Abstract
Deciphering the metabolic functions of organisms requires understanding the dynamic responses of living cells upon genetic and environmental perturbations, which in turn can be inferred from enzymatic activity. In this work, we investigate the optimal modes of operation for enzymes in terms of the evolutionary pressure driving them toward increased catalytic efficiency. We develop a framework using a mixed-integer formulation to assess the distribution of thermodynamic forces and enzyme states, providing detailed insights into the enzymatic mode of operation. We use this framework to explore Michaelis-Menten and random-ordered multi-substrate mechanisms. We show that optimal enzyme utilization is achieved by unique or alternative operating modes dependent on reactant concentrations. We find that in a bimolecular enzyme reaction, the random mechanism is optimal over any other ordered mechanism under physiological conditions. Our framework can investigate the optimal catalytic properties of complex enzyme mechanisms. It can further guide the directed evolution of enzymes and fill in the knowledge gaps in enzyme kinetics.