k1 represents the phosphofructo kinase activity
This a model from the article: How yeast cells synchronize their glycolytic oscillations: a perturbation analytic treatment Bier M, Bakker BM, Westerhoff HV. Biophys. J 2000 Mar;78(3):1087-93. 10692299 , Abstract: Of all the lifeforms that obtain their energy from glycolysis, yeast cells are among the most basic. Under certain conditions the concentrations of the glycolytic intermediates in yeast cells can oscillate. Individual yeast cells in a suspension can synchronize their oscillations to get in phase with each other. Although the glycolytic oscillations originate in the upper part of the glycolytic chain, the signaling agent in this synchronization appears to be acetaldehyde, a membrane-permeating metabolite at the bottom of the anaerobic part of the glycolytic chain. Here we address the issue of how a metabolite remote from the pacemaking origin of the oscillation may nevertheless control the synchronization. We present a quantitative model for glycolytic oscillations and their synchronization in terms of chemical kinetics. We show that, in essence, the common acetaldehyde concentration can be modeled as a small perturbation on the "pacemaker" whose effect on the period of the oscillations of cells in the same suspension is indeed such that a synchronization develops.
Department of Surgery, Section of Plastic and Reconstructive Surgery, University of Chicago.
V_in represents the constant glucose inflow