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

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

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

Spatial constraints underlying the retinal mosaics of two types of horizontal cells in cat and macaque

Most types of retinal neurons are spatially positioned in non-random patterns, termed retinal mosaics. Several developmental mechanisms are thought to be important in the formation of these mosaics. Most evidence to date suggests that homotypic constraints within a type of neuron are dominant, and that heterotypic interactions between different types of neuron are rare. In an analysis of macaque H1 and H2 horizontal cell mosaics, W\"assle et al. (2000) suggested that the high regularity index of the combined H1 and H2 mosaic might be caused by heterotypic interactions during development. Here we use computer modelling to suggest that the high regularity index of the combined H1 and H2 mosaic is a by-product of the basic constraint that two neurons cannot occupy the same space. The spatial arrangement of type A and type B horizontal cells in cat retina also follow this same principle

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

From Random to Regular: Variation in the Patterning of Retinal Mosaics

The various types of retinal neurons are each positioned at their respective depths within the retina where they are believed to be assembled as orderly mosaics, in which like-type neurons minimize proximity to one another. Two common statistical analyses for assessing the spatial properties of retinal mosaics include the nearest neighbor analysis, from which an index of their "regularity" is commonly calculated, and the density recovery profile derived from auto-correlation analysis, revealing the presence of an exclusion zone indicative of anti-clustering. While each of the spatial statistics derived from these analyses, the regularity index and the effective radius, can be useful in characterizing such properties of orderly retinal mosaics, they are rarely sufficient for conveying the natural variation in the self-spacing behavior of different types of retinal neurons and the extent to which that behavior generates uniform intercellular spacing across the mosaic. We consider the strengths and limitations of different spatial statistical analyses for assessing the patterning in retinal mosaics, highlighting a number of misconceptions and their frequent misuse. Rather than being diagnostic criteria for determining simply whether a population is "regular", they should be treated as descriptive statistics that convey variation in the factors that influence neuronal positioning. We subsequently apply multiple spatial statistics to the analysis of eight different mosaics in the mouse retina, demonstrating conspicuous variability in the degree of patterning present, from essentially random to notably regular. This variability in patterning has both a developmental as well as a functional significance, reflecting the rules governing the positioning of different types of neurons as the architecture of the retina is assembled (abstract truncated).Comment: 11 Figure

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

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LL5β: a regulator of postsynaptic differentiation identified in a screen for synaptically enriched transcripts at the neuromuscular junction

In both neurons and muscle fibers, specific mRNAs are concentrated beneath and locally translated at synaptic sites. At the skeletal neuromuscular junction, all synaptic RNAs identified to date encode synaptic components. Using microarrays, we compared RNAs in synapse-rich and -free regions of muscles, thereby identifying transcripts that are enriched near synapses and that encode soluble membrane and nuclear proteins. One gene product, LL5β, binds to both phosphoinositides and a cytoskeletal protein, filamin, one form of which is concentrated at synaptic sites. LL5β is itself associated with the cytoplasmic face of the postsynaptic membrane; its highest levels border regions of highest acetylcholine receptor (AChR) density, which suggests a role in “corraling” AChRs. Consistent with this idea, perturbing LL5β expression in myotubes inhibits AChR aggregation. Thus, a strategy designed to identify novel synaptic components led to identification of a protein required for assembly of the postsynaptic apparatus