Computational Study of Neuronal Oscillations In Motor Control Circuits
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In this thesis we used mathematical and computational models to study neuronal net- works that control motor behaviours. Specifically, we modelled two neuronal circuits from two opposite ends of the brain complexity spectrum: the swimming circuit of the hatchling Xenopus tadpole and the human basal ganglia. Due to its relative simplicity, tadpole is a unique animal for studying locomotion us- ing both experiments and models. This allowed us to define three biologically-realistic spiking models to clarify the interplay between the architecture of synaptic connections (structure) and the network’s ability to generate activities that correspond to its swim- ming behaviour (function). First, we investigated how the structural variability of individual circuits produces similar behaviours. To answer this question, we defined a probabilistic model of connectivity and dynamics for the neurons in the spinal cord. Simulations of the model showed that the swimming behaviours generated by different connectivities are remarkably similar. We used graph theory measures to characterise structural properties of networks un- derlying swimming. For example, we applied them to (1) predict the swimming period and (2) detect key neurons and connections that promote the swimming rhythm. Second, we built a minimal model of the central pattern generator (CPG) which repro- duces all the experimentally recorded oscillatory regimes: swimming and synchrony - anti-phase and in-phase oscillations between two body sides, respectively. Using bifurcation theory, we defined stabilities for these regimes and demonstrated the exis- tence of bi-stablity for a physiological range of parameters. Considering a vicinity of the critical parameter values of a saddle-node bifurcation, we explained how long-lasting synchrony transitions can appear both in model and experiment. Third, we expanded our CPG model by adding three sensory pathways. Our modelling is based on available anatomical and physiological data and on our new probabilistic ap- proach for modelling connections. The expanded model contains approximately 1700 neurons and about 100,000 connections. The model reproduces the experimentally recorded neuronal activities during the initiation, acceleration, continuation, modula- tion and termination of locomotion. Therefore, it can describe the complete swimming behaviour of the tadpole in response to sensory inputs. Inspired by our study of oscillations and synchronisation in the tadpole nervous sys- tem, we proposed a theoretical model of action selection in the basal ganglia. We use a mathematical formalism known as Arnold tongues to explain how modulatory inputs from the cortex can partially synchronise subsets of neurons in the basal ganglia and generate a rhythmic action. This mechanism can explain how the transitions between multiple oscillatory states might work, thus effectively resolving the switching between competing actions. Although theoretical, the model could serve as a qualitative tool to understand the basic working principles of action selection. For example, model simula- tions match experimental recordings in rodents showing that the cortex can synchronise neurons in the basal ganglia and generate Arnold tongues synchronisation.