sub> = 1, 2, 3 and 4 modes. (<bold>B</bold>) The average value of the log intracluster dispersion for the clustered (open circles) and reference (open diamonds) datasets for each value of k tested in panel (<bold>A</bold>). (<bold>C</bold>) Gap values resulting from the difference between the clustered and reference values for each k in panel (<bold>B</bold>). Many (≥500 in this paper) reference distributions are generated and their mean intracluster dispersion values are subtracted from those arising from the clustered distribution to maximize the reliability of the Gap values. (<bold>D</bold>) A procedure for selecting the optimal k depending on the associated gap values. Quantitative procedure for selecting optimal k (k<sub>est</sub>). ∆Gap values (open circles) are obtained by subtracting from the Gap value of a given k the Gap value for the previous k (∆Gap<sub>k</sub> = Gap<sub>k</sub> – Gap<sub>k-1</sub>). For each ∆Gap<sub>k</sub>, if the ∆Gap value is greater than a threshold (filled triangles) associated with that ∆Gap<sub>k</sub>, that ∆Gap<sub>k</sub> will be k<sub>est</sub>, if no ∆Gap exceeds, the threshold, k<sub>est</sub> = 1. In the figure, for ∆Gap<sub>k</sub> = 2, 3, 4 (brown, pink and cyan), the ∆Gap value exceeds its threshold only when ∆Gap<sub>k</sub> = 3. Therefore k<sub>est</sub> = 3. (<bold>E–G</bold>) Determination of ∆Gap<sub>k</sub> thresholds. (<bold>E</bold>) Histograms of ∆Gap values calculated from 20,000 simulated datasets drawn from uniform distributions for each ∆Gap<sub>k</sub> (brown, pink and cyan, respectively, for ∆Gap<sub>k</sub> = 2, 3, 4) for a single dataset size (n = 40). ∆Gap thresholds (filled triangles) are the values beyond which 1% of the ∆Gap values fall and vary with ∆Gap<sub>k</sub>. (<bold>F</bold>) Histograms of ∆Gap values for a range of dataset sizes (n = 20, 40, 100) and their associated thresholds. (<bold>G</bold>) Plot of the ∆Gap thresholds as a function of dataset size and ∆Gap<sub>k</sub>. For separate ∆Gap<sub>k</sub>, ∆Gap threshold values are fitted well by a hyperbolic function of dataset size. These fits provide a practical method of finding the appropriate ∆Gap threshold for an arbitrary dataset size.</p></caption><graphic mime-subtype="jpeg" mimetype="image" xlink:href="elife-52258.xml.media/fig1-figsupp1.jpg"/></fig><fig id="fig1s2" position="float" specific-use="child-fig"><label>Figure 1—figure supplement 2.</label><caption><title>Discrimination of continuous from modular organizations using the adapted gap statistic algorithm.</title><p>(<bold>A</bold>) Simulated datasets (each n = 40) drawn from continuous (uniform, k = 1 mode) (upper) and modular (multimodal mixture of Gaussians with k = 2 modes) (lower) distributions, and plotted against simulated dorsoventral locations. Also shown are the probability density functions (pdf) used to generate each dataset (light blue) and the densities estimated post-hoc from the generated data as kernel smoothed densities (light gray pdfs). (<bold>B</bold>) Histograms showing the distribution of k<sub>est</sub> from 1000 simulated datasets drawn from each pdf in panel (<bold>A</bold>). k<sub>est</sub> is determined for each dataset by a modified gap statistic algorithm (see <xref ref-type="fig" rid="fig1s1">Figure 1—figure supplement 1</xref> above). When k<sub>est</sub> = 1, the dataset is considered to be continuous (unclustered), when k<sub>est</sub> ≥2, the dataset is considered to be modular (clustered). The algorithm operates only on the feature values and does not use location information. (<bold>C</bold>) Illustration of a set of clustered (k = 2) pdfs with the distance (in standard deviations) between clusters ranging from 2 to 6 (upper). Systematic evaluation of the ability of the modified gap statistic algorithm to detect clustered organization (k<sub>est</sub> ≥2) in simulated datasets of different size (n = 20 to 100) drawn from the clustered (filled blue) and continuous (open blue) pdfs (lower). The proportion of datasets drawn from the continuous distribution that have k<sub>est</sub> ≥2 is the false positive (FP) rate (pFP = ~0.07). The light gray filled circle shows the smallest dataset size (n = 40) with SD = 5, where the proportion of datasets detected as clustered (p<sub>detect</sub>) is ~0.8. (<bold>D</bold>). Plot showing how p<sub>detect</sub> at n = 40, SD = 5 changes when datasets are drawn from pdfs with different numbers of clusters (n modes from 2 to 8). Further evaluation of the analysis of additional clusters is represented in the following figure.</p></caption><graphic mime-subtype="jpeg" mimetype="image" xlink:href="elife-52258.xml.media/fig1-figsupp2.jpg"/></fig><fig id="fig1s3" position="float" specific-use="child-fig"><label>Figure 1—figure supplement 3.</label><caption><title>Additional evaluation of the adapted gap statistic algorithm.</title><p>(<bold>A–C</bold>) Plots showing how p<sub>detect</sub> (the ability of the modified gap statistic algorithm to detect clustered organization) depends on dataset size and separation between cluster modes in simulated datasets drawn from clustered pdfs with different numbers of modes. The gray markers indicate n = 40, SD = 5 (as shown in <xref ref-type="fig" rid="fig1">Figure 1E</xref>). In each plot, p<sub>detect</sub> is shown as a function of simulated dataset size and separation between modes when k = 3 (<bold>A</bold>), k = 5 (<bold>B</bold>) and k = 8 (<bold>C</bold>), which was the maximum number of clusters evaluated. (<bold>D–F</bold>) Histograms showing the counts of k<sub>est</sub> from the 1000 simulated n = 40, SD = 5 datasets (gray filled circles) illustrated in panels (<bold>A–C</bold>), respectively. (<bold>G</bold>) p<sub>detect</sub> as a function of dataset size and mode separation with k = 5 when cluster modes are unevenly sampled. Sample sizes from clusters vary randomly with each dataset. A single mode can contribute from all to none of the points in any simulated dataset. (<bold>H</bold>) p<sub>detect</sub> as a function of dataset size and mode separation with k = 5 when the distance between mode centers increases by a factor of sqrt(2) between sequential cluster pairs. Data are shown for different initial separations (the distance between the first two cluster centers) ranging from 1 to 4 (with corresponding separations between the final cluster pair ranging from 4 to 16).</p></caption><graphic mime-subtype="jpeg" mimetype="image" xlink:href="elife-52258.xml.media/fig1-figsupp3.jpg"/></fig><fig id="fig1s4" position="float" specific-use="child-fig"><label>Figure 1—figure supplement 4.</label><caption><title>Comparing the adapted gap statistic algorithm with discontinuity measures for discreteness.</title><p>(<bold>A</bold>) Counts of log discontinuity ratio scores generated from a simulated uniform data distribution. The data distribution was ordered and then sampled either at positions drawn at random from a uniform distribution (dark blue) or at positions with a fixed increment (light blue). For the data sampled at random positions, approximately half of the scores are >0 and for even sampling all scores are >0. Therefore, a threshold score >0 does not distinguish discrete from continuous distributions. (<bold>B</bold>) Comparison of p<sub>detect</sub> as a function of dataset size for the adapted gap statistic algorithm, the discontinuity (upper) and the discreteness algorithm (lower). Each algorithm is adjusted to yield a 7% false positive rate. Each column shows simulations of data with different numbers of modes (k).</p></caption><graphic mime-subtype="jpeg" mimetype="image" xlink:href="elife-52258.xml.media/fig1-figsupp4.jpg"/></fig><fig id="fig1s5" position="float" specific-use="child-fig"><label>Figure 1—figure supplement 5.</label><caption><title>Evaluation of modularity of grid firing using an adapted gap statistic algorithm.</title><p>Examples of grid spacing for individual neurons (crosses) from different mice. Kernel smoothed densities (KSDs) were generated with either a wide (solid gray) or a narrow (dashed lines) kernel. The number of modes estimated using the modified gap statistic algorithm is ≥ 2 for all but one animal (animal 4) with n ≥ 20 (animals 3 and 7 have < 20 recorded cells). We did not have location information for animal 2.</p></caption><graphic mime-subtype="jpeg" mimetype="image" xlink:href="elife-52258.xml.media/fig1-figsupp5.jpg"/></fig></fig-group><p>Stellate cells in layer 2 (SCs) of the medial entorhinal cortex (MEC) provide a striking example of correspondence between functional organization of neural circuits and variability of electrophysiological features within a single cell type. The MEC contains neurons that encode an animal’s location through grid-like firing fields (<xref ref-type="bibr" rid="bib27">Fyhn et al., 2004</xref>). The spatial scale of grid fields follows a dorsoventral organization (<xref ref-type="bibr" rid="bib42">Hafting et al., 2005</xref>), which is mirrored by a dorsoventral organization in key electrophysiological features of SCs (<xref ref-type="bibr" rid="bib10">Boehlen et al., 2010</xref>; <xref ref-type="bibr" rid="bib21">Dodson et al., 2011</xref>; <xref ref-type="bibr" rid="bib28">Garden et al., 2008</xref>; <xref ref-type="bibr" rid="bib30">Giocomo et al., 2007</xref>; <xref ref-type="bibr" rid="bib33">Giocomo and Hasselmo, 2008a</xref>; <xref ref-type="bibr" rid="bib58">Pastoll et al., 2012a</xref>). Grid cells are further organized into discrete modules (<xref ref-type="bibr" rid="bib71">Stensola et al., 2012</xref>), with the cells within a module having a similar grid scale and orientation (<xref ref-type="bibr" rid="bib6">Barry et al., 2007</xref>; <xref ref-type="bibr" rid="bib40">Gu et al., 2018</xref>; <xref ref-type="bibr" rid="bib71">Stensola et al., 2012</xref>; <xref ref-type="bibr" rid="bib82">Yoon et al., 2013</xref>); progressively more ventral modules are composed of cells with wider grid spacing (<xref ref-type="bibr" rid="bib71">Stensola et al., 2012</xref>). Studies that demonstrate dorsoventral organization of integrative properties of SCs have so far relied on the pooling of relatively few measurements per animal. Hence, it is unclear whether the organization of these cellular properties is modular, as one might expect if they directly set the scale of grid firing fields in individual grid cells (<xref ref-type="bibr" rid="bib30">Giocomo et al., 2007</xref>). The possibility that set points for electrophysiological properties of SCs differ between animals has also not been considered previously.</p><p>Evaluation of variability between and within animals requires statistical approaches that are not typically used in single-cell electrophysiological investigations. Given appropriate assumptions, inter-animal differences can be assessed using mixed effect models that are well established in other fields (<xref ref-type="bibr" rid="bib4">Baayen et al., 2008</xref>; <xref ref-type="bibr" rid="bib29">Geiler-Samerotte et al., 2013</xref>). Because tests of whether data arise from modular as opposed to continuous distributions have received less general attention, to facilitate detection of modularity using relatively few observations, we introduce a modification of the gap statistic algorithm (<xref ref-type="bibr" rid="bib75">Tibshirani et al., 2001</xref>) that estimates the number of modes in a dataset while controlling for observations expected by chance (see 'Materials and methods' and <xref ref-type="fig" rid="fig1s1">Figure 1—figure supplements 1</xref>–<xref ref-type="fig" rid="fig1s5">5</xref>). This algorithm performs well compared with discreteness metrics that are based on the standard deviation of binned data (<xref ref-type="bibr" rid="bib32">Giocomo et al., 2014</xref>; <xref ref-type="bibr" rid="bib71">Stensola et al., 2012</xref>), which we find are prone to high false-positive rates (<xref ref-type="fig" rid="fig1s4">Figure 1—figure supplement 4A</xref>). We find that recordings from approximately 30 SCs per animal should be sufficient to detect modularity using the modified gap statistic algorithm and given the experimentally observed separation between grid modules (see 'Materials and methods' and <xref ref-type="fig" rid="fig1s2">Figure 1—figure supplements 2</xref>–<xref ref-type="fig" rid="fig1s3">3</xref>). Although methods for high-quality recording from SCs in ex-vivo brain slices are well established (<xref ref-type="bibr" rid="bib59">Pastoll et al., 2012b</xref>), typically fewer than five recordings per animal were made in previous studies, which is many fewer than our estimate of the minimum number of observations required to test for modularity.</p><p>We set out to establish the nature of the set points that establish the integrative properties of SCs by measuring intra- and inter-animal variation in key electrophysiological features using experiments that maximize the number of SCs recorded per animal. Our results suggest that set points for individual features of a neuronal cell type are established at the level of neuronal cell populations, differ between animals and follow a continuous organization.</p></sec><sec id="s2" sec-type="results"><title>Results</title><sec id="s2-1"><title>Sampling integrative properties from many neurons per animal</title><p>Before addressing intra- and inter-animal variability, we first describe the data set used for the analyses that follow. We established procedures to facilitate the recording of integrative properties of many SCs from a single animal (see 'Materials and methods'). With these procedures, we measured and analyzed electrophysiological features of 836 SCs (n/mouse: range 11–55; median = 35) from 27 mice (median age = 37 days, age range = 18–57 days). The mice were housed either in a standard home cage (dimensions: 0.2 × 0.37 m, N = 18 mice, n = 583 neurons) or from postnatal day 16 in a 2.4 × 1.2 m cage, which provided a large environment that could be freely explored (N = 9, n = 253, median age = 38 days) (<xref ref-type="fig" rid="fig2s1">Figure 2—figure supplement 1</xref>). For each neuron, we measured six sub-threshold integrative properties (<xref ref-type="fig" rid="fig2">Figure 2A–B</xref>) and six supra-threshold integrative properties (<xref ref-type="fig" rid="fig2">Figure 2C</xref>). Unless indicated otherwise, we report the analysis of datasets that combine the groups of mice housed in standard and large home cages and that span the full range of ages.</p><fig-group><fig id="fig2" position="float"><label>Figure 2.</label><caption><title>Dorsoventral organization of intrinsic properties of stellate cells from a single animal.</title><p>(<bold>A–C</bold>) Waveforms (gray traces) and example responses (black traces) from a single mouse for step (<bold>A</bold>), ZAP (<bold>B</bold>) and ramp (<bold>C</bold>) stimuli (left). The properties derived from each protocol are shown plotted against recording location (each data point is a black cross) (right). KSDs with arbitrary bandwidth are displayed to the right of each data plot to facilitate visualization of the property’s distribution when location information is disregarded (light gray pdfs). (<bold>A</bold>) Injection of a series of current steps enables the measurement of the resting membrane potential (V<sub>rest</sub>) (<bold>i</bold>), the input resistance (IR) (ii), the sag coefficient (sag) (iii) and the membrane time constant (τ<sub>m</sub>) (iv). (<bold>B</bold>) Injection of ZAP current waveform enables the calculation of an impedance amplitude profile, which was used to estimate the resonance resonant frequency (Res. F) (<bold>i</bold>) and magnitude (Res. mag) (ii). (<bold>C</bold>) Injection of a slow current ramp enabled the measurement of the rheobase (i); the slope of the current-frequency relationship (I-F slope) (ii); using only the first five spikes in each response (enlarged zoom, lower left), the AHP minimum value (AHP<sub>min</sub>) (iii); the spike maximum (Spk. max) (iv); the spike threshold (Spk. thr.) (v); and the spike width at half height (Spk. HW) (vi).</p></caption><graphic mime-subtype="jpeg" mimetype="image" xlink:href="elife-52258.xml.media/fig2.jpg"/></fig><fig id="fig2s1" position="float" specific-use="child-fig"><label>Figure 2—figure supplement 1.</label><caption><title>Large environment for housing.</title><p>(<bold>A, B</bold>) The large cage environment viewed from above (<bold>A</bold>) and from inside (<bold>B</bold>).</p></caption><graphic mime-subtype="jpeg" mimetype="image" xlink:href="elife-52258.xml.media/fig2-figsupp1.jpg"/></fig></fig-group><p>Because SCs are found intermingled with pyramidal cells in layer 2 (L2PCs), and as misclassification of L2PCs as SCs would probably confound investigation of intra-SC variation, we validated our criteria for distinguishing each cell type. To establish characteristic electrophysiological properties of L2PCs, we recorded from neurons in layer 2 that were identified by Cre-dependent marker expression in a <italic>Wfs1</italic><sup>Cre</sup> mouse line (<xref ref-type="bibr" rid="bib72">Sürmeli et al., 2015</xref>). Expression of Cre in this line, and in a similar line (<xref ref-type="bibr" rid="bib44">Kitamura et al., 2014</xref>), labels L2PCs that project to the CA1 region of the hippocampus, but does not label SCs (<xref ref-type="bibr" rid="bib44">Kitamura et al., 2014</xref>; <xref ref-type="bibr" rid="bib72">Sürmeli et al., 2015</xref>). We identified two populations of neurons in layer 2 of MEC that were labelled in <italic>Wfs1</italic><sup>Cre</sup> mice (<xref ref-type="fig" rid="fig3">Figure 3A–C</xref>). The more numerous population had properties consistent with L2PCs (<xref ref-type="fig" rid="fig3">Figure 3A,G</xref>) and could be separated from the unidentified population on the basis of a lower rheobase (<xref ref-type="fig" rid="fig3">Figure 3C</xref>). The unidentified population had firing properties that were typical of layer 2 interneurons (<xref ref-type="bibr" rid="bib37">Gonzalez-Sulser et al., 2014</xref>). A principal component analysis (PCA) (<xref ref-type="fig" rid="fig3">Figure 3D–F</xref>) clearly separated the L2PC population from the SC population, but did not identify subpopulations of SCs. The properties of the less numerous population were also clearly distinct from those of SCs (<xref ref-type="fig" rid="fig3">Figure 3A,C</xref>). These data demonstrate that the SC population used for our analyses is distinct from other cell types also found in layer 2 of the MEC.</p><fig id="fig3" position="float"><label>Figure 3.</label><caption><title>Distinct and dorsoventrally organized properties of layer 2 stellate cells.</title><p>(<bold>A</bold>) Representative action potential after hyperpolarization waveforms from a SC (left), a pyramidal cell (middle) and an unidentified cell (right). The pyramidal and unidentified cells were both positively labelled in <italic>Wfs1<sup>C</sup></italic><sup>re</sup> mice. (<bold>B</bold>) Plot of the first versus the second principal component from PCA of the properties of labelled neurons in <italic>Wfs1</italic><sup>Cre</sup> mice reveals two populations of neurons. (<bold>C</bold>) Histogram showing the distribution of rheobase values of cells positively labelled in <italic>Wfs1</italic><sup>Cre</sup> mice. The two groups identified in panel (B) can be distinguished by their rheobase. (<bold>D</bold>) Plot of the first two principal components from PCA of the properties of the L2PC (n = 44, green) and SC populations (n = 836, black). Putative pyramidal cells (x) and SCs (+) are colored according to their dorsoventral location (inset shows the scale). (<bold>E</bold>) Proportion of total variance explained by the first five principal components for the analysis in panel (<bold>D</bold>). (<bold>F</bold>) Histograms of the locations of recorded SCs (upper) and L2PCs (lower). (<bold>G</bold>) All values of measured features from all mice are plotted as a function of the dorsoventral location of the recorded cells. Lines indicate fits of a linear model to the complete datasets for SCs (black) and L2PCs (green). Putative pyramidal cells (x, green) and SCs (+, black). Adjusted R<sup>2</sup> values use the same color scheme.</p></caption><graphic mime-subtype="jpeg" mimetype="image" xlink:href="elife-52258.xml.media/fig3.jpg"/></fig><p>To further validate the large SC dataset, we assessed the location-dependence of individual electrophysiological features, several of which have previously been found to depend on the dorso-ventral location of the recorded neuron (<xref ref-type="bibr" rid="bib10">Boehlen et al., 2010</xref>; <xref ref-type="bibr" rid="bib11">Booth et al., 2016</xref>; <xref ref-type="bibr" rid="bib28">Garden et al., 2008</xref>; <xref ref-type="bibr" rid="bib30">Giocomo et al., 2007</xref>; <xref ref-type="bibr" rid="bib58">Pastoll et al., 2012a</xref>; <xref ref-type="bibr" rid="bib83">Yoshida et al., 2013</xref>). We initially fit the dependence of each feature on dorsoventral position using a standard linear regression model. We found substantial (adjusted R<sup>2</sup> >0.1) dorsoventral gradients in input resistance, sag, membrane time constant, resonant frequency, rheobase and the current-frequency (I-F) relationship (<xref ref-type="fig" rid="fig3">Figure 3G</xref>). In contrast to the situation in SCs, we did not find evidence for dorsoventral organization of these features in L2PCs (<xref ref-type="fig" rid="fig3">Figure 3G</xref>). Thus, our large dataset replicates the previously observed dependence of integrative properties of SCs on their dorsoventral position, and shows that this location dependence further distinguishes SCs from L2PCs.</p></sec><sec id="s2-2"><title>Inter-animal differences in the intrinsic properties of stellate cells</title><p>To what extent does variability between the integrative properties of SCs at a given dorsoventral location arise from differences between animals? Comparing specific features between individual animals suggested that their distributions could be almost completely non-overlapping, despite consistent and strong dorsoventral tuning (<xref ref-type="fig" rid="fig4">Figure 4A</xref>). If this apparent inter-animal variability results from the random sampling of a distribution determined by a common underlying set point, then fitting the complete data set with a mixed model in which animal identity is included as a random effect should reconcile the apparent differences between animals (<xref ref-type="fig" rid="fig4">Figure 4B</xref>). In this scenario, the conditional R<sup>2</sup> estimated from the mixed model, in other words, the estimate of variance explained by animal identity and location, should be similar to the marginal R<sup>2</sup> value, which indicates the variance explained by location only. By contrast, if differences between animals contribute to experimental variability, the mixed model should predict different fitting parameters for each animal, and the estimated conditional R<sup>2</sup> should be greater than the corresponding marginal R<sup>2</sup> (<xref ref-type="fig" rid="fig4">Figure 4C</xref>).</p><fig-group><fig id="fig4" position="float"><label>Figure 4.</label><caption><title>Inter-animal variability and dependence on environment of intrinsic properties of stellate cells.</title><p>(<bold>A</bold>) Examples of rheobase as a function of dorsoventral position for two mice. (<bold>B, C</bold>) Each line is the fit of simulated data from a different subject for datasets in which there is no inter-subject variability (<bold>B</bold>) or in which intersubject variability is present (<bold>C</bold>). Fitting data from each subject independently with linear regression models suggests intersubject variation in both datasets (left). By contrast, after fitting mixed effect models (right) intersubject variation is no longer suggested for the dataset in which it is absent (<bold>B</bold>) but remains for the dataset in which it is present (<bold>C</bold>). (<bold>D</bold>) Each line is the fit of rheobase as a function of dorsoventral location for a single mouse. The fits were carried out independently for each mouse (left) or using a mixed effect model with mouse identity as a random effect (right). (<bold>E</bold>) The intercept (I), sum of the intercept and slope (I + S), and slopes realigned to a common intercept (right) for each mouse obtained by fitting mixed effect models for each property as a function of dorsoventral position.</p></caption><graphic mime-subtype="jpeg" mimetype="image" xlink:href="elife-52258.xml.media/fig4.jpg"/></fig><fig id="fig4s1" position="float" specific-use="child-fig"><label>Figure 4—figure supplement 1.</label><caption><title>Properties of SCs in medial and lateral slices.</title><p>Membrane properties of SCs from slices containing more medial (blue) and more lateral (red) parts of the MEC plotted as a function of dorsal ventral position. Neurons from more medial slices had a higher spike threshold, a lower spike maximum and a less-negative spike after-hyperpolarization (see <xref ref-type="supplementary-material" rid="supp6">Supplementary file 6</xref>). Properties are labelled as in <xref ref-type="fig" rid="fig2">Figure 2</xref>.</p></caption><graphic mime-subtype="jpeg" mimetype="image" xlink:href="elife-52258.xml.media/fig4-figsupp1.jpg"/></fig></fig-group><p>Fitting the experimental measures for each feature with mixed models suggests that differences between animals contribute substantially to the variability in properties of SCs. In contrast to simulated data in which inter-animal differences are absent (<xref ref-type="fig" rid="fig4">Figure 4B</xref>), differences in fits between animals remained after fitting with the mixed model (<xref ref-type="fig" rid="fig4">Figure 4D</xref>). This corresponds with expectations from fits to simulated data containing inter-animal variability (<xref ref-type="fig" rid="fig4">Figure 4C</xref>). To visualize inter-animal variability for all measured features, we plot for each animal the intercept of the model fit (I), the predicted value at a location 1 mm ventral from the intercept (I+S), and the slope (lines) (<xref ref-type="fig" rid="fig4">Figure 4E</xref>). Strikingly, even for features such as rheobase and input resistance (IR) that are highly tuned to a neurons’ dorsoventral position, the extent of variability between animals is similar to the extent to which the property changes between dorsal and mid-levels of the MEC.</p><p>If set points that determine integrative properties of SCs do indeed differ between animals, then mixed models should provide a better account of the data than linear models that are generated by pooling data across all animals. Consistent with this, we found that mixed models for all electrophysiological features gave a substantially better fit to the data than linear models that considered all neurons as independent (adjusted p<2×10<sup>−17</sup> for all models, χ<sup>2</sup> test, <xref ref-type="table" rid="table1">Table 1</xref>). Furthermore, even for properties with substantial (R<sup>2</sup> value >0.1) dorsoventral tuning, the conditional R<sup>2</sup> value for the mixed effect model was substantially larger than the marginal R<sup>2</sup> value (<xref ref-type="fig" rid="fig4">Figure 4D</xref> and <xref ref-type="table" rid="table1">Table 1</xref>). Together, these analyses demonstrate inter-animal variability in key electrophysiological features of SCs, suggesting that the set points that establish the underlying integrative properties differ between animals.</p><table-wrap id="table1" position="float"><label>Table 1.</label><caption><title>Dependence of the electrophysiological features of SCs on dorsoventral position.</title><p>Key statistical parameters from analyses of the relationship between each measured electrophysiological feature and dorsoventral location. The data are ordered according to the marginal R<sup>2</sup> for each property’s relationship with dorsoventral position. Slope is the population slope from fitting a mixed effect model for each feature with location as a fixed effect (mm<sup>−1</sup>), with p(slope) obtained by comparing this model to a model without location as a fixed effect (χ<sup>2</sup> test). For all properties except the spike thereshold, the slope was unlikely to have arisen by chance (p<0.05). The marginal and conditional R<sup>2</sup> values, and the minimum and maximum slopes across all mice, are obtained from the fits of mixed effect models that contain location as a fixed effect. The estimate p(vs linear) is obtained by comparing the mixed effect model containing location as a fixed effect with a corresponding linear model without random effects (χ<sup>2</sup> test). The values of p(slope) and p(vs linear) were adjusted for multiple comparisons using the method of <xref ref-type="bibr" rid="bib9">Benjamini and Hochberg (1995)</xref>. Units for the slope measurements are units for the property mm<sup>−1</sup>. The data are from 27 mice.</p></caption><table frame="hsides" rules="groups"><thead><tr><th>Feature</th><th>Slope</th><th>P (slope)</th><th>Marginal R<sup>2</sup></th><th>Conditional R<sup>2</sup></th><th>Slope (min)</th><th>Slope (max)</th><th>P (vs linear)</th></tr></thead><tbody><tr><td>IR (MΩ)</td><td>11.794</td><td>8.39e-17</td><td>0.383</td><td>0.532</td><td>9.630</td><td>14.262</td><td>4.33e-40</td></tr><tr><td>Rheobase (pA)</td><td>−119.887</td><td>9.07e-15</td><td>0.382</td><td>0.652</td><td>−153.873</td><td>−76.130</td><td>6.55e-43</td></tr><tr><td>I-F slope (Hz/pA)</td><td>0.036</td><td>6.06e-10</td><td>0.228</td><td>0.561</td><td>0.019</td><td>0.087</td><td>6.82e-34</td></tr><tr><td>Tm (ms)</td><td>2.646</td><td>3.70e-12</td><td>0.192</td><td>0.343</td><td>1.809</td><td>3.979</td><td>1.20e-29</td></tr><tr><td>Res. frequency (Hz)</td><td>−1.334</td><td>4.13e-09</td><td>0.122</td><td>0.553</td><td>−2.299</td><td>−0.342</td><td>6.37e-65</td></tr><tr><td>Sag</td><td>0.033</td><td>6.06e-10</td><td>0.121</td><td>0.347</td><td>0.016</td><td>0.043</td><td>1.91e-38</td></tr><tr><td>Spike maximum (mV)</td><td>1.900</td><td>1.85e-05</td><td>0.064</td><td>0.436</td><td>−1.288</td><td>3.297</td><td>1.14e-50</td></tr><tr><td>Res. magnitude</td><td>−0.114</td><td>6.34e-08</td><td>0.064</td><td>0.198</td><td>−0.138</td><td>−0.087</td><td>9.13e-20</td></tr><tr><td>Vm (mV)</td><td>−0.884</td><td>3.67e-05</td><td>0.046</td><td>0.348</td><td>−1.965</td><td>0.150</td><td>8.73e-35</td></tr><tr><td>Spike AHP (mV)</td><td>−0.645</td><td>1.93e-02</td><td>0.011</td><td>0.257</td><td>−1.828</td><td>0.408</td><td>1.82e-17</td></tr><tr><td>Spike width (ms)</td><td>0.017</td><td>1.93e-02</td><td>0.010</td><td>0.643</td><td>−0.021</td><td>0.055</td><td>7.04e-139</td></tr><tr><td>Spike threshold (mV)</td><td>0.082</td><td>8.20e-01</td><td>0.000</td><td>0.510</td><td>−2.468</td><td>2.380</td><td>2.03e-17</td></tr></tbody></table></table-wrap></sec><sec id="s2-3"><title>Experience-dependence of intrinsic properties of stellate cells</title><p>Because neuronal integrative properties may be modified by changes in neural activity (<xref ref-type="bibr" rid="bib85">Zhang and Linden, 2003</xref>), we asked whether experience influences the measured electrophysiological features of SCs. We reasoned that modifying the space through which animals can navigate may drive experience-dependent plasticity in the MEC. As standard mouse housing has dimensions less than the distance between the firing fields of more ventrally located grid cells (<xref ref-type="bibr" rid="bib12">Brun et al., 2008</xref>; <xref ref-type="bibr" rid="bib42">Hafting et al., 2005</xref>), in a standard home cage, only a relatively small fraction of ventral grid cells is likely to be activated, whereas larger housing should lead to the activation of a greater proportion of ventral grid cells. We therefore tested whether the electrophysiological features of SCs differ between mice housed in larger environments (28,800 cm<sup>2</sup>) and those with standard home cages (740 cm<sup>2</sup>).</p><p>We compared the mixed models described above to models in which housing was also included as a fixed effect. To minimize the effects of age on SCs (<xref ref-type="bibr" rid="bib10">Boehlen et al., 2010</xref>; <xref ref-type="bibr" rid="bib16">Burton et al., 2008</xref>; <xref ref-type="supplementary-material" rid="supp2">Supplementary file 2</xref>), we focused these and subsequent analyses on mice between P33 and P44 (N = 25, n = 779). We found that larger housing was associated with a smaller sag coefficient, indicating an increased sag response, a lower resonant frequency and a larger spike half-width (adjusted p<0.05; <xref ref-type="fig" rid="fig4">Figure 4E</xref>, <xref ref-type="supplementary-material" rid="supp3">Supplementary file 3</xref>). These differences were primarily from changes to the magnitude rather than the location-dependence of each feature. Other electrophysiological features appeared to be unaffected by housing.</p><p>To determine whether inter-animal differences remain after accounting for housing, we compared mixed models that include dorsoventral location and housing as fixed effects with equivalent linear regression models in which individual animals were not accounted for. Mixed models incorporating animal identity continued to provide a better account of the data, both for features that were dependent on housing (adjusted p<2.8×10<sup>−21</sup>) and for features that were not (adjusted p<1.4×10<sup>−7</sup>) (<xref ref-type="supplementary-material" rid="supp4">Supplementary file 4</xref>).</p><p>Together, these data suggest that specific electrophysiological features of SCs may be modified by experience of large environments. After accounting for housing, significant inter-animal variation remains, suggesting that additional mechanisms acting at the level of animals rather than individual neurons also determine differences between SCs.</p></sec><sec id="s2-4"><title>Inter-animal differences remain after accounting for additional experimental parameters</title><p>To address the possibility that other experimental or biological variables could contribute to inter-animal differences, we evaluated the effects of home cage size (<xref ref-type="supplementary-material" rid="supp3">Supplementary files 3</xref>–<xref ref-type="supplementary-material" rid="supp4">4</xref>), brain hemisphere (<xref ref-type="supplementary-material" rid="supp5">Supplementary file 5</xref>), mediolateral position (<xref ref-type="fig" rid="fig4s1">Figure 4—figure supplement 1</xref> and <xref ref-type="supplementary-material" rid="supp6">Supplementary file 6</xref>), the identity of the experimenter (<xref ref-type="supplementary-material" rid="supp7">Supplementary file 7</xref>) and time since slice preparation (<xref ref-type="supplementary-material" rid="supp8">Supplementary files 8</xref> and <xref ref-type="supplementary-material" rid="supp9">9</xref>). Several of the variables influenced some measured electrophysiological features, for example properties primarily related to the action potential waveform depended on the mediolateral position of the recorded neuron (<xref ref-type="supplementary-material" rid="supp6">Supplementary file 6</xref>; <xref ref-type="bibr" rid="bib18">Canto and Witter, 2012</xref>; <xref ref-type="bibr" rid="bib83">Yoshida et al., 2013</xref>), but significant inter-animal differences remained after accounting for each variable. We carried out further analyses using models that included housing, mediolateral position, experimenter identity and the direction in which sequential recordings were obtained as fixed effects (<xref ref-type="supplementary-material" rid="supp10">Supplementary file 10</xref>), and using models fit to minimal datasets in which housing, mediolateral position and the recording direction were identical (<xref ref-type="supplementary-material" rid="supp11">Supplementary file 11</xref>). These analyses again found evidence for significant inter-animal differences.</p><p>Inter-animal differences could arise if the health of the recorded neurons differed between brain slices. To minimize this possibility, we standardized our procedures for tissue preparation (see 'Materials and methods'), such that slices were of consistent high quality as assessed by low numbers of unhealthy cells and by visualization of soma and dendrites of neurons in the slice. Several further observations are consistent with comparable quality of slices between experiments. First, if the condition of the slices had differed substantially between animals, then in better quality slices, it should be easier to record from more neurons, in which case features that depend on tissue quality would correlate with the number of recorded neurons. However, the majority (10/12) of the electrophysiological features were not significantly (p>0.2) associated with the number of recorded neurons (<xref ref-type="supplementary-material" rid="supp12">Supplementary file 12</xref>). Second, analyses of inter-animal differences that focus only on data from animals for which >35 recordings were made, which should only be feasible with uniformly high-quality brain slices, are consistent with conclusions from analysis of the larger dataset (<xref ref-type="supplementary-material" rid="supp13">Supplementary file 13</xref>). Third, the conditional R<sup>2</sup> values of electrophysiological features of L2PCs are much lower than those for SCs recorded under the same experimental conditions (<xref ref-type="table" rid="table1">Table 1</xref> and <xref ref-type="supplementary-material" rid="supp1">Supplementary file 1</xref>), suggesting that inter-animal variation may be specific to SCs and cannot be explained by slice conditions. Together, these analyses indicate that differences between animals remain after accounting for experimental and technical factors that might contribute to variation in the measured features of SCs.</p></sec><sec id="s2-5"><title>The distribution of intrinsic properties is consistent with a continuous rather than a modular organization</title><p>The dorsoventral organization of SC integrative properties is well established, but whether this results from within animal variation consistent with a small number of discrete set points that underlie a modular organization (<xref ref-type="fig" rid="fig1">Figure 1B</xref>) is unclear. To evaluate modularity, we used datasets with n ≥ 34 SCs (N = 15 mice, median age = 37 days, age range = 18–43 days). We focus initially on rheobase, which is the property with the strongest correlation to dorsoventral location, and resonant frequency, which is related to the oscillatory dynamics underlying dorsoventral tuning in some models of grid firing (e.g. <xref ref-type="bibr" rid="bib14">Burgess et al., 2007</xref>; <xref ref-type="bibr" rid="bib30">Giocomo et al., 2007</xref>). For n ≥ 34 SCs, we expect that if properties are modular, then this would be detected by the modified gap statistic in at least 50% of animals (<xref ref-type="fig" rid="fig1s2">Figure 1—figure supplements 2C</xref> and <xref ref-type="fig" rid="fig1s3">3</xref>). By contrast, we find that for datasets from the majority of animals, the modified gap statistic identifies only a single mode in the distribution of rheobase values (<xref ref-type="fig" rid="fig5">Figure 5A</xref> and <xref ref-type="fig" rid="fig6">Figure 6</xref>) (N = 13/15) and of resonant frequencies (<xref ref-type="fig" rid="fig5">Figure 5B</xref> and <xref ref-type="fig" rid="fig6">Figure 6</xref>) (N = 14/15), indicating that these properties have a continuous rather than a modular distribution. Consistent with this, smoothed distributions did not show clearly separated peaks for either property (<xref ref-type="fig" rid="fig5">Figure 5</xref>). The mean and 95% confidence interval for the probability of evaluating a dataset as clustered (p<sub>detect</sub>) was 0.133 and 0.02–0.4 for rheobase and 0.067 and 0.002–0.32 for resonant frequency. These values of p<sub>detect</sub> were not significantly different from the proportions expected given the false positive rate of 0.1 in the complete absence of clustering (p=0.28 and 0.66, binomial test). Thus, the rheobase and resonant frequency of SCs, although depending strongly on a neuron’s dorsoventral position, do not have a detectable modular organization.</p><fig id="fig5" position="float"><label>Figure 5.</label><caption><title>Rheobase and resonant frequency do not have a detectable modular organization.</title><p>(<bold>A, B</bold>) Rheobase (<bold>A</bold>) and resonant frequency (<bold>B</bold>) are plotted as a function of dorsoventral position separately for each animal. Marker color and type indicate the age and housing conditions of the animal (‘+’ standard housing, ‘x’ large housing). KSDs (arbitrary bandwidth, same for all animals) are also shown. The number of clusters in the data (k<sub>est</sub>) is indicated for each animal (<inline-formula><mml:math id="inf1"><mml:mstyle displaystyle="true" scriptlevel="0"><mml:mrow><mml:mrow><mml:mover><mml:mrow><mml:mi mathvariant="normal">k</mml:mi></mml:mrow><mml:mo stretchy="false">^</mml:mo></mml:mover></mml:mrow></mml:mrow></mml:mstyle></mml:math></inline-formula>).</p></caption><graphic mime-subtype="jpeg" mimetype="image" xlink:href="elife-52258.xml.media/fig5.jpg"/></fig><fig id="fig6" position="float"><label>Figure 6.</label><caption><title>Significant modularity is not detectable for any measured property.</title><p>(<bold>A, B</bold>) Histograms showing the k<sub>est </sub>(<inline-formula><mml:math id="inf2"><mml:mstyle displaystyle="true" scriptlevel="0"><mml:mrow><mml:mrow><mml:mover><mml:mrow><mml:mi mathvariant="normal">k</mml:mi></mml:mrow><mml:mo stretchy="false">^</mml:mo></mml:mover></mml:mrow></mml:mrow></mml:mstyle></mml:math></inline-formula>) counts across all mice for each different measured sub-threshold (<bold>A</bold>) and supra-threshold (<bold>B</bold>) intrinsic property. The maximum k evaluated was 8. The proportion of each measured property with k<sub>est</sub>>1 was compared using binomial tests (with N = 15) to the proportion expected if the underlying distribution of that property is always clustered with all separation between modes ≥5 standard deviations (pink text), or if the underlying distribution of the property is uniform (purple text). For all measured properties, the values of k<sub>est</sub> (<inline-formula><mml:math id="inf3"><mml:mstyle displaystyle="true" scriptlevel="0"><mml:mrow><mml:mrow><mml:mover><mml:mrow><mml:mi mathvariant="normal">k</mml:mi></mml:mrow><mml:mo stretchy="false">^</mml:mo></mml:mover></mml:mrow></mml:mrow></mml:mstyle></mml:math></inline-formula>) were indistinguishable (p>0.05) from the data generated from a uniform distribution and differed from the data generated from a multi-modal distribution (p<1×10<sup>−6</sup>).</p></caption><graphic mime-subtype="jpeg" mimetype="image" xlink:href="elife-52258.xml.media/fig6.jpg"/></fig><p>When we investigated the other measured integrative properties, we also failed to find evidence for modularity. Across all properties, for any given property, at most 3 out of 15 mice were evaluated as having a clustered organization using the modified gap statistic (<xref ref-type="fig" rid="fig6">Figure 6</xref>). This does not differ significantly from the proportion expected by chance when no modularity is present (p>0.05, binomial test). Consistent with this, the average proportion of datasets evaluated as modular across all measured features was 0.072 ± 0.02 (± SEM), which is similar to the expected false-positive rate. By contrast, the properties of grid firing fields previously recorded with tetrodes in behaving animals (<xref ref-type="bibr" rid="bib71">Stensola et al., 2012</xref>) were detected as having a modular organization using the modified gap statistic (<xref ref-type="fig" rid="fig1s5">Figure 1—figure supplement 5</xref>). For seven grid-cell datasets with n ≥ 20, the mean for p<sub>detect</sub> is 0.86, with 95% confidence intervals of 0.42 to 0.996. We note here that discontinuity algorithms that were previously used to assess the modularity of grid field properties (<xref ref-type="bibr" rid="bib32">Giocomo et al., 2014</xref>; <xref ref-type="bibr" rid="bib71">Stensola et al., 2012</xref>) did indicate significant modularity in the majority of the intrinsic properties measured in our dataset (N = 13/15 and N = 12/15, respectively), but this was attributable to false positives resulting from the relatively even sampling of recording locations (see <xref ref-type="fig" rid="fig1s4">Figure 1—figure supplement 4A</xref>). Therefore, we conclude that it is unlikely that any of the intrinsic integrative properties of SCs that we examined have organization within individual animals resembling the modular organization of grid cells in behaving animals.</p></sec><sec id="s2-6"><title>Multiple sources of variance contribute to diversity in stellate cell intrinsic properties</title><p>Finally, because many of the measured electrophysiological features of SCs emerge from shared ionic mechanisms (<xref ref-type="bibr" rid="bib21">Dodson et al., 2011</xref>; <xref ref-type="bibr" rid="bib28">Garden et al., 2008</xref>; <xref ref-type="bibr" rid="bib58">Pastoll et al., 2012a</xref>), we asked whether dorsoventral tuning reflects a single core mechanism and whether inter-animal differences are specific to this mechanism or manifest more generally.</p><p>Estimation of conditional independence for measurements at the level of individual neurons (<xref ref-type="fig" rid="fig7">Figure 7A</xref>) or individual animals (<xref ref-type="fig" rid="fig7">Figure 7B</xref>) was consistent with the expectation that particular classes of membrane ion channels influence multiple electrophysiologically measured features. The first five dimensions of a principal components analysis (PCA) of all measured electrophysiological features accounted for almost 80% of the variance (<xref ref-type="fig" rid="fig7">Figure 7C</xref>). Examination of the rotations used to generate the principal components suggested relationships between individual features that are consistent with our evaluation of the conditional independence structure of the measured features (<xref ref-type="fig" rid="fig7">Figure 7D and A</xref>). When we fit the principal components using mixed models with location as a fixed effect and animal identity as a random effect, we found that the first two components depended significantly on dorsoventral location (<xref ref-type="fig" rid="fig7">Figure 7E</xref> and <xref ref-type="supplementary-material" rid="supp14">Supplementary file 14</xref>) (marginal R<sup>2</sup> = 0.50 and 0.09 and adjusted p=1.09×10<sup>−15</sup> and 1.05 × 10<sup>−4</sup>, respectively). Thus, the dependence of multiple electrophysiological features on dorsoventral position may be reducible to two core mechanisms that together account for much of the variability between SCs in their intrinsic electrophysiology.</p><fig id="fig7" position="float"><label>Figure 7.</label><caption><title>Feature relationships and inter-animal variability after reducing dimensionality of the data.</title><p>(<bold>A, B</bold>) Partial correlations between the electrophysiological features investigated at the level of individual neurons (<bold>A</bold>) and at the level of animals (<bold>B</bold>). Partial correlations outside of the 95% basic bootstrap confidence intervals are color coded. Non-significant correlations are colored white. Properties shown are the resting membrane potential (Vm), input resistance (IR), membrane potential sag response (sag), membrane time constant (Tm), resonance frequency (Rm), resonance magnitude (Rm), rheobase (Rheo), slope of the current frequency relationship (FI), peak of the action potential after hyperpolarization (AHP), peak of the action potential (Smax) voltage threshold for the action potential (Sthr) and half-width of the action potential (SHW). (<bold>C</bold>) Proportion of variance explained by each principal component. To remove variance caused by animal age and the experimenter identity, the principal component analysis used a reduced dataset obtained by one experimenter and restricted to animals between 32 and 45 days old (N = 25, n = 572). (<bold>D</bold>) Loading plot for the first two principal components. (<bold>E</bold>) The first five principal components plotted as a function of position. (<bold>F</bold>) Intercept (I), intercept plus the slope (I + S) and slopes aligned to the same intercept, for fits for each animal of the first five principal components to a mixed model with location as a fixed effect and animal as a random effect.</p></caption><graphic mime-subtype="jpeg" mimetype="image" xlink:href="elife-52258.xml.media/fig7.jpg"/></fig><p>Is inter-animal variation present in PCA dimensions that account for dorsoventral variation? The intercept, but not the slope of the dependence of the first two principal components on dorsoventral position depended on housing (adjusted p=0.039 and 0.027) (<xref ref-type="fig" rid="fig7">Figure 7E,F</xref> and <xref ref-type="supplementary-material" rid="supp15">Supplementary file 15</xref>). After accounting for housing, the first two principal components were still better fit by models that include animal identity as a random effect (adjusted p=3.3×10<sup>−9</sup> and 4.1 × 10<sup>−86</sup>), indicating remaining inter-animal differences in these components (<xref ref-type="supplementary-material" rid="supp16">Supplementary file 16</xref>). A further nine of the next ten higher-order principal components did not depend on housing (adjusted p>0.1) (<xref ref-type="supplementary-material" rid="supp15">Supplementary file 15</xref>), while eight differed significantly between animals (adjusted p<0.05) (<xref ref-type="supplementary-material" rid="supp16">Supplementary file 16</xref>).</p><p>Together, these analyses indicate that the dorsoventral organization of multiple electrophysiological features of SCs is captured by two principal components, suggesting two main sources of variance, both of which are dependent on experience. Significant inter-animal variation in the major sources of variance remains after accounting for experience and experimental parameters.</p></sec></sec><sec id="s3" sec-type="discussion"><title>Discussion</title><p>Phenotypic variation is found across many areas of biology (<xref ref-type="bibr" rid="bib29">Geiler-Samerotte et al., 2013</xref>), but has received little attention in investigations of mammalian nervous systems. We find unexpected inter-animal variability in SC properties, suggesting that the integrative properties of neurons are determined by set points that differ between animals and are controlled at a circuit level (<xref ref-type="fig" rid="fig8">Figure 8</xref>). Continuous, location-dependent organization of set points for SC integrative properties provides new constraints on models for grid cell firing. More generally, the existence of inter-animal differences in set points has implications for experimental design and raises new questions about how the integrative properties of neurons are specified.</p><fig id="fig8" position="float"><label>Figure 8.</label><caption><title>Models for intra- and inter-animal variation.</title><p>(<bold>A</bold>) The configuration of a cell type can be conceived of as a trough (arrow head) in a developmental landscape (solid line). In this scheme, the trough can be considered as a set point. Differences between cells (filled circles) reflect variation away from the set point. (<bold>B</bold>) Neurons from different animals or located at different dorsoventral positions can be conceptualized as arising from different troughs in the developmental landscape. (<bold>C</bold>) Variation may reflect inter-animal differences in factors that establish gradients (upper left) and in factors that are uniformly distributed (lower left), combining to generate set points that depend on animal identity and location (right). Each line corresponds to schematized properties of a single animal.</p></caption><graphic mime-subtype="jpeg" mimetype="image" xlink:href="elife-52258.xml.media/fig8.jpg"/></fig><sec id="s3-1"><title>A conceptual framework for within cell type variability</title><p>Theoretical models suggest how different cell types can be generated by varying target concentrations of intracellular Ca<sup>2+</sup> or rates of ion channel expression (<xref ref-type="bibr" rid="bib56">O'Leary et al., 2014</xref>). The within cell type variability predicted by these models arises from different initial conditions and may explain the variability in our data between neurons from the same animal at the same dorsoventral location (<xref ref-type="fig" rid="fig8">Figure 8A</xref>). By contrast, the dependence of integrative properties on position and their variation between animals implies additional mechanisms that operate at the circuit level (<xref ref-type="fig" rid="fig8">Figure 8B</xref>). In principle, this variation could be accounted for by inter-animal differences in dorsoventrally tuned or spatially uniform factors that influence ion channel expression or target points for intracellular Ca<sup>2+</sup> (<xref ref-type="fig" rid="fig8">Figure 8C</xref>).</p><p>The mechanisms for within cell type variability that are suggested by our results may differ from inter-animal variation described in invertebrate nervous systems. In invertebrates, inter-animal variability is between properties of individual identified neurons (<xref ref-type="bibr" rid="bib36">Goaillard et al., 2009</xref>), whereas in mammalian nervous systems, neurons are not individually identifiable and the variation that we describe here is at the level of cell populations. From a developmental perspective in which cell identity is considered as a trough in a state-landscape through which each cell moves (<xref ref-type="bibr" rid="bib79">Wang et al., 2011b</xref>), variation in the population of neurons of the same type could be conceived as cell autonomous deviations from set points corresponding to the trough (<xref ref-type="fig" rid="fig8">Figure 8A</xref>). Our finding that variability among neurons of the same type manifests between as well as within animals, could be explained by differences between animals in the position of the trough or set point in the developmental landscape (<xref ref-type="fig" rid="fig8">Figure 8B</xref>).</p><p>Our comparison of neurons from animals in standard and large cages provides evidence for the idea that within cell-type excitable properties are modified by experience (<xref ref-type="bibr" rid="bib85">Zhang and Linden, 2003</xref>). For example, granule cells in the dentate gyrus that receive input from SCs increase their excitability when animals are housed in enriched environments (<xref ref-type="bibr" rid="bib38">Green and Greenough, 1986</xref>; <xref ref-type="bibr" rid="bib57">Ohline and Abraham, 2019</xref>). Our experiments differ in that we increased the size of the environment with the goal of activating more ventral grid cells, whereas previous enrichment experiments have focused on increasing the environmental complexity and availability of objects for exploration. Further investigation will be required to dissociate the influence of each factor on excitability.</p></sec><sec id="s3-2"><title>Implications of continuous dorsoventral organization of stellate cell integrative properties for grid cell firing</title><p>Dorsoventral gradients in the electrophysiological features of SCs have stimulated cellular models for the organization of grid firing (<xref ref-type="bibr" rid="bib15">Burgess, 2008</xref>; <xref ref-type="bibr" rid="bib34">Giocomo and Hasselmo, 2008b</xref>; <xref ref-type="bibr" rid="bib39">Grossberg and Pilly, 2012</xref>; <xref ref-type="bibr" rid="bib55">O'Donnell and Nolan, 2011</xref>; <xref ref-type="bibr" rid="bib81">Widloski and Fiete, 2014</xref>). Increases in spatial scale following deletion of HCN1 channels (<xref ref-type="bibr" rid="bib31">Giocomo et al., 2011</xref>), which in part determine the dorsoventral organization of SC integrative properties (<xref ref-type="bibr" rid="bib28">Garden et al., 2008</xref>; <xref ref-type="bibr" rid="bib35">Giocomo and Hasselmo, 2009</xref>), support a relationship between the electrophysiological properties of SCs and grid cell spatial scales. Our data argue against models that explain this relationship through single cell computations (<xref ref-type="bibr" rid="bib15">Burgess, 2008</xref>; <xref ref-type="bibr" rid="bib14">Burgess et al., 2007</xref>; <xref ref-type="bibr" rid="bib30">Giocomo et al., 2007</xref>), as in this case, the modularity of integrative properties of SCs is required to generate modularity of grid firing. A continuous dorsoventral organization of the electrophysiological properties of SCs could support the modular grid firing generated by self-organizing maps (<xref ref-type="bibr" rid="bib39">Grossberg and Pilly, 2012</xref>) or by synaptic learning mechanisms (<xref ref-type="bibr" rid="bib45">Kropff and Treves, 2008</xref>; <xref ref-type="bibr" rid="bib76">Urdapilleta et al., 2017</xref>). It is less clear how a continuous gradient would affect the organization of grid firing predicted by continuous attractor network models, which can instead account for modularity by limiting synaptic interactions between modules (<xref ref-type="bibr" rid="bib13">Burak and Fiete, 2009</xref>; <xref ref-type="bibr" rid="bib17">Bush and Burgess, 2014</xref>; <xref ref-type="bibr" rid="bib26">Fuhs and Touretzky, 2006</xref>; <xref ref-type="bibr" rid="bib41">Guanella et al., 2007</xref>; <xref ref-type="bibr" rid="bib70">Shipston-Sharman et al., 2016</xref>; <xref ref-type="bibr" rid="bib81">Widloski and Fiete, 2014</xref>; <xref ref-type="bibr" rid="bib82">Yoon et al., 2013</xref>). Modularity of grid cell firing could also arise through the anatomical clustering of calbindin-positive L2PCs (<xref ref-type="bibr" rid="bib63">Ray et al., 2014</xref>; <xref ref-type="bibr" rid="bib64">Ray and Brecht, 2016</xref>). Because many SCs do not appear to generate grid codes and as the most abundant functional cell type in the MEC appears to be non-grid spatial neurons (<xref ref-type="bibr" rid="bib20">Diehl et al., 2017</xref>; <xref ref-type="bibr" rid="bib43">Hardcastle et al., 2017</xref>), the continuous dorsoventral organization of SC integrative properties may also impact grid firing indirectly through modulation of these codes.</p><p>Our results add to previous comparisons of medially and laterally located SCs (<xref ref-type="bibr" rid="bib18">Canto and Witter, 2012</xref>; <xref ref-type="bibr" rid="bib83">Yoshida et al., 2013</xref>). The similar dorsoventral organization of subthreshold integrative properties of SCs from medial and lateral parts of the MEC appears consistent with the organization of grid cell modules recorded in behaving animals (<xref ref-type="bibr" rid="bib71">Stensola et al., 2012</xref>). How mediolateral differences in firing properties (<xref ref-type="fig" rid="fig4s1">Figure 4—figure supplement 1</xref>; <xref ref-type="bibr" rid="bib18">Canto and Witter, 2012</xref>; <xref ref-type="bibr" rid="bib83">Yoshida et al., 2013</xref>) might contribute to spatial computations within the MEC is unclear.</p><p>The continuous dorsoventral variation of the electrophysiological features of SCs suggested by our analysis is consistent with continuous dorsoventral gradients in gene expression along layer 2 of the MEC (<xref ref-type="bibr" rid="bib62">Ramsden et al., 2015</xref>). For example, labelling of the mRNA and protein for the HCN1 ion channel suggests a continuous dorsoventral gradient in its expression (<xref ref-type="bibr" rid="bib53">Nolan et al., 2007</xref>; <xref ref-type="bibr" rid="bib62">Ramsden et al., 2015</xref>). It is also consistent with single-cell RNA sequencing analysis of other brain areas, which indicates that although the expression profiles for some cell types cluster around a point in feature space, others lie along a continuum (<xref ref-type="bibr" rid="bib19">Cembrowski and Menon, 2018</xref>). It will be interesting in future to determine whether gene expression continua establish corresponding continua of electrophysiological features (<xref ref-type="bibr" rid="bib47">Liss et al., 2001</xref>).</p></sec><sec id="s3-3"><title>Functional consequences of within cell type inter-animal variability</title><p>What are the functional roles of inter-animal variability? In the crab stomatogastric ganglion, inter-animal variation correlates with circuit performance (<xref ref-type="bibr" rid="bib36">Goaillard et al., 2009</xref>). Accordingly, variation in intrinsic properties of SCs might correlate with differences in grid firing (<xref ref-type="bibr" rid="bib22">Domnisoru et al., 2013</xref>; <xref ref-type="bibr" rid="bib40">Gu et al., 2018</xref>; <xref ref-type="bibr" rid="bib66">Rowland et al., 2018</xref>; <xref ref-type="bibr" rid="bib68">Schmidt-Hieber and Häusser, 2013</xref>) or behaviors that rely on SCs (<xref ref-type="bibr" rid="bib44">Kitamura et al., 2014</xref>; <xref ref-type="bibr" rid="bib61">Qin et al., 2018</xref>; <xref ref-type="bibr" rid="bib74">Tennant et al., 2018</xref>). It is interesting in this respect that there appear to be inter-animal differences in the spatial scale of grid modules (Figure 5 of <xref ref-type="bibr" rid="bib71">Stensola et al., 2012</xref>). Modification of grid field scaling following deletion of HCN1 channels is also consistent with this possibility (<xref ref-type="bibr" rid="bib31">Giocomo et al., 2011</xref>; <xref ref-type="bibr" rid="bib48">Mallory et al., 2018</xref>). Alternatively, inter-animal differences may reflect multiple ways to achieve a common higher-order phenotype. According to this view, coding of spatial location by SCs would not differ between animals despite lower level variation in their intrinsic electrophysiological features. This is related to the idea of degeneracy at the level of single-cell electrophysiological properties (<xref ref-type="bibr" rid="bib49">Marder and Goaillard, 2006</xref>; <xref ref-type="bibr" rid="bib51">Mittal and Narayanan, 2018</xref>; <xref ref-type="bibr" rid="bib56">O'Leary et al., 2014</xref>; <xref ref-type="bibr" rid="bib73">Swensen and Bean, 2005</xref>), except that here the electrophysiological features differ between animals whereas the higher-order circuit computations may nevertheless be similar.</p><p>In conclusion, our results identify substantial within cell type variation in neuronal integrative properties that manifests between as well as within animals. This has implications for experimental design and model building as the distribution of replicates from the same animal will differ from those obtained from different animals (<xref ref-type="bibr" rid="bib50">Marder and Taylor, 2011</xref>). An important future goal will be to distinguish causes of inter-animal variation. Many behaviors are characterized by substantial inter-animal variation (e.g. <xref ref-type="bibr" rid="bib77">Villette et al., 2017</xref>), which could result from variation in neuronal integrative properties, or could drive this variation. For example, it is possible that external factors such as social interactions may affect brain circuitry (<xref ref-type="bibr" rid="bib78">Wang et al., 2011a</xref>; <xref ref-type="bibr" rid="bib80">Wang et al., 2014</xref>), although these effects appear to be focused on frontal cortical structures rather than circuits for spatial computations (<xref ref-type="bibr" rid="bib80">Wang et al., 2014</xref>). Alternatively, stochastic mechanisms operating at the population level may drive the emergence of inter-animal differences during the development of SCs (<xref ref-type="bibr" rid="bib23">Donato et al., 2017</xref>; <xref ref-type="bibr" rid="bib64">Ray and Brecht, 2016</xref>). Addressing these questions may turn out to be critical to understanding the relationship between cellular biophysics and circuit-level computations in cognitive circuits (<xref ref-type="bibr" rid="bib69">Schmidt-Hieber and Nolan, 2017</xref>).</p></sec></sec><sec id="s4" sec-type="materials|methods"><title>Materials and methods</title><sec id="s4-1"><title>Mouse strains</title><p>All experimental procedures were performed under a United Kingdom Home Office license and with approval of the University of Edinburgh’s animal welfare committee. Recordings of many SCs per animal used C57Bl/6J mice (Charles River). Recordings targeting calbindin cells used a <italic>Wfs1</italic><sup>Cre</sup> line (<italic>Wfs1</italic>-Tg3-CreERT2) obtained from Jackson Labs (Strain name: B6;C3-Tg(<italic>Wfs1</italic>-cre/ERT2)3Aibs/J; stock number:009103) crossed to RCE:loxP (R26R CAG-boosted EGFP) reporter mice (described in <xref ref-type="bibr" rid="bib52">Miyoshi et al., 2010</xref>). To promote expression of Cre in the mice, tamoxifen (Sigma, 20 mg/ml in corn oil) was administered on three consecutive days by intraperitoneal injections, approximately 1 week before experiments. Mice were group housed in a 12 hr light/dark cycle with unrestricted access to food and water (light on 07.30–19.30 hr). Mice were usually housed in standard 0.2 × 0.37 m cages that contained a cardboard roll for enrichment. A subset of the mice was instead housed from pre-weaning ages in a larger 2.4 × 1.2 m cage that was enriched with up to 15 bright plastic objects and eight cardboard rolls (<xref ref-type="fig" rid="fig2s1">Figure 2—figure supplement 1</xref>). Thus, the large cages had more items but at a slightly lower density (large cages — up to 1 item per 0.125 m<sup>2</sup>; standard cages — 1 item per 0.074 m<sup>2</sup>). All experiments in the standard cage used male mice. For experiments in the large cage, two mice were female, six mice were male and one was not identified. Because we did not find significant effects of sex on individual electrophysiologically properties, all mice were included in the analyses reported in the text. When only male mice were included, the effects of housing on the first principal component remained significant, whereas the effects of housing on individual electrophysiologically properties no longer reach statistical significance after correcting for multiple comparisons. Additional analyses that consider only male mice are provided in the code associated with the manuscript.</p></sec><sec id="s4-2"><title>Slice preparation</title><p>Methods for preparation of parasagittal brain slices containing medial entorhinal cortex were based on procedures described previously (<xref ref-type="bibr" rid="bib59">Pastoll et al., 2012b</xref>). Briefly, mice were sacrificed by cervical dislocation and their brains carefully removed and placed in cold (2–4°C) modified ACSF, with composition (in mM): NaCl 86, NaH<sub>2</sub>PO<sub>4</sub> 1.2, KCl 2.5, NaHCO<sub>3</sub> 25, glucose 25, sucrose 75, CaCl<sub>2</sub> 0.5, and MgCl<sub>2</sub> 7. Brains were then hemisected and sectioned, also in modified ACSF at 4–8°C, using a vibratome (Leica VT1200S). To minimize variation in the slicing angle, the hemi-section was cut along the midline of the brain and the cut surface of the brain was glued to the cutting block. After cutting, brains were placed at 36°C for 30 min in standard ACSF, with composition (in mM): NaCl 124, NaH<sub>2</sub>PO4 1.2, KCl 2.5, NaHCO<sub>3</sub> 25, glucose 20, CaCl<sub>2</sub> 2, and MgCl<sub>2</sub> 1. They were then allowed to cool passively to room temperature. All slices were prepared by the same experimenter (HP), who followed the same procedure on each day.</p></sec><sec id="s4-3"><title>Recording methods</title><p>Whole-cell patch-clamp recordings were made between 1 to 10 hr after slice preparation using procedures described previously (<xref ref-type="bibr" rid="bib60">Pastoll et al., 2013</xref>; <xref ref-type="bibr" rid="bib58">Pastoll et al., 2012a</xref>; <xref ref-type="bibr" rid="bib59">Pastoll et al., 2012b</xref>; <xref ref-type="bibr" rid="bib72">Sürmeli et al., 2015</xref>). Recordings were made from slice perfused in standard ACSF maintained at 34–36°C. In these conditions, we observe spontaneous fast inhibitory and excitatory postsynaptic potentials, but do not find evidence for tonic GABAergic or glutamatergic currents. Patch electrodes were filled with the following intracellular solution (in mM): K gluconate 130; KCl 10, HEPES 10, MgCl<sub>2</sub> 2, EGTA 0.1, Na<sub>2</sub>ATP 2, Na<sub>2</sub>GTP 0.3 and NaPhosphocreatine 10. The open tip resistance was 4–5 MΩ, all seal resistances were >2 GΩ and series resistances were <30 MΩ. Recordings were made in current clamp mode using Multiclamp 700B amplifiers (Molecular Devices, Sunnyvale, CA, USA) connected to PCs via Instrutech ITC-18 interfaces (HEKA Elektronik, Lambrecht, Germany) and using Axograph X acquisition software (<ext-link ext-link-type="uri" xlink:href="http://axographx.com/">http://axographx.com/</ext-link>). Pipette capacitance and series resistances were compensated using the capacitance neutralization and bridge-balance amplifier controls. An experimentally measured liquid junction potential of 12.9 mV was not corrected for. Stellate cells were identified by their large sag response and the characteristic waveform of their action potential after hyperpolarization (see <xref ref-type="bibr" rid="bib2">Alonso and Klink, 1993</xref>; <xref ref-type="bibr" rid="bib37">Gonzalez-Sulser et al., 2014</xref>; <xref ref-type="bibr" rid="bib53">Nolan et al., 2007</xref>; <xref ref-type="bibr" rid="bib58">Pastoll et al., 2012a</xref>).</p><p>To maximize the number of cells recorded per animal, we adopted two strategies. First, to minimize the time required to obtain data from each recorded cell, we measured electrophysiological features using a series of three short protocols following initiation of stable whole-cell recordings. We used responses to sub-threshold current steps to estimate passive membrane properties (<xref ref-type="fig" rid="fig2">Figure 2A</xref>), a frequency modulated sinusoidal current waveform (ZAP waveform) to estimate impedance amplitude profiles (<xref ref-type="fig" rid="fig2">Figure 2B</xref>), and a linear current ramp to estimate the action potential threshold and firing properties (<xref ref-type="fig" rid="fig2">Figure 2C</xref>). From analysis of data obtained with these protocols, we obtained 12 quantitative measures that describe the sub- and supra-threshold integrative properties of each recorded cell (<xref ref-type="fig" rid="fig2">Figure 2A–C</xref>). Second, for the majority of mice, two experimenters made recordings in parallel from neurons in two sagittal brain sections from the same hemisphere. The median dorsal-ventral extent of the recorded SCs was 1644 µm (range 0–2464 µm). Each experimenter aimed to sample recording locations evenly across the dorsoventral extent of the MEC, and for most animals, each experimenter recorded sequentially from opposite extremes of the dorsoventral axis. Each experimenter varied the starting location for recording between animals. For several features, the direction of recording affected their measured dependence on dorsoventral location, but the overall dependence of these features on dorsoventral location was robust to this effect (<xref ref-type="supplementary-material" rid="supp9">Supplementary file 9</xref>).</p></sec><sec id="s4-4"><title>Measurement of electrophysiological features and neuronal location</title><p>Electrophysiological recordings were analyzed in Matlab (Mathworks) using a custom-written semi-automated pipeline. We defined each feature as follows (see also <xref ref-type="bibr" rid="bib53">Nolan et al., 2007</xref>; <xref ref-type="bibr" rid="bib58">Pastoll et al., 2012a</xref>): resting membrane potential was the mean of the membrane potential during the 1 s prior to injection of the current steps used to assess subthreshold properties; input resistance was the steady-state voltage response to the negative current steps divided by their amplitude; membrane time constant was the time constant of an exponential function fit to the initial phase of membrane potential responses to the negative current steps; the sag coefficient was the steady-state divided by the peak membrane potential response to the negative current steps; resonance frequency was the frequency at which the peak membrane potential impedance was found to occur; resonance magnitude was the ratio between the peak impedance and the impedance at a frequency of 1 Hz; action potential threshold was calculated from responses to positive current ramps as the membrane potential at which the first derivative of the membrane potential crossed 20 mv ms<sup>−1</sup> averaged across the first five spikes, or fewer if fewer spikes were triggered; rheobase was the ramp current at the point when the threshold was crossed on the first spike; spike maximum was the mean peak amplitude of the action potentials triggered by the positive current ramp; spike width was the duration of the action potentials measured at the voltage corresponding to the midpoint between the spike threshold and spike maximum; the AHP minimum was the negative peak membrane potential of the after hyperpolarization following the first action potential when a second action potential also occurred; and the F-I slope was the linear slope of the relationship between the spike rate and the injected ramp current over a 500 ms window.</p><p>The location of each recorded neuron was estimated as described previously (<xref ref-type="bibr" rid="bib28">Garden et al., 2008</xref>; <xref ref-type="bibr" rid="bib59">Pastoll et al., 2012b</xref>). Following each recording, a low magnification image was taken of the slice with the patch-clamp electrode at the recording location. The image was calibrated and then the distance measured from the dorsal border of the MEC along the border of layers 1 and 2 to the location of the recorded cell.</p></sec><sec id="s4-5"><title>Analysis of location-dependence, experience-dependence and inter-animal differences</title><p>Analyses of location-dependence and inter-animal differences used R 3.4.3 (R Core Team, Vienna, Austria) and R Studio 1.1.383 (R Studio Inc, Boston, MA).</p><p>To fit linear mixed effect models, we used the lme4 package (<xref ref-type="bibr" rid="bib8">Bates et al., 2014</xref>). Features of interest were included as fixed effects and animal identity was included as a random effect. All reported analyses are for models with the minimal a priori random effect structure, in other words the random effect was specified with uncorrelated slope and intercept. We also evaluated models in which only the intercept, or correlated intercept and slope were specified as the random effect. Model assessment was performed using Akaike Information Criterion (AIC) scores. In general, models with either random slope and intercept, or correlated random slope and intercept, had lower AIC scores than random intercept only models, indicating a better fit to the data. We used the former set of models for all analyses of all properties for consistency and because a maximal effect structure may be preferable on theoretical grounds (<xref ref-type="bibr" rid="bib5">Barr et al., 2013</xref>). We evaluated assumptions including linearity, normality, homoscedasticity and influential data points. For some features, we found modest deviations from these assumptions that could be remedied by handling non-linearity in the data using a copula transformation. Model fits were similar following transformation of the data. However, we focus here on analyses of the untransformed data because the physical interpretation of the resulting values for data points is clearer.</p><p>To evaluate the location-dependence of a given feature, p-values were calculated using a χ<sup>2</sup> test comparing models to null models with no location information but identical random effect specification. To calculate marginal and conditional R<sup>2</sup> of mixed effect models, we used the MuMin package (<xref ref-type="bibr" rid="bib7">Bartoń, 2014</xref>). To evaluate additional fixed effects, we used Type II Wald χ<sup>2</sup> test tests provided by the car package (<xref ref-type="bibr" rid="bib25">Fox and Weisberg, 2018</xref>). To compare mixed effect with equivalent linear models, we used a χ<sup>2</sup> test to compare the calculated deviance for each model. For clarity, we have reported key statistics in the main text and provide full test statistics in the Supplemental Tables. In addition, the code from which the analyses can be fully reproduced is available at <ext-link ext-link-type="uri" xlink:href="https://github.com/MattNolanLab/Inter_Intra_Variation">https://github.com/MattNolanLab/Inter_Intra_Variation</ext-link> (<xref ref-type="bibr" rid="bib54">Nolan, 2020</xref>; copy archived at <ext-link ext-link-type="uri" xlink:href="https://github.com/elifesciences-publications/Inter_Intra_Variation">https://github.com/elifesciences-publications/Inter_Intra_Variation</ext-link>).</p><p>To evaluate partial correlations between features, we used the function cor2pcor from the R package corpcor (<xref ref-type="bibr" rid="bib67">Schafer et al., 2017</xref>). Principal components analysis used core R functions.</p></sec><sec id="s4-6"><title>Implementation of tests for modularity</title><p>To establish statistical tests to distinguish ‘modular’ from ‘continuous’ distributions given relatively few observations, we classified datasets as continuous or modular by modifying the gap statistic algorithm (<xref ref-type="bibr" rid="bib75">Tibshirani et al., 2001</xref>). The gap statistic estimates the number of clusters (k<sub>est</sub>) that best account for the data in any given dataset (<xref ref-type="fig" rid="fig1s1">Figure 1—figure supplement 1A-C</xref>). However, this estimate may be prone to false positives, particularly where the numbers of observations are low. We therefore introduced a thresholding mechanism for tuning the sensitivity of the algorithm so that the false-positive rate, which is the rate of misclassifying datasets drawn from continuous (uniform) distributions as ‘modular’, is low, constant across different numbers of cluster modes and insensitive to dataset size (<xref ref-type="fig" rid="fig1s1">Figure 1—figure supplement 1D-G</xref>). With this approach, we are able to estimate whether a dataset is best described as lacking modularity (k<sub>est</sub> = 1), or having a given number of modes (k<sub>est</sub> > 1). Below, we describe tests carried out to validate the approach.</p><p>To illustrate the sensitivity and specificity of the modified gap statistic algorithm, we applied it to simulated datasets drawn either from a uniform distribution (k = 1, n = 40) or from a bimodal distribution with separation between the modes of five standard deviations (k = 2, n = 40, sigma = 5) (<xref ref-type="fig" rid="fig1s2">Figure 1—figure supplement 2A</xref>). We set the thresholding mechanism so that k<sub>est</sub> for each distinct k (where k<sub>est</sub> ≥2) has a false-positive rate of 0.01. In line with this, testing for 2 ≤ k<sub>est</sub> ≤ 8 (the maximum k expected to occur in grid spacing in the MEC), across multiple (N = 1000) simulated datasets drawn from the uniform distribution, produced a low false-positive rate (P(k<sub>est</sub>)≥2 = ~0.07), whereas when the data were drawn from the bimodal distribution, the ability to detect modular organization (p<sub>detect</sub>) was good (P[k<sub>est</sub>]≥2 = ~0.8) (<xref ref-type="fig" rid="fig1s2">Figure 1—figure supplement 2B</xref>). The performance of the statistic improved with larger separation between clusters and with greater numbers of data points per dataset (<xref ref-type="fig" rid="fig1s2">Figure 1—figure supplement 2C</xref>) and is relatively insensitive to the numbers of clusters (<xref ref-type="fig" rid="fig1s2">Figure 1—figure supplement 2D</xref>). The algorithm maintains high rates of p<sub>detect</sub> when modes have varying densities and when sigma between modes varies in a manner similar to grid spacing data (<xref ref-type="fig" rid="fig1s3">Figure 1—figure supplement 3</xref>).</p></sec><sec id="s4-7"><title>Analysis of extracellular recording data from other laboratories</title><p>Recently described algorithms (<xref ref-type="bibr" rid="bib32">Giocomo et al., 2014</xref>; <xref ref-type="bibr" rid="bib71">Stensola et al., 2012</xref>) address the problem of identifying modularity when data are sampled from multiple locations and data values vary as a function of location, as is the case for the mean spacing of grid fields for cells at different dorsoventral locations recorded in behaving animals using tetrodes (<xref ref-type="bibr" rid="bib42">Hafting et al., 2005</xref>). They generate log-normalized discontinuity (which we refer to here as lnDS) or discreteness scores, which are the log of the ratio of discontinuity or discreteness scores for the data points of interest and for the sampling locations, with positive values interpreted as evidence for clustering (<xref ref-type="bibr" rid="bib32">Giocomo et al., 2014</xref>; <xref ref-type="bibr" rid="bib71">Stensola et al., 2012</xref>). However, in simulations of datasets generated from a uniform distribution with evenly spaced recording locations, we find that the lnDS is always greater than zero (<xref ref-type="fig" rid="fig1s4">Figure 1—figure supplement 4A</xref>). This is because evenly spaced locations result in a discontinuity score that approaches zero, and therefore the log ratio of the discontinuity of the data to this score will be positive. Thus, for evenly spaced data, the lnDS is guaranteed to produce false-positive results. When locations are instead sampled from a uniform distribution, approximately half of the simulated datasets have a log discontinuity ratio greater than 0 (<xref ref-type="fig" rid="fig1s4">Figure 1—figure supplement 4A</xref>), which in previous studies would be interpreted as evidence of modularity (<xref ref-type="bibr" rid="bib32">Giocomo et al., 2014</xref>). Similar discrepancies arise for the discreteness measure (<xref ref-type="bibr" rid="bib71">Stensola et al., 2012</xref>). To address these issues, we introduced a log discontinuity ratio threshold, so that the discontinuity method could be matched to produce a similar false-positive rate to the adapted gap statistic algorithm used in the example above. After including this modification, we found that for a given false-positive rate, the adapted gap statistic is more sensitive at detecting modularity in the simulated datasets (<xref ref-type="fig" rid="fig4s1">Figure 4—figure supplement 1B</xref>).</p><p>To establish whether the modified gap statistic detects clustering in experimental data, we applied it to previously published grid cell data recorded with tetrodes from awake behaving animals (<xref ref-type="bibr" rid="bib71">Stensola et al., 2012</xref>). We find that the modified gap statistic identified clustered grid spacing for 6 of 7 animals previously identified as having grid modules and with n ≥ 20. For these animals, the number of modules was similar (but not always identical) to the number of previously identified modules (<xref ref-type="fig" rid="fig1s5">Figure 1—figure supplement 5</xref>). By contrast, the modified gap statistic does not identify clustering in five of six sets of recording locations, confirming that the grid clustering is likely not a result of uneven sampling of locations (we could not test the seventh as location data were not available). The thresholded discontinuity score also detects clustering in the same five of the six tested sets of grid data. From the six grid datasets detected as clustered with the modified gap statistic, we estimated the separation between clusters by fitting the data with a mixture of Gaussians, with the number of modes set by the value of k obtained with the modified gap statistic. This analysis suggested that the largest spacing between contiguous modules in each mouse is always >5.6 standard deviations (mean = 20.5 ± 5.0 standard deviations). Thus, the modified gap statistic detects modularity within the grid system and indicates that previous descriptions of grid modularity are, in general, robust to the possibility of false positives associated with the discreteness and discontinuity methods.</p></sec></sec></body><back><ack id="ack"><title>Acknowledgements</title><p>We thank Vanessa Stempel for comments on the manuscript, Tor Stensola and Edvard Moser for sharing published data, and Lukas Solanka and Lukas Fischer for help with building the large cage. This work was supported by grants to MN from the Wellcome Trust (200855/Z/16/Z) and the BBSRC (BB/L010496/1, BB/1022147/1 and BB/H020284/1).</p></ack><sec id="s5" sec-type="additional-information"><title>Additional information</title><fn-group content-type="competing-interest"><title>Competing interests</title><fn fn-type="COI-statement" id="conf1"><p>No competing interests declared</p></fn></fn-group><fn-group content-type="author-contribution"><title>Author contributions</title><fn fn-type="con" id="con1"><p>Conceptualization, Data curation, Software, Formal analysis, Validation, Investigation, Visualization, Methodology, Writing - original draft, Writing - review and editing</p></fn><fn fn-type="con" id="con2"><p>Formal Analysis, Investigation, Writing - reviewing and editing.</p></fn><fn fn-type="con" id="con3"><p>Formal analysis, Writing - review and editing</p></fn><fn fn-type="con" id="con4"><p>Resources, Methodology, Writing - review and editing</p></fn><fn fn-type="con" id="con5"><p>Conceptualization, Formal analysis, Supervision, Funding acquisition, Visualization, Writing - original draft, Project administration, Writing - review and editing</p></fn></fn-group><fn-group content-type="ethics-information"><title>Ethics</title><fn fn-type="other"><p>Animal experimentation: All experimental procedures were performed under a United Kingdom Home Office license (PC198F2A0) and with approval of the University of Edinburgh's animal welfare committee.</p></fn></fn-group></sec><sec id="s6" sec-type="supplementary-material"><title>Additional files</title><supplementary-material id="supp1"><label>Supplementary file 1.</label><caption><title>Dependence of calbindin cell properties on dorsoventral position.</title><p>Analyses are as described for <xref ref-type="table" rid="table1">Table 1</xref>. Data are from GFP-positive putative pyramidal neurons (n = 42, N = 3).</p></caption><media mime-subtype="docx" mimetype="application" xlink:href="elife-52258-supp1-v4.docx"/></supplementary-material><supplementary-material id="supp2"><label>Supplementary file 2.</label><caption><title>Dependence of SC properties on age.</title><p>The distinguishing electrophysiological features of SCs and their dorsoventral organization were apparent at all ages, with some features depending significantly on age (left columns), consistent with the idea that SCs continue to mature beyond P18 (<xref ref-type="bibr" rid="bib10">Boehlen et al., 2010</xref>; <xref ref-type="bibr" rid="bib16">Burton et al., 2008</xref>). When we considered only animals between P33 and P44, we did not find any significant effect of age (right columns). Significance estimates for the effects of dorsoventral position (dvloc), age (age) and interactions between dorsoventral position and age (dvloc:age) were estimated using type II ANOVA and Wald χ<sup>2</sup> test from fits to mixed models containing age and location as fixed effects and animal identity as random effects. Significance estimates were adjusted for multiple comparisons using the Benjamini and Hochberg method.</p></caption><media mime-subtype="docx" mimetype="application" xlink:href="elife-52258-supp2-v4.docx"/></supplementary-material><supplementary-material id="supp3"><label>Supplementary file 3.</label><caption><title>Dependence of SC properties on housing.</title><p>Analyses suggesting that the membrane potential sag, resonance frequency, and spike half-width of SCs differ between mice housed in standard and large home cages. Significance estimates for the effects of dorsoventral position (dvloc), housing (housing) and interactions between dorsoventral position and housing (dvloc:housing) estimated using type II ANOVA and Wald χ<sup>2</sup> test from fits to mixed models containing age and location as fixed effects and animal identity as random effects. Initial significance estimates (raw p) were adjusted for multiple comparisons (adjusted p) using the Benjamini and Hochberg method.</p></caption><media mime-subtype="docx" mimetype="application" xlink:href="elife-52258-supp3-v4.docx"/></supplementary-material><supplementary-material id="supp4"><label>Supplementary file 4.</label><caption><title>Inter-animal differences in electrophysiological features remain after accounting for housing.</title><p>Results from comparison of a mixed effect model incorporating dorsoventral location and housing with an equivalent linear model. The significance estimate (p) is calculated using a χ<sup>2</sup>test and adjusted for multiple comparisons (p_adj) using the Benjamini and Hochberg method.</p></caption><media mime-subtype="docx" mimetype="application" xlink:href="elife-52258-supp4-v4.docx"/></supplementary-material><supplementary-material id="supp5"><label>Supplementary file 5.</label><caption><title>Dependence of SC properties on hemisphere.</title><p>We did not find significant effects of brain hemisphere on any features except for the relationship between dorsoventral location and sag. Significance estimates for the effects of dorsoventral position (dvloc), brain hemisphere (hemi) and interactions between dorsoventral position and hemisphere (dvloc:hemi) were estimated using type II ANOVA and Wald χ<sup>2</sup> test from fits to mixed models containing age and location as fixed effects and animal identity as random effects. Initial significance estimates (raw p) were adjusted for multiple comparisons (adjusted p) using the Benjamini and Hochberg method.</p></caption><media mime-subtype="docx" mimetype="application" xlink:href="elife-52258-supp5-v4.docx"/></supplementary-material><supplementary-material id="supp6"><label>Supplementary file 6.</label><caption><title>Dependence of SC properties on mediolateral position.</title><p>Mediolateral as well as dorsoventral position has been reported to determine the sub-threshold electrophysiological features of SCs (<xref ref-type="bibr" rid="bib18">Canto and Witter, 2012</xref>). We found significant effects of mediolateral position on all measured electrophysiological features. However, the sizes of the effects of mediolateral position on subthreshold features (vm, ir, sag, tau, resf, resmag, and rheo) were much smaller than for dorsoventral position. By contrast, supra-threshold features (spkthr, spkmax, and ahp) were more greatly affected by mediolateral position, with more medial neurons having a higher spike threshold, and lower amplitudes of the spike peak and of after-hyperpolarization. Fixed effects are the intercept and slope coefficients for mixed models containing dorsoventral and mediolateral location as fixed effects and animal identity as random effects. Significance estimates for the effects of dorsoventral position (dvloc), mediolateral position (ml) and interactions between dorsoventral position and mediolateral position (dvloc:ml) are estimated using type II ANOVA and Wald χ<sup>2</sup> tests from the fits of the mixed models. Initial significance estimates (raw p) were adjusted for multiple comparisons (adjusted p) using the Benjamini and Hochberg method.</p></caption><media mime-subtype="docx" mimetype="application" xlink:href="elife-52258-supp6-v4.docx"/></supplementary-material><supplementary-material id="supp7"><label>Supplementary file 7.</label><caption><title>Dependence of SC properties on experimenter.</title><p>We found that for many electrophysiological features, the identity of the experimenter affected the intercept, but not the slope, of their relationship with dorsoventral position. All features except for spike threshold nevertheless followed a dorsoventral organization after accounting for the experimenter. Significance estimates for the effects of dorsoventral position (dvloc), experimenter (exp) and interactions between dorsoventral position and experimenter (dvloc:exp) were estimated using type II ANOVA and Wald χ<sup>2</sup> tests from fits to mixed models containing age and location as fixed effects and animal identity as random effects. Initial significance estimates (raw p) were adjusted for multiple comparisons (adjusted p) using the Benjamini and Hochberg method.</p></caption><media mime-subtype="docx" mimetype="application" xlink:href="elife-52258-supp7-v4.docx"/></supplementary-material><supplementary-material id="supp8"><label>Supplementary file 8.</label><caption><title>Dependence of SC properties on time since slice preparation.</title><p>We anticipated that the interval between slice preparation and recording may influence the measured electrophysiological features. Consistent with our expectation, analyses of the data were consistent with changes to some electrophysiological features of SCs with time since slice preparation, but dorsoventral gradients could not be explained by these changes. Significance estimates for the effects of dorsoventral position (dvloc), time since slice preparation (rect) and interactions between dorsoventral position and experimenter (dvloc:rect) estimated using type II ANOVA and Wald χ<sup>2</sup> tests from fits to mixed models containing age and location as fixed effects and animal identity as random effects. Initial significance estimates (raw p) were adjusted for multiple comparisons (adjusted p) using the Benjamini and Hochberg method.</p></caption><media mime-subtype="docx" mimetype="application" xlink:href="elife-52258-supp8-v4.docx"/></supplementary-material><supplementary-material id="supp9"><label>Supplementary file 9.</label><caption><title>Dependence of SC properties on direction in which sequential recordings are made.</title><p>In anticipation of the effects of the time since slice preparation on the electrophysiological features of SCS, we varied the direction along the dorsoventral axis from which consecutive recordings were made between experimenters and experimental days (see 'Materials and methods'). Consistent with effects of time on electrophysiological features (see <xref ref-type="supplementary-material" rid="supp7">Supplementary file 7</xref> above), we found that the direction in which sequential recordings were made influenced the slope, but not the intercept of several electrophysiological features. Significance estimates for the effects of dorsoventral position (dvloc), direction in which sequential recordings were made (dir) and interactions between dorsoventral position and recording direction (dvloc:dir) estimated using type II ANOVA and Wald χ<sup>2</sup> tests from fits to mixed models containing age and location as fixed effects and animal identity as random effects. Initial significance estimates (raw p) were adjusted for multiple comparisons (adjusted p) using the Benjamini and Hochberg method.</p></caption><media mime-subtype="docx" mimetype="application" xlink:href="elife-52258-supp9-v4.docx"/></supplementary-material><supplementary-material id="supp10"><label>Supplementary file 10.</label><caption><title>Inter-animal differences in extended models.</title><p>Results from comparison of a mixed effect model incorporating dorsoventral location, housing, mediolateral position, experimenter identity and direction in which recordings were obtained with an equivalent linear model. Data are from animals between 32 and 45 days old. The significance estimate (p) is calculated using a χ<sup>2</sup> test and adjusted for multiple comparisons (p_adj) using the Benjamini and Hochberg method.</p></caption><media mime-subtype="docx" mimetype="application" xlink:href="elife-52258-supp10-v4.docx"/></supplementary-material><supplementary-material id="supp11"><label>Supplementary file 11.</label><caption><title>Inter-animal differences in models fit to minimal datasets.</title><p>Results from comparison of mixed effect models with dorsoventral location as a fixed effect and animal identity as a random effect using minimal datasets obtained by either HP (upper) or DG (lower). Data are from animals between 32 and 45 days old. Because of the smaller size of these datasets, the statistical power to detect inter-animal variation is reduced. Nevertheless, in these analyses, the conditional R<sup>2</sup> of the mixed model fit was again substantially higher than the marginal R<sup>2</sup>, and most (9/12) features were better fit by a mixed model compared to a corresponding linear model in both datasets.</p></caption><media mime-subtype="docx" mimetype="application" xlink:href="elife-52258-supp11-v4.docx"/></supplementary-material><supplementary-material id="supp12"><label>Supplementary file 12.</label><caption><title>Electrophysiological features and the number of recorded neurons.</title><p>Significance estimates for the effects of dorsoventral position (dvloc), number of recorded neurons (counts) and interactions between dorsoventral position and number of recorded neurons (dvloc:counts) estimated using type II ANOVA and Wald χ<sup>2</sup> tests from fits to mixed models containing age and location as fixed effects and animal identity as random effects. Initial significance estimates (raw p) were adjusted for multiple comparisons (adjusted p) using the Benjamini and Hochberg method.</p></caption><media mime-subtype="docx" mimetype="application" xlink:href="elife-52258-supp12-v4.docx"/></supplementary-material><supplementary-material id="supp13"><label>Supplementary file 13.</label><caption><title>Inter-animal differences for experiments with >35 recorded neurons.</title><p>Analyses of inter-animal differences focusing only on data from animals for which > 35 recordings were made (N = 11, n = 459). Comparison of marginal and conditional R<sup>2</sup> values continued to indicate substantial inter-animal variance, and fits obtained with mixed models remained significantly different to fits that did not account for animal identity (p<4.4×10<sup>−5</sup>). Analyses are as for <xref ref-type="supplementary-material" rid="supp1">Supplementary file 1</xref>, but are restricted to experiments in which > 35 neurons were recorded from.</p></caption><media mime-subtype="docx" mimetype="application" xlink:href="elife-52258-supp13-v4.docx"/></supplementary-material><supplementary-material id="supp14"><label>Supplementary file 14.</label><caption><title>Dependence of principal components on dorsoventral position and animal identity.</title><p>Analyses are as described for <xref ref-type="table" rid="table1">Table 1</xref>, but were applied to principal components of the electrophysiological features of SCs.</p></caption><media mime-subtype="docx" mimetype="application" xlink:href="elife-52258-supp14-v4.docx"/></supplementary-material><supplementary-material id="supp15"><label>Supplementary file 15.</label><caption><title>Dependence of principal components of SC properties on housing.</title><p>Analyses are as described for <xref ref-type="supplementary-material" rid="supp3">Supplementary file 3</xref>, but are applied to principal components of the electrophysiological features of SCs.</p></caption><media mime-subtype="docx" mimetype="application" xlink:href="elife-52258-supp15-v4.docx"/></supplementary-material><supplementary-material id="supp16"><label>Supplementary file 16.</label><caption><title>Dependence of principal components on animal identity in models that account for housing.</title><p>Analyses are as for <xref ref-type="supplementary-material" rid="supp10">Supplementary file 10</xref>, but are applied to principal components of the electrophysiological features of SCs.</p></caption><media mime-subtype="docx" mimetype="application" xlink:href="elife-52258-supp16-v4.docx"/></supplementary-material><supplementary-material id="transrepform"><label>Transparent reporting form</label><media mime-subtype="docx" mimetype="application" xlink:href="elife-52258-transrepform-v4.docx"/></supplementary-material></sec><sec id="s7" sec-type="data-availability"><title>Data availability</title><p>Processed data used for analyses and all associated code is available from the GitHub page for the project (<ext-link ext-link-type="uri" xlink:href="https://github.com/MattNolanLab/Inter_Intra_Variation">https://github.com/MattNolanLab/Inter_Intra_Variation</ext-link>, copy archived at <ext-link ext-link-type="uri" xlink:href="https://github.com/elifesciences-publications/Inter_Intra_Variation">https://github.com/elifesciences-publications/Inter_Intra_Variation</ext-link>). Raw data has been made available from our institutional repository and can be found at <ext-link ext-link-type="uri" xlink:href="https://doi.org/10.7488/ds/2765">https://doi.org/10.7488/ds/2765</ext-link>.</p><p>The following dataset was generated:</p><p><element-citation id="dataset1" publication-type="data" specific-use="isSupplementedBy"><person-group person-group-type="author"><name><surname>Hugh</surname><given-names>P</given-names></name><name><surname>Derek</surname><given-names>LG</given-names></name><name><surname>Matthew</surname><given-names>FN</given-names></name></person-group><year iso-8601-date="2020">2020</year><data-title>Inter- and intra-animal variation in the integrative properties of stellate cells in the medial entorhinal cortex</data-title><source>Edinburgh DataShare</source><pub-id assigning-authority="Edinburgh University" pub-id-type="doi">10.7488/ds/2765</pub-id></element-citation></p></sec><ref-list><title>References</title><ref id="bib1"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Adamson</surname> <given-names>CL</given-names></name><name><surname>Reid</surname> <given-names>MA</given-names></name><name><surname>Mo</surname> <given-names>ZL</given-names></name><name><surname>Bowne-English</surname> <given-names>J</given-names></name><name><surname>Davis</surname> <given-names>RL</given-names></name></person-group><year iso-8601-date="2002">2002</year><article-title>Firing features and potassium channel content of murine spiral ganglion neurons vary with cochlear location</article-title><source>The Journal of Comparative Neurology</source><volume>447</volume><fpage>331</fpage><lpage>350</lpage><pub-id pub-id-type="doi">10.1002/cne.10244</pub-id><pub-id pub-id-type="pmid">11992520</pub-id></element-citation></ref><ref id="bib2"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Alonso</surname> <given-names>A</given-names></name><name><surname>Klink</surname> <given-names>R</given-names></name></person-group><year iso-8601-date="1993">1993</year><article-title>Differential electroresponsiveness of stellate and pyramidal-like cells of medial entorhinal cortex layer II</article-title><source>Journal of Neurophysiology</source><volume>70</volume><fpage>128</fpage><lpage>143</lpage><pub-id pub-id-type="doi">10.1152/jn.1993.70.1.128</pub-id><pub-id pub-id-type="pmid">8395571</pub-id></element-citation></ref><ref id="bib3"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Angelo</surname> <given-names>K</given-names></name><name><surname>Rancz</surname> <given-names>EA</given-names></name><name><surname>Pimentel</surname> <given-names>D</given-names></name><name><surname>Hundahl</surname> <given-names>C</given-names></name><name><surname>Hannibal</surname> <given-names>J</given-names></name><name><surname>Fleischmann</surname> <given-names>A</given-names></name><name><surname>Pichler</surname> <given-names>B</given-names></name><name><surname>Margrie</surname> <given-names>TW</given-names></name></person-group><year iso-8601-date="2012">2012</year><article-title>A biophysical signature of network affiliation and sensory processing in mitral cells</article-title><source>Nature</source><volume>488</volume><fpage>375</fpage><lpage>378</lpage><pub-id pub-id-type="doi">10.1038/nature11291</pub-id><pub-id pub-id-type="pmid">22820253</pub-id></element-citation></ref><ref id="bib4"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Baayen</surname> <given-names>RH</given-names></name><name><surname>Davidson</surname> <given-names>DJ</given-names></name><name><surname>Bates</surname> <given-names>DM</given-names></name></person-group><year iso-8601-date="2008">2008</year><article-title>Mixed-effects modeling with crossed random effects for subjects and items</article-title><source>Journal of Memory and Language</source><volume>59</volume><fpage>390</fpage><lpage>412</lpage><pub-id pub-id-type="doi">10.1016/j.jml.2007.12.005</pub-id></element-citation></ref><ref id="bib5"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Barr</surname> <given-names>DJ</given-names></name><name><surname>Levy</surname> <given-names>R</given-names></name><name><surname>Scheepers</surname> <given-names>C</given-names></name><name><surname>Tily</surname> <given-names>HJ</given-names></name></person-group><year iso-8601-date="2013">2013</year><article-title>Random effects structure for confirmatory hypothesis testing: keep it maximal</article-title><source>Journal of Memory and Language</source><volume>68</volume><fpage>255</fpage><lpage>278</lpage><pub-id pub-id-type="doi">10.1016/j.jml.2012.11.001</pub-id></element-citation></ref><ref id="bib6"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Barry</surname> <given-names>C</given-names></name><name><surname>Hayman</surname> <given-names>R</given-names></name><name><surname>Burgess</surname> <given-names>N</given-names></name><name><surname>Jeffery</surname> <given-names>KJ</given-names></name></person-group><year iso-8601-date="2007">2007</year><article-title>Experience-dependent rescaling of entorhinal grids</article-title><source>Nature Neuroscience</source><volume>10</volume><fpage>682</fpage><lpage>684</lpage><pub-id pub-id-type="doi">10.1038/nn1905</pub-id><pub-id pub-id-type="pmid">17486102</pub-id></element-citation></ref><ref id="bib7"><element-citation publication-type="software"><person-group person-group-type="author"><name><surname>Bartoń</surname> <given-names>K</given-names></name></person-group><year iso-8601-date="2014">2014</year><data-title>MuMIn: Multi-Model Inference</data-title><publisher-name>R package version 1.10. 0</publisher-name><ext-link ext-link-type="uri" xlink:href="https://CRAN.R-project.org/package=MuMIn">https://CRAN.R-project.org/package=MuMIn</ext-link></element-citation></ref><ref id="bib8"><element-citation publication-type="preprint"><person-group person-group-type="author"><name><surname>Bates</surname> <given-names>D</given-names></name><name><surname>Mächler</surname> <given-names>M</given-names></name><name><surname>Bolker</surname> <given-names>B</given-names></name><name><surname>Walker</surname> <given-names>S</given-names></name></person-group><year iso-8601-date="2014">2014</year><article-title>Fitting linear Mixed-Effects models using lme4</article-title><source>arXiv</source><ext-link ext-link-type="uri" xlink:href="https://arxiv.org/abs/1406.5823">https://arxiv.org/abs/1406.5823</ext-link></element-citation></ref><ref id="bib9"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Benjamini</surname> <given-names>Y</given-names></name><name><surname>Hochberg</surname> <given-names>Y</given-names></name></person-group><year iso-8601-date="1995">1995</year><article-title>Controlling the false discovery rate: a practical and powerful approach to multiple testing</article-title><source>Journal of the Royal Statistical Society: Series B</source><volume>57</volume><fpage>289</fpage><lpage>300</lpage><pub-id pub-id-type="doi">10.1111/j.2517-6161.1995.tb02031.x</pub-id></element-citation></ref><ref id="bib10"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Boehlen</surname> <given-names>A</given-names></name><name><surname>Heinemann</surname> <given-names>U</given-names></name><name><surname>Erchova</surname> <given-names>I</given-names></name></person-group><year iso-8601-date="2010">2010</year><article-title>The range of intrinsic frequencies represented by medial entorhinal cortex stellate cells extends with age</article-title><source>Journal of Neuroscience</source><volume>30</volume><fpage>4585</fpage><lpage>4589</lpage><pub-id pub-id-type="doi">10.1523/JNEUROSCI.4939-09.2010</pub-id><pub-id pub-id-type="pmid">20357109</pub-id></element-citation></ref><ref id="bib11"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Booth</surname> <given-names>CA</given-names></name><name><surname>Ridler</surname> <given-names>T</given-names></name><name><surname>Murray</surname> <given-names>TK</given-names></name><name><surname>Ward</surname> <given-names>MA</given-names></name><name><surname>de Groot</surname> <given-names>E</given-names></name><name><surname>Goodfellow</surname> <given-names>M</given-names></name><name><surname>Phillips</surname> <given-names>KG</given-names></name><name><surname>Randall</surname> <given-names>AD</given-names></name><name><surname>Brown</surname> <given-names>JT</given-names></name></person-group><year iso-8601-date="2016">2016</year><article-title>Electrical and network neuronal properties are preferentially disrupted in Dorsal, but not ventral, medial entorhinal cortex in a mouse model of tauopathy</article-title><source>Journal of Neuroscience</source><volume>36</volume><fpage>312</fpage><lpage>324</lpage><pub-id pub-id-type="doi">10.1523/JNEUROSCI.2845-14.2016</pub-id><pub-id pub-id-type="pmid">26758825</pub-id></element-citation></ref><ref id="bib12"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Brun</surname> <given-names>VH</given-names></name><name><surname>Solstad</surname> <given-names>T</given-names></name><name><surname>Kjelstrup</surname> <given-names>KB</given-names></name><name><surname>Fyhn</surname> <given-names>M</given-names></name><name><surname>Witter</surname> <given-names>MP</given-names></name><name><surname>Moser</surname> <given-names>EI</given-names></name><name><surname>Moser</surname> <given-names>MB</given-names></name></person-group><year iso-8601-date="2008">2008</year><article-title>Progressive increase in grid scale from dorsal to ventral medial entorhinal cortex</article-title><source>Hippocampus</source><volume>18</volume><fpage>1200</fpage><lpage>1212</lpage><pub-id pub-id-type="doi">10.1002/hipo.20504</pub-id><pub-id pub-id-type="pmid">19021257</pub-id></element-citation></ref><ref id="bib13"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Burak</surname> <given-names>Y</given-names></name><name><surname>Fiete</surname> <given-names>IR</given-names></name></person-group><year iso-8601-date="2009">2009</year><article-title>Accurate path integration in continuous attractor network models of grid cells</article-title><source>PLOS Computational Biology</source><volume>5</volume><elocation-id>e1000291</elocation-id><pub-id pub-id-type="doi">10.1371/journal.pcbi.1000291</pub-id><pub-id pub-id-type="pmid">19229307</pub-id></element-citation></ref><ref id="bib14"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Burgess</surname> <given-names>N</given-names></name><name><surname>Barry</surname> <given-names>C</given-names></name><name><surname>O'Keefe</surname> <given-names>J</given-names></name></person-group><year iso-8601-date="2007">2007</year><article-title>An oscillatory interference model of grid cell firing</article-title><source>Hippocampus</source><volume>17</volume><fpage>801</fpage><lpage>812</lpage><pub-id pub-id-type="doi">10.1002/hipo.20327</pub-id><pub-id pub-id-type="pmid">17598147</pub-id></element-citation></ref><ref id="bib15"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Burgess</surname> <given-names>N</given-names></name></person-group><year iso-8601-date="2008">2008</year><article-title>Grid cells and theta as oscillatory interference: theory and predictions</article-title><source>Hippocampus</source><volume>18</volume><fpage>1157</fpage><lpage>1174</lpage><pub-id pub-id-type="doi">10.1002/hipo.20518</pub-id><pub-id pub-id-type="pmid">19021256</pub-id></element-citation></ref><ref id="bib16"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Burton</surname> <given-names>BG</given-names></name><name><surname>Economo</surname> <given-names>MN</given-names></name><name><surname>Lee</surname> <given-names>GJ</given-names></name><name><surname>White</surname> <given-names>JA</given-names></name></person-group><year iso-8601-date="2008">2008</year><article-title>Development of theta rhythmicity in entorhinal stellate cells of the juvenile rat</article-title><source>Journal of Neurophysiology</source><volume>100</volume><fpage>3144</fpage><lpage>3157</lpage><pub-id pub-id-type="doi">10.1152/jn.90424.2008</pub-id><pub-id pub-id-type="pmid">18829850</pub-id></element-citation></ref><ref id="bib17"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Bush</surname> <given-names>D</given-names></name><name><surname>Burgess</surname> <given-names>N</given-names></name></person-group><year iso-8601-date="2014">2014</year><article-title>A hybrid oscillatory interference/continuous attractor network model of grid cell firing</article-title><source>The Journal of Neuroscience</source><volume>34</volume><fpage>5065</fpage><lpage>5079</lpage><pub-id pub-id-type="doi">10.1523/JNEUROSCI.4017-13.2014</pub-id><pub-id pub-id-type="pmid">24695724</pub-id></element-citation></ref><ref id="bib18"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Canto</surname> <given-names>CB</given-names></name><name><surname>Witter</surname> <given-names>MP</given-names></name></person-group><year iso-8601-date="2012">2012</year><article-title>Cellular properties of principal neurons in the rat entorhinal cortex II the medial entorhinal cortex</article-title><source>Hippocampus</source><volume>22</volume><fpage>1277</fpage><lpage>1299</lpage><pub-id pub-id-type="doi">10.1002/hipo.20993</pub-id><pub-id pub-id-type="pmid">22161956</pub-id></element-citation></ref><ref id="bib19"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Cembrowski</surname> <given-names>MS</given-names></name><name><surname>Menon</surname> <given-names>V</given-names></name></person-group><year iso-8601-date="2018">2018</year><article-title>Continuous variation within cell types of the nervous system</article-title><source>Trends in Neurosciences</source><volume>41</volume><fpage>337</fpage><lpage>348</lpage><pub-id pub-id-type="doi">10.1016/j.tins.2018.02.010</pub-id><pub-id pub-id-type="pmid">29576429</pub-id></element-citation></ref><ref id="bib20"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Diehl</surname> <given-names>GW</given-names></name><name><surname>Hon</surname> <given-names>OJ</given-names></name><name><surname>Leutgeb</surname> <given-names>S</given-names></name><name><surname>Leutgeb</surname> <given-names>JK</given-names></name></person-group><year iso-8601-date="2017">2017</year><article-title>Grid and nongrid cells in medial entorhinal cortex represent spatial location and environmental features with complementary coding schemes</article-title><source>Neuron</source><volume>94</volume><fpage>83</fpage><lpage>92</lpage><pub-id pub-id-type="doi">10.1016/j.neuron.2017.03.004</pub-id><pub-id pub-id-type="pmid">28343867</pub-id></element-citation></ref><ref id="bib21"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Dodson</surname> <given-names>PD</given-names></name><name><surname>Pastoll</surname> <given-names>H</given-names></name><name><surname>Nolan</surname> <given-names>MF</given-names></name></person-group><year iso-8601-date="2011">2011</year><article-title>Dorsal-ventral organization of theta-like activity intrinsic to entorhinal stellate neurons is mediated by differences in stochastic current fluctuations</article-title><source>The Journal of Physiology</source><volume>589</volume><fpage>2993</fpage><lpage>3008</lpage><pub-id pub-id-type="doi">10.1113/jphysiol.2011.205021</pub-id><pub-id pub-id-type="pmid">21502290</pub-id></element-citation></ref><ref id="bib22"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Domnisoru</surname> <given-names>C</given-names></name><name><surname>Kinkhabwala</surname> <given-names>AA</given-names></name><name><surname>Tank</surname> <given-names>DW</given-names></name></person-group><year iso-8601-date="2013">2013</year><article-title>Membrane potential dynamics of grid cells</article-title><source>Nature</source><volume>495</volume><fpage>199</fpage><lpage>204</lpage><pub-id pub-id-type="doi">10.1038/nature11973</pub-id><pub-id pub-id-type="pmid">23395984</pub-id></element-citation></ref><ref id="bib23"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Donato</surname> <given-names>F</given-names></name><name><surname>Jacobsen</surname> <given-names>RI</given-names></name><name><surname>Moser</surname> <given-names>MB</given-names></name><name><surname>Moser</surname> <given-names>EI</given-names></name></person-group><year iso-8601-date="2017">2017</year><article-title>Stellate cells drive maturation of the entorhinal-hippocampal circuit</article-title><source>Science</source><volume>355</volume><elocation-id>eaai8178</elocation-id><pub-id pub-id-type="doi">10.1126/science.aai8178</pub-id><pub-id pub-id-type="pmid">28154241</pub-id></element-citation></ref><ref id="bib24"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Fletcher</surname> <given-names>LN</given-names></name><name><surname>Williams</surname> <given-names>SR</given-names></name></person-group><year iso-8601-date="2019">2019</year><article-title>Neocortical topology governs the dendritic integrative capacity of layer 5 pyramidal neurons</article-title><source>Neuron</source><volume>101</volume><fpage>76</fpage><lpage>90</lpage><pub-id pub-id-type="doi">10.1016/j.neuron.2018.10.048</pub-id><pub-id pub-id-type="pmid">30472076</pub-id></element-citation></ref><ref id="bib25"><element-citation publication-type="book"><person-group person-group-type="author"><name><surname>Fox</surname> <given-names>J</given-names></name><name><surname>Weisberg</surname> <given-names>S</given-names></name></person-group><year iso-8601-date="2018">2018</year><source>An R Companion to Applied Regression</source><publisher-name>SAGE Publications</publisher-name></element-citation></ref><ref id="bib26"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Fuhs</surname> <given-names>MC</given-names></name><name><surname>Touretzky</surname> <given-names>DS</given-names></name></person-group><year iso-8601-date="2006">2006</year><article-title>A spin glass model of path integration in rat medial entorhinal cortex</article-title><source>Journal of Neuroscience</source><volume>26</volume><fpage>4266</fpage><lpage>4276</lpage><pub-id pub-id-type="doi">10.1523/JNEUROSCI.4353-05.2006</pub-id><pub-id pub-id-type="pmid">16624947</pub-id></element-citation></ref><ref id="bib27"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Fyhn</surname> <given-names>M</given-names></name><name><surname>Molden</surname> <given-names>S</given-names></name><name><surname>Witter</surname> <given-names>MP</given-names></name><name><surname>Moser</surname> <given-names>EI</given-names></name><name><surname>Moser</surname> <given-names>MB</given-names></name></person-group><year iso-8601-date="2004">2004</year><article-title>Spatial representation in the entorhinal cortex</article-title><source>Science</source><volume>305</volume><fpage>1258</fpage><lpage>1264</lpage><pub-id pub-id-type="doi">10.1126/science.1099901</pub-id><pub-id pub-id-type="pmid">15333832</pub-id></element-citation></ref><ref id="bib28"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Garden</surname> <given-names>DL</given-names></name><name><surname>Dodson</surname> <given-names>PD</given-names></name><name><surname>O'Donnell</surname> <given-names>C</given-names></name><name><surname>White</surname> <given-names>MD</given-names></name><name><surname>Nolan</surname> <given-names>MF</given-names></name></person-group><year iso-8601-date="2008">2008</year><article-title>Tuning of synaptic integration in the medial entorhinal cortex to the organization of grid cell firing fields</article-title><source>Neuron</source><volume>60</volume><fpage>875</fpage><lpage>889</lpage><pub-id pub-id-type="doi">10.1016/j.neuron.2008.10.044</pub-id><pub-id pub-id-type="pmid">19081381</pub-id></element-citation></ref><ref id="bib29"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Geiler-Samerotte</surname> <given-names>KA</given-names></name><name><surname>Bauer</surname> <given-names>CR</given-names></name><name><surname>Li</surname> <given-names>S</given-names></name><name><surname>Ziv</surname> <given-names>N</given-names></name><name><surname>Gresham</surname> <given-names>D</given-names></name><name><surname>Siegal</surname> <given-names>ML</given-names></name></person-group><year iso-8601-date="2013">2013</year><article-title>The details in the distributions: why and how to study phenotypic variability</article-title><source>Current Opinion in Biotechnology</source><volume>24</volume><fpage>752</fpage><lpage>759</lpage><pub-id pub-id-type="doi">10.1016/j.copbio.2013.03.010</pub-id><pub-id pub-id-type="pmid">23566377</pub-id></element-citation></ref><ref id="bib30"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Giocomo</surname> <given-names>LM</given-names></name><name><surname>Zilli</surname> <given-names>EA</given-names></name><name><surname>Fransén</surname> <given-names>E</given-names></name><name><surname>Hasselmo</surname> <given-names>ME</given-names></name></person-group><year iso-8601-date="2007">2007</year><article-title>Temporal frequency of subthreshold oscillations scales with entorhinal grid cell field spacing</article-title><source>Science</source><volume>315</volume><fpage>1719</fpage><lpage>1722</lpage><pub-id pub-id-type="doi">10.1126/science.1139207</pub-id><pub-id pub-id-type="pmid">17379810</pub-id></element-citation></ref><ref id="bib31"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Giocomo</surname> <given-names>LM</given-names></name><name><surname>Hussaini</surname> <given-names>SA</given-names></name><name><surname>Zheng</surname> <given-names>F</given-names></name><name><surname>Kandel</surname> <given-names>ER</given-names></name><name><surname>Moser</surname> <given-names>MB</given-names></name><name><surname>Moser</surname> <given-names>EI</given-names></name></person-group><year iso-8601-date="2011">2011</year><article-title>Grid cells use HCN1 channels for spatial scaling</article-title><source>Cell</source><volume>147</volume><fpage>1159</fpage><lpage>1170</lpage><pub-id pub-id-type="doi">10.1016/j.cell.2011.08.051</pub-id><pub-id pub-id-type="pmid">22100643</pub-id></element-citation></ref><ref id="bib32"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Giocomo</surname> <given-names>LM</given-names></name><name><surname>Stensola</surname> <given-names>T</given-names></name><name><surname>Bonnevie</surname> <given-names>T</given-names></name><name><surname>Van Cauter</surname> <given-names>T</given-names></name><name><surname>Moser</surname> <given-names>MB</given-names></name><name><surname>Moser</surname> <given-names>EI</given-names></name></person-group><year iso-8601-date="2014">2014</year><article-title>Topography of head direction cells in medial entorhinal cortex</article-title><source>Current Biology</source><volume>24</volume><fpage>252</fpage><lpage>262</lpage><pub-id pub-id-type="doi">10.1016/j.cub.2013.12.002</pub-id><pub-id pub-id-type="pmid">24440398</pub-id></element-citation></ref><ref id="bib33"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Giocomo</surname> <given-names>LM</given-names></name><name><surname>Hasselmo</surname> <given-names>ME</given-names></name></person-group><year iso-8601-date="2008">2008a</year><article-title>Time constants of h current in layer ii stellate cells differ along the dorsal to ventral Axis of medial entorhinal cortex</article-title><source>Journal of Neuroscience</source><volume>28</volume><fpage>9414</fpage><lpage>9425</lpage><pub-id pub-id-type="doi">10.1523/JNEUROSCI.3196-08.2008</pub-id><pub-id pub-id-type="pmid">18799674</pub-id></element-citation></ref><ref id="bib34"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Giocomo</surname> <given-names>LM</given-names></name><name><surname>Hasselmo</surname> <given-names>ME</given-names></name></person-group><year iso-8601-date="2008">2008b</year><article-title>Computation by oscillations: implications of experimental data for theoretical models of grid cells</article-title><source>Hippocampus</source><volume>18</volume><fpage>1186</fpage><lpage>1199</lpage><pub-id pub-id-type="doi">10.1002/hipo.20501</pub-id><pub-id pub-id-type="pmid">19021252</pub-id></element-citation></ref><ref id="bib35"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Giocomo</surname> <given-names>LM</given-names></name><name><surname>Hasselmo</surname> <given-names>ME</given-names></name></person-group><year iso-8601-date="2009">2009</year><article-title>Knock-out of HCN1 subunit flattens dorsal-ventral frequency gradient of medial entorhinal neurons in adult mice</article-title><source>Journal of Neuroscience</source><volume>29</volume><fpage>7625</fpage><lpage>7630</lpage><pub-id pub-id-type="doi">10.1523/JNEUROSCI.0609-09.2009</pub-id><pub-id pub-id-type="pmid">19515931</pub-id></element-citation></ref><ref id="bib36"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Goaillard</surname> <given-names>JM</given-names></name><name><surname>Taylor</surname> <given-names>AL</given-names></name><name><surname>Schulz</surname> <given-names>DJ</given-names></name><name><surname>Marder</surname> <given-names>E</given-names></name></person-group><year iso-8601-date="2009">2009</year><article-title>Functional consequences of animal-to-animal variation in circuit parameters</article-title><source>Nature Neuroscience</source><volume>12</volume><fpage>1424</fpage><lpage>1430</lpage><pub-id pub-id-type="doi">10.1038/nn.2404</pub-id><pub-id pub-id-type="pmid">19838180</pub-id></element-citation></ref><ref id="bib37"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Gonzalez-Sulser</surname> <given-names>A</given-names></name><name><surname>Parthier</surname> <given-names>D</given-names></name><name><surname>Candela</surname> <given-names>A</given-names></name><name><surname>McClure</surname> <given-names>C</given-names></name><name><surname>Pastoll</surname> <given-names>H</given-names></name><name><surname>Garden</surname> <given-names>D</given-names></name><name><surname>Sürmeli</surname> <given-names>G</given-names></name><name><surname>Nolan</surname> <given-names>MF</given-names></name></person-group><year iso-8601-date="2014">2014</year><article-title>GABAergic projections from the medial septum selectively inhibit interneurons in the medial entorhinal cortex</article-title><source>Journal of Neuroscience</source><volume>34</volume><fpage>16739</fpage><lpage>16743</lpage><pub-id pub-id-type="doi">10.1523/JNEUROSCI.1612-14.2014</pub-id><pub-id pub-id-type="pmid">25505326</pub-id></element-citation></ref><ref id="bib38"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Green</surname> <given-names>EJ</given-names></name><name><surname>Greenough</surname> <given-names>WT</given-names></name></person-group><year iso-8601-date="1986">1986</year><article-title>Altered synaptic transmission in Dentate Gyrus of rats reared in complex environments: evidence from hippocampal slices maintained in vitro</article-title><source>Journal of Neurophysiology</source><volume>55</volume><fpage>739</fpage><lpage>750</lpage><pub-id pub-id-type="doi">10.1152/jn.1986.55.4.739</pub-id><pub-id pub-id-type="pmid">3009728</pub-id></element-citation></ref><ref id="bib39"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Grossberg</surname> <given-names>S</given-names></name><name><surname>Pilly</surname> <given-names>PK</given-names></name></person-group><year iso-8601-date="2012">2012</year><article-title>How entorhinal grid cells may learn multiple spatial scales from a dorsoventral gradient of cell response rates in a self-organizing map</article-title><source>PLOS Computational Biology</source><volume>8</volume><elocation-id>e1002648</elocation-id><pub-id pub-id-type="doi">10.1371/journal.pcbi.1002648</pub-id><pub-id pub-id-type="pmid">23055909</pub-id></element-citation></ref><ref id="bib40"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Gu</surname> <given-names>Y</given-names></name><name><surname>Lewallen</surname> <given-names>S</given-names></name><name><surname>Kinkhabwala</surname> <given-names>AA</given-names></name><name><surname>Domnisoru</surname> <given-names>C</given-names></name><name><surname>Yoon</surname> <given-names>K</given-names></name><name><surname>Gauthier</surname> <given-names>JL</given-names></name><name><surname>Fiete</surname> <given-names>IR</given-names></name><name><surname>Tank</surname> <given-names>DW</given-names></name></person-group><year iso-8601-date="2018">2018</year><article-title>A Map-like Micro-Organization of grid cells in the medial entorhinal cortex</article-title><source>Cell</source><volume>175</volume><fpage>736</fpage><lpage>750</lpage><pub-id pub-id-type="doi">10.1016/j.cell.2018.08.066</pub-id><pub-id pub-id-type="pmid">30270041</pub-id></element-citation></ref><ref id="bib41"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Guanella</surname> <given-names>A</given-names></name><name><surname>Kiper</surname> <given-names>D</given-names></name><name><surname>Verschure</surname> <given-names>P</given-names></name></person-group><year iso-8601-date="2007">2007</year><article-title>A model of grid cells based on a twisted torus topology</article-title><source>International Journal of Neural Systems</source><volume>17</volume><fpage>231</fpage><lpage>240</lpage><pub-id pub-id-type="doi">10.1142/S0129065707001093</pub-id><pub-id pub-id-type="pmid">17696288</pub-id></element-citation></ref><ref id="bib42"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Hafting</surname> <given-names>T</given-names></name><name><surname>Fyhn</surname> <given-names>M</given-names></name><name><surname>Molden</surname> <given-names>S</given-names></name><name><surname>Moser</surname> <given-names>MB</given-names></name><name><surname>Moser</surname> <given-names>EI</given-names></name></person-group><year iso-8601-date="2005">2005</year><article-title>Microstructure of a spatial map in the entorhinal cortex</article-title><source>Nature</source><volume>436</volume><fpage>801</fpage><lpage>806</lpage><pub-id pub-id-type="doi">10.1038/nature03721</pub-id><pub-id pub-id-type="pmid">15965463</pub-id></element-citation></ref><ref id="bib43"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Hardcastle</surname> <given-names>K</given-names></name><name><surname>Maheswaranathan</surname> <given-names>N</given-names></name><name><surname>Ganguli</surname> <given-names>S</given-names></name><name><surname>Giocomo</surname> <given-names>LM</given-names></name></person-group><year iso-8601-date="2017">2017</year><article-title>A multiplexed, heterogeneous, and adaptive code for navigation in medial entorhinal cortex</article-title><source>Neuron</source><volume>94</volume><fpage>375</fpage><lpage>387</lpage><pub-id pub-id-type="doi">10.1016/j.neuron.2017.03.025</pub-id><pub-id pub-id-type="pmid">28392071</pub-id></element-citation></ref><ref id="bib44"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Kitamura</surname> <given-names>T</given-names></name><name><surname>Pignatelli</surname> <given-names>M</given-names></name><name><surname>Suh</surname> <given-names>J</given-names></name><name><surname>Kohara</surname> <given-names>K</given-names></name><name><surname>Yoshiki</surname> <given-names>A</given-names></name><name><surname>Abe</surname> <given-names>K</given-names></name><name><surname>Tonegawa</surname> <given-names>S</given-names></name></person-group><year iso-8601-date="2014">2014</year><article-title>Island cells control temporal association memory</article-title><source>Science</source><volume>343</volume><fpage>896</fpage><lpage>901</lpage><pub-id pub-id-type="doi">10.1126/science.1244634</pub-id><pub-id pub-id-type="pmid">24457215</pub-id></element-citation></ref><ref id="bib45"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Kropff</surname> <given-names>E</given-names></name><name><surname>Treves</surname> <given-names>A</given-names></name></person-group><year iso-8601-date="2008">2008</year><article-title>The emergence of grid cells: intelligent design or just adaptation?</article-title><source>Hippocampus</source><volume>18</volume><fpage>1256</fpage><lpage>1269</lpage><pub-id pub-id-type="doi">10.1002/hipo.20520</pub-id><pub-id pub-id-type="pmid">19021261</pub-id></element-citation></ref><ref id="bib46"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Kuba</surname> <given-names>H</given-names></name><name><surname>Yamada</surname> <given-names>R</given-names></name><name><surname>Fukui</surname> <given-names>I</given-names></name><name><surname>Ohmori</surname> <given-names>H</given-names></name></person-group><year iso-8601-date="2005">2005</year><article-title>Tonotopic specialization of auditory coincidence detection in nucleus laminaris of the chick</article-title><source>Journal of Neuroscience</source><volume>25</volume><fpage>1924</fpage><lpage>1934</lpage><pub-id pub-id-type="doi">10.1523/JNEUROSCI.4428-04.2005</pub-id><pub-id pub-id-type="pmid">15728832</pub-id></element-citation></ref><ref id="bib47"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Liss</surname> <given-names>B</given-names></name><name><surname>Franz</surname> <given-names>O</given-names></name><name><surname>Sewing</surname> <given-names>S</given-names></name><name><surname>Bruns</surname> <given-names>R</given-names></name><name><surname>Neuhoff</surname> <given-names>H</given-names></name><name><surname>Roeper</surname> <given-names>J</given-names></name></person-group><year iso-8601-date="2001">2001</year><article-title>Tuning pacemaker frequency of individual dopaminergic neurons by Kv4.3L and KChip3.1 transcription</article-title><source>The EMBO Journal</source><volume>20</volume><fpage>5715</fpage><lpage>5724</lpage><pub-id pub-id-type="doi">10.1093/emboj/20.20.5715</pub-id><pub-id pub-id-type="pmid">11598014</pub-id></element-citation></ref><ref id="bib48"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Mallory</surname> <given-names>CS</given-names></name><name><surname>Hardcastle</surname> <given-names>K</given-names></name><name><surname>Bant</surname> <given-names>JS</given-names></name><name><surname>Giocomo</surname> <given-names>LM</given-names></name></person-group><year iso-8601-date="2018">2018</year><article-title>Grid scale drives the scale and long-term stability of place maps</article-title><source>Nature Neuroscience</source><volume>21</volume><fpage>270</fpage><lpage>282</lpage><pub-id pub-id-type="doi">10.1038/s41593-017-0055-3</pub-id><pub-id pub-id-type="pmid">29335607</pub-id></element-citation></ref><ref id="bib49"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Marder</surname> <given-names>E</given-names></name><name><surname>Goaillard</surname> <given-names>JM</given-names></name></person-group><year iso-8601-date="2006">2006</year><article-title>Variability, compensation and homeostasis in neuron and network function</article-title><source>Nature Reviews Neuroscience</source><volume>7</volume><fpage>563</fpage><lpage>574</lpage><pub-id pub-id-type="doi">10.1038/nrn1949</pub-id><pub-id pub-id-type="pmid">16791145</pub-id></element-citation></ref><ref id="bib50"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Marder</surname> <given-names>E</given-names></name><name><surname>Taylor</surname> <given-names>AL</given-names></name></person-group><year iso-8601-date="2011">2011</year><article-title>Multiple models to capture the variability in biological neurons and networks</article-title><source>Nature Neuroscience</source><volume>14</volume><fpage>133</fpage><lpage>138</lpage><pub-id pub-id-type="doi">10.1038/nn.2735</pub-id><pub-id pub-id-type="pmid">21270780</pub-id></element-citation></ref><ref id="bib51"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Mittal</surname> <given-names>D</given-names></name><name><surname>Narayanan</surname> <given-names>R</given-names></name></person-group><year iso-8601-date="2018">2018</year><article-title>Degeneracy in the robust expression of spectral selectivity, subthreshold oscillations, and intrinsic excitability of entorhinal stellate cells</article-title><source>Journal of Neurophysiology</source><volume>120</volume><fpage>576</fpage><lpage>600</lpage><pub-id pub-id-type="doi">10.1152/jn.00136.2018</pub-id><pub-id pub-id-type="pmid">29718802</pub-id></element-citation></ref><ref id="bib52"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Miyoshi</surname> <given-names>G</given-names></name><name><surname>Hjerling-Leffler</surname> <given-names>J</given-names></name><name><surname>Karayannis</surname> <given-names>T</given-names></name><name><surname>Sousa</surname> <given-names>VH</given-names></name><name><surname>Butt</surname> <given-names>SJ</given-names></name><name><surname>Battiste</surname> <given-names>J</given-names></name><name><surname>Johnson</surname> <given-names>JE</given-names></name><name><surname>Machold</surname> <given-names>RP</given-names></name><name><surname>Fishell</surname> <given-names>G</given-names></name></person-group><year iso-8601-date="2010">2010</year><article-title>Genetic fate mapping reveals that the caudal ganglionic eminence produces a large and diverse population of superficial cortical interneurons</article-title><source>Journal of Neuroscience</source><volume>30</volume><fpage>1582</fpage><lpage>1594</lpage><pub-id pub-id-type="doi">10.1523/JNEUROSCI.4515-09.2010</pub-id><pub-id pub-id-type="pmid">20130169</pub-id></element-citation></ref><ref id="bib53"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Nolan</surname> <given-names>MF</given-names></name><name><surname>Dudman</surname> <given-names>JT</given-names></name><name><surname>Dodson</surname> <given-names>PD</given-names></name><name><surname>Santoro</surname> <given-names>B</given-names></name></person-group><year iso-8601-date="2007">2007</year><article-title>HCN1 channels control resting and active integrative properties of stellate cells from layer II of the entorhinal cortex</article-title><source>Journal of Neuroscience</source><volume>27</volume><fpage>12440</fpage><lpage>12451</lpage><pub-id pub-id-type="doi">10.1523/JNEUROSCI.2358-07.2007</pub-id><pub-id pub-id-type="pmid">18003822</pub-id></element-citation></ref><ref id="bib54"><element-citation publication-type="software"><person-group person-group-type="author"><name><surname>Nolan</surname> <given-names>MF</given-names></name></person-group><year iso-8601-date="2020">2020</year><data-title>Analyses for investigation of large scale organisation of stellate cell properties</data-title><source>GitHub</source><version designator="85056ea">85056ea</version><ext-link ext-link-type="uri" xlink:href="https://github.com/MattNolanLab/Inter_Intra_Variation">https://github.com/MattNolanLab/Inter_Intra_Variation</ext-link></element-citation></ref><ref id="bib55"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>O'Donnell</surname> <given-names>C</given-names></name><name><surname>Nolan</surname> <given-names>MF</given-names></name></person-group><year iso-8601-date="2011">2011</year><article-title>Tuning of synaptic responses: an organizing principle for optimization of neural circuits</article-title><source>Trends in Neurosciences</source><volume>34</volume><fpage>51</fpage><lpage>60</lpage><pub-id pub-id-type="doi">10.1016/j.tins.2010.10.003</pub-id><pub-id pub-id-type="pmid">21067825</pub-id></element-citation></ref><ref id="bib56"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>O'Leary</surname> <given-names>T</given-names></name><name><surname>Williams</surname> <given-names>AH</given-names></name><name><surname>Franci</surname> <given-names>A</given-names></name><name><surname>Marder</surname> <given-names>E</given-names></name></person-group><year iso-8601-date="2014">2014</year><article-title>Cell types, network homeostasis, and pathological compensation from a biologically plausible ion channel expression model</article-title><source>Neuron</source><volume>82</volume><fpage>809</fpage><lpage>821</lpage><pub-id pub-id-type="doi">10.1016/j.neuron.2014.04.002</pub-id><pub-id pub-id-type="pmid">24853940</pub-id></element-citation></ref><ref id="bib57"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Ohline</surname> <given-names>SM</given-names></name><name><surname>Abraham</surname> <given-names>WC</given-names></name></person-group><year iso-8601-date="2019">2019</year><article-title>Environmental enrichment effects on synaptic and cellular physiology of hippocampal neurons</article-title><source>Neuropharmacology</source><volume>145</volume><fpage>3</fpage><lpage>12</lpage><pub-id pub-id-type="doi">10.1016/j.neuropharm.2018.04.007</pub-id></element-citation></ref><ref id="bib58"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Pastoll</surname> <given-names>H</given-names></name><name><surname>Ramsden</surname> <given-names>HL</given-names></name><name><surname>Nolan</surname> <given-names>MF</given-names></name></person-group><year iso-8601-date="2012">2012a</year><article-title>Intrinsic electrophysiological properties of entorhinal cortex stellate cells and their contribution to grid cell firing fields</article-title><source>Frontiers in Neural Circuits</source><volume>6</volume><elocation-id>17</elocation-id><pub-id pub-id-type="doi">10.3389/fncir.2012.00017</pub-id><pub-id pub-id-type="pmid">22536175</pub-id></element-citation></ref><ref id="bib59"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Pastoll</surname> <given-names>H</given-names></name><name><surname>White</surname> <given-names>M</given-names></name><name><surname>Nolan</surname> <given-names>M</given-names></name></person-group><year iso-8601-date="2012">2012b</year><article-title>Preparation of parasagittal slices for the investigation of Dorsal-ventral organization of the rodent medial entorhinal cortex</article-title><source>Journal of Visualized Experiments</source><elocation-id>e3802</elocation-id><pub-id pub-id-type="doi">10.3791/3802</pub-id></element-citation></ref><ref id="bib60"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Pastoll</surname> <given-names>H</given-names></name><name><surname>Solanka</surname> <given-names>L</given-names></name><name><surname>van Rossum</surname> <given-names>MC</given-names></name><name><surname>Nolan</surname> <given-names>MF</given-names></name></person-group><year iso-8601-date="2013">2013</year><article-title>Feedback inhibition enables θ-nested γ oscillations and grid firing fields</article-title><source>Neuron</source><volume>77</volume><fpage>141</fpage><lpage>154</lpage><pub-id pub-id-type="doi">10.1016/j.neuron.2012.11.032</pub-id><pub-id pub-id-type="pmid">23312522</pub-id></element-citation></ref><ref id="bib61"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Qin</surname> <given-names>H</given-names></name><name><surname>Fu</surname> <given-names>L</given-names></name><name><surname>Hu</surname> <given-names>B</given-names></name><name><surname>Liao</surname> <given-names>X</given-names></name><name><surname>Lu</surname> <given-names>J</given-names></name><name><surname>He</surname> <given-names>W</given-names></name><name><surname>Liang</surname> <given-names>S</given-names></name><name><surname>Zhang</surname> <given-names>K</given-names></name><name><surname>Li</surname> <given-names>R</given-names></name><name><surname>Yao</surname> <given-names>J</given-names></name><name><surname>Yan</surname> <given-names>J</given-names></name><name><surname>Chen</surname> <given-names>H</given-names></name><name><surname>Jia</surname> <given-names>H</given-names></name><name><surname>Zott</surname> <given-names>B</given-names></name><name><surname>Konnerth</surname> <given-names>A</given-names></name><name><surname>Chen</surname> <given-names>X</given-names></name></person-group><year iso-8601-date="2018">2018</year><article-title>A Visual-Cue-Dependent memory circuit for place navigation</article-title><source>Neuron</source><volume>99</volume><fpage>47</fpage><lpage>55</lpage><pub-id pub-id-type="doi">10.1016/j.neuron.2018.05.021</pub-id><pub-id pub-id-type="pmid">29909996</pub-id></element-citation></ref><ref id="bib62"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Ramsden</surname> <given-names>HL</given-names></name><name><surname>Sürmeli</surname> <given-names>G</given-names></name><name><surname>McDonagh</surname> <given-names>SG</given-names></name><name><surname>Nolan</surname> <given-names>MF</given-names></name></person-group><year iso-8601-date="2015">2015</year><article-title>Laminar and dorsoventral molecular organization of the medial entorhinal cortex revealed by large-scale anatomical analysis of gene expression</article-title><source>PLOS Computational Biology</source><volume>11</volume><elocation-id>e1004032</elocation-id><pub-id pub-id-type="doi">10.1371/journal.pcbi.1004032</pub-id><pub-id pub-id-type="pmid">25615592</pub-id></element-citation></ref><ref id="bib63"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Ray</surname> <given-names>S</given-names></name><name><surname>Naumann</surname> <given-names>R</given-names></name><name><surname>Burgalossi</surname> <given-names>A</given-names></name><name><surname>Tang</surname> <given-names>Q</given-names></name><name><surname>Schmidt</surname> <given-names>H</given-names></name><name><surname>Brecht</surname> <given-names>M</given-names></name></person-group><year iso-8601-date="2014">2014</year><article-title>Grid-layout and theta-modulation of layer 2 pyramidal neurons in medial entorhinal cortex</article-title><source>Science</source><volume>343</volume><fpage>891</fpage><lpage>896</lpage><pub-id pub-id-type="doi">10.1126/science.1243028</pub-id><pub-id pub-id-type="pmid">24457213</pub-id></element-citation></ref><ref id="bib64"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Ray</surname> <given-names>S</given-names></name><name><surname>Brecht</surname> <given-names>M</given-names></name></person-group><year iso-8601-date="2016">2016</year><article-title>Structural development and dorsoventral maturation of the medial entorhinal cortex</article-title><source>eLife</source><volume>5</volume><elocation-id>e13343</elocation-id><pub-id pub-id-type="doi">10.7554/eLife.13343</pub-id><pub-id pub-id-type="pmid">27036175</pub-id></element-citation></ref><ref id="bib65"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Regev</surname> <given-names>A</given-names></name><name><surname>Teichmann</surname> <given-names>SA</given-names></name><name><surname>Lander</surname> <given-names>ES</given-names></name><name><surname>Amit</surname> <given-names>I</given-names></name><name><surname>Benoist</surname> <given-names>C</given-names></name><name><surname>Birney</surname> <given-names>E</given-names></name><name><surname>Bodenmiller</surname> <given-names>B</given-names></name><name><surname>Campbell</surname> <given-names>P</given-names></name><name><surname>Carninci</surname> <given-names>P</given-names></name><name><surname>Clatworthy M</surname> <given-names>O</given-names></name></person-group><year iso-8601-date="2017">2017</year><article-title>Science forum: the human cell atlas</article-title><source>eLife</source><volume>6</volume><elocation-id>e27041</elocation-id><pub-id pub-id-type="doi">10.7554/eLife.27041</pub-id></element-citation></ref><ref id="bib66"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Rowland</surname> <given-names>DC</given-names></name><name><surname>Obenhaus</surname> <given-names>HA</given-names></name><name><surname>Skytøen</surname> <given-names>ER</given-names></name><name><surname>Zhang</surname> <given-names>Q</given-names></name><name><surname>Kentros</surname> <given-names>CG</given-names></name><name><surname>Moser</surname> <given-names>EI</given-names></name><name><surname>Moser</surname> <given-names>MB</given-names></name></person-group><year iso-8601-date="2018">2018</year><article-title>Functional properties of stellate cells in medial entorhinal cortex layer II</article-title><source>eLife</source><volume>7</volume><elocation-id>e36664</elocation-id><pub-id pub-id-type="doi">10.7554/eLife.36664</pub-id><pub-id pub-id-type="pmid">30215597</pub-id></element-citation></ref><ref id="bib67"><element-citation publication-type="software"><person-group person-group-type="author"><name><surname>Schafer</surname> <given-names>J</given-names></name><name><surname>Opgen-Rhein</surname> <given-names>R</given-names></name><name><surname>Zuber</surname> <given-names>V</given-names></name><name><surname>Ahdesmaki</surname> <given-names>M</given-names></name><name><surname>Silva</surname> <given-names>APD</given-names></name><name><surname>Strimmer</surname> <given-names>K</given-names></name></person-group><year iso-8601-date="2017">2017</year><data-title>corpcor: Efficient estimation of covariance and (partial) correlation</data-title><publisher-name>R package version 1.6. 9</publisher-name></element-citation></ref><ref id="bib68"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Schmidt-Hieber</surname> <given-names>C</given-names></name><name><surname>Häusser</surname> <given-names>M</given-names></name></person-group><year iso-8601-date="2013">2013</year><article-title>Cellular mechanisms of spatial navigation in the medial entorhinal cortex</article-title><source>Nature Neuroscience</source><volume>16</volume><fpage>325</fpage><lpage>331</lpage><pub-id pub-id-type="doi">10.1038/nn.3340</pub-id></element-citation></ref><ref id="bib69"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Schmidt-Hieber</surname> <given-names>C</given-names></name><name><surname>Nolan</surname> <given-names>MF</given-names></name></person-group><year iso-8601-date="2017">2017</year><article-title>Synaptic integrative mechanisms for spatial cognition</article-title><source>Nature Neuroscience</source><volume>20</volume><fpage>1483</fpage><lpage>1492</lpage><pub-id pub-id-type="doi">10.1038/nn.4652</pub-id><pub-id pub-id-type="pmid">29073648</pub-id></element-citation></ref><ref id="bib70"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Shipston-Sharman</surname> <given-names>O</given-names></name><name><surname>Solanka</surname> <given-names>L</given-names></name><name><surname>Nolan</surname> <given-names>MF</given-names></name></person-group><year iso-8601-date="2016">2016</year><article-title>Continuous attractor network models of grid cell firing based on excitatory-inhibitory interactions</article-title><source>The Journal of Physiology</source><volume>594</volume><fpage>6547</fpage><lpage>6557</lpage><pub-id pub-id-type="doi">10.1113/JP270630</pub-id><pub-id pub-id-type="pmid">27870120</pub-id></element-citation></ref><ref id="bib71"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Stensola</surname> <given-names>H</given-names></name><name><surname>Stensola</surname> <given-names>T</given-names></name><name><surname>Solstad</surname> <given-names>T</given-names></name><name><surname>Frøland</surname> <given-names>K</given-names></name><name><surname>Moser</surname> <given-names>MB</given-names></name><name><surname>Moser</surname> <given-names>EI</given-names></name></person-group><year iso-8601-date="2012">2012</year><article-title>The entorhinal grid map is discretized</article-title><source>Nature</source><volume>492</volume><fpage>72</fpage><lpage>78</lpage><pub-id pub-id-type="doi">10.1038/nature11649</pub-id><pub-id pub-id-type="pmid">23222610</pub-id></element-citation></ref><ref id="bib72"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Sürmeli</surname> <given-names>G</given-names></name><name><surname>Marcu</surname> <given-names>DC</given-names></name><name><surname>McClure</surname> <given-names>C</given-names></name><name><surname>Garden</surname> <given-names>DLF</given-names></name><name><surname>Pastoll</surname> <given-names>H</given-names></name><name><surname>Nolan</surname> <given-names>MF</given-names></name></person-group><year iso-8601-date="2015">2015</year><article-title>Molecularly defined circuitry reveals Input-Output segregation in deep layers of the medial entorhinal cortex</article-title><source>Neuron</source><volume>88</volume><fpage>1040</fpage><lpage>1053</lpage><pub-id pub-id-type="doi">10.1016/j.neuron.2015.10.041</pub-id><pub-id pub-id-type="pmid">26606996</pub-id></element-citation></ref><ref id="bib73"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Swensen</surname> <given-names>AM</given-names></name><name><surname>Bean</surname> <given-names>BP</given-names></name></person-group><year iso-8601-date="2005">2005</year><article-title>Robustness of burst firing in dissociated purkinje neurons with acute or long-term reductions in sodium conductance</article-title><source>Journal of Neuroscience</source><volume>25</volume><fpage>3509</fpage><lpage>3520</lpage><pub-id pub-id-type="doi">10.1523/JNEUROSCI.3929-04.2005</pub-id><pub-id pub-id-type="pmid">15814781</pub-id></element-citation></ref><ref id="bib74"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Tennant</surname> <given-names>SA</given-names></name><name><surname>Fischer</surname> <given-names>L</given-names></name><name><surname>Garden</surname> <given-names>DLF</given-names></name><name><surname>Gerlei</surname> <given-names>KZ</given-names></name><name><surname>Martinez-Gonzalez</surname> <given-names>C</given-names></name><name><surname>McClure</surname> <given-names>C</given-names></name><name><surname>Wood</surname> <given-names>ER</given-names></name><name><surname>Nolan</surname> <given-names>MF</given-names></name></person-group><year iso-8601-date="2018">2018</year><article-title>Stellate cells in the medial entorhinal cortex are required for spatial learning</article-title><source>Cell Reports</source><volume>22</volume><fpage>1313</fpage><lpage>1324</lpage><pub-id pub-id-type="doi">10.1016/j.celrep.2018.01.005</pub-id><pub-id pub-id-type="pmid">29386117</pub-id></element-citation></ref><ref id="bib75"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Tibshirani</surname> <given-names>R</given-names></name><name><surname>Walther</surname> <given-names>G</given-names></name><name><surname>Hastie</surname> <given-names>T</given-names></name></person-group><year iso-8601-date="2001">2001</year><article-title>Estimating the number of clusters in a data set via the gap statistic</article-title><source>Journal of the Royal Statistical Society: Series B</source><volume>63</volume><fpage>411</fpage><lpage>423</lpage><pub-id pub-id-type="doi">10.1111/1467-9868.00293</pub-id></element-citation></ref><ref id="bib76"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Urdapilleta</surname> <given-names>E</given-names></name><name><surname>Si</surname> <given-names>B</given-names></name><name><surname>Treves</surname> <given-names>A</given-names></name></person-group><year iso-8601-date="2017">2017</year><article-title>Selforganization of modular activity of grid cells</article-title><source>Hippocampus</source><volume>27</volume><fpage>1204</fpage><lpage>1213</lpage><pub-id pub-id-type="doi">10.1002/hipo.22765</pub-id><pub-id pub-id-type="pmid">28768062</pub-id></element-citation></ref><ref id="bib77"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Villette</surname> <given-names>V</given-names></name><name><surname>Levesque</surname> <given-names>M</given-names></name><name><surname>Miled</surname> <given-names>A</given-names></name><name><surname>Gosselin</surname> <given-names>B</given-names></name><name><surname>Topolnik</surname> <given-names>L</given-names></name></person-group><year iso-8601-date="2017">2017</year><article-title>Simple platform for chronic imaging of hippocampal activity during spontaneous behaviour in an awake mouse</article-title><source>Scientific Reports</source><volume>7</volume><elocation-id>43388</elocation-id><pub-id pub-id-type="doi">10.1038/srep43388</pub-id><pub-id pub-id-type="pmid">28240275</pub-id></element-citation></ref><ref id="bib78"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Wang</surname> <given-names>F</given-names></name><name><surname>Zhu</surname> <given-names>J</given-names></name><name><surname>Zhu</surname> <given-names>H</given-names></name><name><surname>Zhang</surname> <given-names>Q</given-names></name><name><surname>Lin</surname> <given-names>Z</given-names></name><name><surname>Hu</surname> <given-names>H</given-names></name></person-group><year iso-8601-date="2011">2011a</year><article-title>Bidirectional control of social hierarchy by synaptic efficacy in medial prefrontal cortex</article-title><source>Science</source><volume>334</volume><fpage>693</fpage><lpage>697</lpage><pub-id pub-id-type="doi">10.1126/science.1209951</pub-id><pub-id pub-id-type="pmid">21960531</pub-id></element-citation></ref><ref id="bib79"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Wang</surname> <given-names>J</given-names></name><name><surname>Zhang</surname> <given-names>K</given-names></name><name><surname>Xu</surname> <given-names>L</given-names></name><name><surname>Wang</surname> <given-names>E</given-names></name></person-group><year iso-8601-date="2011">2011b</year><article-title>Quantifying the Waddington landscape and biological paths for development and differentiation</article-title><source>PNAS</source><volume>108</volume><fpage>8257</fpage><lpage>8262</lpage><pub-id pub-id-type="doi">10.1073/pnas.1017017108</pub-id><pub-id pub-id-type="pmid">21536909</pub-id></element-citation></ref><ref id="bib80"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Wang</surname> <given-names>F</given-names></name><name><surname>Kessels</surname> <given-names>HW</given-names></name><name><surname>Hu</surname> <given-names>H</given-names></name></person-group><year iso-8601-date="2014">2014</year><article-title>The mouse that roared: neural mechanisms of social hierarchy</article-title><source>Trends in Neurosciences</source><volume>37</volume><fpage>674</fpage><lpage>682</lpage><pub-id pub-id-type="doi">10.1016/j.tins.2014.07.005</pub-id><pub-id pub-id-type="pmid">25160682</pub-id></element-citation></ref><ref id="bib81"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Widloski</surname> <given-names>J</given-names></name><name><surname>Fiete</surname> <given-names>IR</given-names></name></person-group><year iso-8601-date="2014">2014</year><article-title>A model of grid cell development through spatial exploration and spike time-dependent plasticity</article-title><source>Neuron</source><volume>83</volume><fpage>481</fpage><lpage>495</lpage><pub-id pub-id-type="doi">10.1016/j.neuron.2014.06.018</pub-id><pub-id pub-id-type="pmid">25033187</pub-id></element-citation></ref><ref id="bib82"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Yoon</surname> <given-names>K</given-names></name><name><surname>Buice</surname> <given-names>MA</given-names></name><name><surname>Barry</surname> <given-names>C</given-names></name><name><surname>Hayman</surname> <given-names>R</given-names></name><name><surname>Burgess</surname> <given-names>N</given-names></name><name><surname>Fiete</surname> <given-names>IR</given-names></name></person-group><year iso-8601-date="2013">2013</year><article-title>Specific evidence of low-dimensional continuous attractor dynamics in grid cells</article-title><source>Nature Neuroscience</source><volume>16</volume><fpage>1077</fpage><lpage>1084</lpage><pub-id pub-id-type="doi">10.1038/nn.3450</pub-id><pub-id pub-id-type="pmid">23852111</pub-id></element-citation></ref><ref id="bib83"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Yoshida</surname> <given-names>M</given-names></name><name><surname>Jochems</surname> <given-names>A</given-names></name><name><surname>Hasselmo</surname> <given-names>ME</given-names></name></person-group><year iso-8601-date="2013">2013</year><article-title>Comparison of properties of medial entorhinal cortex layer II neurons in two anatomical dimensions with and without cholinergic activation</article-title><source>PLOS ONE</source><volume>8</volume><elocation-id>e73904</elocation-id><pub-id pub-id-type="doi">10.1371/journal.pone.0073904</pub-id><pub-id pub-id-type="pmid">24069244</pub-id></element-citation></ref><ref id="bib84"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Zeng</surname> <given-names>H</given-names></name><name><surname>Sanes</surname> <given-names>JR</given-names></name></person-group><year iso-8601-date="2017">2017</year><article-title>Neuronal cell-type classification: challenges, opportunities and the path forward</article-title><source>Nature Reviews Neuroscience</source><volume>18</volume><fpage>530</fpage><lpage>546</lpage><pub-id pub-id-type="doi">10.1038/nrn.2017.85</pub-id><pub-id pub-id-type="pmid">28775344</pub-id></element-citation></ref><ref id="bib85"><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Zhang</surname> <given-names>W</given-names></name><name><surname>Linden</surname> <given-names>DJ</given-names></name></person-group><year iso-8601-date="2003">2003</year><article-title>The other side of the Engram: experience-driven changes in neuronal intrinsic excitability</article-title><source>Nature Reviews Neuroscience</source><volume>4</volume><fpage>885</fpage><lpage>900</lpage><pub-id pub-id-type="doi">10.1038/nrn1248</pub-id><pub-id pub-id-type="pmid">14595400</pub-id></element-citation></ref></ref-list></back><sub-article article-type="decision-letter" id="sa1"><front-stub><article-id pub-id-type="doi">10.7554/eLife.52258.sa1</article-id><title-group><article-title>Decision letter</article-title></title-group><contrib-group><contrib contrib-type="editor"><name><surname>Giocomo</surname><given-names>Lisa</given-names></name><role>Reviewing Editor</role><aff><institution>Stanford School of Medicine</institution><country>United States</country></aff></contrib></contrib-group><contrib-group><contrib contrib-type="reviewer"><name><surname>Hasselmo</surname><given-names>Michael E</given-names></name><role>Reviewer</role><aff><institution>Boston University</institution><country>United States</country></aff></contrib></contrib-group></front-stub><body><boxed-text><p>In the interests of transparency, eLife publishes the most substantive revision requests and the accompanying author responses.</p></boxed-text><p><bold>Acceptance summary:</bold></p><p>In this study, the authors examined the electrophysiological properties of entorhinal cortical layer II stellate cells along the dorsal-ventral axis both within and across animals. They confirm, as previously reported, that a number of stellate cell biophysical features differ along this axis. Using sophisticated statistical methods, the authors then ask if these features follow a continuum pattern or a modular pattern along the dorsal-ventral axis. This has been an important question in the field since a discrete modular/clustered distribution of grid cell spacing was first described (Barry et al., 2007) and later work showed discrete modules (populations) of neurons with shared features of grid cell spacing, orientation, and elliptical shape (Stensola et al., 2012). The authors of the current paper systematically show that even with large numbers of neurons from single animals (N>35) they do not find evidence of modular/clustered patterns in the intrinsic properties of entorhinal stellate cells. The authors' findings add to the notion that the module cell organization of grid cells may reflect microcircuit activity. This is an important and rigorous paper that provides an important addition to the field and contributes to our understanding of the generation of spatial coding and circuits in the MEC.</p><p><bold>Decision letter after peer review:</bold></p><p>Thank you for submitting your article "Inter-and intra-animal variation of integrative properties of stellate cells in the medial entorhinal cortex" for consideration by <italic>eLife</italic>. Your article has been reviewed by three peer reviewers, and the evaluation has been overseen by a Reviewing Editor and Laura Colgin as the Senior Editor. The following individuals involved in review of your submission have agreed to reveal their identity: Michael E. Hasselmo (Reviewer #2); Andrea Burgalossi (Reviewer #3).</p><p>The reviewers have discussed the reviews with one another and the Reviewing Editor has drafted this decision to help you prepare a revised submission.</p><p>Essential revisions:</p><p>1) The authors have also studied the inter-animal variability among stellate cell excitability. They find that there is considerable inter animal variability, which is not unexpected given that there are a number of uncontrollable factors such as social interaction between animals as the authors allude to in their discussion. A number of studies have also reported that neuronal properties differ between animals at a single cell level in diverse regions (e.g. Villette et al., 2017). One possible issue for this variability, which the authors should address, is the fact that the slice quality, and therefore cell quality, might differ substantially between animals, even if this procedure is performed by the same experimenter. In particular, slight changes in cutting angles might impact factors such as the number of dendrites that are retained or cut off. Additional analyses on this front should be performed and considered in the discussion. Further, the synaptic connections onto the cells might also be variable between slices. I note that there are no glutamate or GABA receptor inhibitors included and thus baseline synaptic activity might be different between slices which might impact electrophysiological properties.</p><p>2) Given that the larger housing does have an effect on cell properties (Figure 4) it would be important to perform further analysis to determine if the number of objects that were in the cages within a specified area were the same in the larger housing versus standard cages. Additional objects in cages has been proposed to be an important factor in altering the properties of, for example, dentate gyrus adult new-born neurons.</p><p>3) The reviewers noted several discussion points that should be included in the Discussion section or relevant Results sections:</p><p>a) It is accepted that stellate cells are directly or indirectly involved in the generation of grid cell firing. However, grid cells are still a minority of all units recorded in MEC (and even in L2). By far, the most abundant functional cell type are non-grid spatial neurons (e.g. Diehl et al., 2017). Additional discussion on this point in relation to how their findings impact grid cell models should be considered.</p><p>b) One conclusion from the present work is that the intrinsic properties of stellate cells are not modularly organized – hence, the anatomical/cellular correlate of the functional grid cells modules remains to be elucidated. However, the L2 calbindin-positive neurons are indeed modularly organized, since they are anatomically clustered. This is an important organization principle of MEC L2 should at least be discussed (or commented upon) in the discussion.</p><p>c) Could the authors include a distribution of recordings along the medial-lateral axis?</p><p>d) Supplementary file 6: The physiological properties of neurons along the mediolateral dimension were also analyzed in Yoshida, Jochems and Hasselmo, 2013. This article should be cited and discussed. In addition, Figure 2, the apparent absence of dorsoventral differences in AHP differs from previous data showing a significant dorsoventral gradient of spike frequency adaptation and mAHP in the work by Yoshida et al., 2013. They should address this apparent difference in results.</p></body></sub-article><sub-article article-type="reply" id="sa2"><front-stub><article-id pub-id-type="doi">10.7554/eLife.52258.sa2</article-id><title-group><article-title>Author response</article-title></title-group></front-stub><body><disp-quote content-type="editor-comment"><p>Essential revisions:</p><p>1) The authors have also studied the inter-animal variability among stellate cell excitability. They find that there is considerable inter animal variability, which is not unexpected given that there are a number of uncontrollable factors such as social interaction between animals as the authors allude to in their discussion. A number of studies have also reported that neuronal properties differ between animals at a single cell level in diverse regions (e.g. Villette et al., 2017).</p></disp-quote><p>We now mention results from the study by Villete et al. (paragraph two subsection “Functional consequences of within cell type inter-animal variability”). We note however that this study describes inter-animal differences in motor behaviour and activity of hippocampal neurons but does not address the neuronal properties that we investigate here. We’re not aware of previous studies that have systematically explored inter-animal variation in the intrinsic properties of mammalian neurons.</p><disp-quote content-type="editor-comment"><p>One possible issue for this variability, which the authors should address, is the fact that the slice quality, and therefore cell quality, might differ substantially between animals, even if this procedure is performed by the same experimenter. In particular, slight changes in cutting angles might impact factors such as the number of dendrites that are retained or cut off. Additional analyses on this front should be performed and considered in the discussion.</p></disp-quote><p>To address the possibility of variation in slice quality we now highlight in the results the standardisation of the slicing procedure and several observations that argue against there being substantial differences in slice quality (paragraph two subsection “Inter-animal differences remain after accounting for additional experimental parameters”).</p><p>We appreciate the possibility that variation in slice angle could in principle alter the number of proportion of dendrites that are cut off. This appears unlikely to be an issue for several reasons:</p><p>1) Our method for preparation of sagittal slices involves hemi-section along the midline of the brain and then gluing the cut surface of the brain to the cutting block. Because the midline of the brain serves is a reliable guide for orientation, variation is minimal. This is in contrast with preparation of horizontal slices for which there is no obvious landmark to use for orientation and is therefore harder to make reproducible.</p><p>2) The same experimenter (HP) prepared all of the slices.</p><p>3) After each patch-clamp experiment we took images of the slice. While the images were primarily to enable assessment of the dorsoventral location of the recorded neurons, they did not suggest any substantial variation in slice angle.</p><p>4) Stellate cells dendrites are oriented in all directions from the soma. Therefore we expect the number of dendrites to be independent of the slicing angle. In other ongoing work we have found this to be the case.</p><p>We have modified the Materials and methods section to highlight how are dissection procedure minimises potential issues related to variation in the slice angle (subsection “Slice preparation”).</p><disp-quote content-type="editor-comment"><p>Further, the synaptic connections onto the cells might also be variable between slices. I note that there are no glutamate or GABA receptor inhibitors included and thus baseline synaptic activity might be different between slices which might impact electrophysiological properties.</p></disp-quote><p>To address possible roles of glutamate or GABA receptor inputs we have carried out additional experiments.</p><p>To detect tonic and phasic GABA receptor mediated synaptic inputs we have recorded spontaneous synaptic activity and the holding current at a potential of -70 mV in conditions in which the Cl<sup>–</sup> equilibrium potential is 0 mV (symmetrical intra- and extracellular Cl<sup>-</sup>concentration) (<xref ref-type="fig" rid="respfig1">Author response image 1</xref>). This is different to our standard recording conditions but is designed to maximise the amplitude of any GABA-A receptor mediated effects. In these conditions we find that application of GABA-A receptor antagonists abolishes spontaneous inhibitory synaptic currents but causes only a very small tonic outward current (6.4 +/- 14.7 pA). Consistent with this, we did not find any detectable change in input resistance when we applied blockers of GABA-A receptors to stellate cells (control: 31.6 ± 3.6 MΩ, GABAzine: 31.9 ± 4.1 MΩ, p = 0.89, n = 6, N = 5). Similar experiments using blockers of AMPA and NMDA suggest there is very little tonic glutamatergic input to stellate cells in our standard slice conditions (change in holding current: 8.5 +/- 13.8 pA; control input resistance: 30.0 ± 5.8 MΩ, input resistance in NBQΧ and D-APV: 31.4 ± 5.6 MΩ, n = 2, N = 2).</p><p>These data argue against baseline synaptic activity explaining our results. We now address this in the Materials and methods.</p><fig id="respfig1"><label>Author response image 1.</label><caption><title>Absence of a tonic GABA-A receptor mediated input to entorhinal cortex stellate cells.</title><p>(<bold>A–B</bold>) Continuous voltage-clamp recording of spontaneous synaptic activity from a stellate cell in control conditions (<bold>A</bold>) and during perfusion of GABAzine to block GABA-A receptors (<bold>B</bold>). (<bold>C–D</bold>) Perfusion of GABAzine did not affect the holding current (<bold>C–D</bold>) or input resistance (<bold>E</bold>) but abolished fast spontaneous inhibitory currents (<bold>F</bold>).</p></caption><graphic mime-subtype="jpeg" mimetype="image" xlink:href="elife-52258.xml.media/resp-fig1.jpg"/></fig><disp-quote content-type="editor-comment"><p>2) Given that the larger housing does have an effect on cell properties (Figure 4) it would be important to perform further analysis to determine if the number of objects that were in the cages within a specified area were the same in the larger housing versus standard cages. Additional objects in cages has been proposed to be an important factor in altering the properties of, for example, dentate gyrus adult new-born neurons.</p></disp-quote><p>This is an interesting idea. There were 10 – 15 plastic objects and 8 cardboard rolls in the large cages. The standard cages contained one cardboard roll and did not contain plastic objects. The area ratio of the large cage to a standard cage is approximately 39:1 (standard cage dimensions of 20 x 37 cm; floor area of 0.074 m<sup>2</sup> vs 2.88 m<sup>2</sup> for the large cage). Therefore, while there were more objects in the large cage, their density was slightly lower (up to 1/0.125 m -2 vs 1/0.074 m<sup>2</sup>). We now add this information to the Materials and methods (subsection “Mouse strains”).</p><p>We appreciate the idea of investigating whether the number or density of objects influences intrinsic properties of stellate cells or other neurons. However, our experiments aimed to test whether the excitable properties of stellate cells are modifiable by an environment that would maximise activation of ventral grid cells. Because we did not attempt to systematically vary the number of objects in the large maze we are not able to analyse the effect of the number of objects separately from the size of the cage. This could be an important question for future studies. We note that because our data suggest that effect sizes when addressing this question are likely to be quite small, obtaining adequate statistical power will likely require a large scale study with many more animals in each experimental group than we use here. To address the reviewers’ point in the manuscript we have modified the Discussion to consider the role of the number of objects (paragraph three subsection “A conceptual framework for within cell type variability”).</p><disp-quote content-type="editor-comment"><p>3) The reviewers noted several discussion points that should be included in the Discussion section or relevant Results sections:</p><p>a) It is accepted that stellate cells are directly or indirectly involved in the generation of grid cell firing. However, grid cells are still a minority of all units recorded in MEC (and even in L2). By far, the most abundant functional cell type are non-grid spatial neurons (e.g. Diehl et al., 2017). Additional discussion on this point in relation to how their findings impact grid cell models should be considered.</p></disp-quote><p>We have modified the Discussion to highlight this point (subsection “Implications of continuous dorsoventral organisation of stellate cell integrative properties for grid cell firing”).</p><disp-quote content-type="editor-comment"><p>b) One conclusion from the present work is that the intrinsic properties of stellate cells are not modularly organized – hence, the anatomical/cellular correlate of the functional grid cells modules remains to be elucidated. However, the L2 calbindin-positive neurons are indeed modularly organized, since they are anatomically clustered. This is an important organization principle of MEC L2 should at least be discussed (or commented upon) in the discussion.</p></disp-quote><p>We now mention this possibility in the Discussion (subsection “Implications of continuous dorsoventral organisation of stellate cell integrative properties for grid cell firing”).</p><disp-quote content-type="editor-comment"><p>c) Could the authors include a distribution of recordings along the medial-lateral axis?</p></disp-quote><p>Because our experiments used para-sagittal slices we only obtained two slices per hemisphere that contained the MEC. To show the distribution of data between these slices we now include a figure comparing properties from slices containing the more medial with the more lateral parts of the MEC (Figure 4—figure supplement 1, referred to on p 5, subsection “Inter-animal differences remain after accounting for additional experimental parameters”).</p><disp-quote content-type="editor-comment"><p>d) Supplementary file 6: The physiological properties of neurons along the mediolateral dimension were also analyzed in Yoshida, Jochems and Hasselmo, 2013. This article should be cited and discussed.</p></disp-quote><p>We apologise for overlooking the study by Yoshida and colleagues. We now cite this study (Results and Discussion section). We have added Discussion of the mediolateral organisation of SC properties (subsection “Implications of continuous dorsoventral organisation of stellate cell integrative properties for grid cell firing”).</p><disp-quote content-type="editor-comment"><p>In addition, Figure 2, the apparent absence of dorsoventral differences in AHP differs from previous data showing a significant dorsoventral gradient of spike frequency adaptation and mAHP in the work by Yoshida et al., 2013. They should address this apparent difference in results.</p></disp-quote><p>Differences between the results from Yoshida et al. and the results we present here likely result from different stimulus waveforms used to drive action potential firing. In Yoshida et al. spike frequency adaptation was measured in response to step currents that generated spike trains with frequency > 20 Hz and the action potential AHP was measured from a baseline membrane potential of -60 mV after triggering a single spike with a 1ms current step. In contrast, we measured action potentials activated during injection of a positive current ramp. Because we were using a current ramp we were unable to quantify adaptation. Moreover, the maximum spike frequency reached during the ramp was typically < 10 Hz (e.g. Figure 1C). Across this lower frequency range stellate cells show very little spike frequency adaptation (cf. Nolan et al., 2007, Pastoll et al., 2012). The dorsoventral gradient in the duration of AHPs reported by Yoshida et al. following single action potentials is consistent with our previous results in conditions similar to those used here (cf. Pastoll et al., 2012). We’re not sure why we don’t see the dorsoventral gradient in AHP amplitude reported by Yoshida et al., but this may reflect different driving forces for currents generating AHPs at the different baseline membrane potentials in each experiment (-60 mV in Yoshida et al. and approximately -40 mV here). Because the mechanisms by which SCs generate their AHP is not well understood it is difficult to speculate further. Therefore, because the two studies do not measure the AHP in the same way, and given that differences are likely to be technical and not related to the main hypotheses of the experiments in the study, we have not added any further discussion of the differences to the manuscript.</p></body></sub-article></article>