2008/01/16 by Diego A. Oyarzún, Brian Ingalls, Oyarzún, Diego +5
Biochemistry, Genetics and Molecular Biology · #Enzyme Catalysis and Immobilization #FOS: Biological sciences #FOS: Mathematics #Gene Regulatory Network Analysis #Microbial Metabolic Engineering and Bioproduction #Molecular Networks (q-bio.MN) #Optimization and Control (math.OC) #Quantitative Methods (q-bio.QM)
paper · doi:10.48550/arxiv.0801.2447
openalex publication_date 2008/01/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/04
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.