How synaptic transmission influences the dynamics of populations of spiking neurons

Abstract

In recent years, models of quadratic integrate-and-fire (QIF) neurons have become ubiquitous in the mathematical neuroscience field. The election of an appropriate synaptic transmission model, either current-based (CUBA) or conductance-based (COBA), is a major challenge that arises from these neuronal frameworks. This problem has been approached using large-scale numerical simulations. However, the lack of use of low-dimensional models obviated the possibility to study how CUBA and COBA approaches shape the dynamics of spiking neurons networks (SNNs) from a general perspective. For this purpose, in this thesis we use a set of exact macroscopic equations for SNNs. This neural mass model (NMM) allows us to perform a comprehensive mathematical analysis of the system’s dynamics, making possible a comparison between the networks’ behavior in terms of the mean membrane voltage and the mean firing rate. Through simulations of different scenarios, including single neuron dynamics and large populations with recurrency, this work uncovers the mechanisms of microscopic and macroscopic state of spiking neurons.The comparison of these approaches advances our understanding of how neuronal signalling is modulated in terms of computational synapses. The results concluded that, unlike the CUBA approach, the COBA model exhibits a non-monotonic and complex dynamics. In this framework, conductance plays a crucial role in shaping the SNNs responses. These findings can be directly correlated with previous research studies where synaptic conductance induced the so-called high-conductance state when tested in vivo.