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Section: New Results

Human vision understanding through joint experimental and modeling studies, for normal and distrophic vision

Recurrent network dynamics reconciles visual motion segmentation and integration

Participants : N.v. Kartheek Medathati, James Rankin [University of Exeter (Department of Mathematics, Exeter, UK)] , Andrew I. Meso [Institut de Neurosciences de la Timone (CNRS and Aix-Marseille Université, France)] , Pierre Kornprobst, Guillaume S. Masson [Institut de Neurosciences de la Timone (CNRS and Aix-Marseille Université, France)] .

In sensory systems, different computational rules are postulated to be implemented by different neuronal subpopulations characterised by their tuning function. For instance, in primate cortical area MT, different classes of direction-selective cells have been identified and related to either motion integration, segmentation or transparency. Still, how such different tuning properties are constructed is unclear. The dominant theoretical viewpoint based on linear-nonlinear feedforward cascade does not account for their complex temporal dynamics and their versatility when facing different input statistics. Here, we demonstrate that a recurrent network model of visual motion processing can reconcile these different properties. Using a ring network, we show how excitatory and inhibitory interactions can implement different computational rules such as vector averaging, winner-take-all or superposition. The model also captures ordered temporal transitions between these behaviours. In particular, depending on the inhibition regime the ring network can switch from motion integration to motion segmentation, thus being able to compute either a single pattern motion or to superpose multiple inputs as in motion transparency. We thus demonstrate that recurrent architectures can adaptively give rise to different cortical computational regimes depending upon the input statistics, thus reconciling the twin blows of sensory processing: integration and segmentation.

This work was published in [20]

Retinal waves

Participants : Dora Karvouniari, Lionel Gil [Institut Non Linéaire de Nice (INLN, Université Côte d'Azur (France), France)] , Olivier Marre [Institut de la Vision (Paris, France)] , Serge Picaud [Institut de la Vision (Paris, France)] , Bruno Cessac.

Retinal waves are bursts of activity occurring spontaneously in the developing retina of vertebrate species, contributing to the shaping of the visual system organization: retina circuitry shaping, retinotopy, eye segregation   [77], [56], [72], [57]. They stop a few weeks after birth. Wave activity begins in the early development, long before the retina is responsive to light. It was recently found that they can be reinitiated pharmacologically in the adult mammalian retina  [54]. This could have deep consequences on therapy for several degenerative retinal diseases. The mechanism of their generation, in imature, or adult retinas, remains however incompletely understood  [78].

We have proposed a model for stage II retinal waves - induced by bursting Starburst Amacrine Cells (SACs) coupled by acetylcholine - with 2 objectives: (i) being sufficiently close to biophysics to explain and propose experiments and (ii) affording a mathematical analysis. From a bifurcations analysis we have highlighted several relevant biophysical parameters controlling waves generation, mainly regulating potassium and calcium dynamics. We thus explain how SACs in different species exhibit a large variability in their bursting periods with a common mechanism. We have proposed a testable experimental prediction providing a possible link of the evolution of voltage-dependent potassium channels along development with their role on the excitability properties of SACs. We have reproduced experimental findings (statistical characteristics of waves size, duration and frequency of appearance) and analyzed how the evolution of cholinergic conductance due to the maturation of nicotinic receptors dramatically changes the retinal wave characteristics. We have also shown that the nonlinear dynamics generates heterogeneous local spatial structures inside which retinal waves propagate. This induces a wide variability in waves characteristics even though the network is perfectly homogeneous.

This work has been presented in [36], [34], [24], [25], [38], [37]

Pan-retinal characterisation of light responses from ganglion cells in the developing mouse retina

Participants : Gerrit Hilgen [Institute of Neuroscience (ION, Newcastle, UK)] , Sahar Pirmoradian [Institute for Adaptive and Neural Computation (ANC, School of Informatics University of Edinburgh, UK)] , Daniela Pamplona [ENSTA ParisTech, Autonomous Systems and Robotics (Paris, France)] , Pierre Kornprobst, Bruno Cessac, Matthias H. Hennig [Institute for Adaptive and Neural Computation (ANC, School of Informatics University of Edinburgh, UK)] , Evelyne Sernagor [Institute of Neuroscience (ION, Newcastle, UK)] .

We have investigated the ontogeny of light-driven responses in mouse retinal ganglion cells (RGCs). Using a large-scale, high-density multielectrode array, we recorded from hundreds to thousands of RGCs simultaneously at pan-retinal level, including dorsal and ventral locations. Responses to different contrasts not only revealed a complex developmental profile for ON, OFF and ON-OFF RGC types, but also unveiled differences between dorsal and ventral RGCs. At eye-opening, dorsal RGCs of all types were more responsive to light, perhaps indicating an environmental priority to nest viewing for pre-weaning pups. The developmental profile of ON and OFF RGCs exhibited antagonistic behaviour, with the strongest ON responses shortly after eye-opening, followed by an increase in the strength of OFF responses later on. Further, we found that with maturation receptive field (RF) center sizes decrease, responses to light get stronger, and centers become more circular while seeing differences in all of them between RGC types. These findings show that retinal functionality is not spatially homogeneous, likely reflecting ecological requirements that favour the early development of dorsal retina, and reflecting different roles in vision in the mature animal.

This work has been published in [19].

Trajectory anticipation, from retina to V1

Participants : Selma Souihel, Bruno Cessac.

Global motion processing is a major computational task of biological visual systems. When an object moves across the visual field, the sequence of visited positions is strongly correlated in space and time, forming a trajectory. These correlated images generate a sequence of local activation of the feedforward stream. At the present stage of knowledge, it is still unclear how the early visual system processes motion trajectories. Motion integration, anticipation and prediction would be jointly achieved through the interactions between feed-forward, lateral and feedback propagations within a common spatial reference frame, the retinotopic maps. Addressing this problem is particularly challenging, as it requires to probe these sequences of events at multiple scales (from individual cells to large networks) and multiple stages (retina, primary visual cortex (V1).

In the context of the ANR Trajectory we are working on such an integrated approach. We aim at modelling the population responses at two key stages of visual motion encoding: the retina and V1 based on simultaneous micro- and mesoscopic recordings made by our partners Institut de Neurosciences de la Timone (CNRS and Aix-Marseille Université, France) and Institut de la Vision (Paris, France), and design a simulator of retinal output feeding V1. This study is a step toward understanding mechanisms of motion coding and anticipation with strong impact on our understanding of the visual system.

We have implemented in our retina simulator, PRANAS, gain control mechanisms allowing to reproduce motion anticipation for simple motions. We developed a simple decoding algorithm that reconstructs the stimulus using firing rates, with the goal of comparing the performance of the different models of gain control. We have also designed a biologically inspired model of connectivity, mimicking short and long range connections between ganglion cells via amacrine cells. This has allowed us to compare the pairwise correlations between ganglion cells, under the influence of a moving object both, in vivo and in silico. These results have been presented in [40], [41], [39]

Dimensionality reduction in spatio-temporal MaxEnt models and analysis of retinal ganglion cell spiking activity in experiments

Participants : Rubén Herzog [Centro Interdisciplinario de Neurociencia de Valparaíso (CINV, Valparaíso, Chile)] , Maria-Jose Escobar [Universidad Tecnico Federico Santa María (Electronics Engineering Department, Valparaíso, Chile)] , Adrian Palacios [Centro Interdisciplinario de Neurociencia de Valparaíso (CINV, Valparaíso, Chile)] , Bruno Cessac.

Retinal spike response to stimuli is constrained, on one hand by short range correlations (receptive field overlap) and on the other hand by lateral connectivity (cells connectivity). This last effect is difficult to handle from statistics because it requires to consider spatio-temporal correlations with a time delay long enough to take into account the time of propagation along synapses. Although MaxEnt models are useful to fit optimal model (maximizing entropy) under the constraints of reproducing observed correlations, they do address spatio-temporal correlations in their classical form (Ising or higher order interactions but without time delay). Binning in such models somewhat integrates propagation effects, but in an implicit form, and increasing binning severely bias data. To resolve this issue we have considered spatio-temporal MaxEnt model formerly developed e.g. by Vasquez et al. [75]. The price to pay, however is a huge set of parameters that must be fitted to experimental data to explain the observed spiking patterns statistics. There is no a priori knowledge of which parameters are relevant and which ones are contributing to overfitting. We propose here a method of dimension reduction, i.e. a projection on a relevant subset of parameters, relying on the so-called Susceptibility matrix closely related to the Fisher information. In contrast to standard methods in information geometry though, this matrix handles space and time correlations. We have applied this method for retina data obtained in a diurnal rodent (Octodon degus, having 30% of cones photoreceptors) and a 252-MEA system. Three types of stimuli were used: spatio-temporal uniform light, white noise and a natural movie. We show the role played by time-delayed pairwise interactions in the neural response to stimuli both for close and distant cells. Our conclusion is that, to explain the population spiking statistics we need both short-distance interactions as well as long-distance interactions, meaning that the relevant functional correlations are mediated not only by common input (i.e. receptive field overlap, electrical coupling; spillover) but also by long range connections.

This work has been submitted to Plos Comp Bio.

On the mathematical consequences of binning spike trains

Participants : Bruno Cessac, Arnaud Le Ny [Laboratoire d'Analyse et de Mathématiques Appliquées (LAMA, (Université Paris-Est, France)] , Eva Loecherbach [Laboratoire d'Analyse, Géométrie et Modélisation (AGM) and Département de Mathématiques (Cergy-Pontoise, France)] .

We initiate a mathematical analysis of hidden effects induced by binning spike trains of neurons. Assuming that the original spike train has been generated by a discrete Markov process, we show that binning generates a stochastic process which is not Markovian any more, but is instead a Variable Length Markov Chain (VLMC) with unbounded memory. We also show that the law of the binned raster is a Gibbs measure in the DLR (Dobrushin-Lanford-Ruelle) sense coined in mathematical statistical mechanics. This allows the derivation of several important consequences on statistical properties of binned spike trains. In particular, we introduce the DLR framework as a natural setting to mathematically formalize anticipation, i.e. to tell "how good" our nervous system is at making predictions. In a probabilistic sense, this corresponds to condition a process by its future and we discuss how binning may affect our conclusions on this ability. We finally comment what could be the consequences of binning in the detection of spurious phase transitions or in the detection of wrong evidences of criticality.

This work has been published in [17].

Linear response of general observables in spiking neuronal network models

Participants : Bruno Cessac, Rodrigo Cofré [Université de Genève (Switzerland) and Centro Interdisciplinario de Neurociencia de Valparaíso (CINV, Valparaíso, Chile)] .

The activity of a neuronal network, characterized by action potentials (spikes), is constrained by the intrinsic properties of neurons and their interactions. When a neuronal network is submitted to external stimuli, the statistics of spikes changes, and it is difficult to disentangle the influence of the stimuli from the intrinsic dynamics. Using the formalism of Gibbs distributions, which are a generalization of Maximum Entropy distributions to non-stationary distributions, and generalization of Markov chains to infinite memory, we analyze this problem in a specific model (Conductance-based Integrate-and-Fire), where the neuronal dynamics depends on the history of spikes of the network. We derive a linear response formula allowing to quantify the influence of a weak amplitude external stimuli on the average value of arbitrary observables. This formula clearly disentangles the effect of the stimuli, intrinsic neuronal dynamics, and network connectivity. Upon some approximations, it reduces to a convolution, allowing to recover a standard formulation in computational neuroscience.

This work has been submitted to Journal of Mathematical Neurosciences [33].

A bio-inspired synergistic virtual retina model for tone mapping

Participants : Marco Benzi, Maria-Jose Escobar [Universidad Tecnico Federico Santa María (Electronics Engineering Department, Valparaíso, Chile)] , Pierre Kornprobst.

Real-world radiance values span several orders of magnitudes which have to be processed by artificial systems in order to capture visual scenes with a high visual sensitivity. Interestingly, it has been found that similar processing happens in biological systems, starting at the retina level. So our motivation in this paper is to develop a new video tone mapping operator (TMO) based on a synergistic model of the retina. We start from the so-called Virtual Retina model  [76], which has been developed in computational neuroscience. We show how to enrich this model with new features to use it as a TMO, such as color management, luminance adaptation at photoreceptor level and readout from a heterogeneous population activity. Our method works for video but can also be applied to static images (by repeating images in time). It has been carefully evaluated on standard benchmarks in the static case, giving comparable results to the state-of-the-art using default parameters, while offering user control for finer tuning. Results on HDR videos are also promising, specifically w.r.t. temporal luminance coherency. As a whole, this paper shows a promising way to address computational photography challenges by exploiting the current research in neuroscience about retina processing.

This work was published in [15].