Toby W. Allen

Permeation of Ions Across the Potassium Channel: Brownian Dynamics Studies

The physical mechanisms underlying the transport of ions across a model potassium channel are described. The shape of the model channel corresponds closely to that deduced from crystallography. From electrostatic calculations, we show that an ion permeating the channel, in the absence of any residual charges, encounters an insurmountable energy barrier arising from induced surface charges. Carbonyl groups along the selectivity filter, helix dipoles near the oval chamber, and mouth dipoles near the channel entrances together transform the energy barrier into a deep energy well. Two ions are attracted to this well, and their presence in the channel permits ions to diffuse across it under the influence of an electric field. Using Brownian dynamics simulations, we determine the magnitude of currents flowing across the channel under various conditions. The conductance increases with increasing dipole strength and reaches its maximum rapidly; a further increase in dipole strength causes a steady decrease in the channel conductance. The current also decreases systematically when the effective dielectric constant of the channel is lowered. The conductance with the optimal choice of dipoles reproduces the experimental value when the dielectric constant of the channel is assumed to be 60. The current-voltage relationship obtained with symmetrical solutions is linear when the applied potential is less than approximately 100 mV but deviates from Ohms law at a higher applied potential. The reversal potentials obtained with asymmetrical solutions are in agreement with those predicted by the Nernst equation. The conductance exhibits the saturation property observed experimentally. We discuss the implications of these findings for the transport of ions across the potassium channels and membrane channels in general.

Mechanisms of permeation and selectivity in calcium channels.

The mechanisms underlying ion transport and selectivity in calcium channels are examined using electrostatic calculations and Brownian dynamics simulations. We model the channel as a rigid structure with fixed charges in the walls, representing glutamate residues thought to be responsible for ion selectivity. Potential energy profiles obtained from multi-ion electrostatic calculations provide insights into ion permeation and many other observed features of L-type calcium channels. These qualitative explanations are confirmed by the results of Brownian dynamics simulations, which closely reproduce several experimental observations. These include the current-voltage curves, current-concentration relationship, block of monovalent currents by divalent ions, the anomalous mole fraction effect between sodium and calcium ions, attenuation of calcium current by external sodium ions, and the effects of mutating glutamate residues in the amino acid sequence.

Molecular Dynamics Study of the KcsA Potassium Channel

The structural, dynamical, and thermodynamic properties of a model potassium channel are studied using molecular dynamics simulations. We use the recently unveiled protein structure for the KcsA potassium channel from Streptomyces lividans. Total and free energy profiles of potassium and sodium ions reveal a considerable preference for the larger potassium ions. The selectivity of the channel arises from its ability to completely solvate the potassium ions, but not the smaller sodium ions. Self-diffusion of water within the narrow selectivity filter is found to be reduced by an order of magnitude from bulk levels, whereas the wider hydrophobic section of the pore maintains near-bulk self-diffusion. Simulations examining multiple ion configurations suggest a two-ion channel. Ion diffusion is found to be reduced to approximately 1/3 of bulk diffusion within the selectivity filter. The reduced ion mobility does not hinder the passage of ions, as permeation appears to be driven by Coulomb repulsion within this multiple ion channel.

The potassium channel: Structure, selectivity and diffusion

We employ the entire experimentally determined protein structure for the KcsA potassium channel from Streptomyces lividans in molecular dynamics calculations to observe hydrated channel protein structure, ion solvation, selectivity, multiple ion configurations, and diffusion. Free energy perturbation calculations display a significant ion discrimination of ∼9 kT in favor of the larger K+ ion. The protein forming the channel is very flexible yet is unable to fully solvate the Na+ ion because of its smaller size and large solvation energy. There is evidence that acidic and basic sidechains may dissociate in the presence of multiple K+ ions to explain experimental ion density maps. K+ diffusion is found to vary from approximately 10%–90% of bulk, supporting the high channel currents observed experimentally.

Study of Ionic Currents across a Model Membrane Channel Using Brownian Dynamics

Brownian dynamics simulations have been carried out to study ionic currents flowing across a model membrane channel under various conditions. The model channel we use has a cylindrical transmembrane segment that is joined to a catenary vestibule at each side. Two cylindrical reservoirs connected to the channel contain a fixed number of sodium and chloride ions. Under a driving force of 100 mV, the channel is virtually impermeable to sodium ions, owing to the repulsive dielectric force presented to ions by the vestibular wall. When two rings of dipoles, with their negative poles facing the pore lumen, are placed just above and below the constricted channel segment, sodium ions cross the channel. The conductance increases with increasing dipole strength and reaches its maximum rapidly; a further increase in dipole strength does not increase the channel conductance further. When only those ions that acquire a kinetic energy large enough to surmount a barrier are allowed to enter the narrow transmembrane segment, the channel conductance decreases monotonically with the barrier height. This barrier represents those interactions between an ion, water molecules, and the protein wall in the transmembrane segment that are not treated explicitly in the simulation. The conductance obtained from simulations closely matches that obtained from ACh channels when a step potential barrier of 2-3 kTr is placed at the channel neck. The current-voltage relationship obtained with symmetrical solutions is ohmic in the absence of a barrier. The current-voltage curve becomes nonlinear when the 3 kTr barrier is in place. With asymmetrical solutions, the relationship approximates the Goldman equation, with the reversal potential close to that predicted by the Nernst equation. The conductance first increases linearly with concentration and then begins to rise at a slower rate with higher ionic concentration. We discuss the implications of these findings for the transport of ions across the membrane and the structure of ion channels.

Gramicidin A channel as a test ground for molecular dynamics force fields

We use the well-known structural and functional properties of the gramicidin A channel to test the appropriateness of force fields commonly used in molecular dynamics (MD) simulations of ion channels. For this purpose, the high-resolution structure of the gramicidin A dimer is embedded in a dimyristoylphosphatidylcholine bilayer, and the potential of mean force of a K(+) ion is calculated along the channel axis using the umbrella sampling method. Calculations are performed using two of the most common force fields in MD simulations: CHARMM and GROMACS. Both force fields lead to large central barriers for K(+) ion permeation, that are substantially higher than those deduced from the physiological data by inverse methods. In long MD simulations lasting over 60 ns, several ions are observed to enter the binding site but none of them crossed the channel despite the presence of a large driving field. The present results, taken together with many earlier studies, highlights the shortcomings of the standard force fields used in MD simulations of ion channels and calls for construction of more appropriate force fields for this purpose.

Modeling Diverse Range of Potassium Channels with Brownian Dynamics

Using the experimentally determined KcsA structure as a template, we propose a plausible explanation for the diversity of potassium channels seen in nature. A simplified model of KcsA is constructed from its atomic resolution structure by smoothing out the protein-water boundary and representing the atoms forming the channel protein as a homogeneous, low dielectric medium. The properties of the simplified and atomic-detail models, deduced from electrostatic calculations and Brownian dynamics simulations, are shown to be qualitatively similar. We then study how the current flowing across the simplified model channel changes as the shape of the intrapore region is modified. This is achieved by increasing the radius of the intracellular pore systematically from 1.5 to 5 A while leaving the dimensions of the selectivity filter and inner chamber unaltered. The strengths of the dipoles located near the entrances of the channel, the carbonyl groups lining the selectivity filter, and the helix macrodipoles are kept constant. The channel conductance increases steadily as the radius of the intracellular pore is increased. The rate-limiting step for both the outward and inward current is the time it takes for an ion to cross the residual energy barrier located in the intrapore region. The current-voltage relationship obtained with symmetrical solutions is linear when the applied potential is less than approximately 100 mV but deviates slightly from Ohms law at higher applied potentials. The nonlinearity in the current-voltage curve becomes less pronounced as the radius of the intracellular pore is increased. When the strengths of the dipoles near the intracellular entrance are reduced, the channel shows a pronounced inward rectification. Finally, the conductance exhibits the saturation property observed experimentally. We discuss the implications of these findings on the transport of ions across the potassium channels and membrane channels in general.

The effect of hydrophobic and hydrophilic channel walls on the structure and diffusion of water and ions

Molecular dynamics simulations are carried out to determine the effects of channel wall structure on water and ion properties. We compare hydrophobic (Lennard-Jones 5-3 and atomic) and molecular-hydrophilic cylindrical pores of 2–6 A in effective radius, relevant to the study of most significant biological ion channels including gramicidin A, ACh, and potassium channels, and to the study of many microporous materials. Large variations in levels of self-diffusion and rotational correlation within hydrophobic channels are explained in terms of water geometry, hydrogen bonding, and dipole correlation. The differing levels of water structure and self-diffusion in hydrophobic and hydrophilic pores arise because of marked differences in the preferred orientation of water dipole moments, and due to hydrogen bonding with molecules on the pore lining. Axial sodium ion diffusion does not experience large variations with pore size, despite anomalous stability in moderate-sized hydrophobic pores. We attribute this to...

Molecular dynamics estimates of ion diffusion in model hydrophobic and KcsA potassium channels

Molecular dynamics simulations are carried out to obtain estimates of diffusion coefficients of biologically important Na+, K+, Ca2+ and Cl- ions in hydrophobic cylindrical channels with varying radii and large reservoirs. Calculations for the cylindrical channels are compared to those for the KcsA potassium channel, for which the protein structure has recently been determined from X-ray diffraction experiments. Our results show that ion diffusion is maintained at reasonably high levels even within narrow channels, and does not support the very small diffusion coefficients used in some continuum models in order to fit experimental data. The present estimates of ion diffusion coefficients are useful in the calculation of channel conductance using the Poisson-Nernst-Planck theory, or Brownian dynamics.

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.