Bayesian experiment design and estimation for probabilistic modeling of biological systems

Author(s): Martin Casas, Marc | Advisor(s): Mesbah, Ali | Abstract: Computational models have emerged as a key tool to study and characterize the behavior of biological systems. In order to accurately describe biological systems, computational models need to capture inherently complex features of biological behavior, such as nonlinear and probabilistic dynamics. Probabilistic models of biological systems can account for our lack of knowledge in model structure or parameters (uncertainty), as well as the physical sources of probabilistic behavior leading to heterogeneity. Uncertainty quantification and optimal experiment design frameworks play a key role in the development of probabilistic models for biological systems, as they can enable system learning from informative experimental data by improving the accuracy of model structures and parameter estimates. Despite the extensive implementation of uncertainty quantification and experimental design frameworks in complex engineering systems, their application in biological systems has been lagging. This is because of their high computational cost, which can be further exacerbated when accounting for the large number of parameters and cellular constituents that characterize biological models. There is a need for computationally efficient tools that can capture complex biological properties to enable learning of biological systems in a systematic manner. In this thesis, we present novel uncertainty quantification and optimal experiment design tools that can capture complex traits of biological behavior, namely uncertainty, heterogeneity, nonlinearities, and large numbers of parameters and cellular constituents. More specifically, we introduce novel surrogate modeling methods for fast propagation of sources of uncertainty and heterogeneity, which enable the application of uncertainty quantification and optimal experiment design tools in biological systems. Subsequently, we introduce novel Bayesian methods for the estimation of genome-scale model parameters from noisy, sparse, and incomplete biological datasets. Additionally, we introduce computationally efficient methods to design experiments that yield informative data to refine parameter estimates and model structures in an offline and online manner (i.e., in the course of an experiment). The contributions of this thesis will create new opportunities for seamless implementation of uncertainty quantification and optimal experiment design for systematic and hypothesis-based modeling in biological systems.