Bayesian Parameter Estimation for Dynamical Models in Systems Biology

TL;DR

This paper introduces a Bayesian framework for estimating parameters in dynamical systems models of systems biology, addressing challenges like data noise, sparsity, and nonlinearities to improve model accuracy and uncertainty quantification.

Contribution

It presents a comprehensive Bayesian approach for parameter estimation in complex biological models, incorporating uncertainty quantification and analysis of data and model influences.

Findings

Parameter estimation is affected by data sparsity and noise.

Model structure influences the accuracy of parameter estimates.

Uncertainty quantification enhances the analysis of biological systems.

Abstract

Dynamical systems modeling, particularly via systems of ordinary differential equations, has been used to effectively capture the temporal behavior of different biochemical components in signal transduction networks. Despite the recent advances in experimental measurements, including sensor development and '-omics' studies that have helped populate protein-protein interaction networks in great detail, modeling in systems biology lacks systematic methods to estimate kinetic parameters and quantify associated uncertainties. This is because of multiple reasons, including sparse and noisy experimental measurements, lack of detailed molecular mechanisms underlying the reactions, and missing biochemical interactions. Additionally, the inherent nonlinearities with respect to the states and parameters associated with the system of differential equations further compound the challenges of parameter estimation. In this study, we propose a comprehensive framework for Bayesian parameter estimation and complete quantification of the effects of uncertainties in the data and models. We apply these methods to a series of signaling models of increasing mathematical complexity. Systematic analysis of these dynamical systems showed that parameter estimation depends on data sparsity, noise level, and model structure, including the existence of multiple steady states. These results highlight how focused uncertainty quantification can enrich systems biology modeling and enable additional quantitative analyses for parameter estimation.