The most probable trajectory for ion flux through large-pore channel

Large-pore channels are β-barrel proteins that transverse the bacterial outer membrane, forming partially selective pores that are ∼50 Å long and ∼30 Å wide. Through these proteins, whose structures were determined up to 2 Å resolution, small solutes permeate into the periplasmic space of the bacteria. In the present study, we investigated the propagation of ions inside the channel space using a combination of sub-nanosecond time-resolved fluorescence measurements and numeric reconstruction of propagation dynamics in order to characterize the properties of the diffusion space inside the channel. The experimental system consisted of the insertion of a single pyranine molecule at the center of the ion-conducting large-pore channel protein (PhoE) and synchronous dissociation of the pyranine molecules by a laser flash. Time-resolved fluorescence monitored the recombination of the excited pyranine anion with the released proton. The electrostatic potential inside the ion-conducting channel was calculated by the DelPhi program, using as input the three-dimensional structure of the protein. The propagation of the proton in the diffusion space was carried out stepwise; first the most probable trajectory was defined, thus reducing the system into an 1D diffusion problem. Once the trajectory was determined, the variation of the entropy along the propagation pathway was calculated. The gradients of the electrostatic potential and the entropy were combined into a transition probability term that determined the probability of a proton to propagate along the trajectory. The propagation algorithm was used sequentially, with the intra-cavity dielectric constant as an adjustable parameter, until the calculated dynamics were super-positioned over the experimental signal. The dielectric constant of the aqueous space inside the channel has a value of ε_intra-cavity=50±5. The validity of the procedure was tested by applying the same algorithms for calculating the passage time of positive and negative charges through five proteins of the large-pore channel family. The calculated first passage times were within ±50% of the experimentally determined mean passage times reported in the literature.