Sequential activation of metabolic pathways: a dynamic optimization approach

Oyarzún, Diego A. and Ingalls, Brian P. and Middleton, Richard H. and Kalamatianos, Dimitrios (2009) Sequential activation of metabolic pathways: a dynamic optimization approach. Bulletin of Mathematical Biology . ISSN 0092-8240

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The regulation of cellular metabolism facilitates robust cellular operation in the face of changing external conditions. The cellular response to this varying environment may include the activation or inactivation of appropriate metabolic pathways. Experimental and numerical observations of sequential timing in pathway activation have been reported in the literature. It has been argued that such patterns can be rationalized by means of an underlying optimal metabolic design. In this paper we pose a dynamic optimization problem that accounts for time-resource minimization in pathway activation under constrained total enzyme abundance. The optimized variables are time-dependent enzyme concentrations that drive the pathway to a steady state characterized by a prescribed metabolic flux. The problem formulation addresses unbranched pathways with irreversible kinetics. Neither specific reaction kinetics nor fixed pathway length are assumed. In the optimal solution, each enzyme follows a switching profile between zero and maximum concentration, following a temporal sequence that matches the pathway topology. This result provides an analytic justification of the sequential activation previously described in the literature. In contrast with the existent numerical approaches, the activationsequence is proven to be optimal for a generic class of monomolecular kinetics. This class includes, but is not limited to, Mass Action, Michaelis–Menten, Hill, and some Power-law models. This suggests that sequential enzyme expression may be a common feature of metabolic regulation, as it is a robust property of optimal pathway activation.

Item Type: Article
Keywords: Metabolic dynamics; Metabolic regulation · Dynamic optimization; Hamilton Institute
Academic Unit: Faculty of Science and Engineering > Research Institutes > Hamilton Institute
Item ID: 1665
Depositing User: Hamilton Editor
Date Deposited: 16 Nov 2009 15:53
Journal or Publication Title: Bulletin of Mathematical Biology
Publisher: Springer Verlag
Refereed: Yes

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