Taming neuronal noise with large networks

How does reliable computation emerge from networks of noisy neurons? While individual neurons are intrinsically noisy, the collective dynamics of populations of neurons taken as a whole can be almost deterministic, supporting the hypothesis that, in the brain, computation takes place at the level of neuronal populations. Mathematical models of networks of noisy spiking neurons allow us to study the effects of neuronal noise on the dynamics of large networks. Classical mean-field models, i.e., models where all neurons are identical and where each neuron receives the average spike activity of the other neurons, offer toy examples where neuronal noise is absorbed in large networks, that is, large networks behave like deterministic systems. In particular, the dynamics of these large networks can be described by deterministic neuronal population equations. In this thesis, I first generalize classical mean-field limit proofs to a broad class of spiking neuron models that can exhibit spike-frequency adaptation and short-term synaptic plasticity, in addition to refractoriness. The mean-field limit can be exactly described by a multidimensional partial differential equation; the long time behavior of which can be rigorously studied using deterministic methods. Then, we show that there is a conceptual link between mean-field models for networks of spiking neurons and latent variable models used for the analysis of multi-neuronal recordings. More specifically, we use a recently proposed finite-size neuronal population equation, which we first mathematically clarify, to design a tractable Expectation-Maximization-type algorithm capable of inferring the latent population activities of multi-population spiking neural networks from the spike activity of a few visible neurons only, illustrating the idea that latent variable models can be seen as partially observed mean-field models. In classical mean-field models, neurons in large networks behave like independent, identically distributed processes driven by the average population activity -- a deterministic quantity, by the law of large numbers. The fact the neurons are identically distributed processes implies a form of redundancy that has not been observed in the cortex and which seems biologically implausible. To show, numerically, that the redundancy present in classical mean-field models is unnecessary for neuronal noise absorption in large networks, I construct a disordered network model where networks of spiking neurons behave like deterministic rate networks, despite the absence of redundancy. This last result suggests that the concentration of measure phenomenon, which generalizes the ``law of large numbers'' of classical mean-field models, might be an instrumental principle for understanding the emergence of noise-robust population dynamics in large networks of noisy neurons

Mean-field limit of age and leaky memory dependent Hawkes processes

We propose a mean-field model of interacting point processes where each process has a memory of the time elapsed since its last event (age) and its recent past (leaky memory), generalizing Age-dependent Hawkes processes. The model is motivated by interacting nonlinear Hawkes processes with Markovian self-interaction and networks of spiking neurons with adaptation and short-term synaptic plasticity. By proving propagation of chaos and using a path integral representation for the law of the limit process, we show that, in the mean-field limit, the empirical measure of the system follows a multidimensional nonlocal transport equation

Long time behavior of an age and leaky memory-structured neuronal population equation

We study the asymptotic stability of a two-dimensional mean-field equation, which takes the form of a nonlocal transport equation and generalizes the time-elapsed neuron network model by the inclusion of a leaky memory variable. This additional variable can represent a slow fatigue mechanism, like spike frequency adaptation or short-term synaptic depression. Even though two-dimensional models are known to have emergent behaviors, like population bursts, which are not observed in standard one-dimensional models, we show that in the weak connectivity regime, two-dimensional models behave like one-dimensional models, i.e. they relax to a unique stationary state. The proof is based on an application of Harris' ergodic theorem and a perturbation argument, adapted to the case of a multidimensional equation with delays

Mesoscopic description of hippocampal replay and metastability in spiking neural networks with short-term plasticity

Bottom-up models of functionally relevant patterns of neural activity provide an explicit link between neuronal dynamics and computation. A prime example of functional activity pattern is hippocampal replay, which is critical for memory consolidation. The switchings between replay events and a low-activity state in neural recordings suggests metastable neural circuit dynamics. As metastability has been attributed to noise and/or slow fatigue mechanisms, we propose a concise mesoscopic model which accounts for both. Crucially, our model is bottom-up: it is analytically derived from the dynamics of finite-size networks of Linear-Nonlinear Poisson neurons with short-term synaptic depression. As such, noise is explicitly linked to spike noise and network size, and fatigue is explicitly linked to synaptic dynamics. To derive the mesosocpic model, we first consider a homogeneous spiking neural network and follow the temporal coarse-graining approach of Gillespie ("chemical Langevin equation"), which can be naturally interpreted as a stochastic neural mass model. The Langevin equation is computationally inexpensive to simulate and enables a thorough study of metastable dynamics in classical setups (population spikes and Up-Down states dynamics) by means of phase-plane analysis. This stochastic neural mass model is the basic component of our mesoscopic model for replay. We show that our model faithfully captures the stochastic nature of individual replayed trajectories. Moreover, compared to the deterministic Romani-Tsodyks model of place cell dynamics, it exhibits a higher level of variability in terms of content, direction and timing of replay events, compatible with biological evidence and could be functionally desirable. This variability is the product of a new dynamical regime where metastability emerges from a complex interplay between finite-size fluctuations and local fatigue.Comment: 43 pages, 8 figure

Mesoscopic modeling of hidden spiking neurons

Can we use spiking neural networks (SNN) as generative models of multi-neuronal recordings, while taking into account that most neurons are unobserved? Modeling the unobserved neurons with large pools of hidden spiking neurons leads to severely underconstrained problems that are hard to tackle with maximum likelihood estimation. In this work, we use coarse-graining and mean-field approximations to derive a bottom-up, neuronally-grounded latent variable model (neuLVM), where the activity of the unobserved neurons is reduced to a low-dimensional mesoscopic description. In contrast to previous latent variable models, neuLVM can be explicitly mapped to a recurrent, multi-population SNN, giving it a transparent biological interpretation. We show, on synthetic spike trains, that a few observed neurons are sufficient for neuLVM to perform efficient model inversion of large SNNs, in the sense that it can recover connectivity parameters, infer single-trial latent population activity, reproduce ongoing metastable dynamics, and generalize when subjected to perturbations mimicking optogenetic stimulation

Visuospatial viewpoint manipulation during full-body illusion modulates subjective first-person perspective

Self-consciousness is based on multisensory signals from the body. In full-body illusion (FBI) experiments, multisensory conflict was used to induce changes in three key aspects of bodily self-consciousness (BSC): self-identification (which body 'I' identify with), self-location (where 'I' am located), and first-person perspective (from where 'I' experience the world; 1PP). Here, we adapted a previous FBI protocol in which visuotactile stroking was administered by a robotic device (tactile stroking) and simultaneously rendered on the back of a virtual body (visual stroking) that participants viewed on a head-mounted display as if filmed from a posterior viewpoint of a camera. We compared the effects of two different visuospatial viewpoints on the FBI and thereby on these key aspects of BSC. During control manipulations, participants saw a no-body object instead of a virtual body (first experiment) or received asynchronous versus synchronous visuotactile stroking (second experiment). Results showed that within-subjects visuospatial viewpoint manipulations affected the subjective 1PP ratings if a virtual body was seen but had no effect for viewing a non-body object. However, visuospatial viewpoint had no effect on self-identification, but depended on the viewed object and visuotactile synchrony. Self-location depended on visuospatial viewpoint (first experiment) and visuotactile synchrony (second experiment). Our results show that the visuospatial viewpoint from which the virtual body is seen during FBIs modulates the subjective 1PP and that such viewpoint manipulations contribute to spatial aspects of BSC. We compare the present data with recent data revealing vestibular contributions to the subjective 1PP and discuss the multisensory nature of BSC and the subjective 1PP

Visuospatial viewpoint manipulation during full-body illusion modulates subjective first-person perspective

Self-consciousness is based on multisensory signals from the body. In full-body illusion (FBI) experiments, multisensory conflict was usedto induce changes in three key aspects of bodily self-consciousness (BSC): self-identification (which body ‘I' identify with), self-location (where ‘I' am located), and first-person perspective (from where ‘I' experience the world; 1PP). Here, we adapted a previous FBI protocol in which visuotactile stroking was administered by a robotic device (tactile stroking) and simultaneously rendered on the back of a virtual body (visual stroking) that participants viewed on a head-mounted display as if filmed from a posterior viewpoint of a camera. We compared the effects of two different visuospatial viewpoints on the FBI and thereby on these key aspects of BSC. During control manipulations, participants saw a no-body object instead of a virtual body (first experiment) or received asynchronous versus synchronous visuotactile stroking (second experiment). Results showed that within-subjects visuospatial viewpoint manipulations affected the subjective 1PP ratings if a virtual body was seen but had no effect for viewing a non-body object. However, visuospatial viewpoint had no effect on self-identification, but depended on the viewed object and visuotactile synchrony. Self-location depended on visuospatial viewpoint (first experiment) and visuotactile synchrony (second experiment). Our results show that the visuospatial viewpoint from which the virtual body is seen during FBIs modulates the subjective 1PP and that such viewpoint manipulations contribute to spatial aspects of BSC. We compare the present data with recent data revealing vestibular contributions to the subjective 1PP and discuss the multisensory nature of BSC and the subjective 1PP

GreenPhylDB v2.0: comparative and functional genomics in plants

GreenPhylDB is a database designed for comparative and functional genomics based on complete genomes. Version 2 now contains sixteen full genomes of members of the plantae kingdom, ranging from algae to angiosperms, automatically clustered into gene families. Gene families are manually annotated and then analyzed phylogenetically in order to elucidate orthologous and paralogous relationships. The database offers various lists of gene families including plant, phylum and species specific gene families. For each gene cluster or gene family, easy access to gene composition, protein domains, publications, external links and orthologous gene predictions is provided. Web interfaces have been further developed to improve the navigation through information related to gene families. New analysis tools are also available, such as a gene family ontology browser that facilitates exploration. GreenPhylDB is a component of the South Green Bioinformatics Platform (http://southgreen.cirad.fr/) and is accessible at http://greenphyl.cirad.fr. It enables comparative genomics in a broad taxonomy context to enhance the understanding of evolutionary processes and thus tends to speed up gene discovery

Evolutionary genomics of a cold-adapted diatom: Fragilariopsis cylindrus

The Southern Ocean houses a diverse and productive community of organisms1, 2. Unicellular eukaryotic diatoms are the main primary producers in this environment, where photosynthesis is limited by low concentrations of dissolved iron and large seasonal fluctuations in light, temperature and the extent of sea ice3, 4, 5, 6, 7. How diatoms have adapted to this extreme environment is largely unknown. Here we present insights into the genome evolution of a cold-adapted diatom from the Southern Ocean, Fragilariopsis cylindrus8, 9, based on a comparison with temperate diatoms. We find that approximately 24.7 per cent of the diploid F. cylindrus genome consists of genetic loci with alleles that are highly divergent (15.1 megabases of the total genome size of 61.1 megabases). These divergent alleles were differentially expressed across environmental conditions, including darkness, low iron, freezing, elevated temperature and increased CO2. Alleles with the largest ratio of non-synonymous to synonymous nucleotide substitutions also show the most pronounced condition-dependent expression, suggesting a correlation between diversifying selection and allelic differentiation. Divergent alleles may be involved in adaptation to environmental fluctuations in the Southern Ocean