8. Quantitative Analysis

The final aim of modeling biochemical processes is to gain a theoretical model which explains and predicts the dynamic behavior of the system in terms of quantities. The limitation of this type of modeling lies rather in the lacking of necessary kinetic data than in the mathematical concepts which are mostly based on coupled ordinary differential equations (ODEs). Whereas kinetic data can be found for some reactions, for the vast majority of pathways kinetic data have not been identified. For many biochemical processes, it still is a task to produce significant experimental data. Continuing efforts in well-designed experiments and data analysis have made kinetic data available for some pathways and some organisms, and with these data at hand quantitative methods become more and more useful. All quantitative methods, applied in modeling of biochemical processes, can easily be adapted to the Petri net formalism. The Petri net formalism offers the advantage of a combination of methods of classical systems biology with discrete Petri net modeling techniques, including an intuitive description of biochemical networks.

The aim of this chapter is to provide an introduction to basic methods for quantitative modeling of biochemical networks and a description in terms of the Petri net formalism. This includes for example, the classical principles of chemical reaction kinetics, the mass action, steady-states, stability and bifurcation analysis, Michaelis–Menten kinetics, and Hill kinetics. Moreover, we provide extensive references for further reading and give references to standard tools in this field.