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Adaptive approach for nonlinear sensitivity analysis of reaction kinetics
Author(s) -
Horenko Illia,
Lorenz Sönke,
Schütte Christof,
Huisinga Wilhelm
Publication year - 2005
Publication title -
journal of computational chemistry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.907
H-Index - 188
eISSN - 1096-987X
pISSN - 0192-8651
DOI - 10.1002/jcc.20234
Subject(s) - ode , sensitivity (control systems) , nonlinear system , ordinary differential equation , context (archaeology) , mathematics , partial differential equation , monte carlo method , statistical physics , differential equation , computer science , physics , mathematical analysis , paleontology , statistics , quantum mechanics , electronic engineering , engineering , biology
We present a unified approach for linear and nonlinear sensitivity analysis for models of reaction kinetics that are stated in terms of systems of ordinary differential equations (ODEs). The approach is based on the reformulation of the ODE problem as a density transport problem described by a Fokker–Planck equation. The resulting multidimensional partial differential equation is herein solved by extending the TRAIL algorithm originally introduced by Horenko and Weiser in the context of molecular dynamics (J. Comp. Chem. 2003, 24, 1921) and discussed it in comparison with Monte Carlo techniques. The extended TRAIL approach is fully adaptive and easily allows to study the influence of nonlinear dynamical effects. We illustrate the scheme in application to an enzyme‐substrate model problem for sensitivity analysis w.r.t. to initial concentrations and parameter values. © 2005 Wiley Periodicals, Inc. J Comput Chem 26: 941–948, 2005