Not only enthalpy: large entropy contribution to ion permeation barriers in single-file channels

The effect of channel length on the barrier for potassium ion permeation through single-file channels has been studied by means of all-atom molecular dynamics simulations. Using series of peptidic gramicidin-like and simplified ring-structured channels, both embedded in model membranes, we obtained two distinct types of behavior: saturation of the central free energy barriers for peptidic channels and a linear increase in simplified ring-structured channels with increasing channel length. The saturation of the central free energy barrier for the peptidic channels occurs at relatively short lengths, and it is correlated with the desolvation from the bulk water. Remarkably, decomposition of free energy barriers into enthalpic and entropic terms reveals an entropic cost for ion permeation. Furthermore, this entropic cost dominates the ion permeation free energy barrier, since the corresponding free energy contribution is higher than the enthalpic barrier. We conclude that the length dependence of the free energy is enthalpy-dominated, but the entropy is the major contribution to the permeation barrier. The decrease in rotational water motion and the reduction of channel mobility are putative origins for the overall entropic penalty.     

Determinants of Water Permeability through Nanoscopic Hydrophilic Channels

Naturally occurring pores show a variety of polarities and sizes that are presumably directly linked to their biological function. Many biological channels are selective toward permeants similar or smaller in size than water molecules, and therefore their pores operate in the regime of single-file water pores. Intrinsic factors affecting water permeability through such pores include the channel-membrane match, the structural stability of the channel, the channel geometry and channel-water affinity. We present an extensive molecular dynamics study on the role of the channel geometry and polarity on the water osmotic and diffusive permeability coefficients. We show that the polarity of the naturally occurring peptidic channels is close to optimal for water permeation, and that the water mobility for a wide range of channel polarities is essentially length independent. By systematically varying the geometry and polarity of model hydrophilic pores, based on the fold of gramicidin A, the water density, occupancy, and permeability are studied. Our focus is on the characterization of the transition between different permeation regimes in terms of the structure of water in the pores, the average pore occupancy and the dynamics of the permeating water molecules. We show that a general relationship between osmotic and diffusive water permeability coefficients in the single-file regime accounts for the time averaged pore occupancy, and that the dynamics of the permeating water molecules through narrow non single file channels effectively behaves like independent single-file columns.     

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. Proteins 2016; 84:305–315. © 2016 Wiley Periodicals, Inc.     

CHAP: A Versatile Tool for the Structural and Functional Annotation of Ion Channel Pores

The control of ion channel permeation requires the modulation of energetic barriers or “gates” within their pores. However, such barriers are often simply identified from the physical dimensions of the pore. Such approaches have worked well in the past, but there is now evidence that the unusual behavior of water within narrow hydrophobic pores can produce an energetic barrier to permeation without requiring steric occlusion of the pathway. Many different ion channels have now been shown to exploit “hydrophobic gating” to regulate ion flow, and it is clear that new tools are required for more accurate functional annotation of the increasing number of ion channel structures becoming available. We have previously shown how molecular dynamics simulations of water can be used as a proxy to predict hydrophobic gates, and we now present a new and highly versatile computational tool, the Channel Annotation Package (CHAP) that implements this methodology.     

Permeation of water through the KcsA K+ channel

Previous studies have reported that the KcsA potassium channel has an osmotic permeability coefficient of 4.8 x 10(-12) cm3/s, giving it a significantly higher osmotic permeability coefficient than that of some membrane channels specialized in water transport. This high osmotic permeability is proposed to occur when the channel is depleted of potassium ions, the presence of which slow down the water permeation process. The atomic structure of the potassium-depleted KcsA channel and the mechanisms of water permeation have not been well characterized so far. Here, all-atom molecular dynamics simulations, in conjunction with an umbrella sampling strategy and a nonequilibrium approach to simulate pressure gradients are employed to illustrate the permeation of water in the absence of ions through the KcsA K+ channel. Equilibrium molecular dynamics simulations (95 ns combined total length) identified a possible structure of the potassium-depleted KcsA channel, and umbrella sampling calculations (160 ns combined total length) revealed that this structure is not permeable by water molecules moving along the channel axis. The simulation of a pressure gradient across the channel (30 ns combined total length) identified an alternative permeation pathway with a computed osmotic permeability of approximately (2.7 +/- 0.9) x 10(-13) cm3/s. Water fluxes along this pathway did not proceed through collective water motions or transitions to vapor state. All of the major results of this study were robust against variations in a wide set of simulation parameters (force field, water model, membrane model, and channel conformation).     

Does CO2 permeate through aquaporin-1?

Aquaporins facilitate water permeation across biological membranes. Additionally, glycerol and other small neutral solutes are permeated by related aquaglyceroporins. The role of aquaporins in gas permeation has been a long-standing and controversially discussed issue. We present an extensive set of atomistic molecular dynamics simulations that address the question of CO(2) permeation through human aquaporin-1. Free energy profiles derived from the simulations display a barrier of approximately 23 kJ/mol in the aromatic/arginine constriction region of the water pore, whereas a barrier of approximately 4 kJ/mol was observed for a palmitoyloleoylphosphatidylethanolamine lipid bilayer membrane. The results indicate that significant aquaporin-1-mediated CO(2) permeation is to be expected only in membranes with a low intrinsic CO(2) permeability.     

Exploring gas permeability of cellular membranes and membrane channels with molecular dynamics

Aquaporins are a family of membrane proteins specialized in rapid water conduction across biological membranes. Whether these channels also conduct gas molecules and the physiological significance of this potential function have not been well understood. Here we report 140 ns of molecular dynamics simulations of membrane-embedded AQP1 and of a pure POPE bilayer addressing these questions. The permeability of AQP1 to two types of gas molecules, O2 and CO2, was investigated using two complementary methods, namely, explicit gas diffusion simulation and implicit ligand sampling. The simulations show that the central (tetrameric) pore of AQP1 can be readily used by either gas molecule to permeate the channel. The two approaches produced similar free energy profiles associated with gas permeation through the central pore: a -0.4 to -1.7 kcal/mol energy well in the middle, and a 3.6-4.6 kcal/mol energy barrier in the periplasmic vestibule. The barrier appears to be mainly due to a dense cluster of water molecules anchored in the periplasmic mouth of the central pore by four aspartate residues. Water pores show a very low permeability to O2, but may contribute to the overall permeation of CO2 due to its more hydrophilic nature. Although the central pore of AQP1 is found to be gas permeable, the pure POPE bilayer provides a much larger cross-sectional area, thus exhibiting a much lower free energy barrier for CO2 and O2 permeation. As such, gas conduction through AQP1 may only be physiologically relevant either in membranes of low gas permeability, or in cells where a major fraction of the cellular membrane is occupied by AQPs.     

Mechanism of anionic conduction across ClC

ClC chloride channels are voltage-gated transmembrane proteins that have been associated with a wide range of regulatory roles in vertebrates. To accomplish their function, they allow small inorganic anions to efficiently pass through, while blocking the passage of all other particles. Understanding the conduction mechanism of ClC has been the subject of many experimental investigations, but until now, the detailed dynamic mechanism was not known despite the availability of crystallographic structures. We investigate Cl(-) conduction by means of an all-atom molecular dynamics simulation of the ClC channel in a membrane environment. Based on our simulation results, we propose a king-of-the-hill mechanism for permeation, in which a lone ion bound to the center of the ClC pore is pushed out by a second ion that enters the pore and takes its place. Although the energy required to extract the single central ion from the pore is enormous, by resorting to this two-ion process, the largest free energy barrier for conduction is reduced to 4 kcal/mol. At the narrowest part of the pore, residues Tyr-445 and Ser-107 stabilize the central ion. There, the bound ion blocks the pore, disrupting the formation of a continuous water file that could leak protons, possibly preventing the passage of uncharged solutes.     

Molecular simulation of permeation behaviour of ethanol/water molecules with single-layer graphene oxide membranes

Graphene oxide (GO)-based materials have shown promise as water-permeating membranes in pervaporation separation. However, the feed permeation and surface affinity of single-layer nanoporous GO sheet for liquid mixtures remain unresolved. Here, the pressure-driven molecular transport of pure ethanol and pure water, as well ethanol-water mixtures, crossing through single-layer nanoporous GO sheet was studied by non-equilibrium molecular dynamics simulations. We show that single-layer GO sheet with controlled pore sizes can effectively reject ethanol and allow water permeation with high permeability. This means that porous GO sheets could act as an effective dehydration membrane, therefore providing the initial barrier for ethanol passage in GO-based membrane. The pore size effect was considered as the separation mechanism. Both ethanol and water molecules in the mixture show comparable affinity with GO surfaces. The hydrogen-bonding coupling interaction between mixture and surface functional groups provide addition influence on the molecular transport through GO pores.     

The influence of geometry, surface character, and flexibility on the permeation of ions and water through biological pores

A hydrophobic constriction site can act as an efficient barrier to ion and water permeation if its diameter is less than the diameter of an ion's first hydration shell. This hydrophobic gating mechanism is thought to operate in a number of ion channels, e.g. the nicotinic receptor, bacterial mechanosensitive channels (MscL and MscS) and perhaps in some potassium channels (e.g. KcsA, MthK and KvAP). Simplified pore models allow one to investigate the primary characteristics of a conduction pathway, namely its geometry (shape, pore length, and radius), the chemical character of the pore wall surface, and its local flexibility and surface roughness. Our extended (about 0.1 micros) molecular dynamic simulations show that a short hydrophobic pore is closed to water for radii smaller than 0.45 nm. By increasing the polarity of the pore wall (and thus reducing its hydrophobicity) the transition radius can be decreased until for hydrophilic pores liquid water is stable down to a radius comparable to a water molecule's radius. Ions behave similarly but the transition from conducting to non-conducting pores is even steeper and occurs at a radius of 0.65 nm for hydrophobic pores. The presence of water vapour in a constriction zone indicates a barrier for ion permeation. A thermodynamic model can explain the behaviour of water in nanopores in terms of the surface tensions, which leads to a simple measure of 'hydrophobicity' in this context. Furthermore, increased local flexibility decreases the permeability of polar species. An increase in temperature has the same effect, and we hypothesize that both effects can be explained by a decrease in the effective solvent-surface attraction which in turn leads to an increase in the solvent-wall surface free energy.     

Water and deuterium oxide permeability through aquaporin 1: MD predictions and experimental verification

Determining the mechanisms of flux through protein channels requires a combination of structural data, permeability measurement, and molecular dynamics (MD) simulations. To further clarify the mechanism of flux through aquaporin 1 (AQP1), osmotic p(f) (cm(3)/s/pore) and diffusion p(d) (cm(3)/s/pore) permeability coefficients per pore of H(2)O and D(2)O in AQP1 were calculated using MD simulations. We then compared the simulation results with experimental measurements of the osmotic AQP1 permeabilities of H(2)O and D(2)O. In this manner we evaluated the ability of MD simulations to predict actual flux results. For the MD simulations, the force field parameters of the D(2)O model were reparameterized from the TIP3P water model to reproduce the experimentally observed difference in the bulk self diffusion constants of H(2)O vs. D(2)O. Two MD systems (one for each solvent) were constructed, each containing explicit palmitoyl-oleoyl-phosphatidyl-ethanolamine (POPE) phospholipid molecules, solvent, and AQP1. It was found that the calculated value of p(f) for D(2)O is approximately 15% smaller than for H(2)O. Bovine AQP1 was reconstituted into palmitoyl-oleoyl-phosphatidylcholine (POPC) liposomes, and it was found that the measured macroscopic osmotic permeability coefficient P(f) (cm/s) of D(2)O is approximately 21% lower than for H(2)O. The combined computational and experimental results suggest that deuterium oxide permeability through AQP1 is similar to that of water. The slightly lower observed osmotic permeability of D(2)O compared to H(2)O in AQP1 is most likely due to the lower self diffusion constant of D(2)O.     

Single-channel water permeabilities of Escherichia coli aquaporins AqpZ and GlpF

From equilibrium molecular dynamics simulations we have determined single-channel water permeabilities for Escherichia coli aquaporin Z (AqpZ) and aquaglyceroporin GlpF with the channels embedded in lipid bilayers. GlpF's osmotic water permeability constant pf exceeds by 2-3 times that of AqpZ and the diffusive permeability constant (pd) of GlpF is found to exceed that of AqpZ 2-9-fold. Achieving complete water selectivity in AqpZ consequently implies lower transport rates overall relative to the less selective, wider channel of GlpF. For AqpZ, the ratio pf/pd congruent with 12 is close to the average number of water molecules in the channel lumen, whereas for GlpF, pf/pd congruent with 4. This implies that single-file structure of the luminal water is more pronounced for AqpZ, the narrower channel of the two. Electrostatics profiles across the pore lumens reveal that AqpZ significantly reinforces water-channel interactions, and weaker water-water interactions in turn suppress water-water correlations relative to GlpF. Consequently, suppressed water-water correlations across the narrow selectivity filter become a key structural determinant for water permeation causing luminal water to permeate slower across AqpZ.     

Cooperativity and allostery in aquaporin 0 regulation by Ca2+

Aquaporin 0 (AQP0) is essential for eye lens homeostasis as is regulation of its water permeability by Ca²⁺, which occurs through interactions with calmodulin (CaM), but the underlying molecular mechanisms are not well understood. Here, we use molecular dynamics (MD) simulations on the microsecond timescale under an osmotic gradient to explicitly model water permeation through the AQP0 channel. To identify any structural features that are specific to water permeation through AQP0, we also performed simulations of aquaporin 1 (AQP1) and a pure mixed lipid bilayer under the same conditions. The relative single-channel water osmotic permeability coefficients (p_f) calculated from all of our simulations are in reasonable agreement with experiment. Our simulations allowed us to characterize the dynamics of the key structural elements that modulate the diffusion of water single-files through the AQP0 and AQP1 pores. We find that CaM binding influences the collective dynamics of the whole AQP0 tetramer, promoting the closing of both the extracellular and intracellular gates by inducing cooperativity between neighboring subunits.     

Water transport in aquaporins: osmotic permeability matrix analysis of molecular dynamics simulations

Single-channel osmotic water permeability (p(f)) is a key quantity for investigating the transport capability of the water channel protein, aquaporin. However, the direct connection between the single scalar quantity p(f) and the channel structure remains unclear. In this study, based on molecular dynamics simulations, we propose a p(f)-matrix method, in which p(f) is decomposed into contributions from each local region of the channel. Diagonal elements of the p(f) matrix are equivalent to the local permeability at each region of the channel, and off-diagonal elements represent correlated motions of water molecules in different regions. Averaging both diagonal and off-diagonal elements of the p(f) matrix recovers p(f) for the entire channel; this implies that correlated motions between distantly-separated water molecules, as well as adjacent water molecules, influence the osmotic permeability. The p(f) matrices from molecular dynamics simulations of five aquaporins (AQP0, AQP1, AQP4, AqpZ, and GlpF) indicated that the reduction in the water correlation across the Asn-Pro-Ala region, and the small local permeability around the ar/R region, characterize the transport efficiency of water. These structural determinants in water permeation were confirmed in molecular dynamics simulations of three mutants of AqpZ, which mimic AQP1.     

The pore helix dipole has a minor role in inward rectifier channel function

Ion channels lower the energetic barrier for ion passage across cell membranes and enable the generation of bioelectricity. Electrostatic interactions between permeant ions and channel pore helix dipoles have been proposed as a general mechanism for facilitating ion passage. Here, using genetic selections to probe interactions of an exemplar potassium channel blocker, barium, with the inward rectifier Kir2.1, we identify mutants bearing positively charged residues in the potassium channel signature sequence at the pore helix C terminus. We show that these channels are functional, selective, resistant to barium block, and have minimally altered conductance properties. Both the experimental data and model calculations indicate that barium resistance originates from electrostatics. We demonstrate that potassium channel function is remarkably unperturbed when positive charges occur near the permeant ions at a location that should counteract pore helix electrostatic effects. Thus, contrary to accepted models, the pore helix dipole seems to be a minor factor in potassium channel permeation.     

Permeability and the hidden area of lipid bilayers

The passive water permeability of a lipid vesicle membrane was studied, related to the hydrostatic (not osmotic) pressure difference between the inner and the outer side of the vesicle in a water environment without additives. Each pressure difference was created by sucking a vesicle into a micropipette at a given sucking pressure. The part of the membrane sucked into the micropipette (the projection length) was measured as a function of time. The time dependence can be divided into two intervals. We put forward the idea that smoothing of membrane defects, accompanied by an increase of the membrane area, takes place during the initial time interval, which results in a faster increase of the projection length. In the second time interval the volume of the vesicle decreases due to the permeability of its membrane and the increase of the projection length is slower. The hidden area and the water permeability of a typical lipid bilayer were estimated. The measured permeability, conjugated to the hydrostatic pressure difference, is an order of magnitude higher than the known value of the permeability, conjugated to the osmotic pressure difference. A hypothesis, based on pore formation, is proposed as an explanation of this experimental result.     

Multiscale modeling shows that dielectric differences make NaV channels faster than KV channels

The generation of action potentials in excitable cells requires different activation kinetics of voltage-gated Na (Na_V) and K (K_V) channels. Na_V channels activate much faster and allow the initial Na⁺ influx that generates the depolarizing phase and propagates the signal. Recent experimental results suggest that the molecular basis for this kinetic difference is an amino acid side chain located in the gating pore of the voltage sensor domain, which is a highly conserved isoleucine in K_V channels but an equally highly conserved threonine in Na_V channels. Mutagenesis suggests that the hydrophobicity of this side chain in Shaker K_V channels regulates the energetic barrier that gating charges cross as they move through the gating pore and control the rate of channel opening. We use a multiscale modeling approach to test this hypothesis. We use high-resolution molecular dynamics to study the effect of the mutation on polarization charge within the gating pore. We then incorporate these results in a lower-resolution model of voltage gating to predict the effect of the mutation on the movement of gating charges. The predictions of our hierarchical model are fully consistent with the tested hypothesis, thus suggesting that the faster activation kinetics of Na_V channels comes from a stronger dielectric polarization by threonine (Na_V channel) produced as the first gating charge enters the gating pore compared with isoleucine (K_V channel).     

Ion transport through membrane-spanning nanopores studied by molecular dynamics simulations and continuum electrostatics calculations

Narrow hydrophobic regions are a common feature of biological channels, with possible roles in ion-channel gating. We study the principles that govern ion transport through narrow hydrophobic membrane pores by molecular dynamics simulation of model membranes formed of hexagonally packed carbon nanotubes. We focus on the factors that determine the energetics of ion translocation through such nonpolar nanopores and compare the resulting free-energy barriers for pores with different diameters corresponding to the gating regions in closed and open forms of potassium channels. Our model system also allows us to compare the results from molecular dynamics simulations directly to continuum electrostatics calculations. Both simulations and continuum calculations show that subnanometer wide pores pose a huge free-energy barrier for ions, but a small increase in the pore diameter to approximately 1 nm nearly eliminates that barrier. We also find that in those wider channels the ion mobility is comparable to that in the bulk phase. By calculating local electrostatic potentials, we show that the long range Coulomb interactions of ions are strongly screened in the wide water-filled channels. Whereas continuum calculations capture the overall energetics reasonably well, the local water structure, which is not accounted for in this model, leads to interesting effects such as the preference of hydrated ions to move along the pore wall rather than through the center of the pore.     

Pore size and negative charge as structural determinants of permeability in the Torpedo nicotinic acetylcholine receptor channel.

To gain an insight into the molecular basis of ion permeation mechanism through the nicotinic acetylcholine receptor (AChR) channel, we have determined permeability ratios of organic cations relative to Na+ of specifically mutated Torpedo californica AChR channels expressed in Xenopus oocytes. The mutations involved mainly the side chains of the amino acid residues in the intermediate ring, where mutations have been found to exert strong effects on single-channel conductance and ion selectivity among alkali metal cations. The results obtained reveal that both the size and the net charge of the side chains of the intermediate ring are involved in determining the permeability, and provide experimental evidence that the pore size at the intermediate ring is a critical determinant of permeability. Our findings further suggest that changes in net charge exert effects on permeability by affecting the pore size of the channel.