Modelling single cell dynamics of protein networks associated with synaptic plasticity

Abstract

Synaptic plasticity, an emergent property of the synaptic networks, has shown strong correlation to one of the essential functions of the brain, memory formation. Through understanding synaptic plasticity, we may discover the modulators and mechanisms which trigger memory formation. Mathematical models and computational methods show incredible potential in advancing the understanding of the complex behaviour of biological systems, which may be very difficult to understand using in vitro experiments. In this study, we develop the mathematical models of synaptic plasticity and analyse these models using computational methods to understand the dynamic behaviour of synaptic plasticity as well as the linkages to memory formation.

In the first part, we develop a simplified mathematical model of the NMDAR-mediated pathway of synaptic plasticity. The model is focused on the Ca²⁺ induced dynamics of modulators in the emergence of synaptic plasticity. The model is developed based on the essential synaptic modulators selected from the literature, but maintains the essential features of the modulators and the pathways. Importantly, this model shows the bidirectional behaviour of synaptic plasticity facilitated by the interactions among the modulators using the experimentally estimated kinetic parameters. Analysis of the dynamic behaviour of the model provides us with insights into the effective timescales of the modulators and an overall view of the main factors of the bidirectional behaviour. Using these information, we propose a hypothesised model of the memory system.

In the second part, we develop a theoretical model of the state transition of CaMKII, an important player for the induction of long term potentiation (LTP). This model includes the holoenzyme state transition of CaMKII and establishes a probabilistic framework for the binding between CaMKII and NMDAR. Through the analysis of the model using computational methods, we gain insights into the relationships among the autophosphorylation of CaMKII, the formation of CaMKII-NMDAR complex and LTP. Moreover, we study the implication of the autophosphorylation in LTP, which has diverse conclusions in the literature.