Determinants of water permeability through nanoscopic hydrophilic channels

A hard sphere model for single-file water transport across biological membranes

We use Gürsey's statistical mechanics of a one-dimensional fluid to find a formula for theP f / P d ratio in the transport of hard spheres across a membrane through a narrow channel that can accommodate molecular movement only in single file. P f is the membrane permeability for osmotic flow and P d the permeability for exchange across the membrane in the absence of osmotic flow. The deviation of the ratio from unity indicates the degree of cooperative transport relative to ordinary diffusion of independent molecules. In contrast to an early idea thatP f / P d must be equal to the number of molecules in the channel, regardless of the physical nature of the interactions among the molecules, we find a functional dependence on the fractional occupancy of the length of the channel by the hard spheres. We also attempt a random walk calculation for P d individually, which gives a result for P f as well when combined with the ratio.

The physical basis of osmosis

Osmosis is an important force in all living organisms, yet the molecular basis of osmosis is widely misunderstood as arising from diffusion of water across a membrane separating solutions of differing osmolarities, and hence different water concentrations. In 1923, Peter Debye proposed a physical model for a semipermeable membrane emphasizing the repulsive forces between solute molecules and membrane that prevent the solute from entering the membrane. His work was hardly noticed at the time and slipped out of view. We show that Debye's analysis of van 't Hoff's law for osmotic equilibrium also provides a consistent and plausible mechanism for osmotic flow. A difference in osmolyte concentrations in solutions separated by a semipermeable membrane leads to different pressures at the two water-membrane interfaces because the total repulsive force between solute molecules and the membrane is different at the two interfaces. Water is therefore driven through the membrane for exactly the same reason that pure water flows in response to an imposed hydrostatic pressure difference. In this paper, we present the Debye model in both equilibrium and flow conditions. We point out its applicability regardless of the nature of the membrane with examples ranging from the predominantly convective flow of water through synthetic membranes and capillary walls to the purely diffusive flow of independent water molecules through a lipid bilayer and the flow of a single-file column of water molecules in narrow protein channels.

Tutorial for Stopped-Flow Water Flux Measurements: Why a Report about “Ultrafast Water Permeation through Nanochannels with a Densely Fluorous Interior Surface” Is Flawed

Millions of years of evolution have produced proteinaceous water channels (aquaporins) that combine perfect selectivity with a transport rate at the edge of the diffusion limit. However, Itoh et al. recently claimed in Science that artificial channels are 100 times faster and almost as selective. The published deflation kinetics of vesicles containing channels or channel elements indicate otherwise, since they do not demonstrate the facilitation of water transport. In an illustrated tutorial on the experimental basis of stopped-flow measurements, we point out flaws in data processing. In contrast to the assumption voiced in Science, individual vesicles cannot simultaneously shrink with two different kinetics. Moreover, vesicle deflation within the dead time of the instrument cannot be detected. Since flawed reports of ultrafast water channels in Science are not a one-hit-wonder as evidenced by a 2018 commentary by Horner and Pohl in Science, we further discuss the achievable limits of single-channel water permeability. After analyzing (i) diffusion limits for permeation through narrow channels and (ii) hydrodynamics in the surrounding reservoirs, we conclude that it is unlikely to fundamentally exceed the evolutionarily optimized water-channeling performance of the fastest aquaporins while maintaining near-perfect selectivity.

The Hidden Intricacies of Aquaporins: Remarkable Details in a Common Structural Scaffold

Evolution turned aquaporins (AQPs) into the most efficient facilitators of passive water flow through cell membranes at no expense of solute discrimination. In spite of a plethora of solved AQP structures, many structural details remain hidden. Here, by combining extensive sequence- and structural-based analysis of a unique set of 20 non-redundant high-resolution structures and molecular dynamics simulations of four representatives, key aspects of AQP stability, gating, selectivity, pore geometry, and oligomerization, with a potential impact on channel functionality, are identified. The general view of AQPs possessing a continuous open water pore is challenged and it is depicted that AQPs' selectivity is not exclusively shaped by pore-lining residues but also by the relative arrangement of transmembrane helices. Moreover, this analysis reveals that hydrophobic interactions constitute the main determinant of protein thermal stability. Finally, a numbering scheme of the conserved AQP scaffold is established, facilitating direct comparison of, for example, disease-causing mutations and prediction of potential structural consequences. Additionally, the results pave the way for the design of optimized AQP water channels to be utilized in biotechnological applications.

Osmotic and diffusive flows in single-file pores: new approach to modeling pore occupancy states

Background

The relation between osmotic permeability, P_f, diffusion permeability, P_d, and the number of water molecules, N_p, in the single-file membrane pore remains an open question. Theoretical analyses, empirical studies on aquaporins and nanotubes, and molecular dynamics simulations have yet to provide a consensus view.

Results

This paper presents a new combinatorial analysis of the different pore states formed from water molecules and the presence of a vacancy that differs from the several previous combinatorial approaches to analyzing pore states. It is the first such analysis to show that P_f / P_d = N_p. It is rooted in the concept of different classes of pore occupancy states, tracer states and tracer exit states, present in the pore. This includes pores with and without a single vacancy. The concepts of knock-on collisions and concerted Brownian fluctuations provide the mechanisms underlying the behaviors of the tracer and vacancy as each moves through the pore during osmotic or diffusive flow. It develops the important role of the knock-on collision mechanism for osmotic flow. An essential feature of the model is the presence, or absence, of a single vacancy in the pore. The vacancy slows down tracer translocation through the pore. Its absence facilitates osmotic flow.

Conclusions

The full pore states and the single vacancy states together with the knock-on and Brownian mechanisms account for the relative values of P_f and P_d during osmotic and diffusive flow through the single-file pore. The new approach to combinatorial analysis differs from previous approaches and is the first to show a simple intuitive basis for the relation P_f / P_d = N_p. This resolves a long persisting dichotomy.

PoreDesigner for tuning solute selectivity in a robust and highly permeable outer membrane pore

Monodispersed angstrom-size pores embedded in a suitable matrix are promising for highly selective membrane-based separations. They can provide substantial energy savings in water treatment and small molecule bioseparations. Such pores present as membrane proteins (chiefly aquaporin-based) are commonplace in biological membranes but difficult to implement in synthetic industrial membranes and have modest selectivity without tunable selectivity. Here we present PoreDesigner, a design workflow to redesign the robust beta-barrel Outer Membrane Protein F as a scaffold to access three specific pore designs that exclude solutes larger than sucrose (>360 Da), glucose (>180 Da), and salt (>58 Da) respectively. PoreDesigner also enables us to design any specified pore size (spanning 3-10 Å), engineer its pore profile, and chemistry. These redesigned pores may be ideal for conducting sub-nm aqueous separations with permeabilities exceeding those of classical biological water channels, aquaporins, by more than an order of magnitude at over 10 billion water molecules per channel per second.

Model of osmosis in a single-file pore

Single-file transport of water and other small molecules through narrow pores in osmosis has drawn considerable attention in recent years due to its extensive application in biology and industry. In this work, we propose a discrete model to describe nonideal osmosis through single-file pores. Every site is assumed to be occupied by a molecule according to experiments and simulations. Hence, a dense chain can always be found, and collective hopping is the only movement method enabling the molecular chain to move. The roles of solute in osmosis are clarified in this model. Those molecules reflected at the pore entrance produce osmotic pressure, and those inside the pore contribute to the flow resistance of the molecular chain. The solute molecules that can enter the pore but cannot penetrate it may significantly reduce the osmotic flux, although they are all rejected by the pore. This conclusion can help to clarify the emerging debate about whether the reflection coefficient of the fully rejected solute can be less than 1. The design of highly efficient membrane pores may also benefit from this study.

Water Determines the Structure and Dynamics of Proteins

Water is an essential participant in the stability, structure, dynamics, and function of proteins and other biomolecules. Thermodynamically, changes in the aqueous environment affect the stability of biomolecules. Structurally, water participates chemically in the catalytic function of proteins and nucleic acids and physically in the collapse of the protein chain during folding through hydrophobic collapse and mediates binding through the hydrogen bond in complex formation. Water is a partner that slaves the dynamics of proteins, and water interaction with proteins affect their dynamics. Here we provide a review of the experimental and computational advances over the past decade in understanding the role of water in the dynamics, structure, and function of proteins. We focus on the combination of X-ray and neutron crystallography, NMR, terahertz spectroscopy, mass spectroscopy, thermodynamics, and computer simulations to reveal how water assist proteins in their function. The recent advances in computer simulations and the enhanced sensitivity of experimental tools promise major advances in the understanding of protein dynamics, and water surely will be a protagonist.

Water and ion permeability of a claudin model: A computational study

At present, the three-dimensional structure of the multimeric paracellular claudin pore is unknown. Using extant biophysical data concerning the size of the pore and permeation of water and cations through it, two three-dimensional models of the pore are constructed in silico. Molecular Dynamics (MD) calculations are then performed to compute water and sodium ion permeation fluxes under the influence of applied hydrostatic pressure. Comparison to experiment is made, under the assumption that the hydrostatic pressure applied in the simulations is equivalent to osmotic pressure induced in experimental measurements of water/ion permeability. One model, in which pore-lining charged is distributed evenly over a selectivity filter section 10-16 Å in length, is found to be generally consistent with experimental data concerning the dependence of water and ion permeation on channel pore diameter, pore length, and the sign and magnitude of pore lining charge. The molecular coupling mechanism between water and ion flow under conditions where hydrostatic pressure is applied is computationally elucidated.

Structural determinants of water permeation through the sodium-galactose transporter vSGLT

Sodium-glucose transporters (SGLTs) facilitate the movement of water across the cell membrane, playing a central role in cellular homeostasis. Here, we present a detailed analysis of the mechanism of water permeation through the inward-facing state of vSGLT based on nearly 10 μs of molecular dynamics simulations. These simulations reveal the transient formation of a continuous water channel through the transporter that permits water to permeate the protein. Trajectories in which spontaneous release of galactose is observed, as well as those in which galactose remains in the binding site, show that the permeation rate, although modulated by substrate occupancy, is not tightly coupled to substrate release. Using a, to our knowledge, novel channel-detection algorithm, we identify the key residues that control water flow through the transporter and show that solvent gating is regulated by side-chain motions in a small number of residues on the extracellular face. A sequence alignment reveals the presence of two insertion sites in mammalian SGLTs that flank these outer-gate residues. We hypothesize that the absence of these sites in vSGLT may account for the high water permeability values for vSGLT determined via simulation compared to the lower experimental estimates for mammalian SGLT1.

Equilibrium and dynamic osmotic behaviour of aqueous solutions with varied concentration at constant and variable volume

Osmosis is essential for the living organisms. In biological systems the process usually occurs in confined volumes and may express specific features. The osmotic pressure in aqueous solutions was studied here experimentally as a function of solute concentration (0.05-0.5 M) in two different regimes: of constant and variable solution volume. Sucrose, a biologically active substance, was chosen as a reference solute for the complex tests. A custom made osmotic cell was used. A novel operative experimental approach, employing limited variation of the solution volume, was developed and applied for the purpose. The established equilibrium values of the osmotic pressure are in agreement with the theoretical expectations and do not exhibit any evident differences for both regimes. In contrast, the obtained kinetic dependences reveal striking divergence in the rates of the process at constant and varied solution volume for the respective solute concentrations. The rise of pressure is much faster at constant solution volume, while the solvent influx is many times greater in the regime of variable volume. The results obtained suggest a feasible mechanism for the way in which the living cells rapidly achieve osmotic equilibrium upon changes in the environment.

Energetic and molecular water permeation mechanisms of the human red blood cell urea transporter B

Urea transporter B (UT-B) is a passive membrane channel that facilitates highly efficient permeation of urea. In red blood cells (RBC), while the major function of UT-B is to transport urea, it is assumed that this protein is able to conduct water. Here, we have revisited this last issue by studying RBCs and ghosts from human variants with defects of aquaporin 1 (AQP1) or UT-B. We found that UT-B's osmotic water unit permeability (pfunit) is similar to that of AQP1. The determination of diffusional permeability coefficient (Pd) allowed the calculation of the Pf/Pd ratio, which is consistent with a single-file water transport. Molecular dynamic simulations of water conduction through human UT-B confirmed the experimental finding. From these results, we propose an atomistic description of water-protein interactions involved in this permeation. Inside the UT-B pore, five water molecules were found to form a single-file and move rapidly along a channel by hydrogen bond exchange involving two critical threonines. We further show that the energy barrier for water located in the central region coincides with a water dipole reorientation, which can be related to the proton exclusion observed experimentally. In conclusion, our results indicate that UT-B should be considered as a new member of the water channel family.

Aquaporins: another piece in the osmotic puzzle

Osmolarity not only plays a key role in cellular homeostasis but also challenges cell survival. The molecular understanding of osmosis has not yet been completely achieved, and the discovery of aquaporins as molecular entities involved in water transport has caused osmosis to again become a focus of research. The main questions that need to be answered are the mechanism underlying the osmotic permeability coefficients and the extent to which aquaporins change our understanding of osmosis. Here, attempts to answer these questions are discussed. Critical aspects of the state of the state of knowledge on osmosis, a topic that has been studied since 19th century, are reviewed and integrated with the available information provided by in vivo, in vitro and in silico approaches.

Biomimetic design of a brush-like nanopore: simulation studies

Combining a high degree of selectivity and nanoscale dimensions, biological pores are attractive potential components for nanotechnology devices and applications. Biomimetic design will facilitate production of stable synthetic nanopores with defined functionality. Bacterial porins offer a good source of possible templates for such nanopores as they form stable, selective pores in lipid bilayers. Molecular dynamics simulations have been used to design simple model nanopores with permeation free energy profiles that can be made to mimic a template protein, the OprP porin, which forms pores selective for anions. In particular, we explored the effects of varying the nature of pore-lining groups on free energy profiles for phosphate and chloride ions along the pore axis and the total charge of the permeation pathway of the pore. Cationic side chains lining the model nanopore are required to model the local detail of the OprP permeation landscape, whereas the total charge contributes to its magnitude. These studies indicate that a locally accurate biomimetic design has captured the essentials of the structure/function relationship of the parent protein.

Water Transport through Nanotubes with Varying Interaction Strength between Tube Wall and Water

We present the results from extensive molecular dynamics simulations to study the effect of varying interaction strength, ε_NT-OW, between the nanotube atoms and water's oxygen atom. We find the existence of a narrow transition region (ε_NT-OW ≈ 0.05 - 0.075 kcal/mol) in which water occupancy within a nanotube and flux through it increases dramatically with increasing ε_NT-OW, with the exact location defined by nanotube diameter and length. This transition region narrows with increasing nanotube diameter to nearly a step-change in water transport from no flow to high water flux between ε_NT-OW= 0.05 kcal/mol to 0.055 kcal/mol for tube diameter 1.6 nm. Interestingly, this transition region (ε_NT-OW= 0.05 - 0.075 kcal/mol) also coincides with water contact angles close to 90° on an unrolled nanotube surface hinting at a fundamental link between nanotube wetting characteristics and water transport through it. Finally, we find that the observed water flux is proportional to the average water occupancy divided by the average residence time within the nanotube, with a proportionality constant found to be 0.36, independent of the nanotube diameter and length.

Single-file water in nanopores

Water molecules confined to pores with sub-nanometre diameters form single-file hydrogen-bonded chains. In such nanoscale confinement, water has unusual physical properties that are exploited in biology and hold promise for a wide range of biomimetic and nanotechnological applications. The latter can be realized by carbon and boron nitride nanotubes which confine water in a relatively non-specific way and lend themselves to the study of intrinsic properties of single-file water. As a consequence of strong water-water hydrogen bonds, many characteristics of single-file water are conserved in biological and synthetic pores despite differences in their atomistic structures. Charge transport and orientational order in water chains depend sensitively on and are mainly determined by electrostatic effects. Thus, mimicking functions of biological pores with apolar pores and corresponding external fields gives insight into the structure-function relation of biological pores and allows the development of technical applications beyond the molecular devices found in living systems. In this Perspective, we revisit results for single-file water in apolar pores, and examine the similarities and the differences between these simple systems and water in more complex pores.

Proton transport in biological systems can be probed by two-dimensional infrared spectroscopy

We propose a new method to determine the proton transfer (PT) rate in channel proteins by two-dimensional infrared (2DIR) spectroscopy. Proton transport processes in biological systems, such as proton channels, trigger numerous fundamental biochemical reactions. Due to the limitation in both spatial and time resolution of the traditional experimental approaches, describing the whole proton transport process and identifying the rate limiting steps at the molecular level is challenging. In the present paper, we focus on proton transport through the Gramicidin A channel. Using a kinetic PT model derived from all-atom molecular dynamics simulations, we model the amide I region of the 2DIR spectrum of the channel protein to examine its sensitivity to the proton transport process. We demonstrate that the 2DIR spectrum of the isotope-labeled channel contain information on the PT rate, which may be extracted by analyzing the antidiagonal linewidth of the spectral feature related to the labeled site. Such experiments in combination with detailed numerical simulations should allow the extraction of site dependent PT rates, providing a method for identifying possible rate limiting steps for proton channel transfer.

Water nanoconfinement induced thermal enhancement at hydrophilic quartz interfaces

We report the effect of water nanoconfinement on the thermal transport properties of two neighbor hydrophilic quartz interfaces. A significant increase and a nonintuitive, nonmonotonic dependence of the overall interfacial thermal conductance between the quartz surfaces on the water layer thickness were found. By probing the interfacial structure and vibrational properties of the connected components, we demonstrated that the mechanism of the peak occurring at submonolayer water originates from the freezing of water molecules at extremely confined conditions and the excellent match of vibrational states between trapped water and hydrophilic headgroups on the two contact surfaces. Our results show that incorporation of polar molecules into hydrophilic interfaces is very promising to enhance the thermal transport through thermally smooth connection of these interfaces.