Beyond the diffusion limit: Water flow through the empty bacterial potassium channel

Water will Find Its Way: Transport through Narrow Tunnels in Hydrolases

An aqueous environment is vital for life as we know it, and water is essential for nearly all biochemical processes at the molecular level. Proteins utilize water molecules in various ways. Consequently, proteins must transport water molecules across their internal network of tunnels to reach the desired action sites, either within them or by functioning as molecular pipes to control cellular osmotic pressure. Despite water playing a crucial role in enzymatic activity and stability, its transport has been largely overlooked, with studies primarily focusing on water transport across membrane proteins. The transport of molecules through a protein's tunnel network is challenging to study experimentally, making molecular dynamics simulations the most popular approach for investigating such events. In this study, we focused on the transport of water molecules across three different α/β-hydrolases: haloalkane dehalogenase, epoxide hydrolase, and lipase. Using a 5 μs adaptive simulation per system, we observed that only a few tunnels were responsible for the majority of water transport in dehalogenase, in contrast to a higher diversity of tunnels in other enzymes. Interestingly, water molecules could traverse narrow tunnels with subangstrom bottlenecks, which is surprising given the commonly accepted water molecule radius of 1.4 Å. Our analysis of the transport events in such narrow tunnels revealed a markedly increased number of hydrogen bonds formed between the water molecules and protein, likely compensating for the steric penalty of the process. Overall, these commonly disregarded narrow tunnels accounted for ∼20% of the total water transport observed, emphasizing the need to surpass the standard geometrical limits on the functional tunnels to properly account for the relevant transport processes. Finally, we demonstrated how the obtained insights could be applied to explain the differences in a mutant of the human soluble epoxide hydrolase associated with a higher incidence of ischemic stroke.

Differences in water and vapor transport through angstrom-scale pores in atomically thin membranes

The transport of water through nanoscale capillaries/pores plays a prominent role in biology, ionic/molecular separations, water treatment and protective applications. However, the mechanisms of water and vapor transport through nanoscale confinements remain to be fully understood. Angstrom-scale pores (~2.8-6.6 Å) introduced into the atomically thin graphene lattice represent ideal model systems to probe water transport at the molecular-length scale with short pores (aspect ratio ~1-1.9) i.e., pore diameters approach the pore length (~3.4 Å) at the theoretical limit of material thickness. Here, we report on orders of magnitude differences (~80×) between transport of water vapor (~44.2-52.4 g m^-2 day^-1 Pa^-1) and liquid water (0.6-2 g m^-2 day^-1 Pa^-1) through nanopores (~2.8-6.6 Å in diameter) in monolayer graphene and rationalize this difference via a flow resistance model in which liquid water permeation occurs near the continuum regime whereas water vapor transport occurs in the free molecular flow regime. We demonstrate centimeter-scale atomically thin graphene membranes with up to an order of magnitude higher water vapor transport rate (~5.4-6.1 × 10⁴g m^-2 day^-1) than most commercially available ultra-breathable protective materials while effectively blocking even sub-nanometer (>0.66 nm) model ions/molecules.

The energetic barrier to single-file water flow through narrow channels

Various nanoscopic channels of roughly equal diameter and length facilitate single-file diffusion at vastly different rates. The underlying variance of the energetic barriers to transport is poorly understood. First, water partitioning into channels so narrow that individual molecules cannot overtake each other incurs an energetic penalty. Corresponding estimates vary widely depending on how the sacrifice of two out of four hydrogen bonds is accounted for. Second, entropy differences between luminal and bulk water may arise: additional degrees of freedom caused by dangling OH-bonds increase entropy. At the same time, long-range dipolar water interactions decrease entropy. Here, we dissect different contributions to Gibbs free energy of activation, ΔG ^‡, for single-file water transport through narrow channels by analyzing experimental results from water permeability measurements on both bare lipid bilayers and biological water channels that (i) consider unstirred layer effects and (ii) adequately count the channels in reconstitution experiments. First, the functional relationship between water permeabilities and Arrhenius activation energies indicates negligible differences between the entropies of intraluminal water and bulk water. Second, we calculate ΔG ^‡ from unitary water channel permeabilities using transition state theory. Plotting ΔG ^‡ as a function of the number of H-bond donating or accepting pore-lining residues results in a 0.1 kcal/mol contribution per residue. The resulting upper limit for partial water dehydration amounts to 2 kcal/mol. In the framework of biomimicry, our analysis provides valuable insights for the design of synthetic water channels. It thus may aid in the urgent endeavor towards combating global water scarcity.

Predicting Ion Channel Conductance via Dissipation-Corrected Targeted Molecular Dynamics and Langevin Equation Simulations

Ion channels are important proteins for physiological information transfer and functional control. To predict the microscopic origins of their voltage-conductance characteristics, here we applied dissipation-corrected targeted molecular dynamics in combination with Langevin equation simulations to potassium diffusion through the gramicidin A channel as a test system. Performing a nonequilibrium principal component analysis on backbone dihedral angles, we find coupled protein-ion dynamics to occur during ion transfer. The dissipation-corrected free energy profiles correspond well to predictions from other biased simulation methods. The incorporation of an external electric field in Langevin simulations enables the prediction of macroscopic observables in the form of I-V characteristics.

Biophysical Reviews' "Meet the Councilor Series"-a profile of Peter Pohl

It is my pleasure to write a few words to introduce myself to the readers of Biophysical Reviews as part of the "Meet the Councilor Series." Currently, I am serving the second period as IUPAB councilor after having been elected first in 2017. Initially, I studied Biophysics in Moscow (Russia) and later Medicine in Halle (Germany). My scientific carrier took me from the Medical School of the Martin Luther University of Halle-Wittenberg, via the Leibniz Institute for Molecular Pharmacology (Berlin) and the Institute for Biology at the Humboldt University (Berlin) to the Physics Department of the Johannes Kepler University in Linz (Austria). My key research interests lie in the molecular mechanisms of transport phenomena occurring at the lipid membrane, including (i) spontaneous and facilitated transport of water and other small molecules across membranes in reconstituted systems, (ii) proton migration along the membrane surface, (iii) protein translocation, and (iv) bilayer mechanics. Training of undergraduate, graduate, and postdoctoral researchers from diverse academic disciplines has been-and shall remain-a consistent part of my work.

The Persistent Question of Potassium Channel Permeation Mechanisms

Potassium channels play critical roles in many physiological processes, providing a selective permeation route for K⁺ ions in and out of a cell, by employing a carefully designed selectivity filter, evolutionarily conserved from viruses to mammals. The structure of the selectivity filter was determined at atomic resolution by x-ray crystallography, showing a tight coordination of desolvated K⁺ ions by the channel. However, the molecular mechanism of K⁺ ions permeation through potassium channels remains unclear, with structural, functional and computational studies often providing conflicting data and interpretations. In this review, we will present the proposed mechanisms, discuss their origins, and will critically assess them against all available data. General properties shared by all potassium channels are introduced first, followed by the introduction of two main mechanisms of ion permeation: soft and direct knock-on. Then, we will discuss critical computational and experimental studies that shaped the field. We will especially focus on molecular dynamics (MD) simulations, that provided mechanistic and energetic aspects of K⁺ permeation, but at the same time created long-standing controversies. Further challenges and possible solutions are presented as well.

Functional stability of water wire-carbonyl interactions in an ion channel

Despite the well-characterized structural symmetry of the dimeric transmembrane antibiotic gramicidin A, we show that the symmetry is broken by selective hydrogen bonding between eight waters comprising a transmembrane water wire and a specific subset of the 26 pore-lining carbonyl oxygens of the gramicidin A channel. The ¹⁷O NMR spectroscopic resolution of the carbonyl resonances from the two subunits required the use of a world record high field magnet (35.2 T; 1,500 MHz for ¹H). Uniquely, this result documented the millisecond timescale stability of the water wire orientation within the gramicidin A pore that had been reported to have only subnanosecond stability. These ¹⁷O spectroscopic results portend wide applications in molecular biophysics and beyond.

Water wires are critical for the functioning of many membrane proteins, as in channels that conduct water, protons, and other ions. Here, in liquid crystalline lipid bilayers under symmetric environmental conditions, the selective hydrogen bonding interactions between eight waters comprising a water wire and a subset of 26 carbonyl oxygens lining the antiparallel dimeric gramicidin A channel are characterized by ¹⁷O NMR spectroscopy at 35.2 T (or 1,500 MHz for ¹H) and computational studies. While backbone ¹⁵N spectra clearly indicate structural symmetry between the two subunits, single site ¹⁷O labels of the pore-lining carbonyls report two resonances, implying a break in dimer symmetry caused by the selective interactions with the water wire. The ¹⁷O shifts document selective water hydrogen bonding with carbonyl oxygens that are stable on the millisecond timescale. Such interactions are supported by density functional theory calculations on snapshots taken from molecular dynamics simulations. Water hydrogen bonding in the pore is restricted to just three simultaneous interactions, unlike bulk water environs. The stability of the water wire orientation and its electric dipole leads to opposite charge-dipole interactions for K⁺ ions bound at the two ends of the pore, thereby providing a simple explanation for an ∼20-fold difference in K⁺ affinity between two binding sites that are ∼24 Å apart. The ¹⁷O NMR spectroscopy reported here represents a breakthrough in high field NMR technology that will have applications throughout molecular biophysics, because of the acute sensitivity of the ¹⁷O nucleus to its chemical environment.

Encapsulation versus Self-Aggregation toward Highly Selective Artificial K+ Channels

Natural ion-channel proteins allow ion transport across cell membranes at rates very close to those for ionic diffusion in water. Among them, natural KcsA K⁺ channels present high transport rates and total selectivity for K⁺ cations, rejecting all other cations. Most of the reported artificial ion channels cannot reach this type of activity because of their low selectivity. Several synthetic channels have been designed to mimic the natural KcSA channels, but those presenting an important K⁺/Na⁺ selectivity are limited. High-selectivity issues are determinant for the performance of natural protein channels, but they have been not considered as determinant in controlling the transport activity of the artificial ion channels. This Account discusses the last developments of artificial supramolecular carriers or channels that selectively transport K⁺ cations against other cations. Mimicking the complex structures of protein channels is an important research area. These studies are related to such adaptive biomimetic systems that can self-select their functions, with a specific emphasis on artificial superstructures enabling K⁺ transport like in the natural ones. Alternatively, it is more than interesting to synthetically construct only the active key structures of protein filters or gates that give the chemical selectivity or lead us to describe their dynamic role in the ion pumping and translocation along the channel. Several self-assembled macrocyclic channels are presented here. The macrocyclic binding sites may selectively encapsulate the K⁺ cations or form aggregated H-bonded central pores of self-assembled macrocycles that coordinate the K⁺ cations as hydrating water molecules in aqueous solution, compensating for the energetic cost of cation dehydration. These macrocyclic channels are responsive in the presence of K⁺ cations, even when a large excess of Na⁺ is present. From the mechanistic point of view, these systems express a synergistic dynamic feature: addition of K⁺ cations drives the selection and emergence of specific ion channels that selectively conduct the K⁺ cations that promoted the formation of channel superstructures in the first place. These highly permeable and K⁺-selective artificial channels may be considered as simple primitive biomimetic alternatives of natural KcsA channels that may find interesting applications in chemical separations, selective sensing, and biomedical materials.

Single-file transport of water through membrane channels

Water at interfaces governs many processes on the molecular scale from electrochemical and enzymatic reactions to protein folding. Here we focus on water transport through proteinaceous pores that are so narrow that the water molecules cannot overtake each other in the pore. After a short introduction into the single-file transport theory, we analyze experiments in which the unitary water permeability, pf, of water channel proteins (aquaporins, AQPs), potassium channels (KcsA), and antibiotics (gramicidin-A derivatives) has been obtained. A short outline of the underlying methods (scanning electrochemical microscopy, fluorescence correlation spectroscopy, measurements of vesicle light scattering) is also provided. We conclude that pf increases exponentially with a decreasing number NH of hydrogen bond donating or accepting residues in the channel wall. The variance in NH is responsible for a more than hundredfold change in pf. The dehydration penalty at the channel mouth has a smaller effect on pf. The intricate link between pf and the Gibbs activation energy barrier, ΔG‡t, for water flow suggests that conformational transitions of water channels act as a third determinant of pf.

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.

Quantification of Water Flux in Vesicular Systems

Water transport across lipid membranes is fundamental to all forms of life and plays a major role in health and disease. However, not only typical water facilitators like aquaporins facilitate water flux, but also transporters, ion channels or receptors represent potent water pathways. The efforts directed towards a mechanistic understanding of water conductivity determinants in transmembrane proteins, the development of water flow inhibitors, and the creation of biomimetic membranes with incorporated membrane proteins or artificial water channels depend on reliable and accurate ways of quantifying water permeabilities Pf. A conventional method is to subject vesicles to an osmotic gradient in a stopped-flow device: Fast recordings of scattered light intensity are converted into the time course of vesicle volume change. Even though an analytical solution accurately acquiring Pf from scattered light intensities exists, approximations potentially misjudging Pf by orders of magnitude are used. By means of computational and experimental data we point out that erroneous results such as that the single channel water permeability pf depends on the osmotic gradient are direct results of such approximations. Finally, we propose an empirical solution of which calculated permeability values closely match those calculated with the analytical solution in the relevant range of parameters.

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.

Molecular dynamics simulation of water permeation through the alpha-hemolysin channel

The alpha-hemolysin (AHL) nanochannel is a non-selective channel that allows for uncontrolled transport of small molecules across membranes leading to cell death. Although it is a bacterial toxin, it has promising applications, ranging from drug delivery systems to nano-sensing devices. This study focuses on the transport of water molecules through an AHL nanochannel using molecular dynamics (MD) simulations. Our results show that AHL can quickly transport water across membranes. The first-passage time approach was used to estimate the diffusion coefficient and the mean exit time. To study the energetics of transport, the potential of mean force (PMF) of a water molecule along the AHL nanochannel was calculated. The results show that the energy barriers of water permeation across a nanopore are always positive along the channel and the values are close to thermal energy (kBT). These findings suggest that the observed quick permeation of water is due to small energy barriers and a hydrophobic inner channel surface resulting in smaller friction. We speculate that these physical mechanisms are important in how AHL causes cell death.

Artificial water channels – incipient innovative developments

This Feature Article discusses the incipient developments of the first artificial water channels, including only systems that integrate synthetic elements in their water selective translocation unit.

Theoretical and simulation studies on voltage-gated sodium channels

Voltage-gated sodium (Na_v) channels are indispensable membrane elements for the generation and propagation of electric signals in excitable cells. The successes in the crystallographic studies on prokaryotic Na_v channels in recent years greatly promote the mechanistic investigation of these proteins and their eukaryotic counterparts. In this paper, we mainly review the progress in computational studies, especially the simulation studies, on these proteins in the past years.

Ion permeation in K⁺ channels occurs by direct Coulomb knock-on

Potassium channels selectively conduct K(+) ions across cellular membranes with extraordinary efficiency. Their selectivity filter exhibits four binding sites with approximately equal electron density in crystal structures with high K(+) concentrations, previously thought to reflect a superposition of alternating ion- and water-occupied states. Consequently, cotranslocation of ions with water has become a widely accepted ion conduction mechanism for potassium channels. By analyzing more than 1300 permeation events from molecular dynamics simulations at physiological voltages, we observed instead that permeation occurs via ion-ion contacts between neighboring K(+) ions. Coulomb repulsion between adjacent ions is found to be the key to high-efficiency K(+) conduction. Crystallographic data are consistent with directly neighboring K(+) ions in the selectivity filter, and our model offers an intuitive explanation for the high throughput rates of K(+) channels.

Real-time monitoring of membrane-protein reconstitution by isothermal titration calorimetry

Phase diagrams offer a wealth of thermodynamic information on aqueous mixtures of bilayer-forming lipids and micelle-forming detergents, providing a straightforward means of monitoring and adjusting the supramolecular state of such systems. However, equilibrium phase diagrams are of very limited use for the reconstitution of membrane proteins because of the occurrence of irreversible, unproductive processes such as aggregation and precipitation that compete with productive reconstitution. Here, we exemplify this by dissecting the effects of the K⁺ channel KcsA on the process of bilayer self-assembly in a mixture of Escherichia coli polar lipid extract and the nonionic detergent octyl-β-d-glucopyranoside. Even at starting concentrations in the low micromolar range, KcsA has a tremendous impact on the supramolecular organization of the system, shifting the critical lipid/detergent ratios at the onset and completion of vesicle formation by more than 2-fold. Thus, equilibrium phase diagrams obtained for protein-free lipid/detergent mixtures would be misleading when used to guide the reconstitution process. To address this issue, we demonstrate that, even under such nonequilibrium conditions, high-sensitivity isothermal titration calorimetry can be exploited to monitor the progress of membrane-protein reconstitution in real time, in a noninvasive manner, and at high resolution to yield functional proteoliposomes with a narrow size distribution for further downstream applications.

From natural to bioassisted and biomimetic artificial water channel systems

Within biological systems, natural channels and pores transport metabolites across the cell membranes. Researchers have explored artificial ion-channel architectures as potential mimics of natural ionic conduction. All these synthetic systems have produced an impressive collection of alternative artificial ion-channels. Amazingly, researchers have made far less progress in the area of synthetic water channels. The development of synthetic biomimetic water channels and pores could contribute to a better understanding of the natural function of protein channels and could offer new strategies to generate highly selective, advanced water purification systems. Despite the imaginative work by synthetic chemists to produce sophisticated architectures that confine water clusters, most synthetic water channels have used natural proteins channels as the selectivity components, embedded in the diverse arrays of bioassisted artificial systems. These systems combine natural proteins that present high water conductance states under natural conditions with artificial lipidic or polymeric matrixes. Experimental results have demonstrated that natural biomolecules can be used as bioassisted building blocks for the construction of highly selective water transport through artificial membranes. A next step to further the potential of these systems was the design and construction of simpler compounds that maintain the high conduction activity obtained with natural compounds leading to fully synthetic artificial biomimetic systems. Such studies aim to use constitutional selective artificial superstructures for water/proton transport to select functions similar to the natural structures. Moving to simpler water channel systems offers a chance to better understand mechanistic and structural behaviors and to uncover novel interactive water-channels that might parallel those in biomolecular systems. This Account discusses the incipient development of the first artificial water channels systems. We include only systems that integrate synthetic elements in their water selective translocation unit. Therefore, we exclude peptide channels because their sequences derive from the proteins in natural channels. We review many of the natural systems involved in water and related proton transport processes. We describe how these systems can fit within our primary goal of maintaining natural function within bioassisted artificial systems. In the last part of the Account, we present several inspiring breakthroughs from the last decade in the field of biomimetic artificial water channels. Researchers have synthesized and tested hydrophobic, hydrophilic and hybrid nanotubular systems. All these examples demonstrate how the novel interactive water-channels can parallel biomolecular systems. At the same time these simpler artificial water channels offer a means of understanding the molecular-scale hydrodynamics of water for many biological scenarios.

Filter gate closure inhibits ion but not water transport through potassium channels

The selectivity filter of K(+) channels is conserved throughout all kingdoms of life. Carbonyl groups of highly conserved amino acids point toward the lumen to act as surrogates for the water molecules of K(+) hydration. Ion conductivity is abrogated if some of these carbonyl groups flip out of the lumen, which happens (i) in the process of C-type inactivation or (ii) during filter collapse in the absence of K(+). Here, we show that K(+) channels remain permeable to water, even after entering such an electrically silent conformation. We reconstituted fluorescently labeled and constitutively open mutants of the bacterial K(+) channel KcsA into lipid vesicles that were either C-type inactivating or noninactivating. Fluorescence correlation spectroscopy allowed us to count both the number of proteoliposomes and the number of protein-containing micelles after solubilization, providing the number of reconstituted channels per proteoliposome. Quantification of the per-channel increment in proteoliposome water permeability with the aid of stopped-flow experiments yielded a unitary water permeability pf of (6.9 ± 0.6) × 10(-13) cm(3)⋅s(-1) for both mutants. "Collapse" of the selectivity filter upon K(+) removal did not alter pf and was fully reversible, as demonstrated by current measurements through planar bilayers in a K(+)-containing medium to which K(+)-free proteoliposomes were fused. Water flow through KcsA is halved by 200 mM K(+) in the aqueous solution, which indicates an effective K(+) dissociation constant in that range for a singly occupied channel. This questions the widely accepted hypothesis that multiple K(+) ions in the selectivity filter act to mutually destabilize binding.

Molecular dynamics of ion transport through the open conformation of a bacterial voltage-gated sodium channel

The crystal structure of the open conformation of a bacterial voltage-gated sodium channel pore from Magnetococcus sp. (NaVMs) has provided the basis for a molecular dynamics study defining the channel's full ion translocation pathway and conductance process, selectivity, electrophysiological characteristics, and ion-binding sites. Microsecond molecular dynamics simulations permitted a complete time-course characterization of the protein in a membrane system, capturing the plethora of conductance events and revealing a complex mixture of single and multi-ion phenomena with decoupled rapid bidirectional water transport. The simulations suggest specific localization sites for the sodium ions, which correspond with experimentally determined electron density found in the selectivity filter of the crystal structure. These studies have also allowed us to identify the ion conductance mechanism and its relation to water movement for the NavMs channel pore and to make realistic predictions of its conductance properties. The calculated single-channel conductance and selectivity ratio correspond closely with the electrophysiology measurements of the NavMs channel expressed in HEK 293 cells. The ion translocation process seen in this voltage-gated sodium channel is clearly different from that exhibited by members of the closely related family of voltage-gated potassium channels and also differs considerably from existing proposals for the conductance process in sodium channels. These studies simulate sodium channel conductance based on an experimentally determined structure of a sodium channel pore that has a completely open transmembrane pathway and activation gate.

Molecular wire of urea in carbon nanotube: a molecular dynamics study

We perform molecular dynamics simulations of narrow single-walled carbon nanotubes (SWNTs) in aqueous urea to investigate the structure and dynamical behavior of urea molecules inside the SWNT. Even at low urea concentrations (e.g., 0.5 M), we have observed spontaneous and continuous filling of SWNT with a one-dimensional urea wire (leaving very few water molecules inside the SWNT). The urea wire is structurally ordered, both translationally and orientationally, with a contiguous hydrogen-bonded network and concerted urea's dipole orientations. Interestingly, despite the symmetric nature of the whole system, the potential energy profile of urea along the SWNT is asymmetric, arising from the ordering of asymmetric urea partial charge distribution (or dipole moment) in confined environment. Furthermore, we study the kinetics of confined urea and find that the permeation of urea molecules through the SWNT decreases significantly (by a factor of ∼20) compared to that of water molecules, due to the stronger dispersion interaction of urea with SWNT than water, and a maximum in urea permeation happens around a concentration of 5 M. These findings might shed some light on the better understanding of unique properties of molecular wires (particularly the wires formed by polar organic small molecules) confined within both artificial and biological nanochannels, and are expected to have practical applications such as the electronic devices for signal transduction and multiplication at the nanoscale.

Proton exclusion by an aquaglyceroprotein: a voltage clamp study

BACKGROUND INFORMATION

In silico both orthodox aquaporins and aquaglyceroporins are shown to exclude protons. Supporting experimental evidence is available only for orthodox aquaporins. In contrast, the subset of the aquaporin water channel family that is permeable to glycerol and certain small, uncharged solutes has not yet been shown to exclude protons. Moreover, different aquaglyceroporins have been reported to conduct ions when reconstituted in planar bilayers.

RESULTS

To clarify these discrepancies, we have measured proton permeability through the purified Escherichia coli glycerol facilitator (GlpF). Functional reconstitution into planar lipid bilayers was demonstrated by imposing an osmotic gradient across the membrane and detecting the resulting small changes in ionic concentration close to the membrane surface. The osmotic water flow corresponds to a GlpF single channel water permeability of 0.7x10(-14) cm(3).subunit(-1).s(-1). Proton conductivity measurements carried out in the presence of a pH gradient (1 unit) revealed an upper limit of the H(+) (OH(-)) to H(2)O molecules transport stoichiometry of 2x10(-9). A significant GlpF-mediated ion conductivity was also not detectable.

CONCLUSIONS

The lack of a physiologically relevant GlpF-mediated proton conductivity agrees well with predictions made by molecular dynamics simulations.

Counting ion and water molecules in a streaming file through the open-filter structure of the K channel

The mechanisms underlying the selective permeation of ions through channel molecules are a fundamental issue related to understanding how neurons exert their functions. The "knock-on" mechanism, in which multiple ions in the selectivity filter are hit by an incoming ion, is one of the leading concepts. This mechanism has been supported by crystallographic studies that demonstrated ion distribution in the structure of the Streptomyces lividans (KcsA) potassium channel. These still pictures under equilibrium conditions, however, do not provide a snapshot of the actual, ongoing permeation processes. To understand the dynamics of permeation, we determined the ratio of the ion and water flow [the water-ion coupling ratio (CR(w-i))] through the KcsA channel by measuring the streaming potential (V(stream)) electrophysiologically. The V(stream) value was converted to the CR(w-i) value, which reveals how individual ion and water molecules are queued in the narrow and short filter during permeation. At high K(+) concentrations, the CR(w-i) value was 1.0, indicating that turnover between the alternating ion and water arrays occurs in a single-file manner. At low K(+), the CR(w-i) value was increased to a point over 2.2, suggesting that the filter contained mostly one ion at a time. These average behaviors of permeation were kinetically analyzed for a more detailed understanding of the permeation process. Here, we envisioned the permeation as queues of ion and water molecules and sequential transitions between different patterns of arrays. Under physiological conditions, we predicted that the knock-on mechanism may not be predominant.

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.

A permeation theory for single-file ion channels: one- and two-step models

How many steps are required to model permeation through ion channels? This question is investigated by comparing one- and two-step models of permeation with experiment and MD simulation for the first time. In recent MD simulations, the observed permeation mechanism was identified as resembling a Hodgkin and Keynes knock-on mechanism with one voltage-dependent rate-determining step [Jensen et al., PNAS 107, 5833 (2010)]. These previously published simulation data are fitted to a one-step knock-on model that successfully explains the highly non-Ohmic current-voltage curve observed in the simulation. However, these predictions (and the simulations upon which they are based) are not representative of real channel behavior, which is typically Ohmic at low voltages. A two-step association/dissociation (A/D) model is then compared with experiment for the first time. This two-parameter model is shown to be remarkably consistent with previously published permeation experiments through the MaxiK potassium channel over a wide range of concentrations and positive voltages. The A/D model also provides a first-order explanation of permeation through the Shaker potassium channel, but it does not explain the asymmetry observed experimentally. To address this, a new asymmetric variant of the A/D model is developed using the present theoretical framework. It includes a third parameter that represents the value of the "permeation coordinate" (fractional electric potential energy) corresponding to the triply occupied state n of the channel. This asymmetric A/D model is fitted to published permeation data through the Shaker potassium channel at physiological concentrations, and it successfully predicts qualitative changes in the negative current-voltage data (including a transition to super-Ohmic behavior) based solely on a fit to positive-voltage data (that appear linear). The A/D model appears to be qualitatively consistent with a large group of published MD simulations, but no quantitative comparison has yet been made. The A/D model makes a network of predictions for how the elementary steps and the channel occupancy vary with both concentration and voltage. In addition, the proposed theoretical framework suggests a new way of plotting the energetics of the simulated system using a one-dimensional permeation coordinate that uses electric potential energy as a metric for the net fractional progress through the permeation mechanism. This approach has the potential to provide a quantitative connection between atomistic simulations and permeation experiments for the first time.

Absence of ion-binding affinity in the putatively inactivated low-[K+] structure of the KcsA potassium channel

Potassium channels are membrane proteins that selectively conduct K(+) across cellular membranes. The narrowest part of their pore, the selectivity filter, is responsible for distinguishing K(+) from Na(+), and can also act as a gate through a mechanism known as C-type inactivation. It has been proposed that a conformation of the KcsA channel obtained by crystallization in presence of low concentration of K(+) (PDB 1K4D) could correspond to the C-type inactivated state. Here, we show using molecular mechanics simulations that such conformation has little ion-binding affinity and that ions do not contribute to its stability. The simulations suggest that, in this conformation, the selectivity filter is mostly occupied by water molecules. Whether such ion-free state of the KcsA channel is physiologically accessible and representative of the inactivated state of eukaryotic channels remains unclear.

Energy variational analysis of ions in water and channels: Field theory for primitive models of complex ionic fluids

Ionic solutions are mixtures of interacting anions and cations. They hardly resemble dilute gases of uncharged noninteracting point particles described in elementary textbooks. Biological and electrochemical solutions have many components that interact strongly as they flow in concentrated environments near electrodes, ion channels, or active sites of enzymes. Interactions in concentrated environments help determine the characteristic properties of electrodes, enzymes, and ion channels. Flows are driven by a combination of electrical and chemical potentials that depend on the charges, concentrations, and sizes of all ions, not just the same type of ion. We use a variational method EnVarA (energy variational analysis) that combines Hamilton's least action and Rayleigh's dissipation principles to create a variational field theory that includes flow, friction, and complex structure with physical boundary conditions. EnVarA optimizes both the action integral functional of classical mechanics and the dissipation functional. These functionals can include entropy and dissipation as well as potential energy. The stationary point of the action is determined with respect to the trajectory of particles. The stationary point of the dissipation is determined with respect to rate functions (such as velocity). Both variations are written in one Eulerian (laboratory) framework. In variational analysis, an "extra layer" of mathematics is used to derive partial differential equations. Energies and dissipations of different components are combined in EnVarA and Euler-Lagrange equations are then derived. These partial differential equations are the unique consequence of the contributions of individual components. The form and parameters of the partial differential equations are determined by algebra without additional physical content or assumptions. The partial differential equations of mixtures automatically combine physical properties of individual (unmixed) components. If a new component is added to the energy or dissipation, the Euler-Lagrange equations change form and interaction terms appear without additional adjustable parameters. EnVarA has previously been used to compute properties of liquid crystals, polymer fluids, and electrorheological fluids containing solid balls and charged oil droplets that fission and fuse. Here we apply EnVarA to the primitive model of electrolytes in which ions are spheres in a frictional dielectric. The resulting Euler-Lagrange equations include electrostatics and diffusion and friction. They are a time dependent generalization of the Poisson-Nernst-Planck equations of semiconductors, electrochemistry, and molecular biophysics. They include the finite diameter of ions. The EnVarA treatment is applied to ions next to a charged wall, where layering is observed. Applied to an ion channel, EnVarA calculates a quick transient pile-up of electric charge, transient and steady flow through the channel, stationary "binding" in the channel, and the eventual accumulation of salts in "unstirred layers" near channels. EnVarA treats electrolytes in a unified way as complex rather than simple fluids. Ad hoc descriptions of interactions and flow have been used in many areas of science to deal with the nonideal properties of electrolytes. It seems likely that the variational treatment can simplify, unify, and perhaps derive and improve those descriptions.

Conformational dynamics in the selectivity filter of KcsA in response to potassium ion concentration

Conformational change in the selectivity filter of KcsA as a function of ambient potassium concentration is studied with solid-state NMR. This highly conserved region of the protein is known to chelate potassium ions selectively. We report solid-state NMR chemical shift fingerprints of two distinct conformations of the selectivity filter; significant changes are observed in the chemical shifts of key residues in the filter as the potassium ion concentration is changed from 50 mM to 1 muM. Potassium ion titration studies reveal that the site-specific K(d) for K(+) binding at the key pore residue Val76 is on the order of approximately 7 muM and that a relatively high sample hydration is necessary to observe the low-K(+) conformer. Simultaneous detection of both conformers at low ambient potassium concentration suggests that the high-K(+) and low-K(+) states are in slow exchange on the NMR timescale (k(ex)<500 s(-)(1)). The slow rate and tight binding for evacuating both inner sites simultaneously differ from prior observations in detergent in solution, but agree well with measurements by electrophysiology and appear to result from our use of a hydrated bilayer environment. These observations strongly support a common assumption that the low-K(+) state is not involved in ion transmission, and that during transmission one of the two inner sites is always occupied. On the other hand, these kinetic and thermodynamic characteristics of the evacuation of the inner sites certainly could be compatible with participation in a control mechanism at low ion concentration such as C-type inactivation, a process that is coupled to activation and involves closing of the outer mouth of the channel.

Relevance of quantum mechanics on some aspects of ion channel function

Mathematical modeling of ionic diffusion along K ion channels indicates that such diffusion is oscillatory, at the weak non-Markovian limit. This finding leads us to derive a Schrödinger-Langevin equation for this kind of system within the framework of stochastic quantization. The Planck's constant is shown to be relevant to the Lagrangian action at the level of a single ion channel. This sheds new light on the issue of applicability of quantum formalism to ion channel dynamics and to the physical constraints of the selectivity filter.

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.

Non-Markovian noise mediated through anomalous diffusion within ion channels

It is evident from a wide range of experimental findings that ion channel gating is inherently stochastic. The issue of "memory effects" (diffusional retardation due to local changes in water viscosity) in ionic flow has been recently addressed using Brownian dynamics simulations. The results presented indicate such memory effects are negligible, unless the diffusional barrier is much higher than that of free solute. In this paper using differential stochastic methods we conclude that the Markovian property of exponential dwell times gives rise to a high barrier, resulting in diffusional memory effects that cannot be ignored in determining ionic flow through channels. We have addressed this question using a generalized Langevin equation that contains a combination of Markovian and non-Markovian processes with different time scales. This approach afforded the development of an algorithm that describes an oscillatory ionic diffusional sequence. The resulting oscillatory function behavior, with exponential decay, was obtained at the weak non-Markovian limit with two distinct time scales corresponding to the processes of ionic diffusion and drift. This will be analyzed further in future studies using molecular dynamics simulations. We propose that the rise of time scales and memory effects is related to differences of shear viscosity in the cytoplasm and extracellular matrix.

Intrinsic Free Energy of the Conformational Transition of the KcsA Signature Peptide from Conducting to Nonconducting State

We explore a conformational transition of the TATTVGYG signature peptide of the KcsA ion selectivity filter and its GYG to AYA mutant from the conducting α-strand state into the nonconducting pII-like state using a novel technique for multidimensional optimization of transition path ensembles and free energy calculations. We find that the wild type peptide, unlike the mutant, intrinsically favors the conducting state due to G77 backbone propensities and additional hydrophobic interaction between the V76 and Y78 side chains in water. The molecular mechanical free energy profiles in explicit water are in very good agreement with the corresponding adiabatic energies from the Generalized Born Molecular Volume (GBMV) implicit solvent model. However comparisons of the energies to higher level B3LYP/6-31G(d) Density Functional Theory calculations with Polarizable Continuum Model (PCM) suggest that the nonconducting state might be more favorable than predicted by molecular mechanics simulations. By extrapolating the single peptide results to the tetrameric channel, we propose a novel hypothesis for the ion selectivity mechanism.

Uniform diffusion of acetonitrile inside carbon nanotubes favors supercapacitor performance

An unusual behavior of liquid acetonitrile (AN) confined inside carbon nanotubes (CNTs) is predicted by molecular dynamics simulation. In contrast to water, which shows inhomogeneous variation of both translational and rotational diffusion with CNT diameter [ Nano Lett. 2003, 3, 589; 2004, 4, 619], the diffusion coefficient of AN changes uniformly and can be described by a simple analytic model. At the same time, the reorientation dynamics of AN vary irregularly in smaller CNTs because of specific packing structures. The uniform translational diffusion of the nonaqueous solvent is critical for stable performance of the new generation of supercapacitors [ Nat. Mater. 2006, 5, 987].

Channels for water efflux and influx involved in volume regulation of murine spermatozoa

The nature of the membrane channels mediating water transport in murine spermatozoa adjusting to anisotonic conditions was investigated. The volume of spermatozoa subjected to physiologically relevant hypotonic conditions either simultaneously, or after isotonic pre-incubation, with putative water transport inhibitors was monitored. Experiments in which quinine prevented osmolyte efflux, and thus regulatory volume decrease (RVD), revealed whether water influx or efflux was being inhibited. There was no evidence that sodium-dependent solute transporters or facilitative glucose transporters were involved in water transport during RVD of murine spermatozoa since phloretin, cytochalasin B and phloridzin had no effect on volume regulation. However, there was evidence that Hg(2+)- and Ag(+)-sensitive channels were involved in water transport and the possibility that they include aquaporin 8 is discussed. Toxic effects of these heavy metals were ruled out by evidence that mitochondrial poisons had no such effect on volume regulation.

Bubbles, gating, and anesthetics in ion channels

We suggest that bubbles are the bistable hydrophobic gates responsible for the on-off transitions of single channel currents. In this view, many types of channels gate by the same physical mechanism-dewetting by capillary evaporation-but different types of channels use different sensors to modulate hydrophobic properties of the channel wall and thereby trigger and control bubbles and gating. Spontaneous emptying of channels has been seen in many simulations. Because of the physics involved, such phase transitions are inherently sensitive, unstable threshold phenomena that are difficult to simulate reproducibly and thus convincingly. We present a thermodynamic analysis of a bubble gate using morphometric density functional theory of classical (not quantum) mechanics. Thermodynamic analysis of phase transitions is generally more reproducible and less sensitive to details than simulations. Anesthetic actions of inert gases-and their interactions with hydrostatic pressure (e.g., nitrogen narcosis)-can be easily understood by actions on bubbles. A general theory of gas anesthesia may involve bubbles in channels. Only experiments can show whether, or when, or which channels actually use bubbles as hydrophobic gates: direct observation of bubbles in channels is needed. Existing experiments show thin gas layers on hydrophobic surfaces in water and suggest that bubbles nearly exist in bulk water.

Enhanced flow in smooth single-file channel

We investigate the flux of particles in a smooth single-file channel where particles cannot cross each other as well as in wider channels of varying cross section where particles execute normal diffusion. All the channels are connected to an infinite reservoir at one end and the flux of particles is measured at the other open end. We perform random walk Monte Carlo simulation using lattice model. The flux decreases monotonically as the channel cross section is increased from single-file channel to wider channel and finally reaches a constant value for a sufficiently wide channel. The observation of enhanced flux in single-file channel as compared to a wider channel can be tested for efficient separation of particles through smooth nanochannels.

Determining the conductance of the SecY protein translocation channel for small molecules

The channel formed by the SecY complex must maintain the membrane barrier for ions and other small molecules during the translocation of membrane or secretory proteins. We have tested the permeability of the channel by using planar bilayers containing reconstituted purified E. coli SecY complex. Wild-type SecY complex did not show any conductance for ions or water. Deletion of the "plug," a short helix normally located in the center of the SecY complex, or modification of a cysteine introduced into the plug resulted in transient channel openings; a similar effect was seen with a mutation in the pore ring, a constriction in the center of the channel. Permanent channel opening occurred when the plug was moved out of the way by disulfide-bridge formation. These data show that the resting channel on its own forms a barrier for small molecules, with both the pore ring and the plug required for the seal; channel opening requires movement of the plug.

Ion conductance vs. pore gating and selectivity in KcsA channel: Modeling achievements and perspectives

KcsA potassium channel belongs to a wide family of allosteric proteins that switch between closed and open states conformations in response to a stimulus, and act as a regulator of cation activity in living cells. The gating mechanism and cation selectivity of such channels have been extensively studied in the literature, with a revival emphasis these latter years, due to the publication of the crystallized structure of KcsA. Despite the increasing number of research and review papers on these topics, quantitative interpretation of these processes at the atomic scale is far from achieved. On the basis of available experimental and theoretical data, and by including our recent results, we review the progresses in this field of activity and discuss the weaknesses that should be corrected. In this spirit, we partition the channel into the filter, cavity, extra and intracellular media, in order to analyze separately the specificity of each region. Special emphasis is brought to the study of an open state for the channel and to the different properties generated by the opening. The influence of water as a structural and dynamical component of the channel properties in closed and open states, as well as in the sequential motions of the cations, is analyzed using molecular dynamics simulations and ab initio calculations. The polarization and charge transfer effects on the ions' dynamics and kinetics are discussed in terms of partial charge models.

Electrostatic gating of a nanometer water channel

Water permeation across a single-walled carbon nanotube (SWNT) under the influence of a mobile external charge has been studied with molecular dynamics simulations. This designed nanopore shows an excellent on-off gating behavior by a single external charge (of value +1.0e): it is both sensitive to the available charge signal when it is close (less than a critical distance of 0.85 A or about half the size of a water molecule) and effectively resistant to charge noise, i.e., the effect on the flow and net flux across the channel is found to be negligible when the charge is >0.85 A away from the wall of the nanopore. This critical distance can be estimated from the interaction balance for the water molecule in the SWNT closest to the imposed charge with its neighboring water molecules and with the charge. The flow and net flux decay exponentially with respect to the difference between these two interaction energies when the charge gets closer to the wall of the SWNT and reaches a very small value once the charge crosses the wall, suggesting a dominating effect on the permeation properties from local water molecules near the external charge. These findings might have biological implications because membrane water channels share a similar single-file water chain inside these nanoscale channels.