Ion-specific diffusion rates through transmembrane protein channels. A molecular dynamics study

Non-Markovian noise mediated through anomalous diffusion within ion channels

It is evident from a wide range of experimental findings that ion channel gating is inherently stochastic. The issue of "memory effects" (diffusional retardation due to local changes in water viscosity) in ionic flow has been recently addressed using Brownian dynamics simulations. The results presented indicate such memory effects are negligible, unless the diffusional barrier is much higher than that of free solute. In this paper using differential stochastic methods we conclude that the Markovian property of exponential dwell times gives rise to a high barrier, resulting in diffusional memory effects that cannot be ignored in determining ionic flow through channels. We have addressed this question using a generalized Langevin equation that contains a combination of Markovian and non-Markovian processes with different time scales. This approach afforded the development of an algorithm that describes an oscillatory ionic diffusional sequence. The resulting oscillatory function behavior, with exponential decay, was obtained at the weak non-Markovian limit with two distinct time scales corresponding to the processes of ionic diffusion and drift. This will be analyzed further in future studies using molecular dynamics simulations. We propose that the rise of time scales and memory effects is related to differences of shear viscosity in the cytoplasm and extracellular matrix.

Cellular microtransport processes: intercellular, intracellular, and aggregate behavior

Ionic and molecular transfer among cells occurs by a variety of transport processes operative at different length scales. Cell membrane permeability and electrical conductance derive from channel proteins producing pores at the molecular (ultrastructural) scale. Intracellular mobility involves the dynamics of motion through the complex ultrastructure of the cytoplasm. These phenomena unite in the larger-scale (microscopic) process of gross intercellular transfer. When such movement occurs among sufficiently many cells, it in turn begins to reflect their average collective (macroscopic) behavior as bulk tissue. This article surveys selected aspects of intercellular and intracellular transport, with emphasis on detailed mechanistic theory, experimental probes of cellular permeability, and systematic transcendence from small to large length scales.

Diffusion and kinetic approaches to describe permeation in ionic channels

Diffusion and reaction rate theories provide convenient approaches for describing permeation in ionic channels. Both approaches have strengths and weaknesses. Diffusion theories realistically approximate the physical process of ion movement within an aqueous pore, but those theories do not handle ionic interactions easily. Reaction rate theories are easy to use, and they provide a mathematical summarization of the data that is valuable for communicating experimental results. During ion permeation, however, the basic assumptions of reaction rate theory are not met. Therefore, rate theories do not provide true physical descriptions of ion permeation.

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.

Solid-phase peptide synthesis and solid-state NMR spectroscopy of [Ala3-15N][Val1]gramicidin A

[Ala3-15N][Val1]Gramicidin A has been prepared by solid-phase peptide synthesis and studied by solid-state 15N nuclear magnetic resonance spectroscopy. The synthesis of desformyl[Ala3-15N][Val1]gramicidin A employed N-hydroxysuccinimide esters of 9-fluorenylmethoxycarbonyl-N alpha-amino acids and completely avoided the use of acid. Since deblocking was done with piperidine and the peptide was removed from the resin by treatment with ethanolamine, this synthetic protocol prevented oxidation of the indole rings of this tryptophan-rich peptide and reduced truncations produced by acid hydrolysis. After formylation and purification by anion-exchange and high-pressure liquid chromatography, the peptide was obtained in an overall yield of 30%. Solid-state 15N nuclear magnetic resonance spectra of this peptide and uniformly labeled [15N]gramicidin A' oriented in hydrated lipid bilayers have been obtained, allowing unambiguous assignment of the [15N]Ala3 resonance in the latter. The solid-state 15N nuclear magnetic resonance experiments provide evidence that [Val1]gramicidin A is rotating about an axis that is perpendicular to the plane of the lipid bilayer and that the N--H axis is nearly parallel with the rotational axis. This study demonstrates that site-specifically labeled [15N]gramicidin A analogs prepared by solid-phase peptide synthesis are valuable tools in the study of the solid-state nuclear magnetic resonance spectra of samples in oriented lipid bilayers.

The normal modes of the gramicidin-A dimer channel

The dynamics of the gramicidin-A dimer channel is studied in the harmonic approximation by a vibrational analysis of the atomic motions relative to their equilibrium positions. The system is represented by an empirical potential energy function, and all degrees of freedom (bonds lengths, bond angles, and torsional angles) are allowed to vary. The thermal fluctuations in the backbone dihedral angles phi and psi, atomic root mean square displacements, and the correlations between the different amide planes are computed. It is found that only adjacent dihedral psi i and phi i+1 are strongly correlated, while different hydrogen-bonded amide planes are only weakly correlated. Modes with relatively low vibrational frequencies (75-175 cm-1) make the dominant contributions to the carbonyl librations. The general flexibility of the structure and the role of carbonyl librations in the ion transport mechanism are discussed.

The interaction of Cl- with a gramicidin-like channel

Molecular dynamics simulations have been used to study the interaction of Cl- with a gramicidin-like channel. The results suggest that there is a high-energy barrier at the entrance of the channel, which would correspond to a permeability 10(-9)-times that of a cation of the same size. This could account for the cationic selectivity of the gramicidin channel and indicates that valence selectivity is kinetically controlled.

Structure and dynamics of one-dimensional ionic solutions in biological transmembrane channels

The structure and dynamics of solvated alkali metal cations in transmembrane channels are treated using the molecular dynamics simulation technique. The simulations are based on a modified Fischer-Brickmann model (Fischer, W., and J. Brickmann, 1983, Biophys. Chem., 18:323-337) for gramicidin A-type channels. The trajectories of all particles in the channel as well as two-dimensional pair correlation functions are analyzed. It is found from the analysis of the stationary simulation state that one-dimensional solvation complexes are formed and that the number of water molecules in the channel varies for different alkali metal cations.

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

Molecular dynamics studies for the voltage-driven transport of the alkali metal ions lithium, sodium, and potassium through gramicidin A-type channels filled with water molecules are presented. The number of water molecules in the channel is obtained from a previous study (Skerra, A., and J. Brickmann, 1987, Biophys. J., 51:969-976). It is shown that the selectivity of the intrachannel ion diffusion through our model pore conforms to the experimentally observed selectivity of the gramicidin A channel. It is demonstrated that the number of water molecules in the channel plays a key role for the selectivity.

Why is gramicidin valence selective? A theoretical study

Calculations contrasting the channel solvation energy for cesium ions and chloride ions associated with water in gramicidin-like channels are presented. The energy profile for the cation exhibits a deep well at the channel entrance; within the single file region the solvation energy is roughly constant. The anion exhibits a totally different energy profile. There is an energy barrier at the channel entrance; if the ion could surmount this barrier, it would be quite stable within the channel. At the channel entrance, the calculated solvation energy difference between anion and cation is approximately 15 kcal mol-1. This is completely consistent with the observation that chloride neither permeates nor blocks the channel since the estimated rate of ion entry would be approximately 0.01-10(-5) s-1, far slower than the rate at which the channel dimer dissociates into monomers.

Solvent effects in ionic transport through transmembrane protein channels

Ion transport through a gramicidin A like channel in the presence of solvent molecules with van der Waals parameters of water has been studied by means of the molecular dynamics simulation technique. It was found that the presence of solvent molecules in the channel has a tendency to equalize the effective masses of the ions through "association" thus giving the experimentally found ion selectivity to the gramicidin A channel.

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.

Molecular dynamics simulation of cation motion in water-filled gramicidinlike pores

A model calculation is carried out to study the potential energy profile of a sodium ion with several water molecules inside a simplified model of the gramicidin ion channel. The sodium ion is treated as a Lennard-Jones sphere with a point charge at its center. The Barnes polarizable water model is used to mimic the water molecules. A polarizable and deformable gramicidinlike channel is constructed based on the model obtained by Koeppe and Kimura. Potential minima and saddle points are located and the static energy barriers are computed. The potential minima at the two mouths of the channel exhibit an aqueous solvation structure very different from that at any of the interior minima. These sites are approximately 23.6 and 24.4 A apart for binding of a sodium ion and a cesium ion, respectively. Ionic motion from these exterior sites to the first interior minimum requires substantial rearrangement of the waters of solvation; this rearrangement may be the hydration/dehydration step in ionic permeation through the channel. Based on these results, a mechanism by which the sodium ion moves from the exterior binding site to the interior of the channel is proposed. Our model channel accommodates about eight water molecules and the transport of the ion and water within the channel is found to be single file. Results of less extensive calculations for Cs+ and Li+ ions in a channel with or without water are also reported.