The total quasi-steady-state for multiple alternative substrate reactions

Abstract

The Michaelis-Menten-Brigs-Haldane approximation and its extension, the total quasi-steady-state approximations (tQSSA) are famous assumptions for simplifications of mathematical modeling of enzyme-substrate reactions.These approximations and their validity conditions are well studied for a single substrate reaction system. However, the extension of these studies for the tQSSA of the general case of multiple substrate reactions is yet to be performed precisely due to the consequent non-linear expressions for tQSSA. In this paper, we introduce a linearization method for equations governing the tQSSA of multiple substrate reactions to obtain an analytical solution for the evolution of concentrations of reactants that is valid throughout the whole time period. In addition, we provide the validity conditions of the tQSSA for multiple substrate reaction systems using the singular perturbation analysis method.

Cardiac myosin binding protein-C phosphorylation as a function of multiple protein kinase and phosphatase activities

“…To study the system response at low substrate concentrations (i.e., of similar order of magnitude to the enzyme concentrations) at which the assumptions of Michaelis–Menten type rate laws are violated, we also used a total-quasi-steady-state version of the model following the approach from 48 , 49 . Following this approach, the tQSSA rate law for an irreversible distributive multisite phosphorylation system such as the one considered here can be given by , where j is the index of the j th reaction step in the sequence.…”

“…In vivo, however, substrate and enzyme concentrations may be comparable, violating the assumptions of the Michaelis-Menten approach. We thus repeated the analyses with a total-quasisteady-state rate law valid at lower substrate concentrations 48,49 but found no major qualitative differences, except that the change in PP1/ PP2A ratio was even more pronounced due to a predicted decrease of [PP2A] during HF (Supplementary Figs. 29 and 30).…”