Diffusion-influenced ligand binding to buried sites in macromolecules and transmembrane channels

Abstract

We consider diffusion-influenced binding to a buried binding site that is connected to the surface by a narrow tunnel. Under the single assumption of an equilibrium distribution of ligands over the tunnel cross section, we reduce the calculation of the time-dependent rate coefficient to the solution of a one-dimensional diffusion equation with appropriate boundary conditions. We obtain a simple analytical expression for the steady-state rate that depends on the potential of mean force in the tunnel and the diffusion-controlled rate of binding to the tunnel entrance. Potential applications of our theory include substrate binding to a buried active site of an enzyme and permeant ion binding to an internal site in a transmembrane channel.

Figure 1

(a) Schematic representation of a biding site buried in a tunnel of length L and varying cross-section S(x). (b) The tunnel leading to the active site of acetylcholinesterase. The active-site residues are shown as stick. (c) The M2 proton channel with an internal binding site, consisting of a histidine tetrad. Only two of the four histidines are shown, as stick. In this structure the channel is blocked so proton can access the internal site from just one side of the membrane. Channel activation allows proton release to and binding from the other side of the membrane.

Figure 2

(a) Schematic representation of a binding site located in a conical tunnel of length L with the smallest and the largest tunnel radii equal to r₀ and a, respectively. (b) Schematic representation of a binding site located at depth L in a sphere of radius R; tunnel sides are specified by the polar angle θ₀.