THEORY OF THE DIFFUSION-INFLUENCED SUBSTRATE-BINDING RATE TO A BURIEDAND GATED ACTIVE-SITE

The effects of stochastic gating on the diffusion-influenced substrate binding rate to a buried active site are studied. An approximation in troduced by Samson and Deutch [J. Chem. Phys. 68, 285 (1978)] is shown to be equivalent to making the constant-flux approximation on the ent rance to the active site. The constant-flux approximation is then exte nded to the case where the entrance to the active site is stochastical ly gated because of conformational fluctuations of the enzyme. The sto chastically gated rate constant, k(sg), is found to be given by the re lation 1/k(sg) = 1/k + w(o)/w(c)(w(o) + w(c))(h) over cap(w(o) + w(c)) , where k is the rate constant in the absence of gating, (h) over cap( s) is the Laplace transform of the total flux across the entrance afte r the substrate is started from an equilibrium distribution outside th e entrance, and w(o) and w(c) are the transition rates between the ope n and closed gating states. This relation reduces to an approximate re lation derived earlier for a more restrictive situation, where the rea ctivity within the active site is gated. The leading term in the expan sion of s (h) over cap(s) for large s is DA[exp(-beta U)](s/D)(1/2)/2, where D is the diffusion coefficient of the substrate, A is the total area of the entrance, and [exp(-beta U)] is the average Boltzmann fac tor on the entrance. The time scale of conformational fluctuations, si milar to a few picoseconds, is much shorter than the time scale of dif fusion, so this leading term is useful for estimating (w(o) + w(c))(h) over cap(w(o) + w(c)). A further consequence of the disparity in time scales is that the value of (w(o) + w(c))(h) over cap(w(o) + w(c)) is much larger than k. As a result the decrease of the rate constant due to gating is relatively small (unless the entrance to the active site is closed nearly all the time). This suggests that a buried and gated active site may play the important role of controlling enzyme specifi city without sacrificing efficiency. (C) 1998 American Institute of Ph ysics.