Approximate Inference for Time-Varying Interactions and Macroscopic Dynamics of Neural Populations

The models in statistical physics such as an Ising model offer a convenient way to characterize stationary activity of neural populations. Such stationary activity of neurons may be expected for recordings from in vitro slices or anesthetized animals. However, modeling activity of cortical circuitries of awake animals has been more challenging because both spike-rates and interactions can change according to sensory stimulation, behavior, or an internal state of the brain. Previous approaches modeling the dynamics of neural interactions suffer from computational cost; therefore, its application was limited to only a dozen neurons. Here by introducing multiple analytic approximation methods to a state-space model of neural population activity, we make it possible to estimate dynamic pairwise interactions of up to 60 neurons. More specifically, we applied the pseudolikelihood approximation to the state-space model, and combined it with the Bethe or TAP mean-field approximation to make the sequential Bayesian estimation of the model parameters possible. The large-scale analysis allows us to investigate dynamics of macroscopic properties of neural circuitries underlying stimulus processing and behavior. We show that the model accurately estimates dynamics of network properties such as sparseness, entropy, and heat capacity by simulated data, and demonstrate utilities of these measures by analyzing activity of monkey V4 neurons as well as a simulated balanced network of spiking neurons.DFG, 103586207, GRK 1589: Verarbeitung sensorischer Informationen in neuronalen Systeme

DEVELOPMENT OF A CEREBELLAR MEAN FIELD MODEL: THE THEORETICAL FRAMEWORK, THE IMPLEMENTATION AND THE FIRST APPLICATION

Brain modeling constantly evolves to improve the accuracy of the simulated brain dynamics with the ambitious aim to build a digital twin of the brain. Specific models tuned on brain regions specific features empower the brain simulations introducing bottom-up physiology properties into data-driven simulators. Despite the cerebellum contains 80 % of the neurons and is deeply involved in a wide range of functions, from sensorimotor to cognitive ones, a specific cerebellar model is still missing. Furthermore, its quasi-crystalline multi-layer circuitry deeply differs from the cerebral cortical one, therefore is hard to imagine a unique general model suitable for the realistic simulation of both cerebellar and cerebral cortex. The present thesis tackles the challenge of developing a specific model for the cerebellum. Specifically, multi-neuron multi-layer mean field (MF) model of the cerebellar network, including Granule Cells, Golgi Cells, Molecular Layer Interneurons, and Purkinje Cells, was implemented, and validated against experimental data and the corresponding spiking neural network microcircuit model. The cerebellar MF model was built using a system of interdependent equations, where the single neuronal populations and topological parameters were captured by neuron-specific inter- dependent Transfer Functions. The model time resolution was optimized using Local Field Potentials recorded experimentally with high-density multielectrode array from acute mouse cerebellar slices. The present MF model satisfactorily captured the average discharge of different microcircuit neuronal populations in response to various input patterns and was able to predict the changes in Purkinje Cells firing patterns occurring in specific behavioral conditions: cortical plasticity mapping, which drives learning in associative tasks, and Molecular Layer Interneurons feed-forward inhibition, which controls Purkinje Cells activity patterns. The cerebellar multi-layer MF model thus provides a computationally efficient tool that will allow to investigate the causal relationship between microscopic neuronal properties and ensemble brain activity in health and pathological conditions. Furthermore, preliminary attempts to simulate a pathological cerebellum were done in the perspective of introducing our multi-layer cerebellar MF model in whole-brain simulators to realize patient-specific treatments, moving ahead towards personalized medicine. Two preliminary works assessed the relevant impact of the cerebellum on whole-brain dynamics and its role in modulating complex responses in causal connected cerebral regions, confirming that a specific model is required to further investigate the cerebellum-on- cerebrum influence. The framework presented in this thesis allows to develop a multi-layer MF model depicting the features of a specific brain region (e.g., cerebellum, basal ganglia), in order to define a general strategy to build up a pool of biology grounded MF models for computationally feasible simulations. Interconnected bottom-up MF models integrated in large-scale simulators would capture specific features of different brain regions, while the applications of a virtual brain would have a substantial impact on the reality ranging from the characterization of neurobiological processes, subject-specific preoperative plans, and development of neuro-prosthetic devices

Spike Train Statistics from Empirical Facts to Theory: The Case of the Retina

International audienceThis chapter focuses on methods from statistical physics and probability theory allowing the analysis of spike trains in neural networks. Taking as an example the retina we present recent works attempting to understand how retina ganglion cells encode the information transmitted to the visual cortex via the optical nerve, by analyzing their spike train statistics. We compare the maximal entropy models used in the literature of retina spike train analysis to rigorous results establishing the exact form of spike train statistics in conductance-based Integrate-and-Fire neural networks

Phase transitions in quantum chromodynamics

The current understanding of finite temperature phase transitions in QCD is reviewed. A critical discussion of refined phase transition criteria in numerical lattice simulations and of analytical tools going beyond the mean-field level in effective continuum models for QCD is presented. Theoretical predictions about the order of the transitions are compared with possible experimental manifestations in heavy-ion collisions. Various places in phenomenological descriptions are pointed out, where more reliable data for QCD's equation of state would help in selecting the most realistic scenario among those proposed. Unanswered questions are raised about the relevance of calculations which assume thermodynamic equilibrium. Promising new approaches to implement nonequilibrium aspects in the thermodynamics of heavy-ion collisions are described.Comment: 156 pages, RevTex. Tables II,VIII,IX and Fig.s 1-38 are not included as postscript files. I would like to ask the requestors to copy the missing tables and figures from the corresponding journal-referenc

A Moment-Based Maximum Entropy Model for Fitting Higher-Order Interactions in Neural Data

Correlations in neural activity have been demonstrated to have profound consequences for sensory encoding. To understand how neural populations represent stimulus information, it is therefore necessary to model how pairwise and higher-order spiking correlations between neurons contribute to the collective structure of population-wide spiking patterns. Maximum entropy models are an increasingly popular method for capturing collective neural activity by including successively higher-order interaction terms. However, incorporating higher-order interactions in these models is difficult in practice due to two factors. First, the number of parameters exponentially increases as higher orders are added. Second, because triplet (and higher) spiking events occur infrequently, estimates of higher-order statistics may be contaminated by sampling noise. To address this, we extend previous work on the Reliable Interaction class of models to develop a normalized variant that adaptively identifies the specific pairwise and higher-order moments that can be estimated from a given dataset for a specified confidence level. The resulting “Reliable Moment” model is able to capture cortical-like distributions of population spiking patterns. Finally, we show that, compared with the Reliable Interaction model, the Reliable Moment model infers fewer strong spurious higher-order interactions and is better able to predict the frequencies of previously unobserved spiking patterns

From statistical mechanics to machine learning: effective models for neural activity

In the retina, the activity of ganglion cells, which feed information through the optic nerve to the rest of the brain, is all that our brain will ever know about the visual world. The interactions between many neurons are essential to processing visual information and a growing body of evidence suggests that the activity of populations of retinal ganglion cells cannot be understood from knowledge of the individual cells alone. Modelling the probability of which cells in a population will fire or remain silent at any moment in time is a difficult problem because of the exponentially many possible states that can arise, many of which we will never even observe in finite recordings of retinal activity. To model this activity, maximum entropy models have been proposed which provide probabilistic descriptions over all possible states but can be fitted using relatively few well-sampled statistics. Maximum entropy models have the appealing property of being the least biased explanation of the available information, in the sense that they maximise the information theoretic entropy. We investigate this use of maximum entropy models and examine the population sizes and constraints that they require in order to learn nontrivial insights from finite data. Going beyond maximum entropy models, we investigate autoencoders, which provide computationally efficient means of simplifying the activity of retinal ganglion cells

Critical phenomena in complex networks

The combination of the compactness of networks, featuring small diameters, and their complex architectures results in a variety of critical effects dramatically different from those in cooperative systems on lattices. In the last few years, researchers have made important steps toward understanding the qualitatively new critical phenomena in complex networks. We review the results, concepts, and methods of this rapidly developing field. Here we mostly consider two closely related classes of these critical phenomena, namely structural phase transitions in the network architectures and transitions in cooperative models on networks as substrates. We also discuss systems where a network and interacting agents on it influence each other. We overview a wide range of critical phenomena in equilibrium and growing networks including the birth of the giant connected component, percolation, k-core percolation, phenomena near epidemic thresholds, condensation transitions, critical phenomena in spin models placed on networks, synchronization, and self-organized criticality effects in interacting systems on networks. We also discuss strong finite size effects in these systems and highlight open problems and perspectives.Comment: Review article, 79 pages, 43 figures, 1 table, 508 references, extende

Computational techniques for cell signaling

Cells can be viewed as sophisticated machines that organize their constituent components and molecules to receive, process, and respond to signals. The goal of the scientist is to uncover both the individual operations underlying these processes and the mechanism of the emergent properties of interest that give rise to the various phenomena such as disease, development, recovery or aging. Cell signaling plays a crucial role in all of these areas. The complexity of biological processes coupled with the physical limitations of experiments to observe individual molecular components across small to large scales limits the knowlege that can be gleaned from direct observations. Mathematical modeling can be used to estimate parameters that are hidden or too difficult to observe in experiments, and it can make qualitative predictions that can distinguish between hypotheses of interest. Statistical analysis can be employed to explore the large amounts of data generated by modern experimental techniques such as sequencing and high-throughput screening, and it can integrate the observations from many individual experiments or even separate studies to generate new hypotheses. This dissertation employs mathematical and statistical analyses for three prominent aspects of cell signaling: the physical transfer of signaling molecules between cells, the intracellular protein machinery that organizes into pathways to process these signals, and changes in gene expression in response to cell signaling. Computational biology can be described as an applied discipline in that it aims to further the knowledge of a discipline that is distinct from itself. However, the richness of the problems encountered in biology requires continuous development of better methods equipped to handle the complexity, size, or uncertainty of the data, and to build in constraints motivated by the reality of the underlying biological system. In addition, better computational and mathematical methods are also needed to model the emergent behavior that arises from many components. The work presented in this dissertation fulfills both of these roles. We apply known and existing techniques to analyse experimental data and provide biological meaning, and we also develop new statistical and mathematical models that add to the knowledge and practice of computational biology. Much of cell signaling is initiated by signal transduction from the exterior, either by sensing the environmental conditions or the recpetion of specific signals from other cells. The phenomena of most immediate concern to our species, that of human health and disease, are usually also generated from, and manifest in, our tissues and organs due to the interaction and signaling between cells. A modality of inter-cellular communication that was regarded earlier as an obscure phenomenon but has more recently come to the attention of the scientific community is that of tunneling nanotubes (TNs). TNs have been observed as thin (of the order of 100 nanometers) extensions from a cell to another closely located one. The formation of such structures along with the intercellular exchange of molecules through them, and their interaction with the cytoskeleton, could be involved in many important processes, such as tissue formation and cancer growth. We describe a simple model of passive transport of molecules between cells due to TNs. Building on a few basic assumptions, we derive parametrized, closed-form expressions to describe the concentration of transported molecules as a function of distance from a population of TN-forming cells. Our model predicts how the perfusion of molecules through the TNs is affected by the size of the transferred molecules, the length and stability of nanotube formation, and the differences between membrane-bound and cytosolic proteins. To our knowledge, this is the first published mathematical model of intercellular transfer through tunneling nanotubes. We envision that experimental observations will be able to confirm or improve the assumptions made in our model. Furthermore, quantifying the form of inter-cellular communication in the basic scenario envisioned in our model can help suggest ways to measure and investigate cases of possible regulation of either formation of tunneling nanotubes or transport through them. The next problem we focus on is uncovering how the interactions between the genes and proteins in a cell organize into pathways to process call signals or perform other tasks. The ability to accurately model and deeply understand gene and protein interaction networks of various kinds can be very powerful for prioritizing candidate genes and predicting their role in various signaling pathways and processes. A popular technique for gene prioritization and function prediction is the graph diffusion kernel. We show how the graph diffusion kernel is mathematically similar to the Ising spin graph, a model popular in statistical physics but not usually employed on biological interaction networks. We develop a new method for calculating gene association based on the Ising spin model which is different from the methods common in either bioinformatics or statistical physics. We show that our method performs better than both the graph diffusion kernel and its commonly used equivalent in the Ising model. We present a theoretical argument for understanding its performance based on ideas of phase transitions on networks. We measure its performance by applying our method to link prediction on protein interaction networks. Unlike candidate gene prioritization or function prediction, link prediction does not depend on the existing annotation or characterization of genes for ground truth. It helps us to avoid the confounding noise and uncertainty in the network and annotation data. As a purely network analysis problem, it is well suited for comparing network analysis methods. Once we know that we are accurately modeling the interaction network, we can employ our model to solve other problems like gene prioritization using interaction data. We also apply statistical analysis for a specific instance of a cell signaling process: the drought response in Brassica napus, a plant of scientific and economic importance. Important changes in the cell physiology of guard cells are initiated by abscisic acid, an important phytohormone that signals water deficit stress. We analyse RNA-seq reads resulting from the sequencing of mRNA extracted from protoplasts treated with abscisic acid. We employ sequence analysis, statisitical modeling, and the integration of cross-species network data to uncover genes, pathways, and interactions important in this process. We confirm what is known from other species and generate new gene and interaction candidates. By associating functional and sequence modification, we are also able to uncover evidence of evolution of gene specialization, a process that is likely widespread in polyploid genomes. This work has developed new computational methods and applied existing tools for understanding cellular signaling and pathways. We have applied statistical analysis to integrate expression, interactome, pathway, regulatory elements, and homology data to infer \textit{Brassica napus} genes and their roles involved in drought response. Previous literature suggesting support for our findings from other species based on independent experiments is found for many of of these findings. By relating the changes in regulatory elements, our RNA-seq results and common gene ancestry, we present evidence of its evolution in the context of polyploidy. Our work can provide a scientific basis for the pursuit of certain genes as targets of breeding and genetic engineering efforts for the development of drought tolerant oil crops. Building on ideas from statistical physics, we developed a new model of gene associations in networks. Using link prediction as a metric for the accuracy of modeling the underlying structure of a real network, we show that our model shows improved performance on real protein interaction networks. Our model of gene associations can be use to prioritize candidate genes for a disease or phenotype of interest. We also develop a mathematical model for a novel inter-cellular mode of biomolecule transfer. We relate hypotheses about the dynamics of TN formation, stability, and nature of molecular transport to quantitative predictions that may be tested by suitable experiments. In summary, this work demostrates the application and development of computational analysis of cell signaling at the level of the transcriptome, the interactome, and physical transport

Computational study of resting state network dynamics

Lo scopo di questa tesi è quello di mostrare, attraverso una simulazione con il software The Virtual Brain, le più importanti proprietà della dinamica cerebrale durante il resting state, ovvero quando non si è coinvolti in nessun compito preciso e non si è sottoposti a nessuno stimolo particolare. Si comincia con lo spiegare cos’è il resting state attraverso una breve revisione storica della sua scoperta, quindi si passano in rassegna alcuni metodi sperimentali utilizzati nell’analisi dell’attività cerebrale, per poi evidenziare la differenza tra connettività strutturale e funzionale. In seguito, si riassumono brevemente i concetti dei sistemi dinamici, teoria indispensabile per capire un sistema complesso come il cervello. Nel capitolo successivo, attraverso un approccio ‘bottom-up’, si illustrano sotto il profilo biologico le principali strutture del sistema nervoso, dal neurone alla corteccia cerebrale. Tutto ciò viene spiegato anche dal punto di vista dei sistemi dinamici, illustrando il pionieristico modello di Hodgkin-Huxley e poi il concetto di dinamica di popolazione. Dopo questa prima parte preliminare si entra nel dettaglio della simulazione. Prima di tutto si danno maggiori informazioni sul software The Virtual Brain, si definisce il modello di network del resting state utilizzato nella simulazione e si descrive il ‘connettoma’ adoperato. Successivamente vengono mostrati i risultati dell’analisi svolta sui dati ricavati, dai quali si mostra come la criticità e il rumore svolgano un ruolo chiave nell'emergenza di questa attività di fondo del cervello. Questi risultati vengono poi confrontati con le più importanti e recenti ricerche in questo ambito, le quali confermano i risultati del nostro lavoro. Infine, si riportano brevemente le conseguenze che porterebbe in campo medico e clinico una piena comprensione del fenomeno del resting state e la possibilità di virtualizzare l’attività cerebrale