Modelling of biochemical networks such as signal transduction and gene regulatory circuits are main components of modern systems biology. In the case of experimentally immeasurable biological processes, a mathematical model can be used to observe and analyze the behavior of a particular variable. The behavior of these hidden system states can be crucial to understand the performance of biological systems where measurement is difficult or impractical.
These applications of mathematical modelling have particular relevance to the study of degenerative diseases of age such as Parkinson’s and Alzheimer’s disease that are unique to the human brain and for which animal models reproduce only certain pathological features. Pathogenesis in Parkinson’s and Alzheimer’s disease have been associated to some genetic impairments reflect on mitochondrial dysfunction, oxidative damage, neuro-inflammation, insulin resistance, abnormal protein phosphorylation and aggregation, compromising key functional roles of dopaminergic neurons, memory cells and their survival. Stochastic differential equations and biochemical systems theory based on ordinary differential equations can be used to mathematize biochemical reactions involved in these diseases. Some of the important pathways such as dopaminergic pathway, tau phosphorylation, alpha synuclein aggregation, oxidative stress etc. have been modelled using this software to study the pathophysiology of progression of the disease.
Cellular mechanisms affected by insulin resistance and abnormal protein aggregation as observed in Alzheimer’s and Parkinson’s disease.
