Water in channel-like cavities: structure and dynamics

Structure and dynamics of liquid water from ab initio simulations: adding Minnesota density functionals to Jacob's ladder

The accurate representation of the structural and dynamical properties of water is essential for simulating the unique behavior of this ubiquitous solvent. Here we assess the current status of describing liquid water using ab initio molecular dynamics, with a special focus on the performance of all the later generation Minnesota functionals. Findings are contextualized within the current knowledge on DFT for describing bulk water under ambient conditions and compared to experimental data. We find that, contrary to the prevalent idea that local and semilocal functionals overstructure water and underestimate dynamical properties, M06-L, revM06-L, and M11-L understructure water, while MN12-L and MN15-L overdistance water molecules due to weak cohesive effects. This can be attributed to a weakening of the hydrogen bond network, which leads to dynamical fingerprints that are over fast. While most of the hybrid Minnesota functionals (M06, M08-HX, M08-SO, M11, MN12-SX, and MN15) also yield understructured water, their dynamical properties generally improve over their semilocal counterparts. It emerges that exact exchange is a crucial component for accurately describing hydrogen bonds, which ultimately leads to corrections in both the dynamical and structural properties. However, an excessive amount of exact exchange strengthens hydrogen bonds and causes overstructuring and slow dynamics (M06-HF). As a compromise, M06-2X is the best performing Minnesota functional for water, and its D3 corrected variant shows very good structural agreement. From previous studies considering nuclear quantum effects (NQEs), the hybrid revPBE0-D3, and the rung-5 RPA (RPA@PBE) have been identified as the only two approximations that closely agree with experiments. Our results suggest that the M06-2X(-D3) functionals have the potential to further improve the reproduction of experimental properties when incorporating NQEs through path integral approaches. This work provides further proof that accurate modeling of water interactions requires the inclusion of both exact exchange and balanced (non-local) correlation, highlighting the need for higher rungs on Jacob's ladder to achieve predictive simulations of complex biological systems in aqueous environments.

Self-Assembled Artificial DNA Nanocompartments and Their Bioapplications

Compartmentalization is the strategy evolved by nature to control reactions in space and time. The ability to emulate this strategy through synthetic compartmentalization systems has rapidly evolved in the past years, accompanied by an increasing understanding of the effects of spatial confinement on the thermodynamic and kinetic properties of the guest molecules. DNA nanotechnology has played a pivotal role in this scientific endeavor and is still one of the most promising approaches for the construction of nanocompartments with programmable structural features and nanometer-scaled addressability. In this review, the design approaches, bioapplications, and theoretical frameworks of self-assembled DNA nanocompartments are surveyed. From DNA polyhedral cages to virus-like capsules, the construction principles of such intriguing architectures are illustrated. Various applications of DNA nanocompartments, including their use for programmable enzyme scaffolding, single-molecule studies, biosensing, and as artificial nanofactories, ending with an ample description of DNA nanocages for biomedical purposes, are then reported. Finally, the theoretical hypotheses that make DNA nanocompartments, and nanosystems in general, a topic of great interest in modern science, are described and the progresses that have been done until now in the comprehension of the peculiar phenomena that occur within nanosized environments are summarized.

Water in Nanopores and Biological Channels: A Molecular Simulation Perspective

This Review explores the dynamic behavior of water within nanopores and biological channels in lipid bilayer membranes. We focus on molecular simulation studies, alongside selected structural and other experimental investigations. Structures of biological nanopores and channels are reviewed, emphasizing those high-resolution crystal structures, which reveal water molecules within the transmembrane pores, which can be used to aid the interpretation of simulation studies. Different levels of molecular simulations of water within nanopores are described, with a focus on molecular dynamics (MD). In particular, models of water for MD simulations are discussed in detail to provide an evaluation of their use in simulations of water in nanopores. Simulation studies of the behavior of water in idealized models of nanopores have revealed aspects of the organization and dynamics of nanoconfined water, including wetting/dewetting in narrow hydrophobic nanopores. A survey of simulation studies in a range of nonbiological nanopores is presented, including carbon nanotubes, synthetic nanopores, model peptide nanopores, track-etched nanopores in polymer membranes, and hydroxylated and functionalized nanoporous silica. These reveal a complex relationship between pore size/geometry, the nature of the pore lining, and rates of water transport. Wider nanopores with hydrophobic linings favor water flow whereas narrower hydrophobic pores may show dewetting. Simulation studies over the past decade of the behavior of water in a range of biological nanopores are described, including porins and β-barrel protein nanopores, aquaporins and related polar solute pores, and a number of different classes of ion channels. Water is shown to play a key role in proton transport in biological channels and in hydrophobic gating of ion channels. An overall picture emerges, whereby the behavior of water in a nanopore may be predicted as a function of its hydrophobicity and radius. This informs our understanding of the functions of diverse channel structures and will aid the design of novel nanopores. Thus, our current level of understanding allows for the design of a nanopore which promotes wetting over dewetting or vice versa. However, to design a novel nanopore, which enables fast, selective, and gated flow of water de novo would remain challenging, suggesting a need for further detailed simulations alongside experimental evaluation of more complex nanopore systems.

Density functional theory based molecular dynamics study of solution composition effects on the solvation shell of metal ions

We present an ab initio molecular dynamics study of the alkali metal ions Li+, Na+, K+ and Cs+, and of the alkaline earth metal ions Mg2+ and Ca2+ in both pure water and electrolyte solutions containing the counterions Cl- and SO42-. Simulations were conducted using different density functional theory methods (PBE, BLYP and revPBE), with and without the inclusion of dispersion interactions (-D3). Analysis of the ion-water structure and interaction strength, water exchange between the first and second hydration shell, and hydrogen bond network and low-frequency reorientation dynamics around the metal ions have been used to characterise the influence of solution composition on the ionic solvation shell. Counterions affect the properties of the hydration shell not only when they are directly coordinated to the metal ion, but also when they are at the second coordination shell. Chloride ions reduce the sodium hydration shell and expand the calcium hydration shell by stabilizing under-coordinated hydrated Na(H2O)5+ complexes and over-coordinated Ca(H2O)72+. The same behaviour is observed in CaSO4(aq), where Ca2+ and SO42- form almost exclusively solvent-shared ion pairs. Water exchange between the first and second hydration shell around Ca2+ in CaSO4(aq) is drastically decelerated compared with the simulations of the hydrated metal ion (single Ca2+, no counterions). Velocity autocorrelation function analysis, used to probe the strength of the local ion-water interaction, shows a smoother decay of Mg2+ in MgCl2(aq), which is a clear indication of a looser inter-hexahedral vibration in the presence of chloride ions located in the second coordination shell of Mg2+. The hydrogen bond statistics and orientational dynamics in the ionic solvation shell show that the influence on the water-water network cannot only be ascribed to the specific cation-water interaction, but also to the subtle interplay between the level of hydration of the ions, and the interactions between ions, especially those of opposite charge. As many reactive processes involving solvated metal ions occur in environments that are far from pure water but rich in ions, this computational study shows how the solution composition can result in significant differences in behaviour and function of the ionic solvation shell.

Dynamic Properties of Water Confined in Graphene-Based Membrane: A Classical Molecular Dynamics Simulation Study

We performed molecular dynamics simulations of water molecules inside a hydrophobic membrane composed of stacked graphene sheets. By decreasing the density of water molecules inside the membrane, we observed that water molecules form a droplet through a hydrogen bond with each other in the hydrophobic environment that stacked graphene sheets create. We found that the water droplet translates as a whole body rather than a dissipate. The translational diffusion coefficient along the graphene surface increases as the number of water molecules in the droplet decreases, because the bigger water droplet has a stronger van der Waals interaction with the graphene surface that hampers the translational motion. We also observed a longer hydrogen bond lifetime as the density of water decreased, because the hydrophobic environment limits the libration motion of the water molecules. We also calculated the reorientational correlation time of the water molecules, and we found that the rotational motion of confined water inside the membrane is anisotropic and the reorientational correlation time of confined water is slower than that of bulk water. In addition, we employed steered molecular dynamics simulations for guiding the target molecule, and measured the free energy profile of water and ion penetration through the interstice between graphene sheets. The free energy profile of penetration revealed that the optimum interlayer distance for desalination is ~10 Å, where the minimum distance for water penetration is 7 Å. With a 7 Å interlayer distance between the graphene sheets, water molecules are stabilized inside the interlayer space because of the van der Waals interaction with the graphene sheets where sodium and chloride ions suffer from a 3–8 kcal/mol energy barrier for penetration. We believe that our simulation results would be a significant contribution for designing a new graphene-based membrane for desalination.

Translational and Rotational Diffusion in Liquid Water at Very High Pressure: A Simulation Study

Translational and rotational diffusion coefficients of liquid water have been computed from molecular dynamics simulation with a recent polarizable potential at 298, 400, and 550 K at very high pressure. At 298 K, the model reproduces the initial increase and the occurrence of a maximum for the translational and rotational diffusion coefficients when the pressure increases. At 400 and 550 K, translational and rotational diffusion coefficients are found to monotonically decrease when pressure increases in the gigapascal range, with the translational coefficient decreasing faster than the rotational one. At 400 K, such an evolution of the rotational diffusion coefficient contrasts with quasielastic neutron scattering results predicting a near independence of the rotational diffusion with a pressure increase above ≃0.5 GPa. An interpretation is proposed to explain this discrepancy. The pressure dependence of the translation-rotation coupling is analyzed. The anisotropy of rotational diffusion is investigated by computing the rotational diffusion tensor in a molecular system of axes and the reorientational correlation times of rank 1 and rank 2 of the inertia axes and of the OH bond vector. Deviation of the simulation data with respect to the predictions of the isotropic Debye model of rotational diffusion are quantified and can be used to estimate experimental rotational diffusion coefficients from experimental reorientational correlation times.

Protein Solvent Shell Structure Provides Rapid Analysis of Hydration Dynamics

The solvation layer surrounding a protein is clearly an intrinsic part of protein structure-dynamics-function, and our understanding of how the hydration dynamics influences protein function is emerging. We have recently reported simulations indicating a correlation between regional hydration dynamics and the structure of the solvation layer around different regions of the enzyme Candida antarctica lipase B, wherein the radial distribution function (RDF) was used to calculate the pairwise entropy, providing a link between dynamics (diffusion) and thermodynamics (excess entropy) known as Rosenfeld scaling. Regions with higher RDF values/peaks in the hydration layer (the first peak, within 6 Å of the protein surface) have faster diffusion in the hydration layer. The finding thus hinted at a handle for rapid evaluation of hydration dynamics at different regions on the protein surface in molecular dynamics simulations. Such an approach may move the analysis of hydration dynamics from a specialized venture to routine analysis, enabling an informatics approach to evaluate the role of hydration dynamics in biomolecular function. This paper first confirms that the correlation between regional diffusive dynamics and hydration layer structure (via water center of mass around protein side-chain atom RDF) is observed as a general relationship across a set of proteins. Second, it seeks to devise an approach for rapid analysis of hydration dynamics, determining the minimum amount of information and computational effort required to get a reliable value of hydration dynamics from structural data in MD simulations based on the protein-water RDF. A linear regression model using the integral of the hydration layer in the water-protein RDF was found to provide statistically equivalent apparent diffusion coefficients at the 95% confidence level for a set of 92 regions within five different proteins. In summary, RDF analysis of 10 ns of data after simulation convergence is sufficient to accurately map regions of fast and slow hydration dynamics around a protein surface. Additionally, it is anticipated that a quick look at protein-water RDFs, comparing peak heights, will be useful to provide a qualitative ranking of regions of faster and slower hydration dynamics at the protein surface for rapid analysis when investigating the role of solvent dynamics in protein function.

Photochemistry and Photophysics in Silica-Based Materials: Ultrafast and Single Molecule Spectroscopy Observation

Silica-based materials (SBMs) are widely used in catalysis, photonics, and drug delivery. Their pores and cavities act as hosts of diverse guests ranging from classical dyes to drugs and quantum dots, allowing changes in the photochemical behavior of the confined guests. The heterogeneity of the guest populations as well as the confinement provided by these hosts affect the behavior of the formed hybrid materials. As a consequence, the observed reaction dynamics becomes significantly different and complex. Studying their photobehavior requires advanced laser-based spectroscopy and microscopy techniques as well as computational methods. Thanks to the development of ultrafast (spectroscopy and imaging) tools, we are witnessing an increasing interest of the scientific community to explore the intimate photobehavior of these composites. Here, we review the recent theoretical and ultrafast experimental studies of their photodynamics and discuss the results in comparison to those in homogeneous media. The discussion of the confined dynamics includes solvation and intra- and intermolecular proton-, electron-, and energy transfer events of the guest within the SBMs. Several examples of applications in photocatalysis, (photo)sensors, photonics, photovoltaics, and drug delivery demonstrate the vast potential of the SBMs in modern science and technology.

A slowing down of proton motion from HPTS to water adsorbed on the MCM-41 surface

We report on the steady-state and femtosecond-nanosecond (fs-ns) behaviour of 8-hydroxypyrene-1,3,6-trisulfonate (pyranine, HPTS) and its interaction with mesoporous silica based materials (MCM-41) in both solid-state and dichloromethane (DCM) suspensions in the absence and presence of water. In the absence of water, HPTS forms aggregates which are characterized by a broad emission spectrum and multiexponential behavior (τsolid-state/DCM = 120 ps, 600 ps, 2.2 ns). Upon interaction with MCM41, the aggregate population is found to be lower, leading to the formation of adsorbed monomers. In the presence of water (1%), HPTS with and without MCM41 materials in DCM suspensions undergoes an excited-state intermolecular proton-transfer (ESPT) reaction in the protonated form (ROH*) producing a deprotonated species (RO(-)*). The long-time emission decays of the ROH* in different systems in the presence of water are multiexponential, and are analysed using the diffusion-assisted geminate recombination model. The obtained proton-transfer and recombination rate constants for HPTS and HPTS/MCM41 complexes in DCM suspensions in the presence of water are kPT = 13 ns(-1), krec = 7.5 Å ns(-1), and kPT = 5.4 ns(-1), krec = 2.2 Å ns(-1), respectively, The slowing down of both processes in the latter case is explained in terms of specific interactions of the dye and of the water molecules with the silica surface. The ultrafast dynamics (fs-regime) of the HPTS/MCM41 complexes in DCM suspensions, without and with water, shows two components which are assigned to intramolecular vibrational-energy relaxation (IVR) (∼120 fs vs. ∼0.8 ps), and vibrational relaxation/cooling (VC), and charge transfer (CT) processes (∼2 ps without water and ∼5 ps with water) of the adsorbed ROH*. Our results provide new knowledge on the interactions and the proton-transfer reaction dynamics of HPTS adsorbed on mesoporous materials.

Simulations of outer membrane channels and their permeability

Channels in the outer membrane of Gram-negative bacteria provide essential pathways for the controlled and unidirectional transport of ions, nutrients and metabolites into the cell. At the same time the outer membrane serves as a physical barrier for the penetration of noxious substances such as antibiotics into the bacteria. Most antibiotics have to pass through these membrane channels to either reach cytoplasmic bound targets or to further cross the hydrophobic inner membrane. Considering the pharmaceutical significance of antibiotics, understanding the functional role and mechanism of these channels is of fundamental importance in developing strategies to design new drugs with enhanced permeation abilities. Due to the biological complexity of membrane channels and experimental limitations, computer simulations have proven to be a powerful tool to investigate the structure, dynamics and interactions of membrane channels. Considerable progress has been made in computer simulations of membrane channels during the last decade. The goal of this review is to provide an overview of the computational techniques and their roles in modeling the transport across outer membrane channels. A special emphasis is put on all-atom molecular dynamics simulations employed to better understand the transport of molecules. Moreover, recent molecular simulations of ion, substrate and antibiotics translocation through membrane pores are briefly summarized. This article is part of a Special Issue entitled: Membrane Proteins edited by J.C. Gumbart and Sergei Noskov.

Potassium ions in the cavity of a KcsA channel model

The high rate of ion flux and selectivity of potassium channels has been attributed to the conformation and dynamics of the ions in the filter which connects the channel cavity and the extracellular environment. The cavity serves as the reservoir for potassium ions diffusing from the intracellular medium. The cavity is believed to decrease the dielectric barrier for the ions to enter the filter. We study here the equilibrium and dynamic properties of potassium ions entering the water-filled cavity of a KcsA channel model. Atomistic molecular dynamics simulations that are supplemented by electrostatic calculations reveal the important role of water molecules and the partially charged protein helices at the bottom of the cavity in overcoming the energy barrier and stabilizing the potassium ion in the cavity. We further show that the average time for a potassium ion to enter the cavity is much shorter than the conduction rate of a potassium passing through the filter, and this time duration is insensitive over a wide range of the membrane potential. The conclusions drawn from the study of the channel model are applicable in generalized contexts, including the entry of ions in artificial ion channels and other confined geometries.

Effects of confinement on the structure and dynamics of an intrinsically disordered peptide: a molecular-dynamics study

In vivo, proteins and peptides are exposed to radically different environments than those in bulk. Because of the abundance of other cellular components, proteins perform their function in crowded and confined spaces. Confinement has been shown to alter the structure, dynamics, and folding of proteins that possess a native fold. Little is known, however, of the effects of confinement on biologically important intrinsically disordered proteins or peptides (IDP). Here, we use extensive molecular dynamics simulations to investigate the effects of confinement in an IDP, the Aβ21-30, a central folding nucleus of the full length amyloid β-protein. In this study, we report results derived from 107 μs of molecular dynamics simulations that subjected the Aβ21-30 to two types of confinement: hydrophilic and hydrophobic pores. Results show that turn structures are enhanced as a function of decreasing pore size (increasing confinement) over other structures, including coils, β-hairpins, and bridges. However, the percentage occurrence of the dominant hydrogen bond between amino acids Asp23 and Ser26 shown to stabilize the turn in bulk simulations does not increase as a function of confinement signifying a disconnect between structure and internal hydrogen bonding. Differences in structure and dynamics of the decapeptide due to hydrophilic and hydrophobic confinement are more apparent at the extreme confinement conditions, where a reduction of the available phase space in hydrophilic confinement is explained in terms of interactions between the decapeptide and a layer of water at the interface between the decapeptide and the surface of the pore, and a smaller size of the decapeptide in the hydrophobic pores is rationalized in terms of peptide-surface interactions.

Derivation and assessment of phase-shifted, disordered vector field models for frustrated solvent interactions

The structure and properties of water at biological interfaces differ drastically from bulk due to effects including confinement and the presence of complicated charge distributions. This non-bulk-like behavior generally arises from water frustration, wherein all favorable interactions among water molecules cannot be simultaneously satisfied. While the frustration of interfacial water is ubiquitous in the cell, the role this frustration plays in mediating biophysical processes like protein folding is not well understood. To investigate the impact of frustration at interfaces, we here derive a general field theoretic model for the interaction of bulk and disordered vector fields at an embedded surface. We calculate thermodynamic and correlation functions for the model in two and three dimensions, and we compare our results to Monte Carlo simulations of lattice system analogs. In our analysis, we see that field-field cross correlations near the interface in the model give rise to a loss in entropy like that seen in glassy systems. We conclude by assessing our theory's utility as a coarse-grained model for water at polar biological interfaces.

Quantum Dynamics in Continuum for Proton Transport I: Basic Formulation

Proton transport is one of the most important and interesting phenomena in living cells. The present work proposes a multiscale/multiphysics model for the understanding of the molecular mechanism of proton transport in transmembrane proteins. We describe proton dynamics quantum mechanically via a density functional approach while implicitly model other solvent ions as a dielectric continuum to reduce the number of degrees of freedom. The densities of all other ions in the solvent are assumed to obey the Boltzmann distribution. The impact of protein molecular structure and its charge polarization on the proton transport is considered explicitly at the atomic level. We formulate a total free energy functional to put proton kinetic and potential energies as well as electrostatic energy of all ions on an equal footing. The variational principle is employed to derive nonlinear governing equations for the proton transport system. Generalized Poisson-Boltzmann equation and Kohn-Sham equation are obtained from the variational framework. Theoretical formulations for the proton density and proton conductance are constructed based on fundamental principles. The molecular surface of the channel protein is utilized to split the discrete protein domain and the continuum solvent domain, and facilitate the multiscale discrete/continuum/quantum descriptions. A number of mathematical algorithms, including the Dirichlet to Neumann mapping, matched interface and boundary method, Gummel iteration, and Krylov space techniques are utilized to implement the proposed model in a computationally efficient manner. The Gramicidin A (GA) channel is used to demonstrate the performance of the proposed proton transport model and validate the efficiency of proposed mathematical algorithms. The electrostatic characteristics of the GA channel is analyzed with a wide range of model parameters. The proton conductances are studied over a number of applied voltages and reference concentrations. A comparison with experimental data verifies the present model predictions and validates the proposed model.

Claudin-17 forms tight junction channels with distinct anion selectivity

Barrier properties of tight junctions are determined by the claudin protein family. Many claudins seal this barrier, but others form paracellular channels. Among these, no claudins with general and clear-cut anion selectivity have yet been described, while for claudin-10a and claudin-4, only circumstantial or small anion selectivities have been shown. A claudin with unknown function and tissue distribution is claudin-17. We characterized claudin-17 by overexpression and knock-down in two renal cell lines. Overexpression in MDCK C7 cell layers caused a threefold increase in paracellular anion permeability and switched these cells from cation- to anion-selective. Knockdown in LLC-PK(1) cells indorsed the finding of claudin-17-based anion channels. Mutagenesis revealed that claudin-17 anion selectivity critically depends on a positive charge at position 65. Claudin-17 expression was found in two organs: marginal in brain but abundant in kidney, where expression was intense in proximal tubules and gradually decreased towards distal segments. As claudin-17 is predominantly expressed in proximal nephrons, which exhibit substantial, though molecularly not defined, paracellular chloride reabsorption, we suggest that claudin-17 has a unique physiological function in this process. In conclusion, claudin-17 forms channels within tight junctions with distinct anion preference.

Effect of cosolvents on nano-confined water: a molecular dynamics study

We present results from atomistic molecular dynamics simulations to characterize the effects of cosolvents, such as urea and guanidinium (Gdm) salts, on the water confined in hydrophobic carbon nanotubes. We observed complete drying of the nanotube interiors of diameter ranging from 8 to 17 Å in urea. In contrast, the water population within nanotube cores smaller than 12 Å remains unaffected in GdmCl solution, whereas larger nanotube interiors become partially dehydrated with prevailing presence of stable Gdm(+)-Gdm(+) dimers. The molecular arrangement and the lifetime inside the nanotube were found to be characteristics of a particular cosolvent. In both urea and GdmCl solutions, preferential cosolvent intrusion resulting in nanotube dehydration is driven by the stronger dispersion interaction of cosolvent than water with the nanotube. The partial drying of the hydrophobic core is attributed to guanidinium's better hydration and weaker self-association propensity compared to urea, as well as to its moderate ion-pairing with strongly hydrated chloride ions. The Gdm(+) induced dehydration varies with the charge density of counter-ions, as the presence of high charge-density sulfate ions impedes penetration of guanidinium, and consequent dehydration of the nanotube. These findings provide important insights into the effect of cosolvents on the nano-confined water in a hydrophobic environment.

Temperature and pressure dependence of the optimized soft-sticky dipole-quadrupole-octupole water model

The soft-sticky dipole-quadrupole-octupole (SSDQO) potential energy function for a coarse-grained single-site water model has Lennard-Jones interactions and an approximate multipole expansion for the electrostatics. Here, the Lennard-Jones parameters and multipole moments of SSDQO were optimized so that the structural, thermodynamic, dynamic, and dielectric properties agreed with experimental values of liquid water at ambient conditions. Using these parameters, the temperature and pressure dependence of various properties were shown to be in good agreement with experiment, including a temperature of maximum density at approximately 260 K. This new parametrization, referred to as SSDQO1, is both computationally faster and generally more accurate over a wide range of conditions than traditional three-site water models, which demonstrates that a model with a single dipole, quadrupole, and octupole on each water molecule can reproduce the tetrahedral hydrogen bonded network of water.

Importance of van der Waals interactions in liquid water

We present ab initio molecular dynamics studies on liquid water using density functional theory in conjunction with either dispersion-corrected atom-centered potentials or empirical van der Waals corrections. Our results show that improving the description of van der Waals interactions in DFT-GGA leads to a softening of liquid water's structure with higher mobility. The results obtained with dispersion-corrected atom-centered potentials are especially encouraging. In particular, the radial distribution functions are in better agreement with experiment, and the self-diffusion coefficient increases by more than three-fold compared with the one predicted by the BLYP functional. This work demonstrates that van der Waals interactions are essential in fine-tuning both structural and dynamical properties of liquid water.

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.

Estimating the dielectric constant of the channel protein and pore

When modelling biological ion channels using Brownian dynamics (BD) or Poisson-Nernst-Planck theory, the force encountered by permeant ions is calculated by solving Poisson's equation. Two free parameters needed to solve this equation are the dielectric constant of water in the pore and the dielectric constant of the protein forming the channel. Although these values can in theory be deduced by various methods, they do not give a reliable answer when applied to channel-like geometries that contain charged particles. To determine the appropriate values of the dielectric constants, here we solve the inverse problem. Given the structure of the MthK channel, we attempt to determine the values of the protein and pore dielectric constants that minimize the discrepancies between the experimentally-determined current-voltage curve and the curve obtained from BD simulations. Two different methods have been applied to determine these values. First, we use all possible pairs of the pore dielectric constant of water, ranging from 20 to 80 in steps of 10, and the protein dielectric constant of 2-10 in steps of 2, and compare the simulated results with the experimental values. We find that the best agreement is obtained with experiment when a protein dielectric constant of 2 and a pore water dielectric constant of 60 is used. Second, we employ a learning-based stochastic optimization algorithm to pick out the optimum combination of the two dielectric constants. From the algorithm we obtain an optimum value of 2 for the protein dielectric constant and 64 for the pore dielectric constant.

Dynamical properties of the soft sticky dipole-quadrupole-octupole water model: a molecular dynamics study

The dynamical properties of the soft sticky dipole-quadrupole-octupole (SSDQO) water model using SPC/E moments are calculated utilizing molecular dynamics simulations. This new potential for liquid water describes the water-water interactions by a Lennard-Jones term and a sticky potential, which is an approximate moment expansion with point dipole, quadrupole, and octupole moments, and reproduces radial distribution functions of pure liquid water using the moments of SPC/E [Ichiye and Tan, J. Chem. Phys. 124, 134504 (2006)]. The forces and torques of SSDQO water for the dipole-quadrupole, quadrupole-quadrupole, and dipole-octupole interactions are derived here. The simulations are carried out at 298 K in the microcanonical ensemble employing the Ewald method for the long-range dipole-dipole interactions. Here, various dynamical properties associated with translational and rotational motions of SSDQO water using the moments of SPC/E (SSDQO:SPC/E) water are compared with the results from SPC/E and also experiment. The self-diffusion coefficient of SSDQO:SPC/E water is found to be in excellent agreement with both SPC/E and experiment whereas the single particle orientational relaxation time for dipole vector is better than SPC/E water but it is somewhat smaller than experiment. The dielectric constant of SSDQO:SPC/E is essentially identical to SPC/E, and both are slightly lower than experiment. Also, molecular dynamics simulations of the SSDQO water model are found to be about twice as fast as three-site models such as SPC/E.

Grand canonical Monte Carlo simulations of water in protein environments

The grand canonical simulation algorithm is considered as a general methodology to sample the configuration of water molecules confined within protein environments. First, the probability distribution of the number of water molecules and their configuration in a region of interest for biochemical simulations, such as the active site of a protein, is derived by considering a finite subvolume in open equilibrium with a large system serving as a bulk reservoir. It is shown that the influence of the bulk reservoir can be represented as a many-body potential of mean force acting on the atoms located inside the subvolume. The grand canonical Monte Carlo (GCMC) algorithm, augmented by a number of technical advances to increase the acceptance of insertion attempts, is implemented, and tested for simple systems. In particular, the method is illustrated in the case of a pure water box with periodic boundary conditions. In addition, finite spherical systems of pure water and containing a dialanine peptide, are simulated with GCMC while the influence of the surrounding infinite bulk is incorporated using the generalized solvent boundary potential [W. Im, S. Berneche, and B. Roux, J. Chem. Phys. 114, 2924 (2001)]. As a last illustration of water confined in the interior of a protein, the hydration of the central cavity of the KcsA potassium channel is simulated.

Claudin-8 modulates paracellular permeability to acidic and basic ions in MDCK II cells

Renal net acid excretion requires tubular reabsorption of filtered bicarbonate, followed by secretion of protons and ammonium in the collecting duct, generating steep transtubular gradients for these ions. To prevent passive backleak of these ions, the tight junctions in the collecting duct must be highly impermeable to these ions. We previously generated a Madin-Darby canine kidney (MDCK II) cell line with inducible expression of claudin-8, a tight junction protein expressed in the collecting duct. In these cells, claudin-8 was shown to function as a paracellular barrier to alkali metal and divalent cations. We have now used this model to test the hypothesis that claudin-8 also functions as a paracellular barrier to acidic or basic ions involved in renal acid excretion. We developed a series of precise and unbiased methods, based on a combination of diffusion potential, short-circuit current, and pH stat measurements, to estimate paracellular permeability to protons, ammonium and bicarbonate in MDCK II cells. We found that under control conditions (i.e. in the absence of claudin-8), these cells are highly permeable to the acidic and basic ions tested. Interestingly, proton permeation exhibited an unusually low activation energy similar to that in bulk solution. This suggests that paracellular proton transfer may occur by a Grotthuss mechanism, implying that the paracellular pores are sufficiently wide to accommodate water molecules in a freely mobile state. Induction of claudin-8 expression reduces permeability not only to protons, but also to ammonium and bicarbonate. We conclude that claudin-8 probably functions to limit the passive leak of these three ions via paracellular routes, thereby playing a permissive role in urinary net acid excretion.

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.

Role of water molecules in the KcsA protein channel by molecular dynamics calculations

Molecular dynamics simulations supported by electrostatic calculations have been conducted on the KcsA channel to determine the role of water molecules in the pore. Starting from the X-ray structure of the KcsA channel in its closed state at 2.0 angstroms resolution, the opening of the pore towards a conformation built on the basis of EPR results is studied. We show that water molecules act as a structural element for the K+ ions inside the filter and the hydrophobic cavity of the channel. In the filter, water tends to enhance the depth of the wells occupied by the K+ ions, while in the cavity there is a strong correlation between the water molecules and the cavity ion. As a consequence, the protein remains very stable in the presence of three K+ ions in the selectivity filter and one in the cavity. The analysis of the dynamics of water molecules in the cavity reveals preferred orientations of the dipoles along the pore axis, and a correlated behavior between this dipole orientation and the displacement of the K+ ion during the gating process.

Water molecules in hydroxy/acid networks as a competition between dynamics and bonding. Synthesis of a wet hydrophobic pore

In a model formed by hydroxy acids with a general structure (+/-)-1, we found that solid-state structures depend on steric interactions. Thus, with the exception of molecules 1b and 1e, compounds (+/-)-1a-(+/-)-1m, which possess bulky and conformationally rigid substituents, aggregate by forming tapes and sheets by alternating (+) and (-) subunits held together via carboxylic acid to alcohol hydrogen bonds. Homologue (+/-)-1n with conformationally flexible substituents, which allow conformational deformation gives, by way of the incorporation of water molecules, an efficient hexagonal assembly, which extends to the third-dimension to form tubular H-bonding networks. Each puckered channel can be described as being interconnected by closely packed hexagons in chair-like conformations. The ethyl groups presented in (+/-)-1n provided the volume required to lock the inner hexagonal wall into a rigid structure.

Glycerol conductance and physical asymmetry of the Escherichia coli glycerol facilitator GlpF

The aquaglyceroporin GlpF is a transmembrane channel of Escherichia coli that facilitates the uptake of glycerol by the cell. Its high glycerol uptake rate is crucial for the cell to survive in very low glycerol concentrations. Although GlpF allows both influx and outflux of glycerol, its structure, similar to the structure of maltoporin, exhibits a significant degree of asymmetry. The potential of mean force characterizing glycerol in the channel shows a corresponding asymmetry with an attractive vestibule only at the periplasmic side. In this study, we analyze the potential of mean force, showing that a simplified six-step model captures the kinetics and yields a glycerol conduction rate that agrees well with observation. The vestibule improves the conduction rate by 40% and 75% at 10- micro M and 10-mM periplasmic glycerol concentrations, respectively. In addition, neither the conduction rate nor the conduction probability for a single glycerol (efficiency) depends on the orientation of GlpF. GlpF appears to conduct equally well in both directions under physiological conditions.

Protons in Supercritical Water: A Multistate Empirical Valence Bond Study

Molecular dynamics simulations have been performed to analyze microscopic details related to aqueous solvation of excess protons along the supercritical T = 673 K isotherm, spanning a density interval from a typical liquid down to vapor environments. The simulation methodology relies on a multistate empirical valence bond Hamiltonian model that includes a proton translocation mechanism. Our results predict a gradual stabilization of the solvated Eigen cation [H(3)O.(H(2)O)(3)](+) at lower densities, in detriment of the symmetric Zundel dimer [H.(H(2)O)(2)](+). At all densities, the average solvation structure in the close vicinity of the hydronium is characterized by three hydrogen bond acceptor water molecules and presents minor changes in the solute water distances. Characteristic times for the proton translocation jumps have been computed using population relaxation time correlation functions. Compared to room temperature results, the rates at high densities are 4 times faster and become progressively slower in steamlike environments. Diffusion coefficients for the excess proton have also been computed. In agreement with conductometric data, our results show that contributions from the Grotthus mechanism to the overall proton transport diminish at lower densities and predict that in steamlike environments, the proton diffusion is almost 1 order of magnitude slower than that for pure water. Spectroscopic information for the solvated proton is accordant to the gradual prevalence of proton localization in Eigen-like structures at lower densities.

A novel approach for designing simple point charge models for liquid water with three interaction sites

A simultaneous improvement of the diffusion and dielectric properties of the simple point charge (SPC) model for liquid water appears to be very difficult with conventional reparametrization of the commonly used Lennard-Jones and Coulomb interaction functions and without including a self-energy correction in the effective pair-potential as is done in the SPC/E model. Here, a different approach to circumvent this problem is presented. A short-range interaction term, which corrects the oxygen-oxygen energy at small distances by small amounts of energy, was introduced in the nonbonded interaction function. This additional force-field term allows to derive new parameter sets for SPC-like water models that yield better agreement with experimental data on liquid water. Based on previous investigations of the force-field parameter dependence of the water properties of SPC-like models, the necessary parameter changes to obtain a lower diffusion coefficient and a larger dielectric permittivity were specified and accordingly six new models were developed. They all represent an improvement over SPC in terms of structural and diffusional properties, four of them show better dielectric properties also. One model, SPC/S, has been characterized in more detail, and represents most properties of liquid water better than SPC while avoiding the larger discrepancies with experimental values regarding density, thermal compressibility, energy, and free energy of the SPC/E model. We conclude that the use of a simple, short-ranged additional oxygen-oxygen interaction term makes a simultaneous improvement of the diffusion coefficient and the dielectric properties of water feasible.

Voltage-gated proton channels and other proton transfer pathways

Proton channels exist in a wide variety of membrane proteins where they transport protons rapidly and efficiently. Usually the proton pathway is formed mainly by water molecules present in the protein, but its function is regulated by titratable groups on critical amino acid residues in the pathway. All proton channels conduct protons by a hydrogen-bonded chain mechanism in which the proton hops from one water or titratable group to the next. Voltage-gated proton channels represent a specific subset of proton channels that have voltage- and time-dependent gating like other ion channels. However, they differ from most ion channels in their extraordinarily high selectivity, tiny conductance, strong temperature and deuterium isotope effects on conductance and gating kinetics, and insensitivity to block by steric occlusion. Gating of H(+) channels is regulated tightly by pH and voltage, ensuring that they open only when the electrochemical gradient is outward. Thus they function to extrude acid from cells. H(+) channels are expressed in many cells. During the respiratory burst in phagocytes, H(+) current compensates for electron extrusion by NADPH oxidase. Most evidence indicates that the H(+) channel is not part of the NADPH oxidase complex, but rather is a distinct and as yet unidentified molecule.

Analysis and evaluation of channel models: simulations of alamethicin

Alamethicin is an antimicrobial peptide that forms stable channels with well-defined conductance levels. We have used extended molecular dynamics simulations of alamethicin bundles consisting of 4, 5, 6, 7, and 8 helices in a palmitoyl-oleolyl-phosphatidylcholine bilayer to evaluate and analyze channel models and to link the models to the experimentally measured conductance levels. Our results suggest that four helices do not form a stable water-filled channel and might not even form a stable intermediate. The lowest measurable conductance level is likely to correspond to the pentamer. At higher aggregation numbers the bundles become less symmetrical. Water properties inside the different-sized bundles are similar. The hexamer is the most stable model with a stability comparable with simulations based on crystal structures. The simulation was extended from 4 to 20 ns or several times the mean passage time of an ion. Essential dynamics analyses were used to test the hypothesis that correlated motions of the helical bundles account for high-frequency noise observed in open channel measurements. In a 20-ns simulation of a hexameric alamethicin bundle, the main motions are those of individual helices, not of the bundle as a whole. A detailed comparison of simulations using different methods to treat long-range electrostatic interactions (a twin range cutoff, Particle Mesh Ewald, and a twin range cutoff combined with a reaction field correction) shows that water orientation inside the alamethicin channels is sensitive to the algorithms used. In all cases, water ordering due to the protein structure is strong, although the exact profile changes somewhat. Adding an extra 4-nm layer of water only changes the water ordering slightly in the case of particle mesh Ewald, suggesting that periodicity artifacts for this system are not serious.

Geometrical modelling of Ohmic conductance in ion channels

In an Ohmic model, channel conductivity can be described in terms of the geometry of a conducting cable. The essential features of such devices are the arc length of the curve describing the channel's longitudinal path, and the cross-sectional areas transversal to this curve. In a first approximation, conducting channels can be represented by an average molecular shape with estimated lengths and cross-sectional areas. Whereas the physical shortcomings of this approach are known, its accuracy limitations in practice have not been established. In this work, we discuss an improved model for the channel's shape, one that allows us to gauge how much of the Ohmic conductivity can be assigned purely to geometrical features. In the present algorithm, we investigate all regions inside the pore that are accessible to ions using various choices for the molecular surface of the inner channel. We discuss the agreement with experimental conductances in the case of 12 channels (cholera toxin B-subunit pentamer, Staphylococcus aureus alpha-hemolysin, Streptomyces lividans KcsA channel, seven porins, gramicidin A, and phospholamban). Our results can be regarded as a benchmark for the best performance that can be expected from a geometrical model of conductance. Consequently, significant deviations from experimental trends can safely be assigned to non-geometrical factors, namely the specific composition of the ion channel and the detailed electrostatic interactions between the channel and a particular ion.