Activated enzyme catalysis as a possible realization of the stable linear chemical oscillator model

Abstract

The stable linear chemical oscillator model of a preceding paper is reformulated in such a way that the action of the catalyst is expressed explicitly in terms of elementary reactions that are non-linear. It is shown that it is hardly possible to get a quasi-linear limiting case, if the substance produced on the feedback path is the catalyst itself. This can be achieved, if that substance is only an activator and the total amount of catalyst is constant. Thus, activated enzyme catalysis is a possible realization of the formally linear model. A further requirement is that the formation of the activated enzyme-substrate complex AES and the final reaction advances essentially over E + S ⇌ ES, ES + A ⇌ AES → P + A + E and that the enzyme is almost completely in the form ES. Fourier analysis of the results of computer simulations proves the high linearity in the essential substances even for cases of great amplitude in the limit cycle, while other parts, e.g. E, oscillate in a strongly non-linear way.