On fitting of mathematical models of cell signaling pathways using adjoint systems

Math Biosci Eng. 2005 Jul;2(3):527-34. doi: 10.3934/mbe.2005.2.527.

Abstract

This paper concerns the problem of fitting of mathematical models of cell signaling pathways. Such models frequently take the form of a set of nonlinear ordinary differential equations. While the model is continuous-time, the performance index, used in the fitting procedure, involves measurements taken only at discrete-time moments. Adjoint sensitivity analysis is a tool that can be used for finding a gradient of a performance index in the space of the model's parameters. The paper uses a structural formulation of sensitivity analysis, especially dedicated for hybrid, continuous/discrete-time systems. A numerical example of fitting of the mathematical model of the NF-kB regulatory module is presented.