Simulation of voltage-driven hydrated cation transport through narrow transmembrane channels

Water Transport and Ion Diffusion Investigation of an Amphotericin B-Based Channel Applied to Forward Osmosis: A Simulation Study

The use of an Amphotericin B_Ergosterol (AmBEr) channel as an artificial water channel in forward osmosis filtration (FO) was studied via molecular dynamics (MD) simulation. Three channel models were constructed: a common AmBEr channel and two modified C3deOAmB_Ergosterol (C3deOAmBEr) channels with different diameters (12 Å and 18 Å). During FO filtration simulation, the osmotic pressure of salt-water was a driving force for water permeation. We examined the effect of the modified C3deOAmBEr channel on the water transport performance. By tracing the change of the number of water molecules along with simulation time in the saltwater region, the water permeability of the channel models could be calculated. A higher water permeability was observed for a modified C3deOAmBEr channel, and there was no ion permeation during the entire simulation period. The hydrated ions and water molecules were placed into the channel to explore the ion leakage behavior of the channels. The mean squared displacement (MSD) of ions and water molecules was obtained to study the ion leakage performance. The Amphotericin B-based channels showed excellent selectivity of water molecules against ions. The results obtained on an atomistic scale could assist in determining the properties and the optimal filtration applications for Amphotericin B-based channels.

Harmonic oscillators: the quantization of simple systems in the old quantum theory and their functional roles in biology

This article introduces quantum physics into biology in an intuitive and non-intimidating manner. It extends the quantum aspects of harmonic oscillators, and electromagnetic fields, to their functional roles in biology. Central to this process are the De Broglie wave-particle duality equation, and the adiabatic invariant parameters, magnetic moment, angular momentum and magnetic flux, determined by Ehrenfest as imposing quantum constraints on the dynamics of charges in motion. In mechanisms designed to explain the generation of low-level light emissions in biology we have adopted a biological analog of the electrical circuitry modeled on the parallel plated capacitor, traversed by helical protein structures, capable of generating electromagnetic radiation in the optical spectral region. The charge carrier required for the emissions is an accelerating electron driven, in a cyclotron-type mechanism, by ATP-induced reverse electron transfer with the radial, emission, components, mediated by coulombic forces within the helical configurations. Adenine, an essential nucleotide constituent of DNA, was examined with its long wavelength absorption maximum determining the energetic parameters for the calculations. The calculations were made for a virtual 5-turn helix where each turn of the helix emits a different frequency, generating a biological quantum series. The components of six adiabatic invariant equations were found to be embedded in Planck's constant rendering them discrete, finite, non-random, non-statistical-Planck's constant precludes probability. A mechanism for drug-induced hallucination is described that might provide insights as to the possible role of electromagnetic fields in consciousness. Sodium acceleration through a proposed nerve membrane helical channel generated electromagnetic emissions in the microwave region in confirmation of reported microwave emission for active nerves and may explain saltatory nerve conduction. Theoretical calculations for a helical DNA system gave a conduction resistance in agreement with a experimentally determined parameter.

The proton-driven rotor of ATP synthase: ohmic conductance (10 fS), and absence of voltage gating

The membrane portion of F(0)F(1)-ATP synthase, F(0), translocates protons by a rotary mechanism. Proton conduction by F(0) was studied in chromatophores of the photosynthetic bacterium Rhodobacter capsulatus. The discharge of a light-induced voltage jump was monitored by electrochromic absorption transients to yield the unitary conductance of F(0). The current-voltage relationship of F(0) was linear from 7 to 70 mV. The current was extremely proton-specific (>10(7)) and varied only slightly ( approximately threefold) from pH 6 to 10. The maximum conductance was approximately 10 fS at pH 8, equivalent to 6240 H(+) s(-1) at 100-mV driving force, which is an order-of-magnitude greater than of coupled F(0)F(1). There was no voltage-gating of F(0) even at low voltage, and proton translocation could be driven by deltapH alone, without voltage. The reported voltage gating in F(0)F(1) is thus attributable to the interaction of F(0) with F(1) but not to F(0) proper. We simulated proton conduction by a minimal rotary model including the rotating c-ring and two relay groups mediating proton exchange between the ring and the respective membrane surface. The data fit attributed pK values of approximately 6 and approximately 10 to these relays, and placed them close to the membrane/electrolyte interface.

Electromagnetic field generation by ATP-induced reverse electron transfer

This paper describes a mechanism to explain low-level light emission in biology. A biological analog of the electrical circuitry, modeled on the parallel plate capacitor, traversed by a helical structure, required to generate electromagnetic radiation in the optical spectral range, is described. The charge carrier required for the emissions is determined to be an accelerating electron driven by an ATP-induced reverse electron transfer. The radial velocity component, the emission trajectory, of the moving charges traversing helical protein structures in a cyclotron-type mechanism is proposed to be imposed by the ferromagnetic field components of the iron in the iron-sulfur proteins. The redox systems NADH, riboflavin, and chlorophyll were examined with their long-wavelength absorption maxima determining the energetic parameters for the calculations. Potentials calculated from the axial velocity components for the riboflavin and NADH systems were found to equal the standard redox potentials of these systems as measured electrochemically and enzymatically. The mechanics for the three systems determined the magnetic moments, the angular momenta, and the orbital magnetic fluxes to be adiabatic invariant parameters. The De Broglie dual wave-particle equation, the fundamental equation of wave mechanics, and the key idea of quantum mechanics, establishes the wavelengths for accelerating electrons which, divided into a given radial velocity, gives its respective emission frequency. Electrons propelled through helical structures, traversed by biologically available electric and magnetic fields, make accessible to the internal environment the optical spectral frequency range that the solar spectrum provides to the external environment.

Effective diffusion coefficients of K+ and Cl- ions in ion channel models

We have used molecular dynamics simulations, corresponding to a total simulation time of 11 ns, to investigate the effective short-time local diffusion coefficient of potassium and chloride ions in a series of model ion channels. These models, which include channels formed by the fungal peptide alamethicin, by a synthetic leucine-serine peptide, and by the pore-lining M2 helix bundle of the nicotinic acetylcholine receptor, have a range of different secondary structures, diameters and hydrophobicities. We find that the diffusion coefficients of both ions are appreciably reduced in the narrower channels, the extent of the reduction being similar for both the anionic and cationic species. This suggests that a difference in mobility cannot be the source of the ion selectivity exhibited by some of the channels (for example, the leucine-serine peptide). We find no evidence for a reduction in mobility of either ion in the nAChR model. These results are broadly in line with a previous similar study of Na+ ions, and may be useful in Poisson-Nernst-Planck, Eyring rate theory or Brownian dynamics calculations of channel conductance.

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.

Dynamic properties of individual water molecules in a hydrophobic pore lined with acyl chains: a molecular dynamics study

Recently, a certain class of synthetic molecules has been shown to form ion channels, the pore of which is lined with hydrophobic acyl chains [M. Sokabe, in: F. Oosawa, H. Hayashi, T. Yoshioka (Eds.), Transmembrane Signaling and Sensation, JSSP/VNU Science Press BV, Tokyo, 1984, p. 119; F. Hayashi, M. Sokabe, M. Takagi, K. Hayashi, U. Kishimoto, Biochim. Biophys. Acta, 510 (1978) 305; M.J. Pregel, L. Jullien, J. Canceill, L. Lacombe, J.M. Lehn, J. Chem. Soc. Perkin Trans., 2 (1995) 417; Y. Tanaka, Y. Kobuke, M. Sokabe, Angew. Chem. Int. Ed. Engl., 34 (1995) 693; M. Sokabe, Z. Qi, K. Donowaki, H. Ishida, K. Okubo, Biophys. J., 70 (1996) A201; H. Ishida, K. Donowaki, Y. Inoue, Z. Qi, M. Sokabe, Chem. Lett. (1997) p. 953]. As an initial step towards understanding the physical mechanisms of ion permeation across such a hydrophobic pore, systematic molecular dynamics simulations were performed to investigate dynamic and energetic properties of water molecules inside the pore using a dimer of alanine-N'-acylated cyclic peptide as a channel model. Dynamic energy profiles for water molecules indicated that the energy barrier at the middle region of the pore is approximately 2-3 kcal/mol higher than that in the cap water region which was defined as a vicinity region of the channel entrance. Energetics analyses demonstrated that the mutual interactions among intrapore water molecules are the major factor to give favorable interaction (negative energy contribution) for themselves. The pore, despite being lined with acyl chains, has a favorable van der Waals interaction with intrapore water molecules. These results may help to explain why water-filled channels can be formed by the hydrophobic helices in natural channels.

Simulation of voltage-dependent interactions of alpha-helical peptides with lipid bilayers

Pore formation in lipid bilayers by channel-forming peptides and toxins is thought to follow voltage-dependent insertion of amphipathic alpha-helices into lipid bilayers. We have developed an approximate potential for use within the CHARMm molecular mechanics program which enables one to simulate voltage-dependent interaction of such helices with a lipid bilayer. Two classes of helical peptides which interact with lipid bilayers have been studied: (a) delta-toxin, a 26 residue channel-forming peptide from Staphylococcus aureus; and (b) synthetic peptides corresponding to the alpha 5 and alpha 7 helices of the pore-forming domain of Bacillus thuringiensis CryIIIA delta-endotoxin. Analysis of delta-toxin molecular dynamics (MD) simulations suggested that the presence of a transbilayer voltage stabilized the inserted location of delta-toxin helices, but did not cause insertion per se. A series of simulations for the alpha 5 and alpha 7 peptides revealed dynamic switching of the alpha 5 helix between a membrane-associated and a membrane-inserted state in response to a transbilayer voltage. In contrast the alpha 7 helix did not exhibit such switching but instead retained a membrane associated state. These results are in agreement with recent experimental studies of the interactions of synthetic alpha 5 and alpha 7 peptides with lipid bilayers.

Absence of effects of low-frequency, low-amplitude magnetic fields on the properties of gramicidin A channels

The effects of static and low-frequency magnetic fields on gramicidin A channels have been investigated using bilayer patch clamp recording and a bridge technique capable of detecting 0.3% changes in the conductance of glyceryl monooleate membranes containing many channels. In the bridge technique the conductance was assessed using 10-ms voltage pulses applied at 10 Hz. Measurements were made for LiCl, KCl, and CsCl using magnetic fields of 50, 100, 500, and 5000 microT with the frequency scanned from 10-200 Hz. The combinations of static and low-frequency fields employed include the "cyclotron resonance" conditions at which effects had been predicted to occur. In no case was there any detectable change in conductance when the magnetic fields were applied or changed. Potassium currents through single gramicidin channels have been recorded for patches in which several channels may be open at once. Fields were applied for 2 min periods interleaved with 2 min controls. Methods have been developed to analyze the multichannel records to reveal the amplitude and duration of the channels together with the frequency, depth, and apparent period of flickers. No significant differences were observed between the control and field-exposed recording periods. The peak of the distribution of opening and closing transitions always coincided for fields on and off within the resolution, 0.4%, of the recordings. There are at least two types of flicker, one with typical period less than 0.1 ms, the other with typical period from 0.3-0.8 ms. Most of the latter were not complete closures with the conductance during a flicker 15-20% above the level for a full closure.

Ion transport in a model gramicidin channel. Structure and thermodynamics

The potential of mean force for Na+ and K+ ions as a function of position in the interior of a periodic poly(L,D)-alanine model for the gramicidin beta-helix is calculated with a detailed atomic model and realistic interactions. The calculated free energy barriers are 4.5 kcal/mol for Na+ and 1.0 kcal/mol for K+. A decomposition of the free energy demonstrates that the water molecules make a significant contribution to the free energy of activation. There is an increase in entropy at the transition state associated with greater fluctuations. Analysis reveals that the free energy profile of ions in the periodic channel is controlled not by the large interaction energy involving the ion but rather by the weaker water-water, water-peptide and peptide-peptide hydrogen bond interactions. The interior of the channel retains much of the solvation properties of a liquid in its interactions with the cations. Of particular importance is the flexibility of the helix, which permits it to respond to the presence of an ion in a fluidlike manner. The distortion of the helix is local (limited to a few carbonyls) because the structure is too flexible to transmit a perturbation to large distances. The plasticity of the structure (i.e., the property to deform without generating a large energy stress) appears to be an essential factor in the transport of ions, suggesting that a rigid helix model would be inappropriate.

Ion-water and ion-polypeptide correlations in a gramicidin-like channel. A molecular dynamics study

This work describes a molecular dynamics study of ion-water and ion-polypeptide correlation in a model gramicidin-like channel (the polyglycine analogue) based upon interaction between polarizable, multipolar groups. The model suggests that the vicinity of the dimer junction and of the ethanolamine tail are regions of unusual flexibility. Cs+ binds weakly in the mouth of the channel: there it coordinates five water molecules and the #11CO group with which it interacts strongly and is ideally aligned. In the channel interior it is generally pentacoordinate; at the dimer junction, because of increased channel flexibility, it again becomes essentially hexacoordinate. The ion is also strongly coupled to the #13 CO but not to either #9 or #15, consistent with 13C NMR data. Water in the channel interior is strikingly different from bulk water; it has a much lower mean dipole moment. This correlates with our observation (which differs from that of previous studies) that water-water angular correlations do not persist within the channel, a result independent of ion occupancy or ionic polarity. In agreement with streaming potential measurements, there are seven single file water molecules associated with Cs+ permeation; one of these is always in direct contact with bulk water. At the mouth of an ion-free channel, there is a pattern of dipole moment alteration among the polar groups. Due to differential interaction with water, exo-carbonyls have unusually large dipole moments whereas those of the endo-carbonyls are low. The computed potential of mean force for CS+ translocation is qualitatively reasonable. However, it only exhibits a weakly articulated binding site and it does not quantitatively account for channel energetics. Correction for membrane polarization reduces, but does not eliminate, these problems.

Open channel noise. V. Fluctuating barriers to ion entry in gramicidin A channels

We have measured the fluctuations in the current through gramicidin A (GA) channels in symmetrical solutions of monovalent cations of various concentrations, and compared the spectral density values with those computed using E. Frehland's theory for noise in discrete transport systems (Frehland, E. 1978. Biophys. Chem. 8:255-265). The noise for the transport of NH4+ and Na+ ions in glycerol-monooleate/squalene membranes could be accounted for entirely by "shot noise" in the process of transport through a single-filing pore with two ion binding sites. However, in confirmation of results in a previous paper (Sigworth, F. J., D. W. Urry, and K. U. Prasad. 1987. Biophys. J. 52:1055-1064) currents of Cs+ showed a substantial excess noise at low ion concentrations, as did currents of K+ and Rb+. The excess noise was increased in thicker membranes. The observations are accounted for by a theory that postulates fluctuations of the entry rates of ions into the channel on a time scale of approximately 1 microsecond. These fluctuations occur preferentially when the channel is empty; the presence of bound ions stabilizes the "high conductance" conformation of the channel. The fluctuations are sensed to different degrees by the various ion species, and their kinetics depend on membrane thickness.

The 20-pS chloride channel of the human airway epithelium

The single-channel inside-out patch clamp technique was used to characterize chloride channels in the apical membranes of human airway epithelial cells maintained in primary culture. Patches were obtained from single isolated cells or from cells at the edges of confluent groups. The channel seen most often, in 24% of all patches, had a conductance of approximately 20 pS and had a linear current-voltage relationship in symmetric chloride solutions. The anion selectivity sequence for the channel was NO3- greater than Cl- greater than HCO3-, and it was impermeable to gluconate ions, indicating that the channel diameter lies between 4.7 and 5.5 A. Current through the channel saturated at high chloride concentrations, and the relationship between channel current and chloride concentration could be approximated by the Michaelis-Menten equation. Analysis of the channel's anion permeability and its current vs. concentration relationship indicates that it can be described by the one-ion channel theory, with a relatively weak binding site inside the channel. Histograms of channel open and closed durations were constructed using the log binning technique and could be well fitted by triple exponential distributions, suggesting that the channel has at least three open and three closed states.

Water and polypeptide conformations in the gramicidin channel. A molecular dynamics study

Theoretical studies of ion channels address several important questions. The mechanism of ion transport, the role of water structure, the fluctuations of the protein channel itself, and the influence of structural changes are accessible from these studies. In this paper, we have carried out a 70-ps molecular dynamics simulation on a model structure of gramicidin A with channel waters. The backbone of the protein has been analyzed with respect to the orientation of the carbonyl and the amide groups. The results are in conformity with the experimental NMR data. The structure of water and the hydrogen bonding network are also investigated. It is found that the water molecules inside the channel act as a collective chain; whereas the conformation in which all the waters are oriented with the dipoles pointing along the axis of the channel is a preferred one, others are also accessed during the dynamics simulation. A collective coordinate involving the channel waters and some of the hydrogen bonding peptide partners is required to describe the transition of waters from one configuration to the other.

Stochastic theory of singly occupied ion channels. II. Effects of access resistance and potential gradients extending into the bath

In a previous paper (Jakobsson, E., and S. W. Chiu. 1987. Biophys. J. 52:33-46), we presented the stochastic theory of the singly occupied ion channel as applied to sodium permeation of gramicidin channels, with the assumption of perfect equilibration between the bathing solutions and the ends of the ion channel. In the present paper we couple the previous theory to electrodiffusion of ions from the bulk of the bathing solution to the channel mouth. Our electrodiffusion calculations incorporate estimates of the potential gradients near the channel mouth due to image forces and due to the fraction of the applied potential that falls beyond the ends of the channel. To keep the diffusion calculation one-dimensional, we make the assumption that the electrical potentials in the bath exhibit hemispherical symmetry. As in the previous paper, the flux equations are fit to data on sodium permeation of normal gramicidin A, and gramicidins modified by the fluorination of the valine at the No. 1 position (Barrett Russell, E. W., L. B. Weiss, F. I. Navetta, R. E. Koeppe II, and O. S. Anderson. 1986. Biophys. J. 49:673-686). The conclusions of our previous paper with respect to the effect of fluorination on the mobility, surface potential well depth, and central barrier, are confirmed. However the absolute values of these quantities are somewhat changed when diffusive resistance to the mouth is taken into account, as in the present paper. Future possibilities for more accurate calculations by other methods are outlined.

Application of Brownian motion theory to the analysis of membrane channel ionic trajectories calculated by molecular dynamics

This paper shows how Brownian motion theory can be used to analyze features of individual ion trajectories in channels as calculated by molecular dynamics, and that its use permits more precise determinations of diffusion coefficients than would otherwise be possible. We also show how a consideration of trajectories of single particles can distinguish between effects due to the magnitude of the diffusion coefficient and effects due to barriers and wells in the potential profile, effects which can not be distinguished by consideration of average fluxes.

Kinetics of channelized membrane ions in magnetic fields

The cyclotron resonance model for channel ion transport in weak magnetic fields is extended to include damping losses. The conductivity tensor is obtained for different electric field configurations, including the circuital field E phi normal to the channel axis. The conductivity behavior close to the cyclotron resonance frequency omega c is compared to existing Ca2+-efflux data in the literature. A collision time of .023 s results from this comparison under the assumption that K+ ions are transiting in a 0.35 G field. We estimate a mean kinetic energy of 3.5 eV for this ion at resonance. This model leads to discrete modes of vibration (eigenfrequencies) in the ion-lattice interaction, such that omega n = n omega c. The presence of such harmonics is compatible with recent results by Blackman et al. [1985b] and McLeod et al. [1986] with the interesting exception that even modes do not appear in their observations, whereas the present model has no restriction on n. This harmonic formalism is also consistent with another reported phenomenon, that of quantized multiple conductances in single patch-clamped channels.

On the cyclotron resonance mechanism for magnetic field effects on transmembrane ion conductivity

The cyclotron resonance model, recently proposed to account for physiological response to weak environmental magnetic fields, is shown to violate the laws of classical mechanics. Further, it is argued that the ubiquitous presence of dynamic friction in fluid media precludes significant magnetic effects on membrane ion transport.