Symbolic Derivation Research Articles

The simulation and analysis by digital computer of biochemical systems in terms of kinetic models IV. Automatic derivation of enzymic rate laws

The application of the steady-state assumption to the enzyme species in kinetic models of biochemical systems is described. A set of rules for the derivation of the rate laws of complex enzymes under this assumption is available (King & Altman, 1956). Two programmes, which carry out a symbolic derivation of this kind, and can be used as part of a generator system for simulation by this method, are described in detail. The limitations and advantages of this approach are discussed.

Symbolic derivatives without list processing, subroutines, or recursion

A routine has been developed which computes and prints out the symbolic derivative of an absolutely continuous elementary function of one or several variables. No use is made of list processing languages. The chain rule is applied and the result is edited to produce results as elegant and efficient as those obtained by hand computation. A subset may be imbedded in a formula translator to introduce a differentiation operator into an “algebraic” programming language.