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.