7 Summary
It has been discussed for a long time whether living systems can be
mathematically conceptualized using simple theories as they possess
very complex dynamic and emergent behaviors, and many times
display unpredictable outcomes [47]. In this chapter, we have
looked at several complex response dynamics of living cells, and
have shown simple biochemical models, based on linear and non-
linear differential equations, which can be used to successfully
understand or interpret the data. For linear models, the reaction
topology rather than kinetics plays crucial and sensitive roles
[4, 19]. For nonlinear dynamics, the parameters need to be precise
or the response cannot be accurately determined due to the stability
issue. For single-cell response, stochastic modeling can be useful in
understanding the diversifying cell fates or heterogeneous
response. We, therefore, believe mathematical models will continue
to play significant roles in unlocking further secrets on the complex
behaviors of living systems.References
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