Projection-Based Model Order Reduction for Biochemical Systems

Abstract

Biochemical systems represent a process that involves di erent biological species linked by a network of chemical reactions. To analyze the behavior of the system, we perform experiments either on the actual system or on the mathematical model of the system. In this thesis, our focus is on modeling and analysis (computer sim- ulation) of biochemical systems. The problem with mathematical models is their complexity. The desire for more details and accurate results often generate large scale complex models. Numerical simulation of such complex models is computa- tionally expensive. Model order reduction can be utilized to tackle this issue of complexity by trying to take out those parts of a reaction network that are mathe- matically contributing very little in our parameters of interest. In this thesis we are using an important projection based model reduction technique that is called IRKA for model reduction of biochemical systems. To clarify the application of IRKA in reduction of biochemical systems, we consider an example of biochemical system from the literature and presents the key steps of modeling, conservation, lineariza- tion and reduction. The results of IRKA are compared with lumping, which is a common reduction technique for chemical reactions. It is observed that the approx- imation error through IRKA is much better as compared to the lumping technique. Keywords: model order reduction, complexity, mathematical modeling, chemical reaction.