Computational Studies of Small Molecule Permeation across Membrane Channels

Abstract

Membrane channels are an essential part of any life form. They conduct the selective flux across the cell membrane of many important molecules that would otherwise not permeate. Experimental studies on membrane channels have led to the structural and functional characterization of many of them, yet many underlying physico-chemical mechanisms are somewhat out of reach. The aim of this thesis is to gain quantitative understanding on the structural and functional properties of these proteins by means of computational methods, such as Molecular Dynamics (MD) and free energy calculations. One of the most common approaches to study the selectivity and permeation mechanisms of a channel is the calculation of the Potential of Mean Force (PMF) for solute permeation across the pore. Usually, PMFs are calculated via MD simulations, which requires a significant amount of computational power. Hence, we compared the capability of MD with that of 3-Dimensional Reference Interaction-Site Model (3D-RISM), allegedly as accurate as MD but much more computationally efficient, to compute PMFs of solute permeation across Urea Transporter B (UT-B) and Aquaporin 1 (AQP1). We found a remarkable agreement between the PMFs for water permeation calculated from both techniques. However, for the rest of tested solutes, namely ammonia, urea, molecular oxygen, and methanol, we found critical discrepancies between 3D-RISM and with MD, which were found to be independent of the closure relation, the choice of the reaction coordinate, or the fluctuations of the protein. This suggests that, whilst 3D-RISM may provide reasonable approximations on PMFs for the permeation of water, it is not appropriate to study the permeation of uncharged non-water solutes. We further investigated, via a combination of MD simulations and free energy calculations, the structure and function of the fluoride-specific channel Fluc-Bpe. The free energy calculations allowed us to ascertain the specific nature of five isolated electron densities found in the crystal structure of Fluc, four of which were provisionaly assigned to fluoride, and the remaining one to sodium. We conducted two different kinds of binding free energy calculations: i) relative binding free energy differences ∆∆Gbind, and ii) absolute binding free energy ∆Gbind. Notably, the calculation of ∆∆Gbind allowed us to determine, between two putative molecular species, namely water and fluoride, which species was more likely to bind at a certain binding site. The resulting free energies were partly dependent on fluoride-phenylalanine interactions, which we found to be underestimated by ~ 30 kJ mol-1 in current additive force-fields. Thus, the disctimination of one species over the other was only possible because the ∆∆Gbind. values largely deviated from zero. In turn, the calculation of ∆Gbind allowed us to confirm whether a certain species would bind per se to Fluc-Bpe. Besides, short, free MD simulations proved to be key to assess the structural stability of the channel in different conditions, which, together with the free energy calculations, indicated that the four densities assigned to fluoride rather corresponded to ordered water molecules, and that the last electron density corresponded to a structural sodium. We finally evaluated, using MD simulations, the response of Fluc-Bpe to the presence of fluoride ions restrained at the permeating pore. The results suggested that the channel would undergo an opening transition, after which water molecules enter the pore to solvate the ions. Then, we calculated the PMFs for the permeation of water, fluoride and chloride using Umbrella Sampling (US) simulations. The profiles of solute permeation across the open structure indicated that water, fluoride, chloride would efficiently permeate the channel, being in stark contrast with the experimental evidence, which demonstrates that Fluc channels permeate fluoride by a ~ 100-fold ratio over chloride. We suspect that our results might be affected by the inaccurate modelling of ion-protein contacts highlighted before. The proper modelling of ion-protein interactions is extremely important for the establishment of salt-bridges, the structural stability of proteins, or the permeation of ions. Therefore, we conclude that our results regarding the permeation mechanism in Fluc-Bpe mainly reflect the imperfections of current additive force-fields, and that the usage of polarizable force-fields and development of accurate ion-protein interactions may certainly aid future research.