Periodic Signal Transmission through Metabolic Pathways with Michaelian Kinetics

Abstract

The propagation of oscillations in metabolite concentrations mediated by simple Michaelis−Menten enzymes is studied from a theoretical viewpoint. Sinusoidal input waves are investigated, and the resulting output velocities are analyzed. As a first approach, both irreversible and reversible reactions with linear kinetics are examined. Analytical expressions result for the ratios of output to input amplitudes (damping factors), as well as for phase shifts. It is shown that transmission of sinusoidal oscillations by Michaelis enzymes is approximately linear around the mean input flux even for high amplitudes of the velocity. Accordingly, contributions of superior harmonics to the overall waveform can be neglected. The predicted maximum phase shift for these systems is a quarter of a cycle per reaction step, which occurs at high frequencies. Effective rate constants are introduced that are needed for the accurate prediction of output amplitudes. By using them, calculations are presented suggesting that complete transmission can be expected for low- or medium-saturated glycolytic enzymes.