Optimal metabolic pathway activation

TL;DR

This paper formulates an optimal control model for enzyme activation in biochemical pathways, revealing that enzyme activation occurs sequentially and in a bang-bang manner, consistent across various enzyme kinetics.

Contribution

It introduces a biologically meaningful optimal control framework for pathway activation, demonstrating the sequential and bang-bang nature of enzyme activation across different kinetic models.

Findings

Enzyme activation follows a bang-bang control pattern.

Reactions are activated sequentially in pathway order.

Results are valid for multiple enzyme kinetic models.

Abstract

This paper deals with temporal enzyme distribution in the activation of biochemical pathways. Pathway activation arises when production of a certain biomolecule is required due to changing environmental conditions. Under the premise that biological systems have been optimized through evolutionary processes, a biologically meaningful optimal control problem is posed. In this setup, the enzyme concentrations are assumed to be time dependent and constrained by a limited overall enzyme production capacity, while the optimization criterion accounts for both time and resource usage. Using geometric arguments we establish the bang-bang nature of the solution and reveal that each reaction must be sequentially activated in the same order as they appear in the pathway. The results hold for a broad range of enzyme dynamics which includes, but is not limited to, Mass Action, Michaelis-Menten and Hill Equation kinetics.