540—Evolution with time of the zero-current potential of a gold electrode in Escherichia coli cultures supplied with lipoic acid : Part I. Mathematical modeling and computer simulation

Abstract

Zero-current potential measurements (gold electrode) are suitable for continuously following the oxidation—reduction reactions of exogenic lipoic acid during Escherichia coli bacterial growth. This paper relates to a mathematical modeling of the experimental time-courses of potential. First, an empirical mathematical relation was obtained in vitro (i.e. in a sterile culture broth) between the zero-current potential and the concentrations of electroactive species that coexist and prevail in vivo (i.e. during the cultures). Secondly, a system of simple kinetic equations was proposed to express the metabolic, physical or chemical processes responsible for the in vivo time evolutions of the concentrations of electroactive species from which the time evolution of the electrode potential during the cultures was obtained. Most of these equations have been standardized by direct measurements. Numerical values could be applied to the remaining parameters of the model by comparing the computer-simulated time-courses of potential with experimental potential—time signals. The model properly fitted the experimental reality. It substantiated a theoretical correlation between the time evolutions of potential and the reductive activity of cultures by means of growth parameters relative to the population of organisms and transport or consumption parameters relative to the bacterial cell.