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.     

Molecular dynamics simulations of ion distribution in nanochannels

Molecular dynamics simulations of ion distribution in a nanochannel were performed using a three region simulation domain including two bulk regions on each side of the nanochannel. This scheme allows the study of ion concentration and distribution inside the nanochannel under a given bulk electrolyte concentration, i.e. when the molecular system reaches equilibrium, the concentrations of the counter- and co-ions inside the nanochannel corresponding to a bulk electrolyte will emerge naturally. Our approach is in sharp contrast to the common practice in modeling electric double layers where the number of ions in the nanochannel is assigned somewhat arbitrarily, corresponding to an unknown bulk concentration.     

Molecular dynamics simulations of Leu-enkephalin in water and DMSO.

The structure of Leu-enkephalin (L-Enk) and Met-enkephalin (M-Enk) have frequently been studied, in particular by nuclear magnetic resonance spectroscopy. After more than 20 years of research, it was concluded that enkephalins have no preferred structure in aqueous solution, but that they may have in other solvents. We have performed molecular dynamics simulations of zwitterionic L-Enk in water, and zwitterionic as well as neutral L-Enk dimethyl sulfoxide (DMSO). In water the peptide is very flexible, although there seems to be a preference for compact conformations. In DMSO, the peptide forms a clear salt bridge in the zwitterionic form, but has no preferred conformation in the neutral form. This difference in conformation may provide an explanation for measurements in DMSO in which multiple conformations were found to exist. In this paper we introduce a new formulation for a dihedral angle autocorrelation function, and apply it to study side-chain dynamics in L-Enk. We find that the side-chain dynamics of the large Tyr and Phe residues cannot be adequately sampled in 2.0-ns simulations, while this does seem to be possible for the smaller Leu side chain.     

Molecular dynamics simulations

Molecular dynamics simulations have become a standard tool for the investigation of biomolecules. Simulations are performed of ever bigger systems using more realistic boundary conditions and better sampling due to longer sampling times. Recently, realistic simulations of systems as complex as transmembrane channels have become feasible. Simulations aid our understanding of biochemical processes and give a dynamic dimension to structural data; for example, the transformation of harmless prion protein into the disease-causing agent has been modeled.     

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.     

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 mechanics and dynamics simulations of various dispersant models on the water surface (001)

Five dispersant-molecule models of succinimide, acrylate, imide, phenylsulfonic and salicyl were used to study their interactions with the water surface (001). The interaction energy, molecular configuration, charge distribution and radial distribution function (RDF) curve for each of the dispersant molecules were analyzed from the molecular mechanics (MM) and molecular dynamics (MD) simulation results. It can be seen that the system energies, mostly electrostatic and hydrogen bond energies, were reduced significantly when the dispersant molecules interacted with the water surface. The hydrophilic group of a dispersant molecule can attach itself to the water surface firmly and reach for a stable energy-minimized configuration, which is helpful to the dispersants' dispersancy. The influence exerted by the hydrophobic group of the dispersant molecule, which was the substituted hydrocarbon chain of n-octadecanyl in this paper, is discussed in comparison with the naked polar headgroup. Steric configuration, charge distribution and substitute hydrocarbon chain of the dispersant molecule influenced the interaction between dispersants and polar water surface.     

Simulation of molecular dynamics of water movement in ion channels

The motion of water molecules in a gramicidin-like channel was studied by the molecular dynamics method. Water molecules are presented in the ST2 model. The structure of the channel was presented in the form of channel's helix frame possessing mobile dipole groups. The interaction of all mobile particles with the membrane channel's walls was taken into account. The calculation consisted of 50,000 integration steps of delta t = 5 x 10(-16) s which corresponded to a total elapsed time of 25 ps. It was shown that water molecules in the channel did not possess rigid spatial structure but exhibited a structure oriented along the channel axis. The motion of water molecules in the channel occurred smoothly, i.e. all water molecules did not have any deep, stable potential wells in the channel. The distribution of water molecules along the radial coordinate of the channel was estimated. Water density was shown to be maximal near the channel axis.     

Molecular dynamics simulations of helix denaturation.

An understanding of the structural transitions that an alpha-helix undergoes will help to elucidate such motions in proteins and their role in protein folding. We present the results of molecular dynamics simulations to investigate these transitions in a short polyalanine peptide (13 residues) both in vacuo and in the presence of solvent. The denaturation of this peptide was monitored as a function of temperature (ranging from 5 to 200 degrees C). In vacuo, the helical state predominated at all temperatures, whereas in solution the helix melted with increasing temperature. The peptide was predominantly helical at low temperature in solution, while at intermediate temperatures the peptide spent the bulk of the time fluctuating between different conformations with intermediate amounts of helix, e.g. not completely helical nor entirely non-helical. Many of these conformations consisted of short helical segments with intervening non-helical residues. At high temperature the peptide unfolded and adopted various collapsed unstructured states. The intrahelical hydrogen bonds that break at high temperature were not fully compensated by hydrogen bonds with water molecules in the partially unfolded forms of the peptide. Increases in temperature disrupted both the helical structure and the peptide-water interactions. Water played a major but indirect role in facilitating unfolding, as opposed to specifically competing for the intrapeptide hydrogen bonds. The implications of our results to protein folding are discussed.     

Molecular dynamics simulations of interaction between sub-bituminous coal and water

The high moisture content of sub-bituminous coal is associated with the interactions between coal and water. Because of complex composition and structure, the graphite surface modified by hydroxyl, carboxyl and carbonyl groups was used to represent the surface model of sub-bituminous coal according to XPS results. Density profiles for oxygen atoms and hydrogen atoms indicate that the coal surface properties affect the structural and dynamic characteristics of the interfacial water molecules. The interfacial water exhibits much more ordering than bulk water. The results of radial distribution functions, mean square displacement and local self-diffusion coefficient for water molecule related to three oxygen moieties confirmed that the water molecules prefer to absorb with carboxylic groups, and adsorption of water molecules at the hydroxy and carbonyl is similar.     

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.     

Molecular dynamics simulations in photosynthesis

Photosynthesis Research - Photosynthesis is regulated by a dynamic interplay between proteins, enzymes, pigments, lipids, and cofactors that takes place on a large spatio-temporal scale. Molecular...     

Tests of continuum theories as models of ion channels. II. Poisson-Nernst-Planck theory versus brownian dynamics

We test the validity of the mean-field approximation in Poisson-Nernst-Planck theory by contrasting its predictions with those of Brownian dynamics simulations in schematic cylindrical channels and in a realistic potassium channel. Equivalence of the two theories in bulk situations is demonstrated in a control study. In simple cylindrical channels, considerable differences are found between the two theories with regard to the concentration profiles in the channel and its conductance properties. These differences are at a maximum in narrow channels with a radius smaller than the Debye length and diminish with increasing radius. Convergence occurs when the channel radius is over 2 Debye lengths. These tests unequivocally demonstrate that the mean-field approximation in the Poisson-Nernst-Planck theory breaks down in narrow ion channels that have radii smaller than the Debye length.     

Tests of continuum theories as models of ion channels. I. Poisson-Boltzmann theory versus Brownian dynamics

Continuum theories of electrolytes are widely used to describe physical processes in various biological systems. Although these are well-established theories in macroscopic situations, it is not clear from the outset that they should work in small systems whose dimensions are comparable to or smaller than the Debye length. Here, we test the validity of the mean-field approximation in Poisson-Boltzmann theory by comparing its predictions with those of Brownian dynamics simulations. For this purpose we use spherical and cylindrical boundaries and a catenary shape similar to that of the acetylcholine receptor channel. The interior region filled with electrolyte is assumed to have a high dielectric constant, and the exterior region representing protein a low one. Comparisons of the force on a test ion obtained with the two methods show that the shielding effect due to counterions is overestimated in Poisson-Boltzmann theory when the ion is within a Debye length of the boundary. As the ion gets closer to the boundary, the discrepancy in force grows rapidly. The implication for membrane channels, whose radii are typically smaller than the Debye length, is that Poisson-Boltzmann theory cannot be used to obtain reliable estimates of the electrostatic potential energy and force on an ion in the channel environment.     

Molecular dynamics simulations of the Cx26 hemichannel: evaluation of structural models with Brownian dynamics

The recently published crystal structure of the Cx26 gap junction channel provides a unique opportunity for elucidation of the structure of the conductive connexin pore and the molecular determinants of its ion permeation properties (conductance, current-voltage [I-V] relations, and charge selectivity). However, the crystal structure was incomplete, most notably lacking the coordinates of the N-terminal methionine residue, which resides within the pore, and also lacking two cytosolic domains. To allow computational studies for comparison with the known channel properties, we completed the structure. Grand canonical Monte Carlo Brownian dynamics (GCMC/BD) simulations of the completed and the published Cx26 hemichannel crystal structure indicate that the pore is too narrow to permit significant ion flux. The GCMC/BD simulations predict marked inward current rectification and almost perfect anion selectivity, both inconsistent with known channel properties. The completed structure was refined by all-atom molecular dynamics (MD) simulations (220 ns total) in an explicit solvent and POPC membrane system. These MD simulations produced an equilibrated structure with a larger minimal pore diameter, which decreased the height of the permeation barrier formed by the N terminus. GCMC/BD simulations of the MD-equilibrated structure yielded more appropriate single-channel conductance and less anion/cation selectivity. However, the simulations much more closely matched experimentally determined I-V relations when the charge effects of specific co- and posttranslational modifications of Cx26 previously identified by mass spectrometry were incorporated. We conclude that the average equilibrated structure obtained after MD simulations more closely represents the open Cx26 hemichannel structure than does the crystal structure, and that co- and posttranslational modifications of Cx26 hemichannels are likely to play an important physiological role by defining the conductance and ion selectivity of Cx26 channels. Furthermore, the simulations and data suggest that experimentally observed heterogeneity in Cx26 I-V relations can be accounted for by variation in co- and posttranslational modifications.     

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.