Brownian dynamics study of ion transport in the vestibule of membrane channels

Theoretical investigation on the effect of terahertz wave on Ca2+ transport in the calcium channel

The question of whether terahertz (THz) waves can interact with ions in channels of nerve cells and cause a further reaction has attracted much attention. To answer this question, we investigate the spontaneous radiation generated by Ca²⁺ moving in calcium channels and the effect of THz radiation on the transport of Ca²⁺ by solving the mathematical physical model through Brownian dynamics (BD) simulations. It is obtained that the moving Ca²⁺ in a calcium channel can generate electromagnetic radiation, the corresponding spectrum of which is concentrated in the THz range. Meanwhile, both the ion number in the channel and the background temperature are proved to have significant effects on the spontaneous emission spectra. The studies also show that external THz radiation can accelerate Ca²⁺ transport through the ion channel. These results are expected to provide a theoretical basis for the future treatment of THz waves in the neurological field.

Computational methods and theory for ion channel research

Ion channels are fundamental biological devices that act as gates in order to ensure selective ion transport across cellular membranes; their operation constitutes the molecular mechanism through which basic biological functions, such as nerve signal transmission and muscle contraction, are carried out. Here, we review recent results in the field of computational research on ion channels, covering theoretical advances, state-of-the-art simulation approaches, and frontline modeling techniques. We also report on few selected applications of continuum and atomistic methods to characterize the mechanisms of permeation, selectivity, and gating in biological and model channels.

How to Enter a Bacterium: Bacterial Porins and the Permeation of Antibiotics

Despite tremendous successes in the field of antibiotic discovery seen in the previous century, infectious diseases have remained a leading cause of death. More specifically, pathogenic Gram-negative bacteria have become a global threat due to their extraordinary ability to acquire resistance against any clinically available antibiotic, thus urging for the discovery of novel antibacterial agents. One major challenge is to design new antibiotics molecules able to rapidly penetrate Gram-negative bacteria in order to achieve a lethal intracellular drug accumulation. Protein channels in the outer membrane are known to form an entry route for many antibiotics into bacterial cells. Up until today, there has been a lack of simple experimental techniques to measure the antibiotic uptake and the local concentration in subcellular compartments. Hence, rules for translocation directly into the various Gram-negative bacteria via the outer membrane or via channels have remained elusive, hindering the design of new or the improvement of existing antibiotics. In this review, we will discuss the recent progress, both experimentally as well as computationally, in understanding the structure-function relationship of outer-membrane channels of Gram-negative pathogens, mainly focusing on the transport of antibiotics.

Frontiers in biomolecular mesh generation and molecular visualization systems

With the development of biomolecular modeling and simulation, especially implicit solvent modeling, higher requirements are set for the stability, efficiency and mesh quality of molecular mesh generation software. In this review, we summarize the recent works in biomolecular mesh generation and molecular visualization. First, we introduce various definitions of molecular surface and corresponding meshing software. Second, as the mesh quality significantly influences biomolecular simulation, we investigate some remeshing methods in the fields of computer graphics and molecular modeling. Then, we show the application of biomolecular mesh in the boundary element method (BEM) and the finite element method (FEM). Finally, to conveniently visualize the numerical results based on the mesh, we present two types of molecular visualization systems.

Computer Simulator of Glycine Receptor Activity: A New Window into a Virtual World

Our study reports computer software that simulates the work of a single glycine receptor (GlyR). GlyRs have been found in various types of tissues, but their most important role seems to be in neurons, where they hyperpolarise membranes by opening chloride transmembrane channels. The software is based on a combination of two blocks. One block describes the Brownian dynamics of charged particle motion in a dielectric medium, and the other block determines the probability and timing of receptor activation. Using this software, the voltage-current dependencies and time curves of the transmembrane current were obtained. The mean value of the simulated anion current (4.5 ± 0.3 pA) is in good agreement with measured values under identical conditions ([Formula: see text] pA). It was shown that there is a condition under which the GlyR anion channel remains active despite a negligible chloride gradient. Virtual experiments allow evaluation of the value of half maximal effective concentration (EC[Formula: see text]) of the GlyR ([Formula: see text] [Formula: see text]M) and confirm that this receptor activates according to a mechanism involving three ligand binding sites. The advantage of the model is the ability to adjust parameters to the precise demands of experimental researchers. Moreover, the introduced algorithm has low computational power demands; therefore, it can be used as a research tool for assistance with structural experiments and applied aspects of neurophysiology.

Effects of electromagnetic field exposure on conduction and concentration of voltage gated calcium channels: A Brownian dynamics study

A three-dimensional Brownian Dynamics (BD) in combination with electrostatic calculations is employed to specifically study the effects of radiation of high frequency electromagnetic fields on the conduction and concentration profile of calcium ions inside the voltage-gated calcium channels. The electrostatic calculations are performed using COMSOL Multiphysics by considering dielectric interfaces effectively. The simulations are performed for different frequencies and intensities. The simulation results show the variations of conductance, average number of ions and the concentration profiles of ions inside the channels in response to high frequency radiation. The ionic current inside the channel increases in response to high frequency electromagnetic field radiation, and the concentration profiles show that the residency of ions in the channel decreases accordingly.

Membrane-Channel Protein System Mesh Construction for Finite Element Simulations

We present a method of constructing the volume meshes of the membrane-channel protein system for finite element simulation of ion channels. The membrane channel system consists of the solvent region and the membrane-protein region. Our method focuses on labeling the tetrahedra in the solvent and membrane-protein regions and collecting the interface triangles between different regions. It contains two stages. Firstly, a volume mesh conforming the surface of the channel protein is generated by the surface and volume mesh generation tools: TMSmesh and TetGen. Then a walk-and-detect algorithm is used to identify the pore region to embed the membrane correctly. This method is shown to be robust because of its independence of the pore structure of the ion channels. In addition, we can also get the information of whether the ion channel is open or closed by the walk-and-detect algorithm. An on-line meshing procedure will be available at our website www.continuummodel.org.

Interacting ions in biophysics: real is not ideal

Ions in water are important throughout biology, from molecules to organs. Classically, ions in water were treated as ideal noninteracting particles in a perfect gas. Excess free energy of each ion was zero. Mathematics was not available to deal consistently with flows, or interactions with other ions or boundaries. Nonclassical approaches are needed because ions in biological conditions flow and interact. The concentration gradient of one ion can drive the flow of another, even in a bulk solution. A variational multiscale approach is needed to deal with interactions and flow. The recently developed energetic variational approach to dissipative systems allows mathematically consistent treatment of the bio-ions Na(+), K(+), Ca(2+), and Cl(-) as they interact and flow. Interactions produce large excess free energy that dominate the properties of the high concentration of ions in and near protein active sites, ion channels, and nucleic acids: the number density of ions is often >10 M. Ions in such crowded quarters interact strongly with each other as well as with the surrounding protein. Nonideal behavior found in many experiments has classically been ascribed to allosteric interactions mediated by the protein and its conformation changes. The ion-ion interactions present in crowded solutions-independent of conformation changes of the protein-are likely to change the interpretation of many allosteric phenomena. Computation of all atoms is a popular alternative to the multiscale approach. Such computations involve formidable challenges. Biological systems exist on very different scales from atomic motion. Biological systems exist in ionic mixtures (like extracellular and intracellular solutions), and usually involve flow and trace concentrations of messenger ions (e.g., 10(-7) M Ca(2+)). Energetic variational methods can deal with these characteristic properties of biological systems as we await the maturation and calibration of all-atom simulations of ionic mixtures and divalents.

Hofmeister effect in confined spaces: halogen ions and single molecule detection

Despite extensive research in the nanopore-sensing field, there is a paucity of experimental studies that investigate specific ion effects in confined spaces, such as in nanopores. Here, the effect of halogen anions on a simple bimolecular complexation reaction between monodisperse poly(ethylene glycol) (PEG) and α-hemolysin nanoscale pores have been investigated at the single-molecule level. The anions track the Hofmeister ranking according to their influence upon the on-rate constant. An inverse relationship was demonstrated for the off-rate and the solubility of PEG. The difference among anions spans several hundredfold. Halogen anions play a very significant role in the interaction of PEG with nanopores although, unlike K(+), they do not bind to PEG. The specific effect appears dominated by a hydration-dehydration process where ions and PEG compete for water. Our findings provide what we believe to be novel insights into physicochemical mechanisms involved in single-molecule interactions with nanopores and are clearly relevant to more complicated chemical and biological processes involving a transient association of two or more molecules (e.g., reception, signal transduction, enzyme catalysis). It is anticipated that these findings will advance the development of devices with nanopore-based sensors for chemical and biological applications.

Testing the applicability of Nernst-Planck theory in ion channels: comparisons with Brownian dynamics simulations

The macroscopic Nernst-Planck (NP) theory has often been used for predicting ion channel currents in recent years, but the validity of this theory at the microscopic scale has not been tested. In this study we systematically tested the ability of the NP theory to accurately predict channel currents by combining and comparing the results with those of Brownian dynamics (BD) simulations. To thoroughly test the theory in a range of situations, calculations were made in a series of simplified cylindrical channels with radii ranging from 3 to 15 Å, in a more complex 'catenary' channel, and in a realistic model of the mechanosensitive channel MscS. The extensive tests indicate that the NP equation is applicable in narrow ion channels provided that accurate concentrations and potentials can be input as the currents obtained from the combination of BD and NP match well with those obtained directly from BD simulations, although some discrepancies are seen when the ion concentrations are not radially uniform. This finding opens a door to utilising the results of microscopic simulations in continuum theory, something that is likely to be useful in the investigation of a range of biophysical and nano-scale applications and should stimulate further studies in this direction.

An improved open-channel structure of MscL determined from FRET confocal microscopy and simulation

Mechanosensitive channels act as molecular transducers of mechanical force exerted on the membrane of living cells by opening in response to membrane bilayer deformations occurring in physiological processes such as touch, hearing, blood pressure regulation, and osmoregulation. Here, we determine the likely structure of the open state of the mechanosensitive channel of large conductance using a combination of patch clamp, fluorescence resonance energy transfer (FRET) spectroscopy, data from previous electron paramagnetic resonance experiments, and molecular and Brownian dynamics simulations. We show that structural rearrangements of the protein can be measured in similar conditions as patch clamp recordings while controlling the state of the pore in its natural lipid environment by modifying the lateral pressure distribution via the lipid bilayer. Transition to the open state is less dramatic than previously proposed, while the N terminus remains anchored at the surface of the membrane where it can either guide the tilt of or directly translate membrane tension to the conformation of the pore-lining helix. Combining FRET data obtained in physiological conditions with simulations is likely to be of great value for studying conformational changes in a range of multimeric membrane proteins.

SIMULATION OF ION CONDUCTION IN α-HEMOLYSIN NANOPORES WITH COVALENTLY ATTACHED β-CYCLODEXTRIN BASED ON BOLTZMANN TRANSPORT MONTE CARLO MODEL

Ion channels, as natures' solution to regulating biological environments, are particularly interesting to device engineers seeking to understand how natural molecular systems realize device-like functions, such as stochastic sensing of organic analytes. What's more, attaching molecular adaptors in desired orientations inside genetically engineered ion channels, enhances the system functionality as a biosensor. In general, a hierarchy of simulation methodologies is needed to study different aspects of a biological system like ion channels. Biology Monte Carlo (BioMOCA), a three-dimensional coarse-grained particle ion channel simulator, offers a powerful and general approach to study ion channel permeation. BioMOCA is based on the Boltzmann Transport Monte Carlo (BTMC) and Particle-Particle-Particle-Mesh (P(3)M) methodologies developed at the University of Illinois at Urbana-Champaign. In this paper, we have employed BioMOCA to study two engineered mutations of α-HL, namely (M113F)(6)(M113C-D8RL2)(1)-β-CD and (M113N)(6)(T117C-D8RL3)(1)-β-CD. The channel conductance calculated by BioMOCA is slightly higher than experimental values. Permanent charge distributions and the geometrical shape of the channels gives rise to selectivity towards anions and also an asymmetry in I-V curves, promoting a rectification largely for cations.

Soft wall ion channel in continuum representation with application to modeling ion currents in α-hemolysin

A soft repulsion (SR) model of short-range interactions between mobile ions and protein atoms is introduced in the framework of continuum representation of the protein and solvent. The Poisson-Nernst-Plank (PNP) theory of ion transport through biological channels is modified to incorporate this soft wall protein model. Two sets of SR parameters are introduced. The first is parametrized for all essential amino acid residues using all atom molecular dynamic simulations; the second is a truncated Lennard-Jones potential. We have further designed an energy-based algorithm for the determination of the ion accessible volume, which is appropriate for a particular system discretization. The effects of these models of short-range interactions were tested by computing current-voltage characteristics of the α-hemolysin channel. The introduced SR potentials significantly improve prediction of channel selectivity. In addition, we studied the effect of the choice of some space-dependent diffusion coefficient distributions on the predicted current-voltage properties. We conclude that the diffusion coefficient distributions largely affect total currents and have little effect on rectifications, selectivity, or reversal potential. The PNP-SR algorithm is implemented in a new efficient parallel Poisson, Poisson-Boltzmann, and PNP equation solver, also incorporated in a graphical molecular modeling package HARLEM.

Ion conduction in ligand-gated ion channels: Brownian dynamics studies of four recent crystal structures

Four x-ray crystal structures of prokaryotic homologs of ligand-gated ion channels have recently been determined: ELIC from Erwinia chrysanthemi, two structures of a proton-activated channel from Gloebacter violaceus (GLIC1 and GLIC2) and that of the E221A mutant (GLIC1M). The availability of numerous structures of channels in this family allows for aspects of channel gating and ion conduction to be examined. Here, we determine the likely conduction states of the four structures as well as IV curves, ion selectivity, and steps involved in ion permeation by performing extensive Brownian dynamics simulations. Our results show that the ELIC structure is indeed nonconductive, but that GLIC1 and GLIC1M are both conductive of ions with properties different from those seen in experimental studies of the channel. GLIC2 appears to reflect an open state of the channel with a predicted conductance of 10.8-12.4 pS in 140 mM NaCl solution, which is comparable to the experimental value 8 +/- 2 pS. The extracellular domain of the channel is shown to have an important influence on the channel current, but a less significant role in ion selectivity.

Single-channel current through nicotinic receptor produced by closure of binding site C-loop

We investigated the initial coupling of agonist binding to channel gating of the nicotinic acetylcholine receptor using targeted molecular-dynamics (TMD) simulation. After TMD simulation to accelerate closure of the C-loops at the agonist binding sites, the region of the pore that passes through the cell membrane expands. To determine whether the structural changes in the pore result in ion conduction, we used a coarse-grained ion conduction simulator, Biology Boltzmann transport Monte Carlo, and applied it to two structural frames taken before and after TMD simulation. The structural model before TMD simulation represents the channel in the proposed "resting" state, whereas the model after TMD simulation represents the channel in the proposed "active" state. Under external voltage biases, the channel in the "active" state was permeable to cations. Our simulated ion conductance approaches that obtained experimentally and recapitulates several functional properties characteristic of the nicotinic acetylcholine receptor. Thus, closure of the C-loop triggers a structural change in the channel sufficient to account for the open channel current. This approach of applying Biology Boltzmann transport Monte Carlo simulation can be used to further investigate the binding to gating transduction mechanism and the structural bases for ion selection and translocation.

Simulation of charge transport in ion channels and nanopores with anisotropic permittivity

Ion channels are part of nature's solution for regulating biological environments. Every ion channel consists of a chain of amino acids carrying a strong and sharply varying permanent charge, folded in such a way that it creates a nanoscopic aqueous pore spanning the otherwise mostly impermeable membranes of biological cells. These naturally occurring proteins are particularly interesting to device engineers seeking to understand how such nanoscale systems realize device-like functions. Availability of high-resolution structural information from X-ray crystallography, as well as large-scale computational resources, makes it possible to conduct realistic ion channel simulations. In general, a hierarchy of simulation methodologies is needed to study different aspects of a biological system like ion channels. Biology Monte Carlo (BioMOCA), a three-dimensional coarse-grained particle ion channel simulator, offers a powerful and general approach to study ion channel permeation. BioMOCA is based on the Boltzmann Transport Monte Carlo (BTMC) and Particle-Particle-Particle-Mesh (P(3)M) methodologies developed at the University of Illinois at Urbana-Champaign. In this paper we briefly discuss the various approaches to simulating ion flow in channel systems that are currently being pursued by the biophysics and engineering communities, and present the effect of having anisotropic dielectric constants on ion flow through a number of nanopores with different effective diameters.

Computational study of the transmembrane domain of the acetylcholine receptor

The nicotinic acetylcholine receptor (nAChR) is a ligand-gated ion channel protein whose transmembrane domain (TM-domain) is believed to be responsible for channel gating via a hydrophobic effect. In this work, we perform molecular dynamics and Brownian dynamics simulations to investigate the effect of transmembrane potential on the conformation and water occupancy of TM-domain, and the resulting ion permeation events. The results show that the behavior of the hydrophobic gate is voltage-dependent. Large hyperpolarized membrane potential can change the conformation of TM-domain and water occupancy in this region, which may enable ion conduction. An electrostatic gating mechanism is also proposed from our simulations, which seems to play a role in addition to the well-known hydrophobic effect.

Role of acetylcholine receptor domains in ion selectivity

The nicotinic acetylcholine receptor (nAChR) is a ligand gated ion channel protein, composed of three domains: a transmembrane domain (TM-domain), extracellular domain (EC-domain), and intracellular domain (IC-domain). Due to its biological importance, much experimental and theoretical research has been carried out to explore its mechanisms of gating and selectivity, but there are still many unresolved issues, especially on the ion selectivity. Moreover, most of the previous theoretical work has concentrated on the TM-domain or EC-domain of nAChR, which may be insufficient to understand the entire structure-function relation. In this work, we perform molecular dynamics, Brownian dynamics simulations and continuum electrostatic calculations to investigate the role of different nAChR domains in ion conduction and selectivity. The results show that although both the EC and IC domains contain strong negative charges that create large cation concentrations at either end of the pore, this alone is not sufficient to create the observed cation selectivity and may play a greater role in determining the channel conductance. The presence of cations in the wide regions of the pore can screen out the protein charge allowing anions to enter, meaning that local regions of the TM-domain are most likely responsible for discriminating between ions. These new results complement our understanding about the ion conduction and selectivity mechanism of nAChR.

Mechanism of KCl enhancement in detection of nonionic polymers by nanopore sensors

The mechanisms of KCl-induced enhancement in identification of individual molecules of poly(ethylene glycol) using solitary alpha-hemolysin nanoscale pores are described. The interaction of single molecules with the nanopore causes changes in the ionic current flowing through the pore. We show that the on-rate constant of the process is several hundred times larger and that the off-rate is several hundred times smaller in 4 M KCl than in 1 M KCl. These shifts dramatically improve detection and make single molecule identification feasible. KCl also changes the solubility of poly(ethylene glycol) by the same order of magnitude as it changes the rate constants. In addition, the polymer-nanopore interaction is determined to be a strong non-monotonic function of voltage, indicating that the flexible, nonionic poly(ethylene glycol) acts as a charged molecule. Therefore, salting-out and Coulombic interactions are responsible for the KCl-induced enhancement. These results will advance the development of devices with sensor elements based on single nanopores.

Brownian dynamics theory for predicting internal and external blockages of tetraethylammonium in the KcsA potassium channel

The theory of Brownian dynamics is used to model permeation and the blocking of KcsA potassium channels by tetraethylammonium (TEA). A novel Brownian dynamics simulation algorithm is implemented that comprises two free energy profiles; one profile is seen by the potassium ions and the other by the TEA molecules whose shape is approximated by a sphere. Our simulations reveal that internally applied TEA blocks the passage of K(+) ions by physically occluding the pore. A TEA molecule in the external reservoir encounters an attractive energy-well created by four tyrosine residues at position 82, in addition to all other attractive and repulsive forces impinging on it. Using Brownian dynamics, we investigate how deep the energy-well needs to be to reproduce the experimentally determined inhibitory constant k(i) for the TEA blockade of KcsA or the mutant Shaker T449Y. The one-dimensional free energy profile obtained from molecular dynamics is first converted into a one-dimensional potential energy profile, and is then transformed into a three-dimensional free energy profile in Brownian dynamics by adding the short-range potential from the channel walls. When converted, the free energy profile calculated from molecular dynamics gives a well-depth of approximately 10 kT. We systematically alter the depths of the profiles, and then use Brownian dynamics simulations to numerically determine the current versus TEA-concentration curves. We show that the sequence of binding and unbinding events of the TEA molecule to the binding pocket can be modeled by a first-order Markov process. The Brownian dynamics simulations also reveal that the probability of a TEA molecule binding to the binding pocket in KcsA potassium channels increases exponentially with TEA concentration and depends also on the applied potential and the K(+) concentration in the simulation assembly.

Conduction properties of KcsA measured using brownian dynamics with flexible carbonyl groups in the selectivity filter

In the narrow segment of an ion conducting pathway, it is likely that a permeating ion influences the positions of the nearby atoms that carry partial or full electronic charges. Here we introduce a method of incorporating the motion of charged atoms lining the pore into Brownian dynamics simulations of ion conduction. The movements of the carbonyl groups in the selectivity filter of the KcsA channel are calculated explicitly, allowing their bond lengths, bond angles, and dihedral angels to change in response to the forces acting upon them. By systematically changing the coefficients of bond stretching and of angle bending, the carbon and oxygen atoms can be made to fluctuate from their fixed positions by varying mean distances. We show that incorporating carbonyl motion in this way does not alter the mechanism of ion conduction and only has a small influence on the computed current. The slope conductance of the channel increases by approximately 25% when the root mean-square fluctuations of the carbonyl groups are increased from 0.01 to 0.61 A. The energy profiles and the number of resident ions in the channel remain unchanged. The method we utilized here can be extended to allow the movement of glutamate or aspartate side chains lining the selectivity filters of other ionic channels.

Self-consistent molecular dynamics formulation for electric-field-mediated electrolyte transport through nanochannels

A self-consistent molecular dynamics (SCMD) formulation is presented for electric-field-mediated transport of water and ions through a nanochannel connected to reservoirs or baths. The SCMD formulation is compared with a uniform field MD approach, where the applied electric field is assumed to be uniform, for 2nm and 3.5nm wide nanochannels immersed in a 0.5M KCl solution. Reservoir ionic concentrations are maintained using the dual-control-volume grand canonical molecular dynamics technique. Simulation results with varying channel height indicate that the SCMD approach calculates the electrostatic potential in the simulation domain more accurately compared to the uniform field approach, with the deviation in results increasing with the channel height. The translocation times and ionic fluxes predicted by uniform field MD can be substantially different from those predicted by the SCMD approach. Our results also indicate that during a 2ns simulation time K+ ions can permeate through a 1nm channel when the applied electric field is computed self-consistently, while the permeation is not observed when the electric field is assumed to be uniform.

Brownian dynamic model of the glycine receptor chloride channel: effect of the position of charged amino acids on ion membrane currents

Glycine is the major inhibitory neurotransmitter in the brainstem and spinal cord, where it participates in a variety of motor and sensory functions. It activates a special type of ligand-gated membrane receptor, which provides for Cl- ion conductance of the neuronal membrane. Computer simulations of a single-channel current through this receptor have been carried out on the basis of Brownian (Langevin) dynamics. The dependence of the currents on pore diameter and the location of the charged amino acid residues have been obtained. It has been shown that the presence and the symmetry of the filter-forming residues determined not only the ion-selectivity of the channel but also increased transmembrane anion current.

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.

An energy-efficient gating mechanism in the acetylcholine receptor channel suggested by molecular and Brownian dynamics

Acetylcholine receptors mediate electrical signaling between nerve and muscle by opening and closing a transmembrane ion conductive pore. Molecular and Brownian dynamics simulations are used to shed light on the location and mechanism of the channel gate. Four separate 5 ns molecular dynamics simulations are carried out on the imaged structure of the channel, a hypothetical open structure with a slightly wider pore and a mutant structure in which a central ring of hydrophobic residues is replaced by polar groups. Water is found to partially evacuate the pore during molecular simulations of the imaged structure, whereas ions face a large energy barrier and do not conduct through the channel in Brownian dynamics simulations. The pore appears to be in a closed configuration despite containing an unobstructed pathway across the membrane as a series of hydrophobic residues in the center of the channel provide an unfavorable home to water and ions. When the channel is widened slightly, water floods into the channel and ions conduct at a rate comparable to the currents measured experimentally in open channels. The pore remains permeable to ions provided the extracellular end of the pore-lining helix is restrained near the putative open configuration to mimic the presence of the ligand binding domain. Replacing some of the hydrophobic residues with polar ones decreases the barrier for ion permeation but does not result in significant currents. The channel is posited to utilize an energy efficient gating mechanism in which only minor conformational changes of the hydrophobic region of the pore are required to create macroscopic changes in conductance.

Electrostatic basis of valence selectivity in cationic channels

We examine how a variety of cationic channels discriminate between ions of differing charge. We construct models of the KcsA potassium channel, voltage gated sodium channel and L-type calcium channel, and show that they all conduct monovalent cations, but that only the calcium channel conducts divalent cations. In the KcsA and sodium channels divalent ions block the channel and prevent any further conduction. We demonstrate that in each case, this discrimination and some of the more complex conductance properties of the channels is a consequence of the electrostatic interaction of the ions with the charges in the channel protein. The KcsA and sodium channels bind divalent ions strongly enough that they cannot be displaced by other ions and thereby block the channel. On the other hand, the calcium channel binds them less strongly such that they can be destabilized by the repulsion of another incoming divalent ion, but not by the lesser repulsion from monovalent ions.

Homology model of the GABAA receptor examined using Brownian dynamics

We have developed a homology model of the GABA(A) receptor, using the subunit combination of alpha1beta2gamma2, the most prevalent type in the mammalian brain. The model is produced in two parts: the membrane-embedded channel domain and the extracellular N-terminal domain. The pentameric transmembrane domain model is built by modeling each subunit by homology with the equivalent subunit of the heteropentameric acetylcholine receptor transmembrane domain. This segment is then joined with the extracellular domain built by homology with the acetylcholine binding protein. The all-atom model forms a wide extracellular vestibule that is connected to an oval chamber near the external surface of the membrane. A narrow, cylindrical transmembrane channel links the outer segment of the pore to a shallow intracellular vestibule. The physiological properties of the model so constructed are examined using electrostatic calculations and Brownian dynamics simulations. A deep energy well of approximately 80 kT accommodates three Cl(-) ions in the narrow transmembrane channel and seven Cl(-) ions in the external vestibule. Inward permeation takes place when one of the ions queued in the external vestibule enters the narrow segment and ejects the innermost ion. The model, when incorporated into Brownian dynamics, reproduces key experimental features, such as the single-channel current-voltage-concentration profiles. Finally, we simulate the gamma2 K289M epilepsy inducing mutation and examine Cl(-) ion permeation through the mutant receptor.

Influence of protein flexibility on the electrostatic energy landscape in gramicidin A

We describe an electrostatic model of the gramicidin A channel that allows protein atoms to move in response to the presence of a permeating ion. To do this, molecular dynamics simulations are carried out with a permeating ion at various positions within the channel. Then an ensemble of atomic coordinates taken from the simulations are used to construct energy profiles using macroscopic electrostatic calculations. The energy profiles constructed are compared to experimentally-determined conductance data by inserting them into Brownian dynamics simulations. We find that the energy landscape seen by a permeating ion changes significantly when we allow the protein atoms to move rather than using a rigid protein structure. However, the model developed cannot satisfactorily reproduce all of the experimental data. Thus, even when protein atoms are allowed to move, the dielectric model used in our electrostatic calculations breaks down when modeling the gramicidin channel.

Ligand-gated ion channels: mechanisms underlying ion selectivity

Anion/cation selectivity is a critical property of ion channels and underpins their physiological function. Recently, there have been numerous mutagenesis studies, which have mapped sites within the ion channel-forming segments of ligand-gated ion channels that are determinants of the ion selectivity. Site-directed mutations to specific amino acids within or flanking the M2 transmembrane segments of the anion-selective glycine, GABA(A) and GABA(C) receptors and the cation-selective nicotinic acetylcholine and serotonin (type 3) receptors have revealed discrete, equivalent regions within the ion channel that form the principal selectivity filter, leading to plausible molecular mechanisms and mathematical models to describe how ions preferentially permeate these channels. In particular, the dominant factor determining anion/cation selectivity seems to be the sign and exposure of charged amino acids lining the selectivity filter region of the open channel. In addition, the minimum pore diameter, which can be influenced by the presence of a local proline residue, also makes a contribution to such ion selectivity in LGICs with smaller diameters increasing anion/cation selectivity and larger ones decreasing it.

Conduction mechanisms of chloride ions in ClC-type channels

The conduction properties of ClC-0 and ClC-1 chloride channels are examined using electrostatic calculations and three-dimensional Brownian dynamics simulations. We create an open-state configuration of the prokaryotic ClC Cl(-) channel using its known crystallographic structure as a basis. Two residues that are occluding the channel are slowly pushed outward with molecular dynamics to create a continuous ion-conducting path with the minimum radius of 2.5 A. Then, retaining the same pore shape, the prokaryotic ClC channel is converted to either ClC-0 or ClC-1 by replacing all the nonconserved dipole-containing and charged amino acid residues. Employing open-state ClC-0 and ClC-1 channel models, current-voltage curves consistent with experimental measurements are obtained. We find that conduction in these pores involves three ions. We locate the binding sites, as well as pinpointing the rate-limiting steps in conduction, and make testable predictions about how the single channel current across ClC-0 and ClC-1 will vary as the ionic concentrations are increased. Finally, we demonstrate that a ClC-0 homology model created from an alternative sequence alignment fails to replicate any of the experimental observations.

Theoretical conformation of the closed and open states of the acetylcholine receptor channel

We conduct a theoretical analysis to show the recently imaged structure of the acetylcholine receptor pore is in a non-conducting state. A hypothesised open state consistent with a lower resolution image is created and shown to have high conductance.

Modeling of ionic relaxation around a biomembrane disk

A simplified Brownian dynamics model and the corresponding software implementation have been developed for the simulation of electrolyte dynamics on the mesoscopic scale. In addition to direct control simulations, the model system has been verified by a quantitative comparison with the Debye-Hückel theory. As a first application, the model was used to simulate ionic relaxation processes following abrupt intramembrane charge rearrangements in the case of a disk shaped membrane. In addition to its general implications, the obtained properties of the relaxation kinetics confirm the assumptions of the theory of the so-called suspension method, a technique capable of tracing molecular charge motions of membrane proteins in three dimensions.

Probing the volume changes during voltage gating of Porin 31BM channel with nonelectrolyte polymers

To probe the volume changes of the voltage-dependent anion-selective channel (VDAC), the nonelectrolyte exclusion technique was taken because it is one of the few existing methods that may define quite accurately the rough geometry of lumen of ion channels (in membranes) for which there is no structural data.Here, we corroborate the data from our previous study [FEBS Lett. 416 (1997) 187] that the gross structural features of VDAC in its highest conductance state are asymmetric with respect to the plane of the membrane, and state that this asymmetry is not dependent on sign of voltage applied. Hence, the plasticity of VDAC does not play a role in the determination of lumen geometry at this state and the asymmetry is an internal property of the channel. We also show that the apparent diameter of the cis segment of the pore decreases slightly from 2 to 1.8 nm when the channel's conductance decreases from its high to low state. However, the trans funnel segment undergoes a more marked change in polymer accessible volume. Specifically, its larger diameter decreases from approximately 4 to 2.4 nm. Supposing the channel's total length is 4.6 nm, the apparent change in channel volume during this transition is estimated to be about 10 nm(3), i.e. about 40% of the channel's volume in the high conductance state.

A model of the glycine receptor deduced from Brownian dynamics studies

We have developed a three-dimensional model of the alpha1 homomeric glycine receptor by using Brownian dynamics simulations to account for its observed physiological properties. The model channel contains a large external vestibule and a shallow internal vestibule, connected by a narrow, cylindrical selectivity filter. Three rings of charged residues from the pore-lining M2 domain are modeled as point charges in the protein. Our simulations reproduce many of the key features of the channel, such as the current-voltage profiles, permeability ratios, and ion selectivity. When we replace the ring of alanine residues lining the selectivity filter with glutamates, the mutant model channel becomes permeable to cations, as observed experimentally. In this mutation, anions act as chaperones for sodium ions in the extracellular vestibule, and together they penetrate deep inside the channel against a steep energy barrier encountered by unaccompanied ions. Two subsequent amino acid mutations increase the cation permeability, enabling monovalent cations to permeate through the channel unaided and divalent cations to permeate when chaperoned by anions. These results illustrate the key structural features and underlying mechanism for charge selectivity in the glycine receptor.

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.

Continuum electrostatics fails to describe ion permeation in the gramicidin channel

We investigate the validity of continuum electrostatics in the gramicidin A channel using a recently determined high-resolution structure. The potential and electric field acting on ions in and around the channel are computed by solving Poisson's equation. These are then used in Brownian dynamics simulations to obtain concentration profiles and the current passing through the channel. We show that regardless of the effective dielectric constant used for water in the channel or the channel protein, it is not possible to reproduce all the experimental data on gramicidin A; thus, continuum electrostatics cannot provide a valid framework for the description of ion dynamics in gramicidin channels. Using experimental data and molecular dynamics simulations as guides, we have constructed potential energy profiles that can satisfactorily describe the available physiological data. These profiles provide useful benchmarks for future potential of mean force calculations of permeating ions from molecular dynamics simulations of gramicidin A. They also offer a convenient starting point for studying structure-function relationships in modified gramicidin channels.

Reservoir boundaries in Brownian dynamics simulations of ion channels

Brownian dynamics (BD) simulations provide a practical method for the calculation of ion channel conductance from a given structure. There has been much debate about the implementation of reservoir boundaries in BD simulations in recent years, with claims that the use of improper boundaries could have large effects on the calculated conductance values. Here we compare the simple stochastic boundary that we have been using in our BD simulations with the recently proposed grand canonical Monte Carlo method. We also compare different methods of creating transmembrane potentials. Our results confirm that the treatment of the reservoir boundaries is mostly irrelevant to the conductance properties of an ion channel as long as the reservoirs are large enough.