Protein machine model of enzymatic reactions gated by enzyme internal dynamics

The slow character of conformational transition dynamics in native proteins, recently becoming more and more apparent, makes conventional theories of chemical reactions inapplicable for the description of enzymatic reactions. Any contemporary statistical theory of biochemical processes has to be based on a possibly simple but realistic model of microscopic dynamics of participating biomolecules. In a model considered in this paper the dynamics of enzymatic protein is approximated by a quasi-continuous diffusive motion of its solid-like structural elements relative to each other. The enzymatic reaction is assumed to involve three steps (a covalent tranformation preceded and followed by association-dissociation processes with the substrate and the product), each step being gated by conformational diffusion. In general, the reaction proceeds in three stages: initial, transient and steady-state. Carefully approximated analytical formulae describing the kinetics in each stage are derived. In the limit of the fast internal dynamics of the enzyme, when compared to the local chemical transformations, the initial stage of reaction, dependent on the initial distribution of enzyme conformations, is absent and all the formulae describing the remaining two stages simplify to those provided by the classical theory of Haldane. However, following recent studies, the rule seems to be that it is the conformational dynamics of the enzyme, and not the details of chemical mechanism, that affects the rate of enzymatic reaction. Apart from the possibility of the initial inhomogeneous kinetics, the important result obtained in the limit of slow conformational dynamics is that the kinetic mechanisms of a reaction differ in general between the transient and steady-state stages. Possibilities of carrying out an experimentum crucis directly discrediting the conventional approach are considered.