The study of neurons is of fundamental importance in biology and medicine. Neurons are the most basic unit of information processing in the nervous system of humans and all other vertebrates and in complex invertebrates. In addition, networks of neurons (the human brain) are the most sophisticated computational devices known, and the study of neurons individually and working in concert is seen as a step toward understanding consciousness and cognition. In the 1950's Hodgkin and Huxley developed a system of nonlinear ordinary differential equations to describe the behavior of a neuron found in the squid. Equations of this form have since been used to model the behavior of a multitude of neurons across a broad spectrum of species. Hodgkin-Huxley type neuron models helped lay the foundation for computational neuroscience, and they remain widely used in the study of neuron behavior almost sixty years after their development. Hodgkin-Huxley type models accept a set of parameters as input and generate data describing the electrical activity of the neuron as a function of time. We develop inversion algorithms to predict a set of input parameter values from the voltage trace data generated by the model. We test our algorithm on data from the Hodgkin-Huxley equations, and we extend the algorithm to solve the inverse problem associated with a more complex Hodgkin-Huxley type model for a lobster stomatogastric neuron. We find strong empirical evidence that the algorithms produce parameter values that generate a good fit to the target voltage trace, and we prove that under certain conditions the inversion algorithm for the Hodgkin-Huxley equations converges to a perfect match. To our knowledge this is the first parameter optimization procedure for which convergence has been shown theoretically. Understanding the relationship between the parameters of a neuron model and its output has implications for designing effective neuron models and for explaining the mechanisms by which neurons regulate their behavior. Inversion algorithms for Hodgkin-Huxley type neuron models are an important theoretical and practical step toward understanding the relationship between model parameters and model behavior, and toward the larger problem of inferring neuronal parameters from behavior observed experimentally.

A neurociência computacional é uma vasta área que tem como objeto de estudo o entendimento ou a emulação da dinâmica cerebral em diversos níveis. Neste trabalho atenta-se ao estudo da dinâmica de neurônios, os quais, no consenso atual, acredita-se serem as unidades fundamentais do processamento cerebral. A importância do estudo sobre o comportamento de neurônios se encontra na diversidade de propriedades que eles podem apresentar. O estudo se torna mais rico quando há interações de sistemas internos ao neurônio em diferentes escalas de tempo, criando propriedades como adaptação, latência e comportamento em rajada, o que pode acarretar em diferentes papéis que os neurônios podem ter na rede. Nesta dissertação é feita uma análise sob o ponto de vista de sistemas dinâmicos e de análise de sensibilidade de seis modelos ao estilo de Hodgkin-Huxley e compartimentais de neurônios encontrados no córtex visual primário de mamíferos. Esses modelos correspondem a seis classes eletrofisiológicas de neurônios corticais e o estudo feito nesta dissertação oferece uma contribuição ao entendimento dos princípios de sistemas dinâmicos subjacentes a essa classificação. / Computational neuroscience is a vast scientific area which has as subject of study the unsderstanding or emulation of brain dynamics at different levels. This work studies the dynamics of neurons, which are believed, according to present consensus, to be the fundamental processing units of the brain. The importance of studying neuronal behavior comes from the diversity of properties they may have. This study becomes richer when there are interactions between distintic neuronal internal systems, in different time scales, creating properties like adaptation, latency and bursting, resulting in different roles that neurons may have in the network. This dissertation contains a study of six reduced compartmental conductance-based models of neurons found in the primary visual cortex of mammals under the dynamical systems and sensitivity analysis viewpoints. These models correspond to six eletrophysiological classes of cortical neurons and this dissertation offers a contribution to the understanding of the dynamical-systems principles underlying such classification.

In the central nervous system, most of the processes ranging from ion channels to neuronal networks occur in a closed loop, where the input to the system depends on its output. In contrast, most experimental preparations and protocols operate autonomously in an open loop and do not depend on the output of the system. Real-time software technology can be an essential tool for understanding the dynamics of many biological processes by providing the ability to precisely control the spatiotemporal aspects of a stimulus and to build activity-dependent stimulus-response closed loops. So far, application of this technology in biological experiments has been limited primarily to the dynamic clamp, an increasingly popular electrophysiology technique for introducing artificial conductances into living cells. Since the dynamic clamp combines mathematical modeling with electrophysiology experiments, it inherits the limitations of both, as well as issues concerning accuracy and stability that are determined by the chosen software and hardware. In addition, most dynamic clamp systems to date are designed for specific experimental paradigms and are not easily extensible to general real-time protocols and analyses. The long-term goal of this research is to develop a suite of real-time tools to evaluate the performance, improve the efficacy, and extend the capabilities of the dynamic clamp technique and real-time neural electrophysiology. We demonstrate a combined dynamic clamp and modeling approach for studying synaptic integration, a software platform for implementing flexible real-time closed-loop protocols, and the potential and limitations of Kalman filter-based techniques for online state and parameter estimation of neuron models.

A neurociência computacional é uma vasta área que tem como objeto de estudo o entendimento ou a emulação da dinâmica cerebral em diversos níveis. Neste trabalho atenta-se ao estudo da dinâmica de neurônios, os quais, no consenso atual, acredita-se serem as unidades fundamentais do processamento cerebral. A importância do estudo sobre o comportamento de neurônios se encontra na diversidade de propriedades que eles podem apresentar. O estudo se torna mais rico quando há interações de sistemas internos ao neurônio em diferentes escalas de tempo, criando propriedades como adaptação, latência e comportamento em rajada, o que pode acarretar em diferentes papéis que os neurônios podem ter na rede. Nesta dissertação é feita uma análise sob o ponto de vista de sistemas dinâmicos e de análise de sensibilidade de seis modelos ao estilo de Hodgkin-Huxley e compartimentais de neurônios encontrados no córtex visual primário de mamíferos. Esses modelos correspondem a seis classes eletrofisiológicas de neurônios corticais e o estudo feito nesta dissertação oferece uma contribuição ao entendimento dos princípios de sistemas dinâmicos subjacentes a essa classificação. / Computational neuroscience is a vast scientific area which has as subject of study the unsderstanding or emulation of brain dynamics at different levels. This work studies the dynamics of neurons, which are believed, according to present consensus, to be the fundamental processing units of the brain. The importance of studying neuronal behavior comes from the diversity of properties they may have. This study becomes richer when there are interactions between distintic neuronal internal systems, in different time scales, creating properties like adaptation, latency and bursting, resulting in different roles that neurons may have in the network. This dissertation contains a study of six reduced compartmental conductance-based models of neurons found in the primary visual cortex of mammals under the dynamical systems and sensitivity analysis viewpoints. These models correspond to six eletrophysiological classes of cortical neurons and this dissertation offers a contribution to the understanding of the dynamical-systems principles underlying such classification.

Ces travaux de thèse, réalisés dans une équipe concevant des circuits analogiques neuromimétiques suivant le modèle d’Hodgkin-Huxley, concernent la modélisation de neurones biologiques, plus précisément, l’estimation des paramètres de modèles de neurones. Une première partie de ce manuscrit s’attache à faire le lien entre la modélisation neuronale et l’optimisation. L’accent est mis sur le modèle d’Hodgkin- Huxley pour lequel il existait déjà une méthode d’extraction des paramètres associée à une technique de mesures électrophysiologiques (le voltage-clamp) mais dont les approximations successives rendaient impossible la détermination précise de certains paramètres. Nous proposons dans une seconde partie une méthode alternative d’estimation des paramètres du modèle d’Hodgkin-Huxley s’appuyant sur l’algorithme d’évolution différentielle et qui pallie les limitations de la méthode classique. Cette alternative permet d’estimer conjointement tous les paramètres d’un même canal ionique. Le troisième chapitre est divisé en trois sections. Dans les deux premières, nous appliquons notre nouvelle technique à l’estimation des paramètres du même modèle à partir de données biologiques, puis développons un protocole automatisé de réglage de circuits neuromimétiques, canal ionique par canal ionique. La troisième section présente une méthode d’estimation des paramètres à partir d’enregistrements de la tension de membrane d’un neurone, données dont l’acquisition est plus aisée que celle des courants ioniques. Le quatrième et dernier chapitre, quant à lui, est une ouverture vers l’utilisation de petits réseaux d’une centaine de neurones électroniques : nous réalisons une étude logicielle de l’influence des propriétés intrinsèques de la cellule sur le comportement global du réseau dans le cadre des oscillations gamma. / These works, which were conducted in a research group designing neuromimetic integrated circuits based on the Hodgkin-Huxley model, deal with the parameter estimation of biological neuron models. The first part of the manuscript tries to bridge the gap between neuron modeling and optimization. We focus our interest on the Hodgkin-Huxley model because it is used in the group. There already existed an estimation method associated to the voltage-clamp technique. Nevertheless, this classical estimation method does not allow to extract precisely all parameters of the model, so in the second part, we propose an alternative method to jointly estimate all parameters of one ionic channel avoiding the usual approximations. This method is based on the differential evolution algorithm. The third chaper is divided into three sections : the first two sections present the application of our new estimation method to two different problems, model fitting from biological data and development of an automated tuning of neuromimetic chips. In the third section, we propose an estimation technique using only membrane voltage recordings – easier to mesure than ionic currents. Finally, the fourth and last chapter is a theoretical study preparing the implementation of small neural networks on neuromimetic chips. More specifically, we try to study the influence of cellular intrinsic properties on the global behavior of a neural network in the context of gamma oscillations.

By exploiting the concept of emergent network properties and the hierarchical nature of networks, we have constructed several levels of models facilitating the investigations of issues in the area of respiratory neural control. The first of such models is an intracellular second messenger pathway model, which has been shown to be an important contributor to intracellular calcium metabolism and mediate responses to neuromodulators such as serotonin. At the next level, we have constructed new single neuron models of respiratory-related neurons (e.g. the pre-Btzinger complex neuron and the Hypoglossal motoneuron), where the electrical activities of the neurons are linked to intracellular mechanisms responsible for chemical homeostasis. Beyond the level of individual neurons, we have constructed models of neuron populations where the effects of different component neurons, varying strengths and types of inter-neuron couplings, as well as network topology are investigated. Our results from these simulation studies at different structural levels are in line with experiment observations. The small-world topology, as observed in previous anatomical studies, has been shown here to support rhythm generation along with a variety of other network-level phenomena. The interactions between different inter-neuron coupling types simultaneously manifesting at time-scales orders of magnitude apart suggest possible explanations for variations in the outputs measured from the XII rootlet in experiments. In addition, we have demonstrated the significance of pacemakers, along with the importance of considering neuromodulations and second-messenger pathways in an attempt to understand important physiological functions such as breathing activities.