Detecting pairwise correlations in spike trains: an objective comparison of methods and application to the study of retinal waves.

Correlations in neuronal spike times are thought to be key to processing in many neural systems. Many measures have been proposed to summarize these correlations and of these the correlation index is widely used and is the standard in studies of spontaneous retinal activity. We show that this measure has two undesirable properties: it is unbounded above and confounded by firing rate. We list properties needed for a measure to fairly quantify and compare correlations and we propose a novel measure of correlation-the spike time tiling coefficient. This coefficient, the correlation index, and 33 other measures of correlation of spike times are blindly tested for the required properties on synthetic and experimental data. Based on this, we propose a measure (the spike time tiling coefficient) to replace the correlation index. To demonstrate the benefits of this measure, we reanalyze data from seven key studies, which previously used the correlation index to investigate the nature of spontaneous activity. We reanalyze data from β2(KO) and β2(TG) mutants, mutants lacking connexin isoforms, and also the age-dependent changes in wild-type and β2(KO) correlations. Reanalysis of the data using the proposed measure can significantly change the conclusions. It leads to better quantification of correlations and therefore better inference from the data. We hope that the proposed measure will have wide applications, and will help clarify the role of activity in retinotopic map formation

Can retinal ganglion cell dipoles seed iso-orientation domains in the visual cortex?

It has been argued that the emergence of roughly periodic orientation preference maps (OPMs) in the primary visual cortex (V1) of carnivores and primates can be explained by a so-called statistical connectivity model. This model assumes that input to V1 neurons is dominated by feed-forward projections originating from a small set of retinal ganglion cells (RGCs). The typical spacing between adjacent cortical orientation columns preferring the same orientation then arises via Moir\'{e}-Interference between hexagonal ON/OFF RGC mosaics. While this Moir\'{e}-Interference critically depends on long-range hexagonal order within the RGC mosaics, a recent statistical analysis of RGC receptive field positions found no evidence for such long-range positional order. Hexagonal order may be only one of several ways to obtain spatially repetitive OPMs in the statistical connectivity model. Here, we investigate a more general requirement on the spatial structure of RGC mosaics that can seed the emergence of spatially repetitive cortical OPMs, namely that angular correlations between so-called RGC dipoles exhibit a spatial structure similar to that of OPM autocorrelation functions. Both in cat beta cell mosaics as well as primate parasol receptive field mosaics we find that RGC dipole angles are spatially uncorrelated. To help assess the level of these correlations, we introduce a novel point process that generates mosaics with realistic nearest neighbor statistics and a tunable degree of spatial correlations of dipole angles. Using this process, we show that given the size of available data sets, the presence of even weak angular correlations in the data is very unlikely. We conclude that the layout of ON/OFF ganglion cell mosaics lacks the spatial structure necessary to seed iso-orientation domains in the primary visual cortex.Comment: 9 figures + 1 Supplementary figure and 1 Supplementary tabl

Bivariate spatial point patterns in the retina: a reproducible review

This is the final version of the article. It first appeared from Societe Française de Statistique via http://journal-sfds.fr/index.php/J-SFdS/article/view/518/490In this article I present a reproducible review of recent research to investigate the spatial positioning of neurons in the nervous system. In particular, I focus on the relative spatial positioning of pairs of cell types within the retina. I examine three different cases by which two types of neurons might be arranged relative to each other. (1) Cells of different type might be effectively independent of each other. (2) Cells of one type are randomly assigned one of two labels to create two related populations. (3) Interactions between cells of different type generate functional dependencies. I show briefly how spatial statistic techniques can be applied to investigate the nature of spatial interactions between two cell types. Finally, I have termed this article a ‘reproducible review’ because all the data and computer code are integrated into the manuscript so that others can repeat the analysis presented here. I close the review with a discussion of this concept

Detecting pairwise correlations in spike trains: an objective comparison of methods and application to the study of retinal waves.

Correlations in neuronal spike times are thought to be key to processing in many neural systems. Many measures have been proposed to summarize these correlations and of these the correlation index is widely used and is the standard in studies of spontaneous retinal activity. We show that this measure has two undesirable properties: it is unbounded above and confounded by firing rate. We list properties needed for a measure to fairly quantify and compare correlations and we propose a novel measure of correlation-the spike time tiling coefficient. This coefficient, the correlation index, and 33 other measures of correlation of spike times are blindly tested for the required properties on synthetic and experimental data. Based on this, we propose a measure (the spike time tiling coefficient) to replace the correlation index. To demonstrate the benefits of this measure, we reanalyze data from seven key studies, which previously used the correlation index to investigate the nature of spontaneous activity. We reanalyze data from β2(KO) and β2(TG) mutants, mutants lacking connexin isoforms, and also the age-dependent changes in wild-type and β2(KO) correlations. Reanalysis of the data using the proposed measure can significantly change the conclusions. It leads to better quantification of correlations and therefore better inference from the data. We hope that the proposed measure will have wide applications, and will help clarify the role of activity in retinotopic map formation.This work was supported by the Wellcome Trust Grant 083205(S.J.E.) and EPSRC (C.S.C.) for funding.This is the final published version. It first appeared at http://www.jneurosci.org/content/34/43/14288.long

Quantitative differences in developmental profiles of spontaneous activity in cortical and hippocampal cultures.

BACKGROUND: Neural circuits can spontaneously generate complex spatiotemporal firing patterns during development. This spontaneous activity is thought to help guide development of the nervous system. In this study, we had two aims. First, to characterise the changes in spontaneous activity in cultures of developing networks of either hippocampal or cortical neurons dissociated from mouse. Second, to assess whether there are any functional differences in the patterns of activity in hippocampal and cortical networks. RESULTS: We used multielectrode arrays to record the development of spontaneous activity in cultured networks of either hippocampal or cortical neurons every 2 or 3 days for the first month after plating. Within a few days of culturing, networks exhibited spontaneous activity. This activity strengthened and then stabilised typically around 21 days in vitro. We quantified the activity patterns in hippocampal and cortical networks using 11 features. Three out of 11 features showed striking differences in activity between hippocampal and cortical networks: (1) interburst intervals are less variable in spike trains from hippocampal cultures; (2) hippocampal networks have higher correlations and (3) hippocampal networks generate more robust theta-bursting patterns. Machine-learning techniques confirmed that these differences in patterning are sufficient to classify recordings reliably at any given age as either hippocampal or cortical networks. CONCLUSIONS: Although cultured networks of hippocampal and cortical networks both generate spontaneous activity that changes over time, at any given time we can reliably detect differences in the activity patterns. We anticipate that this quantitative framework could have applications in many areas, including neurotoxicity testing and for characterising the phenotype of different mutant mice. All code and data relating to this report are freely available for others to use.PC and AM were supported by the Wellcome Trust Genes to Cognition programme. PC received additional support from the Biotechnology and Biological Sciences Research Council (BB/H008608/1). EC was supported by a Wellcome Trust PhD studentship and Cambridge Biomedical Research Centre studentship. SJE was supported by an Engineering and Physical Sciences Research Council grant (EP/E002331/1).This is the final published version. It first appeared at http://link.springer.com/article/10.1186%2Fs13064-014-0028-0

Analysis of spontaneous activity patterns in developing retina: algorithms and results

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Estimating the location and size of retinal injections from orthogonal images of an intact retina.

BACKGROUND: To study the mapping from the retina to the brain, typically a small region of the retina is injected with a dye, which then propagates to the retina's target structures. To determine the location of the injection, usually the retina is dissected out of the eye, flattened and then imaged, causing tears and stretching of the retina. The location of the injection is then estimated from the image of the flattened retina. Here we propose a new method that avoids dissection of the retina. RESULTS: We have developed IntactEye, a software package that uses two orthogonal images of the intact retina to locate focal injections of a dye. The two images are taken while the retina is still inside the eye. This bypasses the dissection step, avoiding unnecessary damage to the retina, and speeds up data acquisition. By using the native spherical coordinates of the eye, we avoid distortions caused by interpreting a curved structure in a flat coordinate system. Our method compares well to the projection method and to the Retistruct package, which both use the flattened retina as a starting point. We have tested the method also on synthetic data, where the injection location is known. Our method has been designed for analysing mouse retinas, where there are no visible landmarks for discerning retinal orientation, but can also be applied to retinas from other species. CONCLUSIONS: IntactEye allows the user to precisely specify the location and size of a retinal injection from two orthogonal images taken of the eye. We are solving the abstract problem of locating a point on a spherical object from two orthogonal images, which might have applications outside the field of neuroscience.SJE and MR gratefully acknowledge the support of the University of Strasbourg Institute for Advanced Study (USIAS). SJE and JJJH were supported by the Wellcome Trust (grant number 083205). The authors wish to thank Ellese Cotterill for analysing synthetic data for verification of accuracy

Homeostatic Activity-Dependent Tuning of Recurrent Networks for Robust Propagation of Activity.

UNLABELLED: Developing neuronal networks display spontaneous bursts of action potentials that are necessary for circuit organization and tuning. While spontaneous activity has been shown to instruct map formation in sensory circuits, it is unknown whether it plays a role in the organization of motor networks that produce rhythmic output. Using computational modeling, we investigate how recurrent networks of excitatory and inhibitory neuronal populations assemble to produce robust patterns of unidirectional and precisely timed propagating activity during organism locomotion. One example is provided by the motor network inDrosophilalarvae, which generates propagating peristaltic waves of muscle contractions during crawling. We examine two activity-dependent models, which tune weak network connectivity based on spontaneous activity patterns: a Hebbian model, where coincident activity in neighboring populations strengthens connections between them; and a homeostatic model, where connections are homeostatically regulated to maintain a constant level of excitatory activity based on spontaneous input. The homeostatic model successfully tunes network connectivity to generate robust activity patterns with appropriate timing relationships between neighboring populations. These timing relationships can be modulated by the properties of spontaneous activity, suggesting its instructive role for generating functional variability in network output. In contrast, the Hebbian model fails to produce the tight timing relationships between neighboring populations required for unidirectional activity propagation, even when additional assumptions are imposed to constrain synaptic growth. These results argue that homeostatic mechanisms are more likely than Hebbian mechanisms to tune weak connectivity based on spontaneous input in a recurrent network for rhythm generation and robust activity propagation. SIGNIFICANCE STATEMENT: How are neural circuits organized and tuned to maintain stable function and produce robust output? This task is especially difficult during development, when circuit properties change in response to variable environments and internal states. Many developing circuits exhibit spontaneous activity, but its role in the synaptic organization of motor networks that produce rhythmic output is unknown. We studied a model motor network, that when appropriately tuned, generates propagating activity as during crawling inDrosophilalarvae. Based on experimental evidence of activity-dependent tuning of connectivity, we examined plausible mechanisms by which appropriate connectivity emerges. Our results suggest that activity-dependent homeostatic mechanisms are better suited than Hebbian mechanisms for organizing motor network connectivity, and highlight an important difference from sensory areas.This work was supported by Cambridge Overseas Research Fund, Trinity College, and Swartz Foundation to J.G. and Wellcome Trust VIP funding to J.F.E. through Program Grant WT075934 to Michael Bate and Matthias Landgraf. J.G. is also supported by Burroughs-Wellcome Fund Career Award at the Scientific Interface.This is the final version of the article. It first appeared from the Society for Neuroscience via https://doi.org/10.1523/JNEUROSCI.2511-15.201