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 epsilon less than or equal to 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 epsilon = 50 +/- 5.