Pressure-induced water transport in membrane channels studied by molecular dynamics

A method is proposed to measure the water permeability of membrane channels by means of molecular dynamics simulations. By applying a constant force to the bulk water molecules and a counter force on the complementary system, a hydrostatic pressure difference across the membrane can be established, producing a net directional water flow. The hydraulic or osmotic permeability can then be determined by the ratio of the water flux and the pressure difference. The method is applied and tested on an aquaglyceroporin channel through a series of simulations totaling 5 ns in duration.     

Molecular dynamics simulations of water within models of ion channels.

The transbilayer pores formed by ion channel proteins contain extended columns of water molecules. The dynamic properties of such waters have been suggested to differ from those of water in its bulk state. Molecular dynamics simulations of ion channel models solvated within and at the mouths of their pores are used to investigate the dynamics and structure of intra-pore water. Three classes of channel model are investigated: a) parallel bundles of hydrophobic (Ala20) alpha-helices; b) eight-stranded hydrophobic (Ala10) antiparallel beta-barrels; and c) parallel bundles of amphipathic alpha-helices (namely, delta-toxin, alamethicin, and nicotinic acetylcholine receptor M2 helix). The self-diffusion coefficients of water molecules within the pores are reduced significantly relative to bulk water in all of the models. Water rotational reorientation rates are also reduced within the pores, particularly in those pores formed by alpha-helix bundles. In the narrowest pore (that of the Ala20 pentameric helix bundle) self-diffusion coefficients and reorientation rates of intra-pore waters are reduced by approximately an order of magnitude relative to bulk solvent. In Ala20 helix bundles the water dipoles orient antiparallel to the helix dipoles. Such dipole/dipole interaction between water and pore may explain how water-filled ion channels may be formed by hydrophobic helices. In the bundles of amphipathic helices the orientation of water dipoles is modulated by the presence of charged side chains. No preferential orientation of water dipoles relative to the pore axis is observed in the hydrophobic beta-barrel models.     

Parallel helix bundles and ion channels: molecular modeling via simulated annealing and restrained molecular dynamics.

A parallel bundle of transmembrane (TM) alpha-helices surrounding a central pore is present in several classes of ion channel, including the nicotinic acetylcholine receptor (nAChR). We have modeled bundles of hydrophobic and of amphipathic helices using simulated annealing via restrained molecular dynamics. Bundles of Ala20 helices, with N = 4, 5, or 6 helices/bundle were generated. For all three N values the helices formed left-handed coiled coils, with pitches ranging from 160 A (N = 4) to 240 A (N = 6). Pore radius profiles revealed constrictions at residues 3, 6, 10, 13, and 17. A left-handed coiled coil and a similar pattern of pore constrictions were observed for N = 5 bundles of Leu20. In contrast, N = 5 bundles of Ile20 formed right-handed coiled coils, reflecting loosened packing of helices containing beta-branched side chains. Bundles formed by each of two classes of amphipathic helices were examined: (a) M2a, M2b, and M2c derived from sequences of M2 helices of nAChR; and (b) (LSSLLSL)3, a synthetic channel-forming peptide. Both classes of amphipathic helix formed left-handed coiled coils. For (LSSLLSL)3 the pitch of the coil increased as N increased from 4 to 6. The M2c N = 5 helix bundle is discussed in the context of possible models of the pore domain of nAChR.     

Computing transient gating charge movement of voltage-dependent ion channels

The opening of voltage-gated sodium, potassium, and calcium ion channels has a steep relationship with voltage. In response to changes in the transmembrane voltage, structural movements of an ion channel that precede channel opening generate a capacitative gating current. The net gating charge displacement due to membrane depolarization is an index of the voltage sensitivity of the ion channel activation process. Understanding the molecular basis of voltage-dependent gating of ion channels requires the measurement and computation of the gating charge, Q. We derive a simple and accurate semianalytic approach to computing the voltage dependence of transient gating charge movement (Q–V relationship) of discrete Markov state models of ion channels using matrix methods. This approach allows rapid computation of Q–V curves for finite and infinite length step depolarizations and is consistent with experimentally measured transient gating charge. This computational approach was applied to Shaker potassium channel gating, including the impact of inactivating particles on potassium channel gating currents.     

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.     

Dynamic properties of Na+ ions in models of ion channels: a molecular dynamics study.

We present simulation results for the effective diffusion coefficients of a sodium ion in a series of model ion channels of different diameters and hydrophobicities, including models of alamethicin, a leucine-serine peptide, and the M2 helix bundle of the nicotinic acetylcholine receptor. The diffusion coefficient, which in the simulations has a value of 0.15(2) A2ps-1 in bulk water, is found to be reduced to as little as 0.02(1) A2ps-1 in the narrower channels, and to about 0.10(5) A2ps-1 in wider channels such as the nicotinic acetylcholine receptor. It is anticipated that this work will be useful in connection with calculations of channel conductivity using such techniques as the Poisson-Nernst-Planck equation, Eyring rate theory, or Brownian dynamics.     

Molecular dynamics study of ion transport in transmembrane protein channels

Ion transport through biological membranes often takes place via pore-like protein channels. The elementary process of this transport can be described as a motion of the ion in a quasi-periodic multi-well potential. In this study molecular dynamics simulations of ion transport in a model channel were performed in order to test the validity of reaction-rate theory for this process. The channel is modelled as a hexagonal helix of infinite length, and the ligand groups interacting with the ion are represented by dipoles lining the central hole of the channel. The dipoles interact electrostatically with each other and are allowed to oscillate around an equilibrium orientation. The coupled equations of motion for the ion and the dipoles were solved simultaneously with the aid of a numerical integration procedure. From the calculated ion trajectories it is seen that, particularly at low temperatures, the ion oscillates back and forth in the trapping site many times before it leaves the site and jumps over the barrier. The observed oscillation frequency was found to be virtually temperature-independent (nu 0 approximately equal to 2 X 10(12) s-1) so that the strong increase of transport rate with temperature results almost exclusively from the Arrhenius-type exponential dependence of jump probability w on 1/T. At higher temperatures simultaneous jumps over several barriers occasionally occur. Although the exponential form of w(T) was in agreement with the predictions of rate theory, the activation energy Ea as determined from w(T) was different from the barrier height which was calculated from the static potential of the ion in the channel; the actual transport rate was 1 X 10(3) times higher than the rate predicted from the calculated barrier height. This observation was interpreted by the notion that ion transport in the channel is strongly influenced by thermal fluctuations in the conformation of the ligand system which in turn give rise to fluctuations of barrier height.     

A molecular model for ion selectivity in membrane channels

In this article, the three-dimensional motion of an ion within a molecular channel is discussed for the first time; escape rates from binding sites are calculated using the transition state method. For a given ligand configuration and a particular pore radius the rates depend upon ion size and mass. It is found that the activation energies depend strongly on the ion size, i.e., they increase with decreasing ion radius. In contrast to the rates obtained from the mass dependence alone, the rates depending on both mass and size of the alkali ions yield the completely inverted sequence, namely the Eisenman sequence I.     

Brownian dynamics simulation of ion flow through porin channels

Bacterial porins, which allow the passage of solutes across the outer bacterial membrane, are structurally well characterized. They therefore lend themselves to detailed studies of the determinants of ion flow through transmembraneous channels. In a comparative study, we have performed Brownian dynamics simulations to obtain statistically significant transfer efficiencies for cations and anions through matrix porin OmpF, osmoporin OmpK36, phosphoporin PhoE and two OmpF charge mutants.The simulations show that the electrostatic potential at the highly charged channel constriction serves to enhance ion permeability of either cations or anions, dependent on the type of porin. At the same time translocation of counterions is not severely impeded. At the constriction, cations and anions follow distinct trajectories, due to the segregation of basic and acidic protein residues.Simulated ion selectivity and relative conductance agree well with experimental values, and are dependent crucially on the charge constellation at the pore constriction. The experimentally observed decrease in ion selectivity and single channel conductance with increasing ionic strength is well reproduced and can be attributed to electrostatic shielding of the pore lining.     

Viral ion channels: molecular modeling and simulation

In a number of membrane-bound viruses, ion channels are formed by integral membrane proteins. These channel proteins include M2 from influenza A, NB from influenza B, and, possibly, Vpu from HIV-1. M2 is important in facilitating uncoating of the influenza A viral genome and is the target of amantadine, an anti-influenza drug. The biological roles of NB and Vpu are less certain. In all cases, the protein contains a single transmembrane alpha-helix close to its N-terminus. Channels can be formed by homo-oligomerization of these proteins, yielding bundles of transmembrane helices that span the membrane and surround a central ion-permeable pore. Molecular modeling may be used to integrate and interpret available experimental data concerning the structure of such transmembrane pores. This has proved successful for the M2 channel domain, where two independently derived models are in agreement with one another, and with solid-state nuclear magnetic resonance (NMR) data. Simulations based on channel models may yield insights into possible ion conduction and selectivity mechanisms.     

Growing momentum in the molecular study of ion channels.

Long the sole domain of physiologists and electrical engineers, ion channel biophysics is going molecular, and with a vengeance. This summary of a recent meeting devoted to ion channel biophysics shows that the integration of techniques, reinforced by active communication among scientists of diverse backgrounds, is extremely potent.     

Semi-Markov models for brownian dynamics permeation in biological ion channels

Constructing accurate computational models that explain how ions permeate through a biological ion channel is an important problem in biophysics and drug design. Brownian dynamics simulations are large-scale interacting particle computer simulations for modeling ion channel permeation but can be computationally prohibitive. In this paper, we show the somewhat surprising result that a small-dimensional semi-Markov model can generate events (such as conduction events and dwell times at binding sites in the protein) that are statistically indistinguishable from brownian dynamics computer simulation. This approach enables the use of extrapolation techniques to predict channel conduction when performing the actual brownian dynamics simulation that is computationally intractable. Numerical studies on the simulation of gramicidin A ion channels are presented.     

Molecular dynamics of synthetic leucine-serine ion channels in a phospholipid membrane

Molecular dynamics calculations were carried out on models of two synthetic leucine-serine ion channels: a tetrameric bundle with sequence (LSLLLSL)(3)NH(2) and a hexameric bundle with sequence (LSSLLSL)(3)NH(2). Each protein bundle is inserted in a palmitoyloleoylphosphatidylcholine bilayer membrane and solvated by simple point charge water molecules inside the pore and at both mouths. Both systems appear to be stable in the absence of an electric field during the 4 ns of molecular dynamics simulation. The water motion in the narrow pore of the four-helix bundle is highly restricted and may provide suitable conditions for proton transfer via a water wire mechanism. In the wider hexameric pore, the water diffuses much more slowly than in bulk but is still mobile. This, along with the dimensions of the pore, supports the observation that this peptide is selective for monovalent cations. Reasonable agreement of predicted conductances with experimentally determined values lends support to the validity of the simulations.     

Structural dynamics in the gating ring of cyclic nucleotide-gated ion channels

For ligand-gated ion channels, the binding of a ligand to an intracellular or extracellular domain generates changes in transmembrane pore-forming helices, which alters ion flow. The molecular mechanism for this allostery, however, remains unknown. Here we explore the structure and conformational rearrangements of the C-terminal gating ring of the cyclic nucleotide-gated channel CNGA1 during activation by cyclic nucleotides with patch-clamp fluorometry. By monitoring fluorescent resonance energy transfer (FRET) between membrane-resident quenchers and fluorophores attached to the channel, we detected no movement orthogonal to the membrane during channel activation. By monitoring FRET between fluorophores within the C-terminal region, we determined that the C-terminal end of the C-linker and the end of the C-helix move apart when channels open. We conclude that during channel activation, a portion of the gating ring moves parallel to the plasma membrane, hinging toward the central axis of the channel.     

Model channel ion currents in NaCl-extended simple point charge water solution with applied-field molecular dynamics.

Using periodic boundary conditions and a constant applied field, we have simulated current flow through an 8.125-A internal diameter, rigid, atomistic channel with polar walls in a rigid membrane using explicit ions and extended simple point charge water. Channel and bath currents were computed from 10 10-ns trajectories for each of 10 different conditions of concentration and applied voltage. An electric field was applied uniformly throughout the system to all mobile atoms. On average, the resultant net electric field falls primarily across the membrane channel, as expected for two conductive baths separated by a membrane capacitance. The channel is rarely occupied by more than one ion. Current-voltage relations are concentration dependent and superlinear at high concentrations.     

Stochastic theory of ion movement in channels with single-ion occupancy. Application to sodium permeation of gramicidin channels.

The electrodiffusion equations were solved for the one-ion channel both by the analytical method due to Levitt and also by Brownian dynamic simulations. For both types of calculations equilibration of ion distribution between the bath and the ends of the channel was assumed. Potential profiles were found that give good fits to published data on Na+ permeation of gramicidin channels. The data were best fit by profiles that have no relative energy maximum at the mouth of the channel. This finding suggests that alignment of waters or channel charged groups inside the channel in response to an ion's approach may provide an energetically favorable situation for entry sufficient to overcome the energy required for removing bulk waters of hydration. An alternative possibility is that the barrier to ion entry is situated outside the region restricted to single-ion occupancy. Replacement of valine with more polar amino acids at the No. 1 location was found to correspond to a deepening of the potential minima near the channel mouths, an increase in height of the central barrier to ion translocation across the channel, and possibly a reduction in the mobility of the ion-water complex in the channel. The Levitt theory was extended to calculate passage times for ions to cross the channel and the blocking effects of ions that entered the channel but didn't cross. These quantities were also calculated by the Brownian dynamics method.     

Plant ion channels: from molecular structures to physiological functions

Progress in identification of plant ion channels and development of electrophysiological analyses in heterologous expression systems and in planta, in combination with reverse genetic approaches, are providing the possibility of associating molecular entities with physiological functions. Recently, the first attempts to determine in vivo functions using knockout mutants demonstrated the roles of root ion channels. The search for proteins interacting with such channels leads to an even more complex view of the concerted action in protein networks.