Bifurcation analysis of metabolic pathways: an illustration from yeast glycolysis

In microorganisms such as bacteria or yeasts, metabolic rates are tightly coupled to growth rate, and therefore to fitness. Although the topology of central pathways are largely conserved across organisms, the enzyme kinetics and their parameters generally vary. This prevents us to understand and predict (changes in) metabolic dynamics. The analytical treatment of metabolic pathways is generally restricted to small models, containing maybe two to four equations. Since such small core models involve much coarse graining, their biological interpretation is often hampered. In this paper we aim to bridge the gap between analytical, more in-depth treatment of small core models and biologically more realistic and detailed models by developing new methods. We illustrate these methods for a model of glycolysis in Saccharo-myces cerevisiae yeast, arguably the best characterised metabolic pathway in the literature. The model is more involved than in previous studies, and involves both ATP/ADP and NADH/NAD householding.A detailed analysis of the steady state equations sheds new light on two recently studied biological phenomena in yeast glycolysis: whether it is to be expected that fructose-1,6-biphosphate (FBP) parameterises all steady states, and the occurrence of bistability between a regular steady state and imbalanced steady state in which glycolytic intermediates keep accumulating.This work shows that the special structure of metabolic pathways does allow for more in-depth bifurcation analyses than is currently the norm. We especially emphasise which of the techniques developed here scale to larger pathways, and which do not.