Structural sensitivity analysis of mathematical models in biology

Sensitivity analysis plays very important and useful role during modeling and analysis of dynamical systems. It answers the question how changes in model parameters affects the model solution. The answer to this question can be useful in solving of many tasks, such as: estimation of model parameters, design of experiments, or the optimization of the structure of the model. Typically, the sensitivity functions with respect to model parameters are calculated but it is possible to perform the sensitivity analysis w.r.t. initial conditions or signals stimulating the system. During the presentation the so-called structural sensitivity analysis will be presented. It assumes that the system is presented in a structural form: as a block diagram. It simplifies the rules for the adjoint system creation and may be treated as a special case of so called automatic differentiation. The adjoint sensitivity analysis for systems of ordinary differential equation (ODE), delayed differential equations (DDE) and cellular automata used for solving partial differential (PDE) will be formulated. Results of application of the approach to parameter estimation and gradient-based optimization for various models will be presented.