Automated sensitivity analysis of stiff biochemical systems using a fourth-order adaptive step size Rosenbrock integration method.

Abstract

Sensitivity analysis is one of the most effective approaches for studying mathematical models of biochemical systems. A stiff Rosenbrock integrator has been developed for sensitivity analysis using a direct sensitivity approach. Automated sparse Jacobian and Hessian calculations of the coupled system (the original model equations and the sensitivity equations) have been implemented in the freely available software package CellSim. The accuracy and efficiency of the integrator are tested extensively on the complex mitogen-activated protein kinase (MAPK) pathway model of Bhalla and Iyengar. Both time-dependent concentration and parameter-based sensitivity coefficients are measured using several integration schemes. The method is shown to perform sensitivity analysis in a manner that is cost effective with moderate accuracy. The error control strategy between the decoupled direct method and the Rosenbrock with direct method is discussed and their computational accuracies are compared. The method is used to analyse the positive feedback loop within the MAPK signal transduction pathway.