Potential of Mean Force Calculations of Solute Permeation Across UT-B and AQP1: A Comparison between Molecular Dynamics and 3D-RISM

Abstract

Membrane channels facilitate the efficient and selective flux of various solutes across biological membranes. A common approach to investigate the selectivity of a channel has been the calculation of potentials of mean force (PMFs) for solute permeation across the pore. PMFs have been frequently computed from molecular dynamics (MD) simulations, yet the three-dimensional reference interaction site model (3D-RISM) has been suggested as a computationally efficient alternative to MD. Whether the two methods yield comparable PMFs for solute permeation has remained unclear. In this study, we calculated potentials of mean force for water, ammonia, urea, molecular oxygen, and methanol across the urea transporter B (UT-B) and aquaporin-1 (AQP1), using 3D-RISM, as well as using MD simulations and umbrella sampling. To allow direct comparison between the PMFs from 3D-RISM and MD, we ensure that all PMFs refer to a well-defined reference area in the bulk or, equivalently, to a well-defined density of channels in the membrane. For PMFs of water permeation, we found reasonable agreement between the two methods, with differences of ≲3 kJ mol. In contrast, we found stark discrepancies for the PMFs for all other solutes. Additional calculations confirm that discrepancies between MD and 3D-RISM are not explained by the choice for the closure relation, the definition the reaction coordinate (center of mass-based versus atomic site-based), details of the molecule force field, or fluctuations of the protein. Comparison of the PMFs suggests that 3D-RISM may underestimate effects from hydrophobic solute-channel interactions, thereby, for instance, missing the urea binding sites in UT-B. Furthermore, we speculate that the orientational averages inherent to 3D-RISM might lead to discrepancies in the narrow channel lumen. These findings suggest that current 3D-RISM solvers provide reasonable estimates for the PMF for water permeation, but that they are not suitable to study the selectivity of membrane channels with respect to uncharged nonwater solutes.

Water in Nanopores and Biological Channels: A Molecular Simulation Perspective

“… 399 A comparison of UT-B and Aqp1 revealed that despite their different folds, the pore constriction radius in both pores was <0.2 nm, presenting a central energetic barrier to water in UT-B of ∼10 kJ/mol. 398 …”

Biomolecular Simulations with the Three-Dimensional Reference Interaction Site Model with the Kovalenko-Hirata Closure Molecular Solvation Theory

“…Among other reports of biomolecular simulations using the 3D-RISM-KH theory, the effect of (micro-) solvent environments on amyloid structure and potential of mean force calculations of solute permeation across UT-B and AQP1 proteins provided further extension of the applications of the 3D-RISM-KH theory based molecular solvation [ 86 , 87 ].…”

Computational Studies of Small Molecule Permeation across Membrane Channels

“…The 3-Dimensional Reference Interaction-Site Model (3D-RISM) was presented as a fast and accurate method for computing PMFs for the permeation of different solutes across aquaporin channels by Phongphanphanee et al (2010) [99]. However, we compared the PMFs calculated with 3D-RISM to the PMFs calculated with Molecular Dynamics (MD) coupled with Umbrella Sampling (US), which is a widely and commonly used computational method to calculate PMFs, and concluded that 3D-RISM is not suitable to compute PMFs of solute permeation across protein channels [65].…”

“…In the crystal, selenourea is bound to S i and S o sites, for which independent computational studies revealed two free energy minima in the Potential of Mean Force (PMF). These urea binding sites are found at both sides of the S m region, in which a free energy maximum is observed [64,65]. Across this selectivity filter, urea permeates by establishing hydrogen bonds along the oxygen ladder without causing much perturbation to the channel (Figure 2.2).…”