Sowohl in der neuronalen als auch in der Kalzium Signalübertragung werden Informationen durch kurze Pulse oder Spikes, übertragen. Obwohl beide Systeme grundlegende Eigenschaften der Spike-Erzeugung teilen, wurden Integrate-and-fire (IF)-Modelle bisher nur auf neuronale Systeme angewendet. Diese Modelle bleiben auch dann behandelbar, wenn sie um Prozesse erweitert werden, die in Übereinstimmung mit Experimenten Spike-Zeiten mit korrelierten Interspike-Intervallen (ISI) erzeugen. Die statistische Analyse solcher nicht erneuerbarer Modelle ist Gegenstand dieser Arbeit. Das zweite Kapitel konzentriert sich auf die Berechnung des seriellen Korrelationskoeffizienten (SCC) in neuronalen Systemen. Es wird ein adaptives Modell betrachtet, das durch einen korrelierten Eingangsstrom getrieben wird. Es zeigt sich, dass neben den langsamen Prozessen auch die Dynamik des Modells den SCC bestimmt. Obwohl die Theorie für schwach gestörte IF-Modelle entwickelt wurde, kann sie auch auf stärker gestörte leitfähigkeitsbasierte Modelle angewendet werden und ist damit in der Lage, ein breites Spektrum biophysikalischer Situationen zu beschreiben. Im dritten Kapitel wird ein IF-Modell zur Beschreibung von Kalzium-Spikes formuliert, das die stochastische Freisetzung von Kalzium aus dem endoplasmatischen Retikulum (ER) und dessen Entleerung berücksichtigt. Die beobachtete Zeitskalentrennung zwischen Kalziumfreisetzung und Spikegenerierung motiviert eine Diffusionsnäherung, die eine analytische Behandlung des Modells ermöglicht. Die experimentell beobachtete Transiente, in der sich die ISIs einem stationären Wert annähern, kann durch die Entleerung des ER beschrieben werden. Es wird untersucht, wie die Statistiken der Transienten mit den stationären Intervallkorrelationen zusammenhängen. Es zeigt sich, dass eine stärkere Anpassung der Intervalle und eine kurze Transiente mit stärkeren Korrelationen einhergehen. Der Vergleich mit experimentellen Daten bestätigt diese Trends qualitativ. / In both neuronal and calcium signaling, information is transmitted by short pulses, so-called spikes. Although both systems share some basic principles of spike generation, integrate-and-fire (IF) models have so far only been applied to neuronal systems. These models remain analytically tractable even when extended to include processes that lead to the generation of spike times with correlated interspike intervals (ISIs) as observed in experiments. The statistical analysis of such non-renewal models is the subject of this thesis. In the second chapter we focus on the calculation of the serial correlation coefficient (SCC) in neural systems. We consider an adaptive model driven by a correlated input current. We show that in addition to the two slow processes, the dynamics of the model also determines the SCC. Although the theory is developed for weakly perturbed IF models, it can also be applied to more strongly perturbed conductance-based models and is thus able to account for a wide range of biophysical situations. In the third chapter, we formulate an IF model to describe the generation of calcium spikes, taking into account the stochastic release of calcium from the endoplasmic reticulum (ER) and its depletion. The observed time-scale separation between calcium release and spike generation motivates a diffusion approximation that allows an analytical treatment of the model. The experimentally observed transient, during which the ISIs approach a steady state value, can be captured by the depletion of the ER. We study how the transient ISI statistics are related to the stationary interval correlations. We show that a stronger adaptation of the intervals as well as a short transient are associated with stronger interval correlations. Comparison with experimental data qualitatively confirms these trends.

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The mystery behind the origin of the pain and the difficulty to propose methodologies for its quantitative characterization fascinated philosophers (and then scientists) from the dawn of our modern society. Nowadays, studying patterns of information flow in mesoscale activity of brain networks is a valuable strategy to offer answers in computational neuroscience. In this paper, complex network analysis was performed on the time-varying brain functional connectomes of a rat model of persistent peripheral neuropathic pain, obtained by means of local field potential and spike train analysis. A wide range of topological network measures (14 in total, the code is publicly released at: https://github.com/biomedical-cybernetics/topological_measures_wide_analysis) was employed to quantitatively investigate the rewiring mechanisms of the brain regions responsible for development and upkeep of pain along time, from three hours to 16 days after nerve injury. The time trend (across the days) of each network measure was correlated with a behavioural test for rat pain, and surprisingly we found that the rewiring mechanisms associated with two local topological measure, the local-community-paradigm and the power-lawness, showed very high statistical correlations (higher than 0.9, being the maximum value 1) with the behavioural test. We also disclosed clear functional connectivity patterns that emerged in association with chronic pain in the primary somatosensory cortex (S1) and ventral posterolateral (VPL) nuclei of thalamus. This study represents a pioneering attempt to exploit network science models in order to elucidate the mechanisms of brain region re-wiring and engram formations that are associated with chronic pain in mammalians. We conclude that the local-community-paradigm is a model of complex network organization that triggers a local learning rule, which seems associated to processing, learning and memorization of chronic pain in the brain functional connectivity. This rule is based exclusively on the network topology, hence was named epitopological learning.

The mystery behind the origin of the pain and the difficulty to propose methodologies for its quantitative characterization fascinated philosophers (and then scientists) from the dawn of our modern society. Nowadays, studying patterns of information flow in mesoscale activity of brain networks is a valuable strategy to offer answers in computational neuroscience. In this paper, complex network analysis was performed on the time-varying brain functional connectomes of a rat model of persistent peripheral neuropathic pain, obtained by means of local field potential and spike train analysis. A wide range of topological network measures (14 in total, the code is publicly released at: https://github.com/biomedical-cybernetics/topological_measures_wide_analysis) was employed to quantitatively investigate the rewiring mechanisms of the brain regions responsible for development and upkeep of pain along time, from three hours to 16 days after nerve injury. The time trend (across the days) of each network measure was correlated with a behavioural test for rat pain, and surprisingly we found that the rewiring mechanisms associated with two local topological measure, the local-community-paradigm and the power-lawness, showed very high statistical correlations (higher than 0.9, being the maximum value 1) with the behavioural test. We also disclosed clear functional connectivity patterns that emerged in association with chronic pain in the primary somatosensory cortex (S1) and ventral posterolateral (VPL) nuclei of thalamus. This study represents a pioneering attempt to exploit network science models in order to elucidate the mechanisms of brain region re-wiring and engram formations that are associated with chronic pain in mammalians. We conclude that the local-community-paradigm is a model of complex network organization that triggers a local learning rule, which seems associated to processing, learning and memorization of chronic pain in the brain functional connectivity. This rule is based exclusively on the network topology, hence was named epitopological learning.

Spontaneous travelling waves of neuronal activity are a prominent feature throughout the developing brain and have been shown to be essential for achieving normal function, but the mechanism of their action on post-synaptic connections remains unknown. A well-known and widespread mechanism for altering synaptic strengths is spike-timing dependent plasticity (STDP), whereby the temporal relationship between the pre- and post-synaptic spikes determines whether a synapse is strengthened or weakened. Here, I answer the theoretical question of how these two phenomenon interact: what types of connectivity patterns can emerge when travelling waves drive a downstream area that implements STDP, and what are the critical features of the waves and the plasticity rules that shape these patterns? I then demonstrate how the theory can be applied to the development of the visual system, where retinal waves are hypothesised to play a role in the refinement of downstream connections. My major findings are as follows. (1) Mathematically, STDP translates the correlated activity of travelling waves into coherent patterns of synaptic connectivity; it maps the spatiotemporal structure in waves into a spatial pattern of synaptic strengths, building periodic structures into feedforward circuits. This is analogous to pattern formation in reaction diffusion systems. The theory reveals a role for the wave speed and time scale of the STDP rule in determining the spatial frequency of the connectivity pattern. (2) Simulations verify the theory and extend it from one-dimensional to two-dimensional cases, and from simplified linear wavefronts to more complex realistic and noisy wave patterns. (3) With appropriate constraints, these pattern formation abilities can be harnessed to explain a wide range of developmental phenomena, including how receptive fields (RFs) in the visual system are refined in size and topography and how simple-cell and direction selective RFs can develop. The theory is applied to the visual system here but generalises across different brain areas and STDP rules. The theory makes several predictions that are testable using existing experimental paradigms.

Neurodegeneration is a progressive loss of neuron function or structure, including death of neurons, and occurs at many different levels of neuronal circuitry. In this thesis I discuss Parkinson’s Disease (PD), the second most common neurodegenerative disease (NDD). PD is a devastating progressive NDD often with delayed diagnosis due to detection methods that depend on the appearance of visible motor symptoms. By the time cardinal symptoms manifest, 60 to 80 percent or more of the dopamine-producing cells in the substantia nigra are irreversibly lost. Although there is currently no cure, earlier detection would be highly beneficial to manage treatment and track disease progression. However, today’s clinical diagnosis methods are limited to subjective evaluations and observation. Onset, symptoms and progression significantly vary from patient to patient across stages and subtypes that exceed the scope of a standardized diagnosis. The goal of this thesis is to provide the basis of a more general approach to study the brain, investigating early detection method for NDD with focus on PD. It details the preliminary development, testing and validation of tools and methods to objectively quantify and extrapolate motor and non-motor features of PD from behavioral and cognitive output during everyday life. Measures of interest are categorized within three domains: the motor system, cognitive function, and brain activity. This thesis describes the initial development of non-intrusive tools and methods to obtain high-resolution movement and speech data from everyday life and feasibility analysis of facial feature extraction and EEG for future integration. I tested and validated a body sensor system and wavelet analysis to measure complex movements and object interaction in everyday living situations. The sensor system was also tested for differentiating between healthy and impaired movements. Engineering and design criteria of the sensor system were tested for usability during everyday life. Cognitive processing was quantified during everyday living tasks with varying loaded conditions to test methods for measuring cognitive function. Everyday speech was analyzed for motor and non-motor correlations related to the severity of the disease. A neural oscillation detection (NOD) algorithm was tested in pain patients and facial expression was analyzed to measure both motor and non-motor aspects of PD. Results showed that the wearable sensor system can measure complex movements during everyday living tasks and demonstrates sensitivity to detect physiological differences between patients and controls. Preliminary engineering design supports clothing integration and development of a smartphone sensor platform for everyday use. Early results from loaded conditions suggest that attentional processing is most affected by cognitive demands and could be developed as a method to detect cognitive decline. Analysis of speech symptoms demonstrates a need to collect higher resolution spontaneous speech from everyday living to measure speech motor and non-motor speech features such as language content. Facial expression classifiers and the NOD algorithm indicated feasibility for future integration with additional validation in PD patients. Thus this thesis describes the initial development of tools and methods towards a more general approach to detecting PD. Measuring speech and movement during everyday life could provide a link between motor and cognitive domains to characterize the earliest detectable features of PD. The approach represents a departure from the current state of detection methods that use single data entities (e.g.one-off imaging procedures), which cannot be easily integrated with other data streams, are time consuming and economically costly. The long-term vision is to develop a non-invasive system to measure and integrate behavioral and cognitive features enabling early detection and progression tracking of degenerative disease.

Les travaux de cette thèse ont pour but de mettre en œuvre des outils de modélisation et de simulation numériques de mécanismes sous-tendant l’activité neuronale, afin de promouvoir la découverte de médicaments pour le traitement des maladies du système nerveux. Les modèles développés s’inscrivent à différentes échelles : 1) les modèles dits « élémentaires » permettent de simuler la dynamique des récepteurs, des canaux ioniques, et les réactions biochimiques des voies de signalisation intracellulaires ; 2) les modèles de neurones permettent d’étudier l’activité électrophysiologique de ces cellules ; et 3) les modèles de microcircuits permettent de comprendre les propriétés émergentes de ces systèmes complexes, tout en conservant les mécanismes élémentaires qui sont les cibles des molécules pharmaceutiques. À partir d’une synthèse bibliographique des éléments de neurobiologie nécessaires, et d’une présentation des outils mathématiques et informatiques mis en œuvre, le manuscrit décrit les différents modèles développés ainsi que leur processus de validation, allant du récepteur de neurotransmetteur au microcircuit. D’autre part, ces développements ont été appliqués à trois études visant à comprendre : 1) la modulation pharmacologique de la potentialisation à long terme (LTP) dans les synapses glutamatergiques de l’hippocampe, 2) les mécanismes de l'hyperexcitabilité neuronale dans l'épilepsie mésio-temporale (MTLE) à partir de résultats expérimentaux in vitro et in vivo, et 3) la modulation cholinergique de l'activité hippocampique, en particulier du rythme thêta associé à la voie septo-hippocampique. / The work of this thesis aims to apply modeling and simulation techniques to mechanisms underlying neuronal activity, in order to promote drug discovery for the treatment of nervous system diseases. The models are developed and integrated at different scales: 1) the so-called "elementary models" permit to simulate dynamics of receptors, ion channels and biochemical reactions in intracellular signaling pathways; 2) models at the neuronal level allow to study the electrophysiological activity of these cells; and 3) microcircuits models help to understand the emergent properties of these complex systems, while maintaining the basic mechanisms that are the targets of pharmaceutical molecules. After a bibliographic synthesis of necessary elements of neurobiology, and an outline of the implemented mathematical and computational tools, the manuscript describes the developed models, as well as their validation process, ranging from the neurotransmitter receptor to the microcircuit. Moreover, these developments have been applied to three studies aiming to understand: 1) pharmacological modulation of the long-term potentiation (LTP) of glutamatergic synapses in the hippocampus, 2) mechanisms of neuronal hyperexcitability in the mesial temporal lobe epilepsy (MTLE), based on in vitro and in vivo experimental results, and 3) cholinergic modulation of hippocampal activity, particularly the theta rhythm associated with septo-hippocampal pathway.

In dieser Dissertation wird ein Modell des visuellen Systems untersucht, basierend auf dem Prinzip des unüberwachten Langsamkeitslernens und des SFA-Algorithmus (Slow Feature Analysis). Dieses Modell wird hier für die invariante Objekterkennung und verwandte Probleme eingesetzt. Das Modell kann dabei sowohl die zu Grunde liegenden diskreten Variablen der Stimuli extrahieren (z.B. die Identität des gezeigten Objektes) als auch kontinuierliche Variablen (z.B. Position und Rotationswinkel). Dabei ist es in der Lage, mit komplizierten Transformationen umzugehen, wie beispielsweise Tiefenrotation. Die Leistungsfähigkeit des Modells wird zunächst mit Hilfe von überwachten Methoden zur Datenanalyse untersucht. Anschließend wird gezeigt, dass auch die biologisch fundierte Methode des Verstärkenden Lernens (reinforcement learning) die Ausgabedaten unseres Modells erfolgreich verwenden kann. Dies erlaubt die Anwendung des Verstärkenden Lernens auf hochdimensionale visuelle Stimuli. Im zweiten Teil der Arbeit wird versucht, das hierarchische Modell mit Top-down Prozessen zu erweitern, speziell für die Rekonstruktion von visuellen Stimuli. Dabei setzen wir die Methode der Vektorquantisierung ein und verbinden diese mit einem Verfahren zum Gradientenabstieg. Die wesentlichen Komponenten der für unsere Simulationen entwickelten Software wurden in eine quelloffene Programmbibliothek integriert, in das ``Modular toolkit for Data Processing'''' (MDP). Diese Programmkomponenten werden im letzten Teil der Dissertation vorgestellt. / This thesis examines a model of the visual system, which is based on the principle of unsupervised slowness learning and using Slow Feature Analysis (SFA). We apply this model to the task of invariant object recognition and several related problems. The model not only learns to extract the underlying discrete variables of the stimuli (e.g., identity of the shown object) but also to extract continuous variables (e.g., position and rotational angles). It is shown to be capable of dealing with complex transformations like in-depth rotation. The performance of the model is first measured with the help of supervised post-processing methods. We then show that biologically motivated methods like reinforcement learning are also capable of processing the high-level output from the model. This enables reinforcement learning to deal with high-dimensional visual stimuli. In the second part of this thesis we try to extend the model with top-down processes, centered around the task of reconstructing visual stimuli. We utilize the method of vector quantization and combine it with gradient descent. The key components of our simulation software have been integrated into an open-source software library, the Modular toolkit for Data Processing (MDP). These components are presented in the last part of the thesis.