This chapter focuses on system's analysis tools and its application to the study of biological systems through mathematical modeling. The tools from classical sensitivity analysis are outlined, and described with application to the unraveling of design principles in complex biophysical networks, particularly with regard to robustness. Applications to optimized experimental design, and hypothesis discrimination are also discussed. In the field of systems biology, sensitivity analysis has been used in a number of applications, including optimized design of synthetic circuits, design of experiments for optimal parameter estimation, and robustness analysis to provide insights into design principles. Examples of how these sensitivity analysis implications and extensions have already been applied to biological systems are provided in this chapter. Sensitivity analysis investigates the changes in a system's behavior in response to infinitesimal parametric perturbations. Results from UPR sensitivity comparisons showed the greatest disparity between the BiP-heterologous unfolded protein binding rate sensitivities for the two models. Sensitivity analysis is also used to explore a stochastic, oscillatory system: the mouse circadian rhythm. The fundamental sensitivity analysis concept, or definition, is quite basic: perturbations in model parameters will affect model outputs. However, its implications, extensions, and applications are profound and numerous in the field of systems biology.
