Quantitative nonlinear analysis of autocatalytic pathways with applications to glycolysis

Autocatalytic pathways are frequently encountered in biological networks. One such pathway, the glycolytic pathway, is of special importance and has been studied extensively. Using tools from linear systems theory, our previous work on a simple two dimensional model of glycolysis demonstrated that autocatalysis can aggravate control performance and contribute to instability. Here, we expand this work and study properties of nonlinear autocatalytic pathway models (of which glycolysis is an example). Changes in the concentration of metabolites and catalyzing enzymes during the lifetime of the cell can perturb the system from the nominal operating point of the pathway. We investigate effects of such perturbations through the estimation of invariant subsets of the region of attraction around nominal operating conditions (i.e., a measure of the set of perturbations from which the cell recovers). Numerical experiments demonstrate that systems that are robust with respect to perturbations in parameter space have easily “verifiable” region of attraction properties in terms of proof complexity.