Statistical analysis of retinal neural coding response: A framework from statistical physics.
Objective: Analyze, at the local network level, the statistical properties of ganglions cells retinal output spike trains thus including adaptation mechanisms.
Methods: Recent advances in multi-electrodes recording have thus brought us closer to understanding how populations of retinal ganglion cells encode visual information. By monitoring the visual responses of many ganglion cells at once, it is now possible to examine how ganglion cells act together to encode a visual scene. To attain this objective, a quantitative and statistical analysis of the ganglion cells spiking activity is required.
This issue is faced to the delicate problem of proposing and validating accurate statistical model fitting the empirical spike trains. It has been shown in (Schneidman et al, 2006; Cessac et al, 2009; Cessac, 2010) that Gibbs measures constitute optimal parametric models, the estimated Gibbs potential allowing to produce population rate, correlations or synchronization pattern, providing an effective statistical tool.
Since, using the Gibbs potential framework allows us to obtain parametric estimations of spike train observables, e.g. the population rate, correlations, or synchronization pattern occurrence probability, this statistical tool appears to be a very interesting way of attaining our objective, allowing us to relate the observed spiking activity to higher scales of observation of the neuronal activity. For instance, the population spiking rate and correlation, or even higher order statistics can be measured using the previous parametric model and then integrated in mean-field mesoscopic models (Faugeras et al, 2009).
We propose to apply an open-source library (EnaS) which estimates a polynomial Gibbs potential over population spike trains and subsequently the population firing rate, correlations, higher order statistics and relative entropy (Vasquez et al, 2010). The software module EnaS has been already validated at the programmatic level (functional tests).
Two types of population spike trains will be studied:
– Simulated spike-trains of well-defined statistics in order to evaluate the quality and precision of the method and,
– Experimental spike-trains provided by CINV in order to evaluate the pertinence and the applicability of the method at the biological level.
The available framework allows the comparison of different statistical models, which is a precious tool to disambiguate the correlations origin. This is illustrated in the following figure where a 2nd order Gibbs-distribution (bgibbs-2) is estimated considering several models, the correct model being easy to detect as the “1st unbiased estimation” (after Vasquez et al, 2010, where a rigorous formalism is proposed).
Task steps:
(i) Artificial spikes-train benchmarks, using statistics as observed in retinal cells.
(ii) Simulated spikes-train benchmarks, as produced by the retinal simulator
(iii) Experimental spike-trains benchmarks, using data from Task1 after “spike-sorting” preprocessing.
