Parameter and topology uncertainty for optimal experimental design

Abstract

A major effort of systems biology is the building of accurate and detailed models of biological systems. Because biological models are large, complex, and highly nonlinear, building accurate models requires large quantities of data and algorithms appropriate to translate this data into a model of the underlying system. This thesis describes the development and application of several algorithms for simulation, quantification of uncertainty, and optimal experimental design for reducing uncertainty. We applied a previously described algorithm for choosing optimal experiments for reducing parameter uncertainty as estimated by the Fisher information matrix. We found, using a computational scenario where the true parameters were unknown, that the parameters of the model could be recovered from noisy data in a small number of experiments if the experiments were chosen well. We developed a method for quickly and accurately approximating the probability distribution over a set of topologies given a particular data set. The method was based on a linearization applied at the maximum a posteriori parameters. This method was found to be about as fast as existing heuristics but much closer to the true probability distribution as computed by an expensive Monte Carlo routine. We developed a method for optimal experimental design to reduce topology uncertainty based on the linear method for topology probability. This method was a Monte Carlo method that used the linear method to quickly evaluate the topology uncertainty that would result from possible data sets of each candidate experiment. We applied the method to a model of ErbB signaling. Finally, we developed a method for reducing the size of models defined as rule-based models. Unlike existing methods, this method handles compartments of models and allows for cycles between monomers. The methods developed here generally improve the detail at which models can be built, as well as quantify how well they have been built and suggest experiments to build them even better.