Systems analysis of stochastic and population balance models for chemically reacting systems

Chemical reaction models present one method of analyzing complex reaction pathways. Most models of chemical reaction networks employ a traditional, deterministic setting. The shortcomings of this traditional framework, namely difficulty in accounting for population heterogeneity and discrete numbers of reactants, motivate the need for more flexible modeling frameworks such as stochastic and cell population balance models. How to efficiently use models to perform systems-level tasks such as parameter estimation and feedback controller design is important in all frameworks. Consequently, this thesis focuses on three main areas: (1) improving the methods used to simulate and perform systems-level tasks using stochastic models, (2) formulating and applying cell population balance models to better account for experimental data, and (3) applying moving-horizon estimation to improve state estimates for nonlinear reaction systems.; For stochastic models, we have derived and implemented techniques that improve simulation efficiency and perform systems-level tasks using these simulations. For discrete stochastic models, these systems-level tasks rely on approximate, biased sensitivities, whereas continuous models (i.e. stochastic differential equations) permit calculation of unbiased sensitivities. Numerous examples illustrate the efficiency of these methods, including an application to modeling of batch crystallization systems.; We have also investigated using cell population balance models to incorporate both intracellular and extracellular levels of information in viral infections. Given experimental images of the focal infection system for vesicular stomatitis virus, we have applied these models to better understand the dynamics of multiple rounds of virus infection and the interferon (antiviral) host response. The model provides estimates of key parameters and suggests that the experimental technique may cause salient features in the data. We have also proposed an efficient and accurate model decomposition that predicts population-level measurements of intracellular and extracellular species.; Finally, we have assessed the capabilities of several state estimators, including moving-horizon estimation (MHE) and the extended Kalman filter (EKF). When multiple optima arise in the estimation problem, the judicious use of constraints and nonlinear optimization as employed by MHE can lead to improved state estimates and closed-loop control performance than the EKE This improvement comes at the price of the computational expense required to solve the MHE optimization.