Master thesis : Sensitivity and robustness analysis of thalamic neuron models at the cellular and network levels

In the early fifties, Hodgkin and Huxley developed a model of the electrical activity of the neuron. Based on a simple RC circuit with non-linear conductances, they reproduced very well the electrical behavior of a squid neuron. Over the last fifty years, thanks to the increase of experimental data and knowledge in neuroscience, scientists have extended the Hodgkin and Huxley’s model to more complex neurons. But they have often increased the complexity which makes their models less robust. This thesis focuses on thalamic neurons. The thalamus is the relay-station for the sensory inputs travelling to the cortex. Depending on the state, the thalamic neurons exhibit two different firing patterns. During sleep, the neurons are bursting, which stops the information processing. During wakefulness, the neurons are spiking and the thalamus processes the inputs. In order to study diseases such as absence seizures in children, or to describe more precisely the thalamic behavior, a robust model of neuron activity switch is necessary. This robustness has to be maintained when the study is performed at the network level. Recent evidences have highlighted the critical role of the slow dynamics of neuronal calcium currents in the switch from spiking to bursting. Inspired by this line of work, this thesis gathers conductancebased models of thalamic neuron in the literature. The major difference between them is the presence of the slow kinetics of the calcium current. The first contribution is their robustness comparison at the cellular level. Models which lack this slow dynamic are fragile when they are subjected to perturbation. The second contribution is to show that this slow dynamic is necessary to reproduce the correct rhythmicity of the thalamus at the network level. The conductance-based models are powerful tools to simulate a neuron with a great biophysical realism. However, they consist in high-dimensional non-linear differential equations that lead to time-consuming simulations. Therefore, the second part of this thesis investigates simple, qualitative modeling of neuron and network activity. This type of model, called hybrid model, is more mathematical; it captures the subthreshold dynamics of the neuron through differential equations and adds a reset rule to mimic the all-or-none nature of the spike. A hybrid model of a thalamic neuron has to be able to switch from spiking to bursting. Its robustness at the cellular level relies on its ability to mimic the slow dynamics of the calcium current without mathematical manipulation. The third contribution of the thesis is to confirm this discussion with a network level analysis. It shows that previously available simple models of thalamocortical neurons such as the well-known Izhikevich models lack the slow dynamics, hence they generate pathological behaviors while connected within a circuit. The key message is the comparison between two classes of thalamic neuron models. The first class integrates the slow dynamics of the calcium current while the second class assumes that this dynamics is fast. This work shows that the first class provides better results in terms of robustness. This demonstration is led at the cellular and network levels, for conductance-based models or reduced models. Therefore, the models belonging to this class are suitable for studies concerning the neuromodulation or the synaptic plasticity.