Mathematical modelling of Alzheimer's disease biomarkers: Targeting Amyloid beta, Tau protein, Apolipoprotein E and Apoptotic pathways.

ABSTRACT

Introduction: The kinetics of brain cell death in Alzheimer's disease (AD) is being studied using mathematical models. These mathematical models utilize techniques like differential equations, stochastic processes, and network theory to explore crucial signalling pathways and interactions between different cell types. One crucial area of research is the intentional cell death known as apoptosis, which is crucial for the nervous system. The main purpose behind the mathematical modelling of this is for identification of which biomarkers and pathways are most influential in the progression of AD. In addition, we can also predict the natural history of the disease, by which we can make early diagnosis. Mathematical modelling of AD Current mathematical models include the Apolipoprotein E (APOE) Gene Model, the Tau Protein Kinetics Model, and the Amyloid Beta Peptide Kinetic Model. The Bcl-2 and Bax apoptosis theories postulate that the balance of pro- and anti-apoptotic proteins in cells determines whether a cell experiences apoptosis, where the Bcl-2 model, depicts the interaction of pro- and anti-apoptotic proteins, it is also being used in research on cell death in a range of cell types, including neurons and glial cells. How peptides are produced and eliminated in the brain is explained by the Amyloid beta Peptide (Aß) Kinetics Model. The tau protein kinetics model focuses on production, aggregation, and clearance of tau protein processes, which are hypothesized to be involved in AD. The APOE gene model investigates the connection between the risk of Alzheimer's disease and the APOE gene. These models have been used to predict how Alzheimer's disease would develop and to evaluate how different inhibitors will affect the illness's course. Conclusion: These mathematical models reflect physiological meaningful characteristics and demonstrates robust fits to training data. Incorporating biomarkers like Aß, Tau, APOE and markers of neuronal loss and cognitive impairment can generate sound predictions of biomarker trajectories over time in Alzheimer's disease.