Allosteric Rate Control of Chaos Governs Reaction Rate Kinetics

Models of metabolic systems have been encapsulated by reaction rate theory, stochastic reaction models, and dynamic flux estimation, amongst others, based on the foundation of Michaelis-Menten kinetics. The limitations of these approaches are well understood and 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 the steady-state 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 nonlinear oscillators based on the concept of rate limitation of the exponential growth in chaotic systems. The method is extended with allosteric properties into Allosteric Rate Control of Chaos (ARCC) to allow robust control of the enzymatic process.

ARCC fully replicates the Michaelis-Menten kinetics as well as allosteric control. The emergent dynamics is insensitive to perturbations and noise but susceptible to regulatory adjustments. This method adapts the control parameters dynamically in the presence of a substrate and a ligand, and permits introduction of energy relations into the control function.

The ARCC method more closely resembles biochemical properties of enzyme mediated reactions and removes the need for quasi-steady-state assumptions and allows the modelling of complex dynamic metabolic systems.

The dynamic nature of the control enables the modelling of the entire complex dynamics of metabolic systems as a large scale free system, potentially addressing metabolic disorders and explain the behaviour of metabolic control.