Formal Analysis of Automated Model Abstractions under Uncertainty: Applications in Systems Biology

In this dissertation, three fundamental problems in modeling of large scale biological systems are addressed.;1. Modeling of chemical reaction under imprecise rate of reactions: A framework is created to model chemical reactions with an interval based approach, incorporating imprecision as well as creating a finite space. Algorithms are presented to construct model abstraction efficiently. The results of the algorithms on a prototype elucidate the model. The formalism presents a novel way to represent continuous data of concentrations for the chemicals and quantitative analysis of temporal behavior of the system.;2. Multiscale formalism in discrete domains: Biological processes are multiscale. We formalize the definition of multiscale modeling in discrete domains. A polynomial algorithm is constructed to compute identifiability of multiscale systems.;3. Formal analysis of gene regulatory network: A formalism that incorporates noise in the data is presented to study gene regulation. Computational efficiency of the formalism is evaluated on a prototype constructed from biological experimental data.