Title :
Adjoint Systems for Models of Cell Signaling Pathways and their Application to Parameter Fitting
Author :
Fujarewicz, Krzysztof ; Kimmel, Marek ; Lipniacki, Tomasz ; êwierniak, Andrzej
Author_Institution :
Silesian Univ. of Technol., Gliwice
Abstract :
The paper concerns the problem of fitting mathematical models of cell signaling pathways. Such models frequently take the form of sets of nonlinear ordinary differential equations. While the model is continuous in time, the performance index used in the fitting procedure involves measurements taken at discrete time moments. Adjoint sensitivity analysis is a tool which can be used for finding the gradient of a performance index in the space of parameters of the model. In the paper, a structural formulation of adjoint sensitivity analysis called the generalized backpropagation through time (GBPTT) is used. The method is especially suited for hybrid, continuous-discrete time systems. As an example, we use the mathematical model NF-kappaB of the regulatory module, which plays a major role in the innate immune response in animals.
Keywords :
backpropagation; biochemistry; cellular biophysics; molecular biophysics; nonlinear differential equations; physiological models; adjoint sensitivity analysis; cell signaling pathways; generalized backpropagation through time; immune response; mathematical model NF-kappaB; nonlinear ordinary differential equations; parameter fitting; Automatic control; Backpropagation; Biological system modeling; Differential equations; Mathematical model; Parameter estimation; Performance analysis; Proteins; Sensitivity analysis; Time measurement; Biology and genetics; modeling; ordinary differential equations; parameter learning; Algorithms; Computer Simulation; Gene Expression; Models, Biological; NF-kappa B; Proteome; Signal Transduction;
Journal_Title :
Computational Biology and Bioinformatics, IEEE/ACM Transactions on
DOI :
10.1109/tcbb.2007.1016