Ultimate limits for the reaction flux and metabolite levels that may be evolutionarily reached in a linear metabolic pathway

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Abstract
A relationship is derived for the maximum steady-state reaction rate that may be supported by an enzyme catalyzing substrate/product interconversion by a generalized Michaelian mechanism for a single-substrate reaction. This relationship is used to characterize the ultimate kinetic and thermodynamic limits for the evolutionary improvement of a linear metabolic sequence of reactions catalyzed by Michaelian enzymes in response to a selective pressure in the direction of increased reaction flux. A mathematical analysis is presented which provides explicit expressions for the maximum reaction flux and metabolite concentrations that can be evolutionarily reached in such a pathway. These expressions may be used to obtain information on the reaction steps that represent ultimate bottlenecks for the attainment of high reaction flux in a certain pathway and to identify the enzymes that ultimately are likely to exert main flux control.