The Green’s function method of sensitivity analysis in chemical kinetics

Abstract

A new approach to the sensitivity analysis of large computational models is presented. The basis for the method is the well-known Green’s function technique. By working with the same differential equations as the conventional direct method, this new approach reduces the number of differential equations to be solved and replaces them by a set of integrals. Altogether, there is only one set of differential equations in the Green’s function method, regardless of the number of system parameters m. Sensitivity coefficients of all orders are expressed in integral form and evaluated in a recursive manner. Since evaluating well-behaved integrals is usually much easier than solving stiff differential equations, substantial savings can be achieved by the method when the number of system parameters is large. It is estimated that if only linear sensitivity coefficients are desired, then the Green’s function method could be advantageous for the case m≳n, where n is the number of dependent variables. However, if both linear and higher order sensitivity coefficients are to be computed, the method could be competitive with other approaches even when m<n. A numerical calculation on a simple linear system is presented to provide a brief illustration of the method.

Sensitivity analysis approaches applied to systems biology models

“…The sensitivity of S with respect to the parameter p can be rewritten with the constructed Green's function (see [17] for details)…”

“…The numerical calculation of (10) was described in [16,17]. The sensitivity coefficients obtained by (10) are the same as those obtained with (6).…”

Mapping global sensitivity of cellular network dynamics: sensitivity heat maps and a global summation law

“…Because it identifies which parameters a given particular aspect of the system is most sensitive to, classical sensitivity analysis (Hwang et al 1978;Kacser et al 1995;Heinrich & Schuster 1996;Campolongo et al 2000;Stelling et al 2004a) is a very useful tool that has been used to address both of these aspects. However, apart from some summation theorems about the control coefficients for period and amplitude of free-running oscillators that are analogous to those derived as in metabolic control analysis (Kacser et al 1995;Heinrich & Schuster 1996;Fell 1997), there is currently rather little general theory about general non-equilibrium networks.…”

Modeling and sensitivity analysis study of the reduction of NO{sub x} by HNCO

“…There have been three approaches to the calculation of sensitivity coefficients for studies of reacting flows: (1) the Fourier amplitude sensitivity test approach of Cukier et al (1973); (2) the direct method of Atherton et al (1975), Dickinson andGalinas (1976), andLutz et al (1991); and (3) the Green's function method of Hwang et al (1978) which has been further developed by Dougherty et al (1979), Rabitz et al (1983), Dacol andRabitz (1984), andYetter et al (1985).…”