Abstract
Conformations and catalytic rates of enzymes fluctuate over a wide range of timescales. Despite these fluctuations, there exist some limiting cases in which the enzymatic catalytic rate follows the macroscopic rate equation such as the Michaelis-Menten law. In this paper we investigate the applicability of macroscopic rate laws for fluctuating enzyme systems in which catalytic transitions are slower than ligand binding-dissociation reactions. In this quasi-equilibrium limit, for an arbitrary reaction scheme we show that the catalytic rate has the same dependence on ligand concentrations as obtained from mass-action kinetics even in the presence of slow conformational fluctuations. These results indicate that the timescale of conformational dynamics – no matter how slow – will not affect the enzymatic rate in quasi-equilibrium limit. Our numerical results for two enzyme-catalyzed reaction schemes involving multiple substrates and inhibitors further support our general theory.
Highlights
Enzymes are biomolecules that catalyze biochemical reactions
Concluding remarks In this paper we developed a generalized formalism to study the kinetics of an enzyme with arbitrary complicated kinetic mechanism in the presence of dynamic disorder
Slow conformational fluctuations which are a source of dynamic disorder are common to many enzymes and can lead to deviations from macroscopic rate laws as predicted by conventional chemical kinetics
Summary
Enzymes are biomolecules that catalyze (i.e., increase the rates of) biochemical reactions. The dependence of enzymatically controlled reaction rate on these concentrations is often referred to as the kinetic law. The kinetic law can be deduced under certain approximation for an enzyme with known kinetic mechanism that is when we know how ligands bind and dissociate from the enzyme and at which state catalytic transitions occur. These kinetic laws have been derived for a variety of reaction schemes with mass-action kinetics and form a solid mathematical foundation of enzymology allowing the researchers to predict the kinetic laws from enzymatic mechanisms and vice versa. Ref. [1] gives a wide collection of examples of such complex enzyme catalyzed reaction mechanisms
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