Speaker
Description
Glycolysis, the process by which energy is extracted from sugar, is known to exhibit oscillations and it has been shown experimentally that these arise in a reaction catalysed by the enzyme phosphofructokinase. Selkov introduced a simple model for this phenomenon which is a system of two ODE with mass action kinetics (in what follows the MA system). It is derived by a limiting process from a system with Michaelis-Menten kinetics (in what follows the MM system). Selkov claimed that the MA system has solutions with unbounded oscillations but that these are an artefact of the limiting process and are not present in the MM model. With Pia
Brechmann we gave a rigorous proof of Selkov's first claim. In this talk I present evidence that his second claim is not correct. A key step in the existence proof was showing that the MA system admits a heteroclinic cycle at infinity. I present a proof that the MM system also admits a heteroclinic cycle at infinity. I then explain what is needed to pass from this statement to the statement that there exist unbounded oscillations in the MM system.
Bibliography
Brechmann, P. and Rendall, A. D. 2021 Unbounded solutions of models for glycolysis. J. Math. Biol. 82, 1.
Selkov, E. E. 1968 Self-oscillations in glycolysis. I. A simple kinetic model. Eur. J. Biochem. 4, 79--86.
