Living systems are known to behave in a complex and sometimes unpredictable manner. Humans, for a very long time, have been intrigued by nature, and have attempted to understand biological processes and mechanisms using numerous experimental and mathematical techniques. In this chapter, we will look at simple theoretical models, using both linear and nonlinear differential equations, that realistically capture complex biochemical and genetic responses of living cells. Even for cases where cellular behaviors are stochastic, as for single-cell responses, randomness added to well-defined deterministic models has elegantly been shown to be useful. The data collectively present evidence for further exploration of the self-organizing rules and laws of living matter.
Keywords: Biological networks; Modeling; Nonlinear dynamics; Oscillation; Systems biology.