Effect of the internal rotations of the reactants in diffusion-controlled chemical reactions: An application to the enzyme kinetic problems

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Abstract
A theoretical model describing the effect of orientational constraints in diffusion-controlled enzymatic reactions is developed. It involves a rototranslational diffusion problem with mixed boundary conditions, which is solved in a diffusion-jump approximation. In this approximation the reactant molecules are partitioned in two classes. One class (I) includes the molecules which have their internal rotational angles, with respect to the enzyme binding site, within a given angular region C. All the other molecules belong to the second class (II). The relative population of the two classes changes according to interconversion rates which, in the present theory, is related to the true rotational diffusion coefficients of the reactants. The molecules of class I are adsorbed inside of a small circular region of the enzyme, while the ones belonging to class II are reflected everywhere at the surface. The solution of this problem leads to a set of integral equations from which the flux of adsorbed reactant molecules can be calculated. The influence of different physical parameters (rotational and translational diffusion coefficients, size of the enzyme binding region, range of the orientational region C) on the total flux has been investigated by numerical calculations, and some interesting limiting cases have been examined.