Beyond Michaelis-Menten: Allosteric Rate Control of Chaos

Abstract: The method developed by Michaelis and Menten was foundational in the development of our understanding of biochemical reaction kinetics. Extended models of metabolism encapsulated by reaction rate theory, stochastic reaction models, and dynamic flux estimation, amongst others, address aspects of this fundamental idea. The limitations of these approaches are well understood, and efforts to overcome those issues so far have been plentiful but with limited success. The known issues can be summarised as the sole dependent relation with substrate concentration, the encapsulation of rate in a single relevant scalar, and the subsequent lack of functional control that results from this assumption. The Rate Control of Chaos (RCC) is a nonlinear control method that has been shown to be effective in controlling the dynamic state of biological oscillators based on the concept of rate limitation of the exponential growth in chaotic systems. Extending RCC with allosteric properties allows robust control of the enzymatic process, and replicates the Michaelis-Menten kinetics. The emergent dynamics is robust to perturbations and noise but susceptible to regulatory adjustments. This control method adapts the control parameters dynamically in the presence of a ligand, and permits introduction of energy relations into the control function. The dynamic nature of the control eliminates the steady-state requirements and allows the modelling of large-scale dynamic behaviour, potentially addressing issues in metabolic disorder and failure of metabolic control.