Dimensionality of Diffusive Exploration at the Protein Interface in Solution

Abstract

The dynamics of water are critically important to the energies of interaction between proteins and substrates and determine the efficiency of transport at the interface. The magnetic field dependence of the nuclear spin-lattice relaxation rate constant 1/T(1) of water protons provides a direct characterization of water diffusional dynamics at the protein interface. We find that the surface-average translational correlation time is 30-40 ps and the magnetic field dependence of the water proton 1/T(1) is characteristic of two-dimensional diffusion of water in the protein interfacial region. The reduced dimensionality substantially increases the intermolecular re-encounter probability and the efficiency of the surface exploration by the small molecule, water in this case. We propose a comprehensive theory of the translational effects of a small diffusing particle confined in the vicinity of a spherical macromolecule as a function of the relative size of the two particles. We show that the change in the apparent dimensionality of the diffusive exploration is a general result of the small diffusing particle encountering a much larger particle that presents a diffusion barrier. Examination of the effects of the size of the confinement relative to the macromolecule size reveals that the reduced dimensionality characterizing the small-molecule diffusion persists to remarkably small radius ratios. The experimental results on several different proteins in solution support the proposed theoretical model, which may be generalized to other small-particle-large-body systems like vesicles and micelles.