Mathematical and Statistical Techniques for Systems Medicine: The Wnt Signaling Pathway as a Case Study

TL;DR

This paper reviews mathematical and statistical techniques, especially ODE models, for analyzing signaling pathways like Wnt in systems medicine, emphasizing model analysis, parameter estimation, and comparison methods.

Contribution

It provides a comprehensive overview of current modeling frameworks and analysis methods for systems medicine, focusing on the Wnt pathway as a case study.

Findings

Demonstrates application of dynamical systems analysis to Wnt models

Introduces Bayesian and algebraic geometry methods for model comparison

Highlights the potential of ODE models in systems biology and medicine

Abstract

The last decade has seen an explosion in models that describe phenomena in systems medicine. Such models are especially useful for studying signaling pathways, such as the Wnt pathway. In this chapter we use the Wnt pathway to showcase current mathematical and statistical techniques that enable modelers to gain insight into (models of) gene regulation, and generate testable predictions. We introduce a range of modeling frameworks, but focus on ordinary differential equation (ODE) models since they remain the most widely used approach in systems biology and medicine and continue to offer great potential. We present methods for the analysis of a single model, comprising applications of standard dynamical systems approaches such as nondimensionalization, steady state, asymptotic and sensitivity analysis, and more recent statistical and algebraic approaches to compare models with data. We present parameter estimation and model comparison techniques, focusing on Bayesian analysis and coplanarity via algebraic geometry. Our intention is that this (non exhaustive) review may serve as a useful starting point for the analysis of models in systems medicine.