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Bruno Cessac

Publications and source records attributed to Bruno Cessac.

At least 19 recordsLinked to original sources
arXiv2025

Macular: a multi-scale simulation platform for the retina and the primary visual system

We developed Macular, a simulation platform with a graphical interface, designed to produce in silico experiment scenarios for the retina and the primary visual system. A scenario consists of generating a three-dimensional structure with interconnected layers, each layer corresponding to a type of 'cell' in the retina or visual cortex. The cells can correspond to neurons or more complex structures (such as cortical columns). The inputs are arbitrary videos. The user can use the cells and synapses provided with the software, or create their own using a graphical interface where they enter the constituent equations in text format (e.g., LaTeX). They also create the three-dimensional structure via the graphical interface. Macular then automatically generates and compiles the C++ code and generates the simulation interface. This allows the user to view the input video and the three-dimensional structure in layers. It also allows the user to select cells and synapses in each layer and view the activity of their state variables. Finally, the user can adjust the phenomenological parameters of the cells or synapses via the interface. We provide several example scenarios, corresponding to published articles, including an example of a retino-cortical model. Macular was designed for neurobiologists and modelers, specialists in the primary visual system, who want to test hypotheses in silico without the need for programming. By design, this tool allows natural or altered conditions (pharmacology, pathology, development) to be simulated.

q-bio.NC↗
arXiv2024

How does the inner retinal network shape the ganglion cells receptive field : a computational study

We consider a model of basic inner retinal connectivity where bipolar and amacrine cells interconnect, and both cell types project onto ganglion cells, modulating their response output to the brain visual areas. We derive an analytical formula for the spatio-temporal response of retinal ganglion cells to stimuli taking into account the effects of amacrine cells inhibition. This analysis reveals two important functional parameters of the network: (i) the intensity of the interactions between bipolar and amacrine cells, and, (ii) the characteristic time scale of these responses. Both parameters have a profound combined impact on the spatiotemporal features of RGC responses to light. %We show that, depending on these parameters value, retinal ganglion cells can change their spatio-temporal response (e.g. from monophasic to biphasic). The validity of the model is confirmed by faithfully reproducing pharmacogenetic experimental results obtained by stimulating excitatory DREADDs (Designer Receptors Exclusively Activated by Designer Drugs) expressed on ganglion cells and amacrine cells subclasses, thereby modifying the inner retinal network activity to visual stimuli in a complex, entangled manner. Our mathematical model allows us to explore and decipher these complex effects in a manner that would not be feasible experimentally and provides novel insights in retinal dynamics.

q-bio.NC↗
arXiv2023

The non linear dynamics of retinal waves

We investigate the dynamics of stage II retinal waves via a dynamical system, grounded on biophysics, and analysed with bifurcation theory. We show how the nonlinear cells coupling and bifurcation structure explain how waves start, propagate, interact and stop. Especially, we analyse how the existence of a small region in parameter space, where dynamics returns in a recurrent way, gives rise to a very rich dynamics. In this context, we propose a non linear transport equation characterizing the waves propagation and interaction.

nlin.AO↗
arXiv2022

Retinal processing: insights from mathematical modelling

The retina is the entrance of the visual system. Although based on common biophysical principles the dynamics of retinal neurons is quite different from their cortical counterparts, raising interesting problems for modellers. In this paper I address some mathematically stated questions in this spirit, discussing, in particular: (1) How could lateral amacrine cell connectivity shape the spatio-temporal spike response of retinal ganglion cells ? (2) How could spatio-temporal stimuli correlations and retinal network dynamics shape the spike train correlations at the output of the retina ? These questions are addressed, first, introducing a mathematically tractable model of the layered retina, integrating amacrine cells lateral connectivity and piecewise linear rectification, allowing to compute the retinal ganglion cells receptive field together with the voltage and spike correlations of retinal ganglion cells resulting from the amacrine cells networks. Then, I review some recent results showing how the concept of spatio-temporal Gibbs distributions and linear response theory can be used to characterize the collective spike response to a spatio-temporal stimulus of a set of retinal ganglion cells, coupled via effective interactions corresponding to the amacrine cells network. On these bases, I briefly discuss several potential consequences of these results at the cortical level.

math.DS↗
arXiv2020

The Retina as a Dynamical System

Considering the retina as a high dimensional, non autonomous, dynamical system, layered and structured, with non stationary and spatially inhomogeneous entries (visual scenes), we present several examples where dynamical systems-, bifurcations-, and ergodic-theory provide useful insights on retinal behaviour and dynamics.

q-bio.NC↗
arXiv2020

Thermodynamic Formalism in Neuronal Dynamics and Spike Train Statistics

The Thermodynamic Formalism provides a rigorous mathematical framework to study quantitative and qualitative aspects of dynamical systems. At its core there is a variational principle corresponding, in its simplest form, to the Maximum Entropy principle. It is used as a statistical inference procedure to represent, by specific probability measures (Gibbs measures), the collective behaviour of complex systems. This framework has found applications in different domains of science. In particular, it has been fruitful and influential in neurosciences. In this article, we review how the Thermodynamic Formalism can be exploited in the field of theoretical neuroscience, as a conceptual and operational tool, to link the dynamics of interacting neurons and the statistics of action potentials from either experimental data or mathematical models. We comment on perspectives and open problems in theoretical neuroscience that could be addressed within this formalism.

q-bio.NC↗
arXiv2020

On the potential role of lateral connectivity in retinal anticipation

We analyse the potential effects of lateral connectivity (amacrine cells and gap junctions) on motion anticipation in the retina. Our main result is that lateral connectivity can-under conditions analysed in the paper-trigger a wave of activity enhancing the anticipation mechanism provided by local gain control [8, 17]. We illustrate these predictions by two examples studied in the experimental literature: differential motion sensitive cells [1] and direction sensitive cells where direction sensitivity is inherited from asymmetry in gap junctions connectivity [73]. We finally present reconstructions of retinal responses to 2D visual inputs to assess the ability of our model to anticipate motion in the case of three different 2D stimuli.

q-bio.QM↗
arXiv2020

Linear response for spiking neuronal networks with unbounded memory

We establish a general linear response relation for spiking neuronal networks, based on chains with unbounded memory. This relation allows us to predict the influence of a weak amplitude time-dependent external stimuli on spatio-temporal spike correlations, from the spontaneous statistics (without stimulus) in a general context where the memory in spike dynamics can extend arbitrarily far in the past. Using this approach, we show how linear response is explicitly related to neuronal dynamics with an example, the gIF model, introduced by M. Rudolph and A. Destexhe. This example illustrates the collective effect of the stimuli, intrinsic neuronal dynamics, and network connectivity on spike statistics. We illustrate our results with numerical simulations.

q-bio.NC↗
arXiv2019

Noise driven broadening of the neural synchronisation transition in stage II retinal waves

Based on a biophysical model of retinal Starburst Amacrine Cell (SAC) \cite{karvouniari-gil-etal:19} we analyse here the dynamics of retinal waves, arising during the visual system development. Waves are induced by spontaneous bursting of SACs and their coupling via acetycholine. We show that, despite the acetylcholine coupling intensity has been experimentally observed to change during development \cite{zheng-lee-etal:04}, SACs retinal waves can nevertheless stay in a regime with power law distributions, reminiscent of a critical regime. Thus, this regime occurs on a range of coupling parameters instead of a single point as in usual phase transitions. We explain this phenomenon thanks to a coherence-resonance mechanism, where noise is responsible for the broadening of the critical coupling strength range.

q-bio.NC↗
arXiv2018

A biophysical model explains the spontaneous bursting behavior in the developing retina

During early development, waves of activity propagate across the retina and play a key role in the proper wiring of the early visual system. During the stage II these waves are triggered by a transient network of neurons, called Starburst Amacrine Cells (SACs), showing a bursting activity which disappears upon further maturation. While several models have attempted to reproduce retinal waves, none of them is able to mimic the rhythmic autonomous bursting of individual SACs and reveal how these cells change their intrinsic properties during development. Here, we introduce a mathematical model, grounded on biophysics, which enables us to reproduce the bursting activity of SACs and to propose a plausible, generic and robust, mechanism that generates it. The core parameters controlling repetitive firing are fast depolarizing $V$-gated calcium channels and hyperpolarizing $V$-gated potassium channels. The quiescent phase of bursting is controlled by a slow after hyperpolarization (sAHP), mediated by calcium-dependent potassium channels. Based on a bifurcation analysis we show how biophysical parameters, regulating calcium and potassium activity, control the spontaneously occurring fast oscillatory activity followed by long refractory periods in individual SACs. We make a testable experimental prediction on the role of voltage-dependent potassium channels on the excitability properties of SACs and on the evolution of this excitability along development. We also propose an explanation on how SACs can exhibit a large variability in their bursting periods, as observed experimentally within a SACs network as well as across different species, yet based on a simple, unique, mechanism. As we discuss, these observations at the cellular level have a deep impact on the retinal waves description.

q-bio.NC↗
arXiv2016

Perspectives on Multi-Level Dynamics

As Physics did in previous centuries, there is currently a common dream of extracting generic laws of nature in economics, sociology, neuroscience, by focalising the description of phenomena to a minimal set of variables and parameters, linked together by causal equations of evolution whose structure may reveal hidden principles. This requires a huge reduction of dimensionality (number of degrees of freedom) and a change in the level of description. Beyond the mere necessity of developing accurate techniques affording this reduction, there is the question of the correspondence between the initial system and the reduced one. In this paper, we offer a perspective towards a common framework for discussing and understanding multi-level systems exhibiting structures at various spatial and temporal levels. We propose a common foundation and illustrate it with examples from different fields. We also point out the difficulties in constructing such a general setting and its limitations.

physics.soc-ph↗
arXiv2014

Exact computation of the Maximum Entropy Potential of spiking neural networks models

Understanding how stimuli and synaptic connectivity in uence the statistics of spike patterns in neural networks is a central question in computational neuroscience. Maximum Entropy approach has been successfully used to characterize the statistical response of simultaneously recorded spiking neurons responding to stimuli. But, in spite of good performance in terms of prediction, the fitting parameters do not explain the underlying mechanistic causes of the observed correlations. On the other hand, mathematical models of spiking neurons (neuro-mimetic models) provide a probabilistic mapping between stimulus, network architecture and spike patterns in terms of conditional proba- bilities. In this paper we build an exact analytical mapping between neuro-mimetic and Maximum Entropy models.

physics.bio-ph↗
arXiv2014

Parameters estimation for spatio-temporal maximum entropy distributions: application to neural spike trains

We propose a numerical method to learn Maximum Entropy (MaxEnt) distributions with spatio-temporal constraints from experimental spike trains. This is an extension of two papers [10] and [4] who proposed the estimation of parameters where only spatial constraints were taken into account. The extension we propose allows to properly handle memory effects in spike statistics, for large sized neural networks.

q-bio.NC↗
arXiv2014

Hearing the Maximum Entropy Potential of neuronal networks

We consider a spike-generating stationary Markov process whose transition probabilities are known. We show that there is a canonical potential whose Gibbs distribution, obtained from the Maximum Entropy Principle (MaxEnt), is the equilibrium distribution of this process. We provide a method to compute explicitly and exactly this potential as a linear combination of spatio-temporal interactions. In particular, our results establish an explicit relation between Maximum Entropy models and neuro-mimetic models used in spike train statistics.

q-bio.NC↗
arXiv2012

Dynamics and spike trains statistics in conductance-based Integrate-and-Fire neural networks with chemical and electric synapses

We investigate the effect of electric synapses (gap junctions) on collective neuronal dynamics and spike statistics in a conductance-based Integrate-and-Fire neural network, driven by a Brownian noise, where conductances depend upon spike history. We compute explicitly the time evolution operator and show that, given the spike-history of the network and the membrane potentials at a given time, the further dynamical evolution can be written in a closed form. We show that spike train statistics is described by a Gibbs distribution whose potential can be approximated with an explicit formula, when the noise is weak. This potential form encompasses existing models for spike trains statistics analysis such as maximum entropy models or Generalized Linear Models (GLM). We also discuss the different types of correlations: those induced by a shared stimulus and those induced by neurons interactions.

physics.bio-ph↗
arXiv2012

Spatio-temporal spike trains analysis for large scale networks using maximum entropy principle and Monte-Carlo method

Understanding the dynamics of neural networks is a major challenge in experimental neuroscience. For that purpose, a modelling of the recorded activity that reproduces the main statistics of the data is required. In a first part, we present a review on recent results dealing with spike train statistics analysis using maximum entropy models (MaxEnt). Most of these studies have been focusing on modelling synchronous spike patterns, leaving aside the temporal dynamics of the neural activity. However, the maximum entropy principle can be generalized to the temporal case, leading to Markovian models where memory effects and time correlations in the dynamics are properly taken into account. In a second part, we present a new method based on Monte-Carlo sampling which is suited for the fitting of large-scale spatio-temporal MaxEnt models. The formalism and the tools presented here will be essential to fit MaxEnt spatio-temporal models to large neural ensembles.

q-bio.NC↗
arXiv2010

Spike trains statistics in Integrate and Fire Models: exact results

We briefly review and highlight the consequences of rigorous and exact results obtained in \cite{cessac:10}, characterizing the statistics of spike trains in a network of leaky Integrate-and-Fire neurons, where time is discrete and where neurons are subject to noise, without restriction on the synaptic weights connectivity. The main result is that spike trains statistics are characterized by a Gibbs distribution, whose potential is explicitly computable. This establishes, on one hand, a rigorous ground for the current investigations attempting to characterize real spike trains data with Gibbs distributions, such as the Ising-like distribution, using the maximal entropy principle. However, it transpires from the present analysis that the Ising model might be a rather weak approximation. Indeed, the Gibbs potential (the formal "Hamiltonian") is the log of the so-called "conditional intensity" (the probability that a neuron fires given the past of the whole network). But, in the present example, this probability has an infinite memory, and the corresponding process is non-Markovian (resp. the Gibbs potential has infinite range). Moreover, causality implies that the conditional intensity does not depend on the state of the neurons at the \textit{same time}, ruling out the Ising model as a candidate for an exact characterization of spike trains statistics. However, Markovian approximations can be proposed whose degree of approximation can be rigorously controlled. In this setting, Ising model appears as the "next step" after the Bernoulli model (independent neurons) since it introduces spatial pairwise correlations, but not time correlations. The range of validity of this approximation is discussed together with possible approaches allowing to introduce time correlations, with algorithmic extensions.

nlin.AO↗