Regulatory crosstalk analysis of biochemical networks in the hippocampus and nucleus accumbens

Abstract

This chapter describes mathematical modeling of neuronal biochemical pathways, especially for pathological and non-pathological features of molecular and cellular mechanisms in the hippocampus and nucleus accumbens. We modeled both types of neurons with a variety of techniques: dynamic equations, constraintbased modeling, and complex network analysis. The last two approaches are called static modeling. In this chapter, we introduced these 3 methods to model the process of signal transduction, metabolism, ion fluxes, and gene regulation in a neuron, and their recent applications to the pathological characterization of the system. (1) The first one is a model of synaptic plasticity in the hippocampal CA1 neurons, which is thought to be relevant for learning and memory. We selected a constraint-based approach to model the cell, which uses constraint conditions in models from the stoichiometry matrix of chemical reactions in the absence of kinetic data. (2) The second model focuses on hippocampal signaling pathways in Alzheimer’s disease, including neurite outgrowth, synaptic plasticity and neuronal death. This is an application of complex network analysis to biological networks, with a particular emphasis on the k shortest path and the k-cycle. (3) The synaptic plasticity in medium spiny neurons in the nucleus accumbens is the main topic of the third model, which is thought to be relevant for reward system. An approach to reveal the dynamic properties of the model is a conventional ordinary differential equation-based modeling and perturbation analysis. Finally, brief concluding remarks appear in Mathematical modeling is aimed at an emergent property of a system, not an entity in a system, which is often intangible, invisible, and non-measurable in nature.