Prediction and Optimal Experimental Design in Systems Biology Models

Abstract

In this dissertation we propose some approaches in model-building and model analysis techniques that can be used for typical systems biology models.

In Chapter 2 we introduce a dynamical model for growth factor receptor signaling and down-regulation. We show how, by quantitatively fitting the model to experimental data, we can infer interactions that are needed to describe the dynamical behavior. We demonstrate that predictions need to be accompanied by uncertainty estimates for both model validation and hypothesis testing. We then introduce some of the techniques from the optimal experimental design literature to reduce the prediction uncertainty for dynamical variables of interest.

In Chapter 3 we analyze the convergence properties of some of the Markov Chain Monte Carlo (MCMC) algorithms that can be used to give more rigorous uncertainty estimates for both parameters and dynamical variables within a model. We lay out a straightforward procedure which gives approximate convergence rates as a function of the tunable parameters of the MCMC method. We show that the method gives good estimates of convergence rates for the one dimensional probability distributions we examine, and it suggests optimal choices for the tunable parameters. We discover that variants of the basic MCMC algorithms which claim to have accelerated convergence often completely fail to converge geometrically in the tails of the probability distribution.

In Chapter 4 we consider a different problem --- how to efficiently simulate stochastic dynamics within a biochemical network. We introduce a mixed dynamics simulation algorithm which describes the biochemical reactions where some of the species can be treated as continuous variables, but other species are naturally described as discrete stochastic variables. We then attempt to describe an approximation to the continuous dynamics in a situation where the discrete variables change on a much faster relative time scale, analogous to the quasi-equilibrium assumption made in fully deterministic systems. However our approximation method mostly fails to capture the true correction to the dynamics; we speculate as to the reasons for this.