Abstract
The investigation of enzyme catalysis has traditionally been based on the rapid equilibrium conditions defined by Henri, Michaelis and Menten. The general rate equations derived by Briggs and Haldane provided incremental progress by assuming near steady-state levels for the enzyme-substrate complex. In situ, however, enzymes may operate far from equilibrium, so that the idealizing assumptions of traditional enzyme kinetics do not hold up and the enzyme becomes an active participant in determining the outcome of a reaction. We used computer modeling of an enzyme-catalyzed reaction with substrate activation to assess the impact of the rate constants on the product production per unit time. Mapping of the parameter space in bifurcation plots displayed ranges of instability that were preceded and succeeded by distinct stable states. To test whether this phenomenon may occur in enzymes without substrate activation, we also analyzed the ordinary differential equations that describe general enzyme catalysis. We found stable responses and limit cycles to rhythmic substrate input, but no chaos. We confirmed, on the basis of theoretical calculations and experiment, that in bifurcating reactions (which are common in situ) the presence or absence of an enzyme in one arm shifts the equilibrium. These results contest the paradigm that enzymes accelerate equilibrium formation in chemical reactions without affecting the reaction outcome.
Highlights
Enzyme catalysis has been studied as a supportive process in biochemical reactions since the 1800s
This notion was formed by decades of analysis of biochemical catalysis under the conditions defined by Henri in 1903, which stipulate that enzyme, substrate and the enzyme-substrate complex are at equilibrium, that a fixed amount of substrate is added at the onset of the reaction, that the substrate concentration is much larger than the enzyme concentration and not affected by the formation of an enzyme-substrate complex, and that there is no change in enzyme concentration over time
The chemical reactions under study can be defined as sets of ordinary differential equations (ODEs) that describe the rate of change of each reactant per time-step
Summary
Enzyme catalysis has been studied as a supportive process in biochemical reactions since the 1800s. This notion was formed by decades of analysis of biochemical catalysis under the conditions defined by Henri in 1903, which stipulate that enzyme, substrate and the enzyme-substrate complex are at equilibrium, that a fixed amount of substrate is added at the onset of the reaction, that the substrate concentration is much larger than the enzyme concentration and not affected by the formation of an enzyme-substrate complex (measurement of initial reaction velocity), and that there is no change in enzyme concentration over time These constraints were developed into the Michaelis-Menten equation (and with the even more restrictive assumption of irreversible reaction steps into the van Slyke equation). It is not reflective of the far-from-equilibrium conditions or the coupled reaction pathways that exist in vivo
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