Free Energy

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Substantial efforts have been devoted to characterize the above interesting phenomenon in the passed several years [7, 16-20, 26, 27]. Water distribution in the crystal structure of AQP1 has suggested the unlikelihood of proton transporting through the channel [7]. Molecular dynamics (MD) simulations utilizing the multi-state empirical valence bond (MS-EVB) model[23, 24, 28-31] have explained the originality of proton blocking behavior in the AQP1 channel [18, 19]. One free energy barrier for proton permeation in wild-type AQP1 originates from a constriction region, or the selectivity filter (SF) domain located at the extracellular pore mouth, which is composed of residue Phe56, His180, Cys189 and Arg195. This domain is also referred as the ar/R region since it provides an aromatic environment with restraints to the incoming solutes inside the protein. In wild-type AQP1, the ar/R region has a diameter of ~ 2 Å and allows the passage of only one water molecule thus a single file water wire is formed along the channel [18, 32]. Such constriction has contributed to the dehydration penalty for the excess proton to pass through [18, 19]. On the other hand, it is suggested that the electrostatic repulsive interaction arising from the positive charge on Arg195 also contributes to the proton permeation free energy barrier which is about 15 kcal/mol higher compared with the channel mouth region [18]. Additionally, a predominant obstacle preventing proton leakage comes from the collective macro-dipole at the Asn-Pro-Ala domain (NPA) located at the center of the channel. This NPA domain is slightly wider in diameter than the SF domain and is considered as fingerprint of the aquaporin family. The two oppositely orientated Asn-Pro-Ala sequence... ... middle of paper ... ... employed to construct a self-consistent potential of meach force (PMF) profile for cation permeation along the reaction coordinate, in each system. Since the channel diameter increases as the excess charge approaches the mouths regions that are close to the bulk water, to ensure that the accessible area of the cation in the x-y plane is similar to that inside the channel and the excess charge moves in a peusdo one-dimension system, additional radial restraints were applied to the cations at both the extracellecuear and cytoplasmic channel mouth regions where the single-file and the bulk water region meet [52]. Statistical error of the free energy curves were evaluated by dividing each umbrella sampling trajectories into two consequent blocks and estimating the standard diviation of the two PMFs calculated by using data from the first block and the second block.
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