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We present a unified approach for linear and non-linear 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 discuss it in comparison with Monte Carlo techniques. The extended TRAIL approach is fully adaptive and easily allows to study the influence of non-linear 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.