This chapter provides an introduction to the formulation and analysis of differential-equation-based models for biological regulatory networks. In the first part, we discuss basic reaction types and the use of mass action kinetics and of simplifying approximations in the development of models for biological signaling. In the second part we introduce phase plane and linear stability analysis to evaluate the time evolution and identify the long-term attractors of dynamic systems. We then discuss the use of bifurcation diagrams to evaluate the parameter dependency of qualitative network behaviors (i.e., the emergence of oscillations or switches), and we give measures for the sensitivity and robustness of the signaling output.
Mathematical modeling ODE models Signaling models
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We thank members of the Iber group for the critical reading of the manuscript. This work was financially supported by SystemsX, the Swiss Initiative for Systems Biology, with an iPhD grant and an RTD grant through the InfectX project.
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