The development of a high-order Taylor expansion solution to the chemical rate equation for the simulation of complex biochemical systems. Comput Appl Biosci 1990 Jul;6(3):173-7
Date
07/01/1990Pubmed ID
2207741DOI
10.1093/bioinformatics/6.3.173Scopus ID
2-s2.0-0025040571 (requires institutional sign-in at Scopus site)Abstract
A numerical method for evaluating chemical rate equations is presented. This method was developed by expressing the system of coupled, first-degree, ordinary differential chemical rate equations as a single tensor equation. The tensorial rate equation is invariant in form for all reversible and irreversible reaction schemes that can be expressed as first- and second-order reaction steps, and can accommodate any number of reactive components. The tensor rate equation was manipulated to obtain a simple formula (in terms of rate constants and initial concentrations) for the power coefficients of the Taylor expansion of the chemical rate equation. The Taylor expansion formula was used to develop a FORTRAN algorithm for analysing the time development of chemical systems. A computational experiment was performed with a Michaelis-Menten scheme in which step size and expansion order (to the 100th term) were varied; the inclusion of high-order terms of the Taylor expansion was shown to reduce truncation and round-off errors associated with Runge-Kutta methods and lead to increased computational efficiency.
Author List
Fischer TH, White GC 2ndAuthor
Gilbert C. White MD Professor in the Medicine department at Medical College of WisconsinMESH terms used to index this publication - Major topics in bold
AlgorithmsBiochemistry
Computer Simulation
Mathematical Computing
Models, Chemical
Programming Languages
Software
Software Design
