ABSTRACT
After constructing a model for the biological system being studied, the next step of the engineering approach is to analyze this model. The goal of analysis is to be able to both reproduce experimental results in silico (i.e., in a computer simulation) as well as make predictions about the system for situations that have not yet been studied in the laboratory. Simulation has the benefit of providing unlimited controllability and observability allowing the computational systems biologist to potentially gain insight about the biological system being studied which would be difficult to achieve in a laboratory setting. The traditional classical chemical kinetics (CCK) model utilizes ordinary
differential equations (ODE) to represent system dynamics. As described in Chapter 1, the law of mass action can be used to translate a chemical reaction model into an ODE model. The differential equations derived in this way are known as reaction rate equations. Solving a set of ODEs is often extremely difficult, so one usually determines the behavior that they specify using numerical simulation. Such simulations, however, are complicated by the trade-off between simulation accuracy and efficiency. Such simulations also only yield results for one set of initial conditions and parameter values. Given the uncertainty in these values in biological systems, it is often quite useful to be able to perform qualitative analysis of an ODE model to better understand the system’s behavior as these values vary. Finally, ODE models usually neglect spatial considerations. Partial differential equations (PDE) are typically utilized when spatial considerations are important. This chapter is organized as follows. First, Section 3.1 describes the classical
chemical kinetics ODE model. Next, Section 3.2 describes the basic concepts and methods for numerical simulation of such ODE models. Then, Section 3.3 presents methods for qualitative analysis of ODE models. Finally, Section 3.4 briefly presents modeling methods that incorporate spatial considerations.
