The barrier for proton transport in aquaporins as a challenge for electrostatic models: The role of protein relaxation in mutational calculations

Abstract

The origin of the barrier for proton transport through the aquaporin channel is a problem of general interest. It is becoming increasingly clear that this barrier is not attributable to the orientation of the water molecules across the channel but rather to the electrostatic penalty for moving the proton charge to the center of the channel. However, the reason for the high electrostatic barrier is still rather controversial. It has been argued by some workers that the barrier is due to the so-called NPA motif and/or to the helix macrodipole or to other specific elements. However, our works indicated that the main reason for the high barrier is the loss of the generalized solvation upon moving the proton charge from the bulk to the center of the channel and that this does not reflect a specific repulsive electrostatic interaction but the absence of sufficient electrostatic stabilization. At this stage it seems that the elucidation and clarification of the origin of the electrostatic barrier can serve as an instructive test case for electrostatic models. Thus, we reexamine the free-energy surface for proton transport in aquaporins using the microscopic free-energy perturbation/umbrella sampling (FEP/US) and the empirical valence bond/umbrella sampling (EVB/US) methods as well as the semimacroscopic protein dipole Langevin dipole model in its linear response approximation version (the PDLD/S-LRA). These extensive studies help to clarify the nature of the barrier and to establish the "reduced solvation effect" as the primary source of this barrier. That is, it is found that the barrier is associated with the loss of the generalized solvation energy (which includes of course all electrostatic effects) upon moving the proton charge from the bulk solvent to the center of the channel. It is also demonstrated that the residues in the NPA region and the helix dipole cannot be considered as the main reasons for the electrostatic barrier. Furthermore, our microscopic and semimacroscopic studies clarify the problems with incomplete alternative calculations, illustrating that the effects of various electrostatic elements are drastically overestimated by macroscopic calculations that use a low dielectric constant and do not consider the protein reorganization. Similarly, it is pointed out that microscopic potential of mean force calculations that do not evaluate the electrostatic barrier relative to the bulk water cannot be used to establish the origin of the electrostatic barrier. The relationship between the present study and calculations of pK(a)s in protein interiors is clarified, pointing out that approaches that are applied to study the aquaporin barrier should be validated by pK(a)s calculations. Such calculations also help to clarify the crucial role of solvation energies in establishing the barrier in aquaporins.

Computational Study of the pKaValues of Potential Catalytic Residues in the Active Site of Monoamine Oxidase B

“…The starting point for our calculations was the high--resolution (1.6 Å) X--ray structure of MAO B in complex with 2--(2--benzofuranyl)--2--imidazoline), 13 pK a calculations were performed using the semi--macroscopic protein dipole / Langevin dipole approach of Warshel and coworkers, in its linear response approximation version (PDLD/S--LRA), 49,[54][55][56] To parameterize the charge distribution of oxidized FAD and dopamine, electrostatic potential derived atomic charges were obtained on the optimized structures at the (PCM)/B3LYP/6-31G(d) level of theory in conjunction with the UFF radii as implemented in Gaussian09 program. 57 The essence of the PDLD/LRA pK a calculation is to convert the problem of evaluating a pK a in a protein to evaluation of the change in "solvation" energy associated with moving the charge from water to the protein.…”

Electrostatic basis for the unidirectionality of the primary proton transfer in cytochrome c oxidase

“…The protein was surrounded by a simplified polarizable membrane, as was done in ref. 23. Ionizable groups were kept at their ionization states in water, except for groups near the main simulation region, where we determined the relevant pK as by the PDLD/S-LRA approach.…”

“…The simulation system represented the membrane by a grid of induced dipoles (e.g., see ref. 23) that were treated explicitly in our polarizable model. The FEP/AC simulations were performed with 51 frames to transform the system between different charged states, where each frame included 80 ps of simulation with 1-fs time steps.…”

“…Note that free energies obtained with the empirical valence bond (EVB) that represent the actual PT process and those obtained with the FEP charging are fully correlated (23). Thus, we adapted here a specialized approach using the regular EVB umbrella sampling (EVB/US) approach (see Methods) to generate the shape of the free energy surfaces but adjusting the PT free energies (by changing the so-called ''EVB gas-phase shifts'' discussed in Methods) to reproduce the PDLD/S-LRA estimates (see SI Text).…”

“…In this respect it is crucial to clarify that we are not dealing with the water orientation effect, which is rather trivial (see references in ref. 23) but rather with the free energy of inserting water molecules in the given PT path.…”