The dielectric properties of water within model transbilayer pores

Nonlinear Effects of Hydrophobic Confinement on the Electronic Structure and Dielectric Response of Water

Fundamental studies of the dielectrics of confined water are critical to understand the ion transport across biological and synthetic nanochannels. The relevance of these fundamental studies, however, surmounts the difficulty of probing water's dielectric constant as a function of a fine variation in confinement. In this work, we explore the computational efficiency of machine learning potentials to derive the confinement effects on the dielectric constant, polarization, and dipole moment of water. Our simulations predict an enhancement of the axial dielectric constant of water under extreme confinement, arising from either the formation of ferroelectric structures of ordered water or larger dipole fluctuations facilitated by the disruption of water's H-bond network. Our study highlights the impact of hydrophobic nanoconfinement on the dielectric constant and on the ionic and electronic structure of water molecules, pointing to the importance of geometric flexibility and electronic polarizability to properly model confinement effects on water.

Reaction within the coulomb-cage; science in retrospect

The Coulomb-cage is defined as the space where the electrostatic interaction between two bodies is more intensive than the thermal energy (k_BT). For small molecule, the Coulomb-cage is a small sphere, extending only few water molecules towards the bulk and its radius is sensitive to the ionic strength of the solution. For charged proteins or membranal structures, the Coulomb-cage can engulf large fraction of the surface and provides a preferred pathway for ion propagation along the surface. Similarly, electrostatic potential at the inner space of a channel can form preferential trajectories passage for ions. The dynamics of ions inside the Coulomb-cage of ions was formulated by the studies of proton-anion recombination of excited photoacids. In the present article, we recount the study of intra- Coulomb-cage reaction taking place on the surface of macro-molecular bodies like micelles, membranes, proteins and intra-protein cavities. The study progressed stepwise, tracing the dynamics of a proton ejected from a photo-acid molecule located at defined sites (on membrane, inter-membrane space, active site of enzyme, inside Large Pore Channels etc.). Accumulation of experimental observations encouraged us to study of the reaction mechanism by molecular dynamics simulations of ions within the Coulomb-cage of proteins surface or inside large pores. The intra-Coulomb-cage proton transfer events follows closely the fine structure of the electrostatic field inside the cage and reflects the shape of nearby dielectric boundaries, the temporal ordering of the solvent molecules and the structural fluctuations of the charged side chains. The article sums some 40 years of research, which in retrospect clarifies the intra-Coulomb-cage reaction mechanism.

Ribosome exit tunnel electrostatics

The impact of ribosome exit tunnel electrostatics on the protein elongation rate or on forces acting upon the nascent polypeptide chain are currently not fully elucidated. In the past, researchers have measured the electrostatic potential inside the ribosome polypeptide exit tunnel at a limited number of spatial points, at least in rabbit reticulocytes. Here we present a basic electrostatic model of the exit tunnel of the ribosome, providing a quantitative physical description of the tunnel interaction with the nascent proteins at all centro-axial points inside the tunnel. We show that a strong electrostatic screening is due to water molecules (not mobile ions) attracted to the ribosomal nucleic acid phosphate moieties buried in the immediate vicinity of the tunnel wall. We also show how the tunnel wall components and local ribosomal protein protrusions impact on the electrostatic potential profile and impede charged amino acid residues from progressing through the tunnel, affecting the elongation rate in a range of -40% to +85% when compared to the average elongation rate. The time spent by the ribosome to decode the genetic encrypted message is constrained accordingly. We quantitatively derive, at single-residue resolution, the axial forces acting on the nascent peptide from its particular sequence embedded in the tunnel. The model sheds light on how the experimental data point measurements of the potential are linked to the local structural chemistry of the inner wall, shape, and size of the tunnel. The model consistently connects experimental observations coming from different fields in molecular biology, x-ray crystallography, physical chemistry, biomechanics, and synthetic and multiomics biology. Our model should be a valuable tool to gain insight into protein synthesis dynamics, translational control, and the role of the ribosome's mechanochemistry in the cotranslational protein folding.

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

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

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.

Water and hydrophobic gates in ion channels and nanopores

Simulations of water behaviour have been used to probe hydrophobic gates in BEST1 and TMEM175, which can reveal important design principles for the engineering of gates in novel biomimetic nanopores.

Ion channel proteins form nanopores in biological membranes which allow the passage of ions and water molecules. Hydrophobic constrictions in such pores can form gates, i.e. energetic barriers to water and ion permeation. Molecular dynamics simulations of water in ion channels may be used to assess whether a hydrophobic gate is closed (i.e. impermeable to ions) or open. If there is an energetic barrier to water permeation then it is likely that a gate will also be impermeable to ions. Simulations of water behaviour have been used to probe hydrophobic gates in two recently reported ion channel structures: BEST1 and TMEM175. In each of these channels a narrow region is formed by three consecutive rings of hydrophobic sidechains and in both cases such analysis demonstrates that the crystal structures correspond to a closed state of the channel. In silico mutations of BEST1 have also been used to explore the effect of changes in the hydrophobicity of the gating constriction, demonstrating that substitution of hydrophobic sidechains with more polar sidechains results in an open gate which allows water permeation. A possible open state of the TMEM175 channel was modelled by the in silico expansion of the hydrophobic gate resulting in the wetting of the pore and free permeation of potassium ions through the channel. Finally, a preliminary study suggests that a hydrophobic gate motif can be transplanted in silico from the BEST1 channel into a simple β-barrel pore template. Overall, these results suggest that simulations of the behaviour of water in hydrophobic gates can reveal important design principles for the engineering of gates in novel biomimetic nanopores.

Gating Charge Calculations by Computational Electrophysiology Simulations

Electrical cell signaling requires adjustment of ion channel, receptor, or transporter function in response to changes in membrane potential. For the majority of such membrane proteins, the molecular details of voltage sensing remain insufficiently understood. Here, we present a molecular dynamics simulation-based method to determine the underlying charge movement across the membrane-the gating charge-by measuring electrical capacitor properties of membrane-embedded proteins. We illustrate the approach by calculating the charge transfer upon membrane insertion of the HIV gp41 fusion peptide, and validate the method on two prototypical voltage-dependent proteins, the Kv1.2 K⁺ channel and the voltage sensor of the Ciona intestinalis voltage-sensitive phosphatase, against experimental data. We then use the gating charge analysis to study how the T1 domain modifies voltage sensing in Kv1.2 channels and to investigate the voltage dependence of the initial binding of two Na⁺ ions in Na⁺-coupled glutamate transporters. Our simulation approach quantifies various mechanisms of voltage sensing, enables direct comparison with experiments, and supports mechanistic interpretation of voltage sensitivity by fractional amino acid contributions.

Macroscopic electric field inside water-filled biological nanopores

Multi-drug resistance bacteria are a challenging problem of contemporary medicine. This is particularly critical for Gram-negative bacteria, where antibiotics are hindered by the outer membrane to reach internal targets. Here more polar antibiotics make use of nanometric water-filled channels to permeate inside. We present in this work a computational all-atom approach, using water as a probe, for the calculation of the macroscopic electric field inside water-filled channels. The method allows one to compare not only different systems but also the same system under different conditions, such as pH and ion concentration. This provides a detailed picture of electrostatics in biological nanopores shedding more light on how the charged residues of proteins determine the electric field inside, and also how medium can tune it. These details are central to unveil the filtering mechanism behind the permeation of small polar molecules through nanometric water-filled channels.

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.

Mechanisms of transfer of bioactive molecules through the cell membrane by electroporation

A short review of biophysical mechanisms for electrotransfer of bioactive molecules through the cell membrane by using electroporation is presented. The concept of transient hydrophilic aqueous pores and membrane electroporation mechanisms of single cells and cells in suspension models are analyzed. Alongside the theoretical approach, some peculiarities of drug and gene electrotransfer into cells and applications in clinical trials are discussed.

Electromagnetic fields (UHF) increase voltage sensitivity of membrane ion channels; possible indication of cell phone effect on living cells

The effects of ultra high frequency (UHF) nonionizing electromagnetic fields (EMF) on the channel activities of nanopore forming protein, OmpF porin, were investigated. The voltage clamp technique was used to study the single channel activity of the pore in an artificial bilayer in the presence and absence of the electromagnetic fields at 910 to 990 MHz in real time. Channel activity patterns were used to address the effect of EMF on the dynamic, arrangement and dielectric properties of water molecules, as well as on the hydration state and arrangements of side chains lining the channel barrel. Based on the varied voltage sensitivity of the channel at different temperatures in the presence and absence of EMF, the amount of energy transferred to nano-environments of accessible groups was estimated to address the possible thermal effects of EMF. Our results show that the effects of EMF on channel activities are frequency dependent, with a maximum effect at 930 MHz. The frequency of channel gating and the voltage sensitivity is increased when the channel is exposed to EMF, while its conductance remains unchanged at all frequencies applied. We have not identified any changes in the capacitance and permeability of membrane in the presence of EMF. The effect of the EMF irradiated by cell phones is measured by Specific Absorption Rate (SAR) in artificial model of human head, Phantom. Thus, current approach applied to biological molecules and electrolytes might be considered as complement to evaluate safety of irradiating sources on biological matter at molecular level.

Transient oscillation of shape and membrane conductivity changes by field pulse-induced electroporation in nano-sized phospholipid vesicles

The results of electrooptical and conductometrical measurements on unilamellar lipid vesicles (of mean radius a = 90 nm), filled with 0.2 M NaCl solution, suspended in 0.33 M sucrose solution of 0.2 mM NaCl, and exposed to a stepwise decaying electric field (time constant τE = 154 μs) in the range 10 ≤ E0 (kV cm(-1)) ≤ 90, are analyzed in terms of cyclic changes in vesicle shape and vesicle membrane conductivity. The two peaks in the dichroitic turbidity relaxations reflect two cycles of rapid membrane electroporation and slower resealing of long-lived electropores. The field-induced changes reflect structural transitions between closed (C) and porated (P) membrane states, qualified by pores of type P1 and of type P2, respectively. The transient change in the membrane conductivity and the transient shape oscillation are based on changes in the pore density of the (larger) P2-pores along a hysteresis cycle. The P2-pore formation leads to transient net ion flows across the P2-pores and to transient changes in the membrane field. The kinetic data are numerically processed in terms of coupled structural relaxation modes. Using the torus-hole pore model, the mean inner pore radii are estimated to be r1 = 0.38 (±0.05) nm and r2 = 1.7 (±0.1) nm, respectively. The observation of a transient oscillation of membrane electroporation and of shape changes in a longer lasting external field pulse is suggestive of potential resonance enhancement, for instance, of electro-uptake by, and of electro-release of biogenic molecules from, biological cells in trains of long-lasting low-intensity voltage pulses.

Polymer translocation through an electrically tunable nanopore in a multilayered semiconductor membrane

We have developed a two-level computational model that enables us to calculate electrostatic fields created by a semiconductor membrane submerged in electrolytic solution and investigate the effects of these fields on the dynamics of a polymer translocating through a nanopore in the membrane. In order to calculate the electrostatic potentials and the ionic concentrations in a solid-state nanopore, we have self-consistently solved Poisson equation within the semiclassical approximation for charge carrier statistics in the membrane and electrolyte. The electrostatic potentials obtained from these simulations are then used in conjunction with Langevin (Brownian) dynamics to model polymer translocation through the nanopore. In this work, we consider single-stranded DNA (ssDNA) translocation through semiconductor membranes consisting of heavily doped p- and n-layers of silicon forming a pn-junction which is capable of creating strong electric fields. We show that the membrane electric field controls dynamics of a biomolecule inside the channel, to either momentarily trap it, slow it down, or allow it to translocate at will.

DOCKING AND MD SIMULATIONS OF THE INTERACTION OF THE POTASSIUM-SPARING DIURETIC AGENT AMILORIDE WITH THE hASIC1a CHANNEL USING A HOMOLOGY MODEL

The interaction of the K+ -sparing agent amiloride — a synthetic chlorinated pyrimidine derivative — with the hASIC1a ion channel is investigated here along homology modeling of the pore region (using the crystal structure of the cASIC1 channel as a template and the known sequence of hASIC1a), automated docking (using the NMR solution structure of amiloride and its conjugated acid, refined by computations), and molecular dynamics simulations. This represents the first modeling and computational chemistry of the pore region of ASIC/DEG/ENaCs/FaNaCh channels. The results agree with the putative amiloride binding site for alphaENaC channel chimeras once the amiloride free base is considered, while its conjugated acid — in contrast with literature beliefs — is poorly scored on a nearby protein pocket. Different protonation conditions of the pore region are irrelevant because histidine residues are far from the binding sites. Mapping the amino acids of the homology model closest to amiloride can have heuristic value in stimulating in silico search of new pore-blocking agents, experimental studies of ASIC channels themselves, and development of code for constant-pH MD simulations.

Voltage dependence of a stochastic model of activation of an alpha helical S4 sensor in a K channel membrane

The voltage dependence of the ionic and gating currents of a K channel is dependent on the activation barriers of a voltage sensor with a potential function which may be derived from the principal electrostatic forces on an S4 segment in an inhomogeneous dielectric medium. By variation of the parameters of a voltage-sensing domain model, consistent with x-ray structures and biophysical data, the lowest frequency of the survival probability of each stationary state derived from a solution of the Smoluchowski equation provides a good fit to the voltage dependence of the slowest time constant of the ionic current in a depolarized membrane, and the gating current exhibits a rising phase that precedes an exponential relaxation. For each depolarizing potential, the calculated time dependence of the survival probabilities of the closed states of an alpha helical S4 sensor are in accord with an empirical model of the ionic and gating currents recorded during the activation process.

Insights on the permeability of wide protein channels: measurement and interpretation of ion selectivity

Ion channels are hollow proteins that have evolved to exhibit discrimination between charged solutes. This property, known as ion selectivity is critical for several biological functions. By using the bacterial porin OmpF as a model system of wide protein channels, we demonstrate that significant insights can be gained when selectivity measurements are combined with electrodiffusion continuum models and simulations based on the atomic structure. A correct interpretation of the mechanisms ruling the many sources of channel discrimination is a first, indispensable step for the understanding of the controlled movement of ions into or out of cells characteristic of many physiological processes. We conclude that the scattered information gathered from several independent approaches should be appropriately merged to provide a unified and coherent picture of the channel selectivity.

Efficiency of the delivery of small charged molecules into cells in vitro

The effectiveness of the delivery of small charged molecules, including anticancer drugs into MH22 hepatoma cells in vitro was investigated. It was shown that for each kind of small molecules one can find a specific set of pulse strength-duration combinations that define electrotransfer of chosen compounds into the same amount of electroporated cells. Analysis of experimental data from the point of theory of hydrophilic aqueous pores and the estimation of the contribution of the electrostatic Born's energy to the change in free energy suggests that the main factors defining small molecules transfer through the membrane are: the charge and size of molecules, the permittivities of external medium, membrane material, and the electropores respectively as well as the size of electropores. The joint impact of all mentioned factors on transfer efficiency is essential.

Determining the orientation of protegrin-1 in DLPC bilayers using an implicit solvent-membrane model

Continuum models that describe the effects of solvent and biological membrane molecules on the structure and behavior of antimicrobial peptides, holds a promise to improve our understanding of the mechanisms of antimicrobial action of these peptides. In such methods, a lipid bilayer model membrane is implicitly represented by multiple layers of relatively low dielectric constant embedded in a high dielectric aqueous solvent, while an antimicrobial peptide is accounted for by a dielectric cavity with fixed partial charge at the center of each one of its atoms. In the present work, we investigate the ability of continuum approaches to predict the most probable orientation of the β-hairpin antimicrobial peptide Protegrin-1 (PG-1) in DLPC lipid bilayers by calculating the difference in the transfer free energy from an aqueous environment to a membrane-water environment for multiple orientations. The transfer free energy is computed as a sum of two terms; polar/electrostatic and non-polar. They both include energetic and entropic contributions to the free energy. We numerically solve the Poisson-Boltzmann equation to calculate the electrostatic contribution to the transfer free energy, while the non-polar contribution to the free energy is approximated using a linear solvent accessible surface area relationships. The most probable orientation of PG-1 is that with the lowest relative transfer free energy. Our simulation results indicate that PG-1 assumes an oblique orientation in DLPC lipid bilayers. The predicted most favorable orientation was with a tilt angle of 19°, which is in qualitative agreement with the experimentally observed orientations derived from solid-state NMR data.

THz investigations of condensed phase biomolecular systems

Terahertz (THz) spectroscopic investigations of crystalline dipeptide nanotubes are discussed in the frequency region from 0.6 (2 cm(-1)) to 3 THz (100 cm(-1)). The THz region provides access to collective modes of biomolecular systems and is therefore sensitive to the large scale motions important for understanding the impact of environmental stimuli in biomolecular systems. The focus of this chapter is on THz spectral changes observed in this region when crystals of alanyl isoleucine (AI) and isoleucyl alanine (IA) nanotubes are exposed to water. Of biological significance is the water permeability through hydrophobic pore regions as exemplified in the disparate behavior of these two dipeptide nanotubes. AI is known from X-ray studies and confirmed here to act reversibly to the exchange of water while IA does not accept water into its pore region. Both quantum chemical and classical calculations are performed to better understand the subtle balance that determines guest molecule absorption and conduction through these hydrophobic channels. Examination of the vibrational character of the THz modes with and without water suggests water mode coupling/decoupling with collective modes of the nanotube may play an important role in the permeability dynamics.

Bacterial mechanosensitive channels: Experiment and theory

Since their discovery in Escherichia coli some 20 years ago, studies of bacterial mechanosensitive (MS) ion channels have been at the forefront of the MS channel research field. Two major events greatly advanced the research on bacterial MS channels: (i) cloning of MscL and MscS, the MS channels of Large and Small conductance, and (ii) solving their 3D crystal structure. These events enabled further experimental studies employing EPR and FRET spectroscopy in addition to patch clamp and molecular biological techniques that have successfully been used in characterization of the structure and function of bacterial MS channels. In parallel with the experimental studies computational modelling has been applied to elucidate the molecular dynamics of MscL and MscS, which has significantly contributed to our understanding of basic physical principles of the mechanosensory transduction in living organisms.

Effects of exogenous electromagnetic fields on a simplified ion channel model

In this paper, we calculate the effect of an exogenous perturbation (an electromagnetic field [EMF] oscillating in the range of microwave frequencies in the range of 1 GHz) on the flux of two ion species through a cylindrical ion channel, implementing a continuous model, the Poisson-Smoluchowski system of equations, to study the dynamics of charged particle density inside the channel. The method was validated through comparison with Brownian dynamics simulations, supposed to be more accurate but computationally more demanding, obtaining a very good agreement. No EMF effects were observed for low field intensities below the level for thermal effects, as the highly viscous regime and the simplicity of the channel do not exhibit resonance phenomena. For high intensities of the external field (>10(5) V/m), we observed slightly different behavior of ion concentration oscillations and ion currents as a function of EMF orientation with respect to the channel axis.

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.

Calcium block of single sodium channels: role of a pore-lining aromatic residue

Extracellular Ca(2+) ions cause a rapid block of voltage-gated sodium channels, manifest as an apparent reduction of the amplitude of single-channel currents. We examined the influence of residue Tyr-401 in the isoform rNa(V)1.4 on both single-channel conductance and Ca(2+) block. An aromatic residue at this position in the outer mouth of the pore plays a critical role in high-affinity block by the guanidinium toxin tetrodotoxin, primarily due to an electrostatic attraction between the cationic blocker and the system of pi electrons on the aromatic face. We tested whether a similar attraction between small metal cations (Na(+) and Ca(2+)) and this residue would enhance single-channel conductance or pore block, using a series of fluorinated derivatives of phenylalanine at this position. Our results show a monotonic decrease in Ca(2+) block as the aromatic ring is increasingly fluorinated, a result in accord with a cation-pi interaction between Ca(2+) and the aromatic ring. This occurred without a change of single-channel conductance, consistent with a greater electrostatic effect of the pi system on divalent than on monovalent cations. High-level quantum mechanical calculations show that Ca(2+) ions likely do not bind directly to the aromatic ring because of the substantial energetic penalty of dehydrating a Ca(2+) ion. However, the complex of a Ca(2+) ion with its inner hydration shell, Ca(2+)(H(2)O)(6), interacts electrostatically with the aromatic ring in a way that affects the local concentration of Ca(2+) ions in the extracellular vestibule.

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.

Mapping the electrostatic potential within the ribosomal exit tunnel

Electrostatic potentials influence interactions among proteins and nucleic acids, the orientation of dipoles and quadrupoles, and the distribution of mobile charges. Consequently, electrostatic potentials can modulate macromolecular folding and conformational stability, as well as rates of catalysis and substrate binding. The ribosomal exit tunnel, along with its resident nascent peptide, is no less susceptible to these consequences. Yet, the electrostatics inside the tunnel have never been measured. Here we map both the electrostatic potential and accessibilities along the length of the tunnel and determine the electrostatic consequences of introducing a charged amino acid into the nascent peptide. To do this we developed novel probes and strategies. Our findings provide new insights regarding the dielectric of the tunnel and the dynamics of its local electric fields.

Charge at the lidocaine binding site residue Phe-1759 affects permeation in human cardiac voltage-gated sodium channels

Our homology molecular model of the open/inactivated state of the Na(+) channel pore predicts, based on extensive mutagenesis data, that the local anaesthetic lidocaine docks eccentrically below the selectivity filter, such that physical occlusion is incomplete. Electrostatic field calculations suggest that the drug's positively charged amine produces an electrostatic barrier to permeation. To test the effect of charge at this pore level on permeation in hNa(V)1.5 we replaced Phe-1759 of domain IVS6, the putative binding site for lidocaine's alkylamino end, with positively and negatively charged residues as well as the neutral cysteine and alanine. These mutations eliminated use-dependent lidocaine block with no effect on tonic/rested state block. Mutant whole cell currents were kinetically similar to wild type (WT). Single channel conductance (gamma) was reduced from WT in both F1759K (by 38%) and F1759R (by 18%). The negatively charged mutant F1759E increased gamma by 14%, as expected if the charge effect were electrostatic, although F1759D was like WT. None of the charged mutations affected Na(+)/K(+) selectivity. Calculation of difference electrostatic fields in the pore model predicted that lidocaine produced the largest positive electrostatic barrier, followed by lysine and arginine, respectively. Negatively charged glutamate and aspartate both lowered the barrier, with glutamate being more effective. Experimental data were in rank order agreement with the predicted changes in the energy profile. These results demonstrate that permeation rate is sensitive to the inner pore electrostatic field, and they are consistent with creation of an electrostatic barrier to ion permeation by lidocaine's charge.

Electrostatic properties of the mechanosensitive channel of small conductance MscS

The mechanosensitive channel of small conductance (MscS) belongs to a family of membrane proteins that are gated in response to changes in membrane tension, thereby protecting the cell from hypo-osmotic shock. Here we report on passive ion transport simulations of MscS in a POPC bilayer using a coarse-grained particle-based description based on the Boltzmann transport Monte Carlo method. Single channel current-voltage curves are computed over hundreds of nanoseconds for channel conformations derived from all-atom molecular dynamics simulations reaching an overall simulation time of over 5 micros. Channel conformations similar to that of the crystal structure exhibit low conductance, whereas conformations reached after opening the channel by means of steered molecular dynamics simulations match experimentally determined conductances. However, while experiments indicate a slight preference for anionic currents, the simulated channel strongly selects anions over cations and the direction of rectification at high voltages is opposite to what is observed in experiments. Three-dimensional maps of time-averaged ion distribution and equilibrium occupancy profiles constructed from trajectory data indicate separation of anions and cations inside and in the immediate vicinity of the large cytoplasmic domain of MscS, in accordance with earlier molecular dynamics simulations. This separation arises from the distribution of ionizable residues of MscS and suggests a specific, yet unknown, functional purpose.

Acidity of a Cu-Bound Histidine in the Binuclear Center of CytochromecOxidase

Cytochrome c oxidase (CcO) is a crucial enzyme in the respiratory chain. Its function is to couple the reduction of molecular oxygen, which takes place in the Fea3-CuB binuclear center, to proton translocation across the mitochondrial membrane. Although several high-resolution structures of the enzyme are known, the molecular basis of proton pumping activation and its mechanism remain to be elucidated. We examine a recently proposed scheme (J. Am. Chem. Soc. 2004, 126, 1858; FEBS Lett. 2004, 566, 126) that involves the deprotonation of the CuB-bound imidazole ring of a histidine (H291 in mammalian CcO) as a key element in the proton pumping mechanism. The central feature of that proposed mechanism is that the pKa values of the imidazole vary significantly depending on the redox state of the metals in the binuclear center. We use density functional theory in combination with continuum electrostatics to calculate the pKa values, successively in bulk water and within the protein, of the Cu-bound imidazole in various Cu- and Cu-Fe complexes. From pKas in bulk water, we derived a value of -266.34 kcal.mol(-1) for the proton solvation free energy (Delta). This estimate is in close agreement with the experimental value of -264.61 kcal.mol(-1) (J. Am. Chem. Soc. 2001, 123, 7314), which reinforces the conclusion that Delta is more negative than previous values used for pKa calculations. Our approach, on the basis of the study of increasingly more detailed models of the CcO binuclear center at different stages of the catalysis, allows us to examine successively the effect of each of the two metals' redox states and of solvation on the acidity of imidazole, whose pKa is approximately 14 in bulk water. This analysis leads to the following conclusions: first, the effect of Cu ligation on the imidazole acidity is negligible regardless of the redox state of the metal. Second, results obtained for Cu-Fe complexes in bulk water indicate that Cu-bound imidazole pKa values lie within the range of 14.8-16.6 throughout binuclear redox states corresponding to the catalytic cycle, demonstrating that the effect of the Fe oxidation states is also negligible. Finally, the low-dielectric CcO proteic environment shifts the acid-base equilibrium toward a neutral imidazole, further increasing the corresponding pKa values. These results are inconsistent with the proposed role of the Cu-bound histidine as a key element in the pumping mechanism. Limitations of continuum solvation models in pKa calculations are discussed.

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.

Electrostatic model of S4 motion in voltage-gated ion channels

The S4 transmembrane domain of the family of voltage-gated ion channels is generally thought to be the voltage sensor, whose translocation by an applied electric field produces the gating current. Experiments on hSkMI Na(+) channels and both Shaker and EAG K(+) channels indicate which S4 residues cross the membrane-solution interface during activation gating. Using this structural information, we derive the steady-state properties of gating-charge transfer for wild-type and mutant Shaker K(+) channels. Assuming that the energetics of gating is dominated by electrostatic forces between S4 charges and countercharges on neighboring transmembrane domains, we calculate the total energy as a function of transmembrane displacement and twist of the S4 domain. The resulting electrostatic energy surface exhibits a series of deep energy minima, corresponding to the transition states of the gating process. The steady-state gating-charge distribution is then given by a Boltzmann distribution among the transition states. The resulting gating-charge distributions are compared to experimental results on wild-type and charge-neutralized mutants of the Shaker K(+) channel.

Fields and forces acting on a planar membrane with a conducting channel

Modeling electric fields and forces around a channel in a planar membrane is still an open problem. Until now, most of the existing theories have oversimplified the electric field distribution by placing the electrode directly at the entry of the channel. However, in any relevant experimental setup the electrodes are placed far away in the electrolyte solution. We demonstrate that long-range deformation of the electric field distribution appears around the membrane, spanning on distances of the order of the distance between the membrane and the electrode. The forces acting due to this distribution are in most of the cases negligible. They can be important for channels with radii of the order of the thickness of the layer of structured water at the oil-water interface.

Improved 3D continuum calculations of ion flux through membrane channels

A continuum model, based on the Poisson-Nernst-Planck (PNP) theory, is applied to simulate steady-state ion flux through protein channels. The PNP equations are modified to explicitly account (1) for the desolvation of mobile ions in the membrane pore and (2) for effects related to ion sizes. The proposed algorithm for a three-dimensional self-consistent solution of PNP equations, in which final results are refined by a focusing technique, is shown to be suitable for arbitrary channel geometry and arbitrary protein charge distribution. The role of the pore shape and protein charge distribution in formation of basic electrodiffusion properties, such as channel conductivity and selectivity, as well as concentration distributions of mobile ions in the pore region, are illustrated by simulations on model channels. The influence of the ionic strength in the bulk solution and of the externally applied electric field on channel properties are also discussed.

Effect of salts on water viscosity in narrow membrane pores

The effect of various salts on the viscosity, and by implication structure, of water in polymeric membrane pores of radius approximately 1.69 nm and low charge density has been studied. Permeation of pure water and various electrolyte solutions was analyzed using the Hagen-Poiseuille equation expressed in a ratio form to exclude membrane-specific quantities such as pore radius and length. The analysis produced viscosity ratios of electrolyte to pure water inside the membrane pores. Comparing the viscosity ratios inside the pores with their bulk counterparts showed that confinement significantly increased the sensitivity of water structure to the presence of ions. It has been found that, in relative terms in the pores, Cl- was a strong structure breaker, K+ was a moderately strong structure breaker, Na+ was a weak structure breaker, SO4(2-) was a weak structure maker, and Mg2+ was a strong structure maker. Predictive modeling of membrane separation performance would benefit from such effects being taken into account in cases where the pore ion concentrations may be high.

Role of the dielectric constants of membrane proteins and channel water in ion permeation

Using both analytical solutions obtained from simplified systems and numerical results from more realistic cases, we investigate the role played by the dielectric constant of membrane proteins epsilon(p) and pore water epsilon(w) in permeation of ions across channels. We show that the boundary and its curvature are the crucial factors in determining how an ion's potential energy depends on the dielectric constants near an interface. The potential energy of an ion outside a globular protein has a dominant 1/epsilon(w) dependence, but this becomes 1/epsilon(p) for an ion inside a cavity. For channels, where the boundaries are in between these two extremes, the situation is more complex. In general, we find that variations in epsilon(w) have a much larger impact on the potential energy of an ion compared to those in epsilon(p). Therefore a better understanding of the effective epsilon(w) values employed in channel models is desirable. Although the precise value of epsilon(p) is not a crucial determinant of ion permeation properties, it still needs to be chosen carefully when quantitative comparisons with data are made.

Pores formed by the nicotinic receptor m2delta Peptide: a molecular dynamics simulation study

The M2delta peptide self-assembles to form a pentameric bundle of transmembrane alpha-helices that is a model of the pore-lining region of the nicotinic acetylcholine receptor. Long (>15 ns) molecular dynamics simulations of a model of the M2delta(5) bundle in a POPC bilayer have been used to explore the conformational dynamics of the channel assembly. On the timescale of the simulation, the bundle remains relatively stable, with the polar pore-lining side chains remaining exposed to the lumen of the channel. Fluctuations at the helix termini, and in the helix curvature, result in closing/opening transitions at both mouths of the channel, on a timescale of approximately 10 ns. On average, water within the pore lumen diffuses approximately 4x more slowly than water outside the channel. Examination of pore water trajectories reveals both single-file and path-crossing regimes to occur at different times within the simulation.

Recent advances in ion channel research

The field of ion channels has entered into a rapid phase of development in the last few years, partly due to the breakthroughs in determination of the crystal structures of membrane proteins and advances in computer simulations of biomolecules. These advances have finally enabled the long-dreamed goal of relating function of a channel to its underlying molecular structure. Here we present simplified accounts of the competing permeation theories and then discuss their application to the potassium, gramicidin A and calcium channels.

Movement and crevices around a sodium channel S3 segment

Voltage sensing is due mainly to the movement of positively charged S4 segments through the membrane electric field during changes of membrane potential. The roles of other transmembrane segments are under study. The S3 segment of domain 4 (D4/S3) in the sodium channel Na(v)1.4 carries two negatively charged residues and has been implicated in voltage-dependent gating. We substituted cysteines into nine putative "high impact" sites along the complete length of D4/S3 and evaluated their accessibilities to extracellular sulfhydryl reagents. Only the four outermost substituted cysteines (L1433C, L1431C, G1430C, and S1427C) are accessible to extracellular sulfhydryl reagents. We measured the voltage-dependent modification rates of the two cysteines situated at the extreme ends of this accessible region, L1433C and S1427C. Independent of the charge on the sulfhydryl reagents, depolarization increases the reactivity of both of these residues. Thus, the direction of the voltage dependence is opposite to that expected for a negatively charged voltage sensor, namely an inward translational movement in response to depolarization. Intrinsic electrostatic potentials were probed by charged sulfhydryl reagents and were either negative or positive, respectively, near L1433C and S1427C. The magnitude of the electrostatic potential near S1427C decreases with depolarization, suggesting that the extracellular crevice next to it widens during depolarization. S1427C experiences 44% of the electric field, as probed by charged cysteine reagents. To further explore movements around D4/S3, we labeled cysteines with the photoactivatable cross-linking reagent benzophenone-4-carboxamidocysteine methanethiosulfonate and examined the effects of UV irradiation on channel gating. After labeling with this reagent, all accessible cysteine mutants show altered gating upon brief UV irradiation. In each case, the apparent insertion efficiency of the photoactivated benzophenone increases with depolarization, indicating voltage-dependent movement near the extracellular end of D4/S3.

Electrostatic properties of the anion selective porin Omp32 from Delftia acidovorans and of the arginine cluster of bacterial porins

The functional properties of the anion-selective porin Omp32 from the bacterium Delftia acidovorans, formerly Comamonas acidovorans, are determined by the particularly narrow channel constriction and the electrostatic field inside and outside the pore. A cluster of arginines (Arg 38, Arg 75, and Arg 133) determines the electrostatic field close to the constriction zone. Stacked amino acids carrying charges are prone to drastic pK(a) shifts. However, optimized calculations of the titration behavior of charged groups, based on the finite-difference Poisson-Boltzmann technique, suggest that all the arginines are charged at physiological pH. Protonation of the clustered arginines is stabilized by one buried glutamate residue (Glu 58), which is strongly interacting with Arg 75 and Arg 38. This functional arrangement of three charged amino acid residues is of general significance because it is found in the constriction zones of all known 16-stranded porins from the alpha-, beta-, and gamma-proteobacteria.

Conducting-state properties of the KcsA potassium channel from molecular and Brownian dynamics simulations

The mechanisms underlying transport of ions across the potassium channel are examined using electrostatic calculations and three-dimensional Brownian dynamics simulations. We first build open-state configurations of the channel with molecular dynamics simulations, by pulling the transmembrane helices outward until the channel attains the desired interior radius. To gain insights into ion permeation, we construct potential energy profiles experienced by an ion traversing the channel in the presence of other resident ions. These profiles reveal that in the absence of an applied field the channel accommodates three potassium ions in a stable equilibrium, two in the selectivity filter and one in the central cavity. In the presence of a driving potential, this three-ion state becomes unstable, and ion permeation across the channel is observed. These qualitative explanations are confirmed by the results of three-dimensional Brownian dynamics simulations. We find that the channel conducts when the ionizable residues near the extracellular entrance are fully charged and those near the intracellular side are partially charged. The conductance increases steeply as the radius of the intracellular mouth of the channel is increased from 2 A to 5 A. Our simulation results reproduce several experimental observations, including the current-voltage curves, conductance-concentration relationships, and outward rectification of currents.

Brownian dynamics study of an open-state KcsA potassium channel

Three-dimensional Brownian dynamics simulations are used to study conductance of the KcsA potassium channel using the known crystallographic structure. Employing an open-state channel created by molecular dynamics simulations, current-voltage and current-concentration curves broadly consistent with experimental measurements are obtained. In the absence of an applied potential, the channel houses three potassium ions at positions that are in close agreement with X-ray diffraction maps.

Mechanisms of permeation and selectivity in calcium channels

The mechanisms underlying ion transport and selectivity in calcium channels are examined using electrostatic calculations and Brownian dynamics simulations. We model the channel as a rigid structure with fixed charges in the walls, representing glutamate residues thought to be responsible for ion selectivity. Potential energy profiles obtained from multi-ion electrostatic calculations provide insights into ion permeation and many other observed features of L-type calcium channels. These qualitative explanations are confirmed by the results of Brownian dynamics simulations, which closely reproduce several experimental observations. These include the current-voltage curves, current-concentration relationship, block of monovalent currents by divalent ions, the anomalous mole fraction effect between sodium and calcium ions, attenuation of calcium current by external sodium ions, and the effects of mutating glutamate residues in the amino acid sequence.

Electrostatics and the gating pore of Shaker potassium channels

Various experiments have suggested that the S4 segment in voltage-dependent Na(+) and K(+) channels is in contact with a solvent-accessible cavity. We explore the consequences of the existence of such a cavity through the electrostatic effects on the gating currents of Shaker K(+) channels under conditions of reduced ionic strength S. We observe that approximately 10-fold reductions of intracellular S produce reductions of the measured gating charge of approximately 10%. These effects continue at even lower values of S. The reduction of gating charge when S is reduced by 10-fold at the extracellular surface is much smaller (approximately 2%). Shifts of the Q(V) curve because of a reduced S are small (<10 mV in size), which is consistent with very little fixed surface charge. Continuum electrostatic calculations show that the S effects on gating charge can be explained by the alteration of the local potential in an intracellular conical cavity of 20-24-A depth and 12-A aperture, and a smaller extracellular cavity of 3-A depth and the same aperture. In this case, the attenuation of the membrane potential at low S leads to reduction of the apparent gating charge. We suggest that this cavity is made by a bundle of transmembrane helices, and that the gating charge movement occurs by translocation of charged residues across a thin septum of approximately 3-7 A thickness.

Simulations of ion channels--watching ions and water move

Ion channels mediate electrical excitability in neurons and muscle. Three-dimensional structures for model peptide channels and for a potassium (K+) channel have been combined with computer simulations to permit rigorous exploration of structure-function relations of channels. Water molecules and ions within transbilayer pores tend to diffuse more slowly than in bulk solutions. In the narrow selectivity filter of the bacterial K+ channel (i.e. the region of the channel that discriminates between different species of ions) a column of water molecules and K+ ions moves in a concerted fashion. By combining atomistic simulations (in which all atoms of the channel molecule, water and ions are treated explicitly) with continuum methods (in which the description of the channel system is considerably simplified) it is possible to simulate some of the physiological properties of channels.