Each neuron needs to maintain a careful balance between the changes implicit in experience, and the demands of stability required by its function. This balance tips depending on the neuronal system, but in any role, disease or neural disorders can develop when the regulatory mechanisms involved in neuronal stability fail. The objective of this thesis was to characterize mechanisms underlying neuronal stability and activity maintenance, in the hopes that further understanding of these processes might someday lead to novel interventions for neurological disorders. The pyloric circuit of decapod crustaceans controls the rhythmic contractions of the foregut musculature, and has long been recognized as an excellent model system in which to study neuronal network stability. Recent experimental evidence has shown that each neuronal cell type of this circuit exhibits a unique set of positive linear correlations between ionic membrane conductances, which suggests that coordinated expression of ion channels plays a role in constraining neuronal electrical activity. In Aim 1, we hypothesized a causal relationship between expressed conductance correlations and features of cellular identity, namely electrical activity type. We partitioned an existing database of conductance-based model neurons based on various measures of intrinsic activity to approximate distinctions between biological cell types. We then tested individual conductance pairs for linear dependence to identify correlations. Similar to experimental results, each activity type investigated had a unique combination of correlated conductances. Furthermore, we found that populations of models that conform to a specific conductance correlation have a higher likelihood of exhibiting a particular feature of electrical activity. We conclude that regulating conductance ratios can support proper electrical activity of a wide range of cell types, particularly when the identity of the cell is well-defined by one or two features of its activity. The phenomenon of pyloric network recovery after removal of top-down neuromodulatory input--a process termed decentralization--is seen as a classic model of homeostatic change after injury. After decentralization, the pyloric central pattern generator briefly loses its characteristic rhythmic activity, but the same activity profile is recovered 3-5 days later via poorly understood homeostatic changes. This re-emergence of the pyloric rhythm occurs without the full pre-decentralization set of fixed conductance ratios. If conductance ratios stabilize pyloric activity before decentralization as we showed in Aim 1, then other mechanisms must account for the return of the pyloric rhythm after network recovery. Based on vertebrate studies demonstrating a role for the extracellular matrix (ECM) in activity regulation, we hypothesized in Aim 2 that the ECM was participating in activity maintenance in the stomatogastric nervous system. We used the enzyme chondroitinase ABC (chABC) to degrade extracellular chondroitin sulfate (CS) in the stomatogastric ganglion while in organ culture. Our results are the first to demonstrate the presence of CS in the crustacean nervous system via immunochemistry. Furthermore, we show that while ongoing activity is not disrupted by chABC treatment, recovery of pyloric activity after decentralization was significantly delayed without intact extracellular CS. Our results are the first to show that CS has a role in neuronal activity maintenance in crustaceans, and suggest that CS may be involved in initiating or directing activity maintenance needed in times of neuronal stress.

In this work, we present a set of methods aimed at improving the discriminative power of time-varying features of signals that contain noise. These methods use properties of noise signals as well as information theoretic techniques to factor types of noise and support signal inference for electroencephalographic (EEG) based brain-machine interfaces (BMI). EEG data were collected over two studies aimed at addressing Psychophysiological issues involving symmetry and mental rotation processing. The Psychophysiological data gathered in the mental rotation study also tested the feasibility of using dissociations of mental rotation tasks correlated with rotation angle in a BMI. We show the feasibility of mental rotation for BMI by showing comparable bitrates and recognition accuracy to state-of-the-art BMIs. The conclusion is that by using the feature selection methods introduced in this work to dissociate mental rotation tasks, we produce bitrates and recognition rates comparable to current BMIs.

The dynamics of biological neural networks are of great interest to neuroscientists and are frequently studied using conductance-based compartmental neuron models. For speed and ease of use, neuron models are often reduced in morphological complexity. This reduction may affect input processing and prevent the accurate reproduction of neural dynamics. However, such effects are not yet well understood. Therefore, for my first aim I analyzed the processing capabilities of 'branched' or 'unbranched' reduced models by collapsing the dendritic tree of a morphologically realistic 'full' globus pallidus neuron model while maintaining all other model parameters. Branched models maintained the original detailed branching structure of the full model while the unbranched models did not. I found that full model responses to somatic inputs were generally preserved by both types of reduced model but that branched reduced models were better able to maintain responses to dendritic inputs. However, inputs that caused dendritic sodium spikes, for instance, could not be accurately reproduced by any reduced model. Based on my analyses, I provide recommendations on how to construct reduced models and indicate suitable applications for different levels of reduction. In particular, I recommend that unbranched reduced models be used for fast searches of parameter space given somatic input output data. The intrinsic electrical properties of neurons depend on the modifiable behavior of their ion channels. Obtaining a quality match between recorded voltage traces and the output of a conductance based compartmental neuron model depends on accurate estimates of the kinetic parameters of the channels in the biological neuron. Indeed, mismatches in channel kinetics may be detectable as failures to match somatic neural recordings when tuning model conductance densities. In my first aim, I showed that this is a task for which unbranched reduced models are ideally suited. Therefore, for my second aim I optimized unbranched reduced model parameters to match three experimentally characterized globus pallidus neurons by performing two stages of automated searches. In the first stage, I set conductance densities free and found that even the best matches to experimental data exhibited unavoidable problems. I hypothesized that these mismatches were due to limitations in channel model kinetics. To test this hypothesis, I performed a second stage of searches with free channel kinetics and observed decreases in the mismatches from the first stage. Additionally, some kinetic parameters consistently shifted to new values in multiple cells, suggesting the possibility for tailored improvements to channel models. Given my results and the potential for cell specific modulation of channel kinetics, I recommend that experimental kinetic data be considered as a starting point rather than as a gold standard for the development of neuron models.

The work we present in this thesis is a series of studies of how heterogeneities in coupling affect the synchronization of coupled neural oscillators. We begin by examining how heterogeneity in coupling strength affects the equilibrium phase difference of a pair of coupled, spiking neurons when compared to the case of identical coupling. This study is performed using pairs of Hodgkin-Huxley and Wang-Buzsaki neurons. We find that heterogeneity in coupling strength breaks the symmetry of the bifurcation diagrams of equilibrium phase difference versus the synaptic rate constant for weakly coupled pairs of neurons. We observe important qualitative changes such as the loss of the ubiquitous in-phase and anti-phase solutions found when the coupling is identical and regions of parameter space where no phase locked solution exists. Another type of heterogeneity can be found by having different types of coupling between oscillators. Synaptic coupling between neurons can either be exciting or inhibiting. We examine the synchronization dynamics when a pair of neurons is coupled with one excitatory and one inhibitory synapse. We also use coupled pairs of Hodgkin-Huxley neurons and Wang-Buzsaki neurons for this work. We then explore the existance of 1:n coupled states for a coupled pair of theta neurons. We do this in order to reproduce an observed effect called quantal slowing. Quantal slowing is the phenomena where jumping between different $1:n$ coupled states is observed instead of gradual changes in period as a parameter in the system is varied. All of these topics fall under the general heading of coupled, non-linear oscillators and specifically weakly coupled, neural oscillators. The audience for this thesis is most likely going to be a mixed crowd as the research reported herein is interdisciplinary. Choosing the content for the introduction proved far more challenging than expected. It might be impossible to write a maximally useful introductory portion of a thesis when it could be read by a physicist, mathematician, engineer or biologist. Undoubtedly readers will find some portion of this introduction elementary. At the risk of boring some or all of my readers we decided it was best to proceed so that enough of the mathematical (biological) background is explained in the introduction so that a biologist (mathematician) is able to appreciate the motivations for the research and the results presented. We begin with a introduction in nonlinear dynamics explaining the mathematical tools we use to characterize the excitability of individual neurons, as well as oscillations and synchrony in neural networks. The next part of the introductory material is an overview of the biology of neurons. We then describe the neuron models used in this work and finally describe the techniques we employ to study coupled neurons.

Many molecules and the complex interactions between them underlie plasticity in the cerebellum. However, the exact relationship between cerebellar plasticity and the different signalling cascades remains unclear. Calcium-calmodulin dependent protein kinase II (CaMKII) regulates many forms of synaptic plasticity, but very little is known about its function during plasticity induction in the cerebellum. The aim of this thesis is to contribute to a better understanding of the molecular mechanisms that regulate the induction of synaptic plasticity in cerebellar Purkinje cells (PCs). The focus of the thesis is to investigate the role of CaMKII isoforms in the bidirectional modulation of plasticity induction at parallel fibre (PF)-PC synapses. For this investigation, computational models that represent the CaMKII activation and the signalling network that mediates plasticity induction at these synapses were constructed. The model of CaMKII activation by calcium-calmodulin developed by Dupont et al (2003) replicates the experiments by De Koninck and Schulman (1998). Both theoretical and experimental studies have argued that the phosphorylation and activation of CaMKII depends on the frequency of calcium oscillations. Using a simplified version of the Dupont model, it was demonstrated that the CaMKII phosphorylation is mostly determined by the average calcium-calmodulin concentration, and therefore depends only indirectly on the actual frequency of calcium oscillations. I have shown that a pulsed application of calcium-calmodulin is, in fact, not required at all. These findings strongly indicate that the activation of CaMKII depends on the average calcium-calmodulin concentration and not on the oscillation frequency per se as asserted in those studies. This thesis also presents the first model of AMPA receptor phosphorylation that simulates the induction of long-term depression (LTD) and potentiation (LTP) at the PF-PC synapse. The results of computer simulations of a simple mathematical model suggest that the balance of CaMKII-mediated phosphorylation and protein phosphatase 2B (PP2B)-mediated dephosphorylation of AMPA receptors determines whether LTD or LTP occurs in cerebellar PCs. This model replicates the experimental observations by Van Woerden et al (2009) that indicate that CaMKII controls the direction of plasticity at PF-PC synapses. My computer simulations support Van Woerden et al’s original suggestion that filamentous actin binding can enable CaMKII to regulate bidirectional plasticity at these synapses. The computational models of intracellular signalling constructed in this thesis advance the understanding of the mechanisms of synaptic plasticity induction in the cerebellum. These simple models are significant tools for future research by the scientific community.

A stochastic leaky integrate-and-fire neuron model was implemented in this study to simulate the spiking activity of the electrosensory "P-unit" receptor neurons of the weakly electric fish Apteronotus leptorhynchus. In the context of sensory coding, these cells have been previously shown to respond in experiment to natural random narrowband signals with either a linear or nonlinear coding scheme, depending on the intrinsic firing rate of the cell in the absence of external stimulation. It was hypothesised in this study that this duality is due to the relation of the stimulus to the neuron's excitation threshold. This hypothesis was validated with the model by lowering the threshold of the neuron or increasing its intrinsic noise, or randomness, either of which made the relation between firing rate and input strength more linear. Furthermore, synchronous P-unit firing to a common input also plays a role in decoding the stimulus at deeper levels of the neural pathways. Synchronisation and desynchronisation between multiple model responses for different types of natural communication signals were shown to agree with experimental observations. A novel result of resonance-induced synchrony enhancement of P-units to certain communication frequencies was also found.

The thesis presents a new paradigm for studying the importance of interactions between an organism and its environment using a combination of biology and technology: embodying cultured cortical neurons via robotics. From this platform, explanations of the emergent neural network properties leading to cognition are sought through detailed electrical observation of neural activity. By growing the networks of neurons and glia over multi-electrode arrays (MEA), which can be used to both stimulate and record the activity of multiple neurons in parallel over months, a long-term real-time 2-way communication with the neural network becomes possible. A better understanding of the processes leading to biological cognition can, in turn, facilitate progress in understanding neural pathologies, designing neural prosthetics, and creating fundamentally different types of artificial cognition. Here, methods were first developed to reliably induce and detect neural plasticity using MEAs. This knowledge was then applied to construct sensory-motor mappings and training algorithms that produced adaptive goal-directed behavior. To paraphrase the results, most any stimulation could induce neural plasticity, while the inclusion of temporal and/or spatial information about neural activity was needed to identify plasticity. Interestingly, the plasticity of action potential propagation in axons was observed. This is a notion counter to the dominant theories of neural plasticity that focus on synaptic efficacies and is suggestive of a vast and novel computational mechanism for learning and memory in the brain. Adaptive goal-directed behavior was achieved by using patterned training stimuli, contingent on behavioral performance, to sculpt the network into behaviorally appropriate functional states: network plasticity was not only induced, but could be customized. Clinically, understanding the relationships between electrical stimulation, neural activity, and the functional expression of neural plasticity could assist neuro-rehabilitation and the design of neuroprosthetics. In a broader context, the networks were also embodied with a robotic drawing machine exhibited in galleries throughout the world. This provided a forum to educate the public and critically discuss neuroscience, robotics, neural interfaces, cybernetics, bio-art, and the ethics of biotechnology.

Actualment, no hi ha consens científic respecte a la informació representada en la activitat de les célules del hipocamp. D'una banda, experiments amb humans sostenen una visión de la funció de l'hipocamp com a un sistema per l'emmagatzematge de memóries episódiques, mentre que la recerca amb rodents enfatitza una visió com a sistema cognitiu espacial. Tot i que existeix abundant evidència experimental que indica una possible sobreposició d'ambdues teories, aquesta dissociació també es manté en part en base a dades fisiològiques aparentment incompatibles. Aquesta tèsi poposa que l'hippocamp té un rol funcional que s'hauría d'analitzar en termes de la seva estructura i funció, enlloc de mitjança estudis correlació entre activitat neuronal i comportament. La identificació d'un codi a l'hipocamp, es a dir, el conjunt de principis computacionals que conformen les transformacions d'entrada i sortida de l'activitat neuronal, hauría de proporcionar un explicació unificada de la seva funció. En aquesta tèsi presentem un model teòric que descriu quantitativament i que interpreta la selectivitat de certes regions de l'hipocamp en funció de variables espaials i no-espaials, tal i com observada en experiments amb rates. Aquest resultat suggereix que multiples aspectes de la memòria expressada en humans i rodents deriven d'uns mateixos principis. Per aquest motius, proposem nous principis per la memòria, l'auto-completat de patrons i plasticitat. A més, mitjançant aplicacions robòtiques, creem d'un nexe causal entre el circuit neural i el comportament amb el que demostrem la naturalesa conjuntiva de la selectivitat neuronal observada en el hipocamp es necessària per la solució de problemes pràctics comuns, com per example la cerca d'aliments. Tot plegat, aquests resultats avancen en l'idea general de que el codi de l'hipocamp es genèric i aplicable als diversos tipus de memòries estudiades en la literatura. / There is no consensual understanding on what the activity of the hippocampus neurons represents. While experiments with humans foster a dominant view of an episodic memory system, experiments with rodents promote its role as a spatial cognitive system. Although there is abundant evidence pointing to an overlap between these two theories, the dissociation is sustained by conflicting physiological data. This thesis proposes that the functional role of the hippocampus should be analyzed in terms of its structure and function rather than by the correlation of neuronal activity and behavioral performance. The identification of the hippocampus code, i.e. the set of computational principles underlying the input-output transformations of neural activity, might ultimately provide a unifying understanding of its role. In this thesis we present a theoretical model that quantitatively describes and interprets the selectivity of regions of the hippocampus to spatial and non-spatial variables observed in experiments with rats. The results suggest that the multiple aspects of memory expressed in human and rodent data are derived form similar principles. This approach suggests new principles for memory, pattern completion and plasticity. In addition, by creating a causal tie between the neural circuitry and behavior through a robotic control framework we show that the conjunctive nature of neural selectivity observed in the hippocampus is needed for effective problem solving in real-world tasks such as foraging. Altogether, these results advance the concept that the hippocampal code is generic to the different aspects of memory highlighted in the literature.

Este trabalho descreve o desenvolvimento de um sistema de simulação de circuitos neuronais, com interface de utilização amigável e arquitetura baseada em web. O sistema é direcionado ao estudo de redes de neurônios da medula espinhal, responsáveis pelo controle motor, sujeitas à ativação por vias superiores e periféricas ou por estímulos elétricos. Sua utilidade está relacionada à criação de hipóteses ou teorias sobre o processamento neuronal realizado no caso são ou patológico, a atividades como a interpretação de resultados de experimentos eletrofisiológicos realizados em humanos e no direcionamento e validação de procedimentos experimentais. Para os propósitos deste projeto, a simulação computacional é o recurso mais indicado a se utilizar, considerando o grande número de variáveis envolvidas e o caráter não-linear dos elementos constituintes. As simulações devem retratar de maneira fidedigna as principais propriedades que caracterizam os núcleos neuronais a se estudar. Essas propriedades estão associadas ao recrutamento de unidades motoras, às relações de entrada-saída dos conjuntos neuronais, à influência das vias aferentes sobre os motoneurônios, ao papel da inibição recorrente e da inibição recíproca, à geração de força e do sinal eletromiográfico, entre outros. A simulação do reflexo H, que é uma técnica muito importante utilizada em estudos neurofisiológicos, está presente neste trabalho. Pretende-se que o sistema de simulação aqui proposto seja uma ferramenta útil para pesquisa e ensino da neurofisiologia do controle motor, provendo subsídios que levem a um melhor entendimento dos circuitos neuronais modelados. / This work describes the development of a simulation system of neuronal circuitry, having a user-friendly interface and based on web architecture. The system is intended for studying spinal cord neuronal networks responsible for muscle control, subjected to descending drive or electrical stimulation. It is potentially useful in many activities, such as the interpretation of electrophysiological experiments conducted with humans, the proposition of hypotheses or theories on neuronal processing. Computer simulation is the most indicated approach to attain the objectives of this project because of the huge number of variables and the non-linear characteristics of the constituting elements. The simulations should mimic in a faithful way the main properties related to the modeled neuronal nuclei. These properties are associated with: i) motor-unit recruitment, ii) neuronal nuclei input-output relations, iii) afferent tract influence on motoneurons, iv) effects of recurrent inhibition and reciprocal inhibition, v) generation of force and electromyogram, and others. The generation of the H-reflex by the Ia-motoneuron pool system, which is an important tool in human neurophysiology, is included in the simulation system. The biological reality obtained with the present simulator and its web-based implementation make it a powerful tool for researchers in neurophysiology.

L’évaluation expérimentale des mécanismes de l’initiation, de la propagation, et de la fin des crises d’épilepsie est un problème complexe. Cette thèse consiste en le développement d’un modèle de réseau de neurones aux caractéristiques biologiques pertinentes à la compréhension des mécanismes de genèse et de propagation de crises d’épilepsie. Nous démontrons que les décharges de type pointes ondes peuvent être générées par les neurones inhibiteurs seuls, tandis que les décharges rapides sont dues en grande partie aux neurones excitateurs. Nous concluons que les variations lentes d’excitabilité globale du système, dues aux fluctuations du milieu extracellulaire, et les interactions électro-tonique par jonctions communicantes sont les facteurs favorisant la genèse de crise localement, tandis qu’à plus large échelle spatiale les communications synaptiques excitatrices et le couplage extracellulaire qui participe davantage à la propagation des crises d’une région du cerveau à une autre. / This thesis consists in the development of a network model of spiking neurons and the systematic investigation of conditions under which the network displays the emergent dynamic behaviors known from the Epileptor, a well-investigated abstract model of epileptic neural activity. We find that exogenous fluctuations from extracellular environment and electro-tonic couplings between neurons play an essential role in seizure genesis. We demonstrate that spike-waves discharges, including interictal spikes, can be generated primarily by inhibitory neurons only, whereas excitatory neurons are responsible for the fast discharges during the wave part. We draw the conclusion that slow variations of global excitability, due to exogenous fluctuations from extracellular environment, and gap junction communication push the system into paroxysmal regimes locally, and excitatory synaptic and extracellular couplings participate in seizure spread globally across brain regions.