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

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.

[1]  J. L. Bos,et al.  ras oncogenes in human cancer: a review. , 1989, Cancer research.

[2]  Mark A. Kramer,et al.  Sensitivity analysis of systems of differential and algebraic equations , 1985 .

[3]  Ji Shen,et al.  A DIRECT METHOD OF CALCULATING SENSITIVITY COEFFICIENTS OF CHEMICAL KINETICS , 1999 .

[4]  Boris N Kholodenko,et al.  MAP kinase cascade signaling and endocytic trafficking: a marriage of convenience? , 2002, Trends in cell biology.

[5]  David H. Slater,et al.  Mechanism and Kinetics of Propane Pyrolysis , 1979 .

[6]  Robert J. Gelinas,et al.  Sensitivity analysis of ordinary differential equation systems—A direct method , 1976 .

[7]  B. Sokhansanj,et al.  Spatiotemporal Systems Biology , 2006 .

[8]  Prahlad T. Ram,et al.  MAP Kinase Phosphatase As a Locus of Flexibility in a Mitogen-Activated Protein Kinase Signaling Network , 2002, Science.

[9]  D. Lauffenburger,et al.  Computational modeling of the EGF-receptor system: a paradigm for systems biology. , 2003, Trends in cell biology.

[10]  C. Der,et al.  Increasing Complexity of the Ras Signaling Pathway* , 1998, The Journal of Biological Chemistry.

[11]  Tien D. Bui.  Some A-Stable and L-Stable Methods for the Numerical Integration of Stiff Ordinary Differential Equations , 1979, JACM.

[12]  G. Carmichael,et al.  Direct and adjoint sensitivity analysis of chemical kinetic systems with KPP: Part I—theory and software tools , 2003, Atmospheric Environment.

[13]  Eugene P. Dougherty,et al.  Computational kinetics and sensitivity analysis of hydrogen–oxygen combustion , 1980 .

[14]  Gerhard Wanner,et al.  A study of Rosenbrock-type methods of high order , 1981 .

[15]  G. Carmichael,et al.  Direct and adjoint sensitivity analysis of chemical kinetic systems with KPP: II—numerical validation and applications , 2003 .

[16]  W. E. Stewart,et al.  Sensitivity analysis of initial value problems with mixed odes and algebraic equations , 1985 .

[17]  D. Bar-Sagi,et al.  Ras effectors and their role in mitogenesis and oncogenesis , 1997, Journal of Molecular Medicine.

[18]  C. Der,et al.  The Ras signal transduction pathway , 1994, Cancer and Metastasis Reviews.

[19]  Jeff R. Cash.  Semi-Implicit Runge-Kutta Procedures with Error Estimates for the Numerical Integration of Stiff Systems of Ordinary Differential Equations , 1976, JACM.

[20]  I. A. Vardanyan,et al.  The rate constant of the reaction HO2 + COCO2 + OH , 1975 .

[21]  P. Rentrop,et al.  Generalized Runge-Kutta methods of order four with stepsize control for stiff ordinary differential equations , 1979 .

[22]  W. Kolch.  Meaningful relationships: the regulation of the Ras/Raf/MEK/ERK pathway by protein interactions. , 2000, The Biochemical journal.

[23]  Lawrence F. Shampine,et al.  Implementation of Rosenbrock Methods , 1982, TOMS.

[24]  A. M. Dunker.  The decoupled direct method for calculating sensitivity coefficients in chemical kinetics , 1984 .

[25]  Avijit Ghosh,et al.  Automated oncogene detection in complex protein networks with applications to the MAPK signal transduction pathway. , 2005, Biophysical chemistry.

[26]  Eugene P. Dougherty,et al.  Further developments and applications of the Green’s function method of sensitivity analysis in chemical kinetics , 1979 .

[27]  U. Bhalla,et al.  Emergent properties of networks of biological signaling pathways. , 1999, Science.

[28]  E. Gilles,et al.  Computational modeling of the dynamics of the MAP kinase cascade activated by surface and internalized EGF receptors , 2002, Nature Biotechnology.

[29]  William H. Press,et al.  Numerical recipes in C , 2002 .