Gauging of the PhoE channel by a single freely diffusing proton

In the present study we combined a continuum approximation with a detailed mapping of the electrostatic potential inside an ionic channel to define the most probable trajectory for proton propagation through the channel (propagation along a structure-supported trajectory (PSST)). The conversion of the three-dimensional diffusion space into propagation along a one-dimensional pathway permits reconstruction of an ion motion by a short calculation (a few seconds on a state-of-the-art workstation) rather than a laborious, time-consuming random walk simulations. The experimental system selected for testing the accuracy of this concept was the reversible dissociation of a proton from a single pyranine molecule (8-hydroxypyrene-1,2,3-trisulfonate) bound by electrostatic forces inside the PhoE ionic channel of the Escherichia coli outer membrane. The crystal structure coordinates were used for calculation of the intra-cavity electrostatic potential, and the reconstruction of the observed fluorescence decay curve was carried out using the dielectric constant of the intra-cavity space as an adjustable parameter. The fitting of past experimental observations (Shimoni, E., Y. Tsfadia, E. Nachliel, and M. Gutman. 1993. Biophys. J. 64:472-479) was carried out by a modified version of the Agmon geminate recombination program (Krissinel, E. B., and N. Agmon. 1996. J. Comp. Chem. 17:1085-1098), where the gradient of the electrostatic potential and the entropic terms were calculated by the PSST program. The best-fitted reconstruction of the observed dynamics was attained when the water in the cavity was assigned ε ≤ 55, corroborating the theoretical estimation of Sansom (Breed, J. R., I. D. Kerr, and M. S. P. Sansom. 1996. Biophys. J. 70:1643-1661). The dielectric constant calculated for reversed micelles of comparable size (Cohen, B., D. Huppert, K. M. Solntsev, Y. Tsfadia, E. Nachliel, and M. Gutman. 2002. JACS. 124:7539-7547) allows us to set a margin of ε = 50 ± 5.