Modeling the Effects of the Extracellular Matrix on Neuron Dynamics

Abstract

In this thesis I have taken a step towards establishing a mathematical model of the effect of the extracellular matrix on the firing rate of the neuron it surrounds, namely the Kazantsev model, as a model that can be used to further research the effects of the extracellular matrix in general, and the perineuronal nets in particular. Part of this work has been studying the dynamics of the model system, where we see that the model facilitates two separate activity dependent steady states, and how a short period of high activity can lead to a shift between these states. In the activity region between these states we see a tendency for the system to fluctuate relatively strongly in terms of the concentration of the ECM components. It remains to be studied further whether this fluctuation is simply an artifact in the model, or if it reflects legitimate behavior. The model describes a system where two contrasting time scales are at play, and to facilitate this I have an effort to make the model more computationally inexpensive by simplifying the spike modeling within the model. This is done by means of a simple integrate-and-fire model.