Modeling, Simulating, and Parameter Fitting of Biochemical Kinetic Experiments

TL;DR

This paper discusses methods for constructing, simulating, and fitting parameters in nonlinear differential equation models of biochemical systems, exemplified by estrogen receptor dimerization, to interpret experimental data.

Contribution

It provides a comprehensive pedagogical example of integrating mathematical, computational, and statistical techniques for biochemical model analysis and parameter estimation.

Findings

Successful parameter estimation for estrogen receptor dimerization

Demonstration of model reduction and simulation techniques

Guidance for future experimental design and modeling

Abstract

In many chemical and biological applications, systems of differential equations containing unknown parameters are used to explain empirical observations and experimental data. The DEs are typically nonlinear and difficult to analyze, requiring numerical methods to approximate the solutions. Compounding this difficulty are the unknown parameters in the DE system, which must be given specific numerical values in order for simulations to be run. Estrogen receptor protein dimerization is used as an example to demonstrate model construction, reduction, simulation, and parameter estimation. Mathematical, computational, and statistical methods are applied to empirical data to deduce kinetic parameter estimates and guide decisions regarding future experiments and modeling. The process demonstrated serves as a pedagogical example of quantitative methods being used to extract parameter values from biochemical data models.