MCMC Techniques for Parameter Estimation of ODE Based Models in Systems Biology

Gloria I Valderrama-Bahamóndez,Holger Fröhlich

doi:10.3389/fams.2019.00055

Abstract

Ordinary differential equation systems (ODEs) are frequently used for dynamical system modelling in many science fields such as economics, physics, engineering, and systems biology. A special challenge in systems biology is that ODE systems typically contain kinetic rate parameters, which are unknown and have to be estimated from data. However, non-linearity of ODE systems together with noise in the data raise severe identifiability issues. Hence, Markov Chain Monte Carlo (MCMC) approaches have been frequently used to estimate posterior distributions of rate parameters. However, designing a good MCMC sampler for high dimensional and multi-modal parameter distributions remains a challenging task. Here we performed a systematic comparison of different MCMC techniques for this purpose using five public domain models. The comparison included Metropolis-Hastings, parallel tempering MCMC, adaptive MCMC and parallel adaptive MCMC. In conclusion, we found specifically parallel adaptive MCMC to produce superior parameter estimates while benefitting from inclusion of our suggested informative Bayesian priors for rate parameters and noise variance.

Highlights

Ordinary differential equations systems (ODEs) have been widely used for modeling dynamical systems
Convergence could be assessed in all cases for parallel tempering and single adaptive Markov Chain Monte Carlo (MCMC), but not for multi-chain adaptive MCMC
We focused this comparison on single chain adaptive MCMC and Metropolis-Hastings with the same noise level as in the previous paragraph

Summary

Introduction

Ordinary differential equations systems (ODEs) have been widely used for modeling dynamical systems. Models based on ODEs have applications in many science fields such as economics, physics, engineering, and systems biology. Together with the initial conditions, the value of parameters in the ODE system determine the dynamical behavior of the model. A special challenge in systems biology is that parameters (typically kinetic rate parameters) are often unknown and have to be estimated from data. Non-trivial challenges in that context comprise non-linearity of ODE systems together with noise in observable data. Noise is inherent in all natural processes on molecular level up to whole ecosystems [1]. Observable data is affected by noise inherent into the applied measurement techniques

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Methods

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Conclusion