A quantitative framework For large-scale model estimation and discrimination In systems biology

Abstract

Using models to simulate and analyze biological networks requires principled approaches to parameter estimation and model discrimination. We use Bayesian and Monte Carlo methods to recover the full probability distributions of free parameters (initial protein concentrations and rate constants) for mass action models of receptor-mediated cell death. The width of the individual parameter distributions is largely determined by non-identifiability but co-variation among parameters, even those that are poorly determined, encodes essential information. Knowledge of joint parameter distributions makes it possible to compute the uncertainty of model-based predictions whereas ignoring it (e.g. by treating parameters as a simple list of values and variances) yields nonsensical predictions. Computing the Bayes factor from joint distributions yields the odds ratio (~20-fold) for competing "direct" and "indirect" apoptosis models having different numbers of parameters. The methods presented in this thesis were then extended to make predictions in eight apoptosis mini-models. Despite topological uncertainty, the simulated predictions can be used to drive experimental design. Our results illustrate how Bayesian approaches to model calibration and discrimination combined with single-cell data represent a generally useful and rigorous approach to discriminating between competing hypotheses in the face of parametric and topological uncertainty.