Quantifying Uncertainty and Sensitivity in an Alzheimer's Disease Model: A Mathematical Approach.

Area of Science:

• Computational Biology
• Neuroscience
• Mathematical Modeling

Background:

• Alzheimer's disease (AD) is characterized by the aggregation of disease-related proteins, immune cell activation, and inflammation.
• The complex interplay between these factors significantly influences AD pathogenesis.
• Mathematical models are crucial for dissecting these intricate biological dynamics.

Purpose of the Study:

• To develop a generalized mathematical model of Alzheimer's disease dynamics.
• To represent key biological interactions, including protein aggregation, immune response, and inflammation.
• To identify critical parameters influencing disease progression.

Main Methods:

• Formulation of a generalized mathematical model incorporating protein aggregation, immune cell activation, and inflammation.
• Analysis of system dynamics, including steady states, stability, and parameter identification.
• Parameter estimation using biological literature and data fitting.
• Sensitivity and uncertainty analyses (Partial Rank Correlation Coefficient, scatter plots) to identify influential parameters.

Main Results:

• Identification of biologically feasible steady states and stability properties.
• Sensitivity analysis revealed key parameters governing disease dynamics.
• Lower microglial activation rates and higher proliferation rates were associated with reduced toxic protein aggregates.

Conclusions:

• Mathematical modeling provides insights into Alzheimer's disease mechanisms.
• Modulating microglial activation and proliferation represents a potential therapeutic strategy to slow early disease progression.
• Further research can refine these models for targeted interventions.