Web interface for Brownian dynamics simulation of ion transport and its applications to beta-barrel pores.

Brownian dynamics (BD) based on accurate potential of mean force is an efficient and accurate method for simulating ion transport through wide ion channels. Here, a web-based graphical user interface (GUI) is presented for carrying out grand canonical Monte Carlo (GCMC) BD simulations of channel proteins: http://www.charmm-gui.org/input/gcmcbd. The webserver is designed to help users avoid most of the technical difficulties and issues encountered in setting up and simulating complex pore systems. GCMC/BD simulation results for three proteins, the voltage dependent anion channel (VDAC), α-Hemolysin (α-HL), and the protective antigen pore of the anthrax toxin (PA), are presented to illustrate the system setup, input preparation, and typical output (conductance, ion density profile, ion selectivity, and ion asymmetry). Two models for the input diffusion constants for potassium and chloride ions in the pore are compared: scaling of the bulk diffusion constants by 0.5, as deduced from previous all-atom molecular dynamics simulations of VDAC, and a hydrodynamics based model (HD) of diffusion through a tube. The HD model yields excellent agreement with experimental conductances for VDAC and α-HL, while scaling bulk diffusion constants by 0.5 leads to underestimates of 10-20%. For PA, simulated ion conduction values overestimate experimental values by a factor of 1.5-7 (depending on His protonation state and the transmembrane potential), implying that the currently available computational model of this protein requires further structural refinement.

Ouabain binding site in a functioning Na+/K+ ATPase.

The Na(+)/K(+) ATPase is an almost ubiquitous integral membrane protein within the animal kingdom. It is also the selective target for cardiotonic derivatives, widely prescribed inhibitors for patients with heart failure. Functional studies revealed that ouabain-sensitive residues distributed widely throughout the primary sequence of the protein. Recently, structural work has brought some consensus to the functional observations. Here, we use a spectroscopic approach to estimate distances between a fluorescent ouabain and a lanthanide binding tag (LBT), which was introduced at five different positions in the Na(+)/K(+) ATPase sequence. These five normally functional LBT-Na(+)/K(+) ATPase constructs were expressed in the cell membrane of Xenopus laevis oocytes, operating under physiological internal and external ion conditions. The spectroscopic data suggest two mutually exclusive distances between the LBT and the fluorescent ouabain. From the estimated distances and using homology models of the LBT-Na(+)/K(+) ATPase constructs, approximate ouabain positions could be determined. Our results suggest that ouabain binds at two sites along the ion permeation pathway of the Na(+)/K(+) ATPase. The external site (low apparent affinity) occupies the same region as previous structural findings. The high apparent affinity site is, however, slightly deeper toward the intracellular end of the protein. Interestingly, in both cases the lactone ring faces outward. We propose a sequential ouabain binding mechanism that is consistent with all functional and structural studies.

Ion selectivity of the KcsA channel: a perspective from multi-ion free energy landscapes.

Potassium (K(+)) channels are specialized membrane proteins that are able to facilitate and regulate the conduction of K(+) through cell membranes. Comprising five specific cation binding sites (S(0)-S(4)) formed by the backbone carbonyl groups of conserved residues common to all K(+) channels, the narrow selectivity filter allows fast conduction of K(+) while being highly selective for K(+) over Na(+). To extend our knowledge of the microscopic mechanism underlying selectivity in K(+) channels, we characterize the free energy landscapes governing the entry and translocation of a Na(+) or a K(+) from the extracellular side into the selectivity filter of KcsA. The entry process of an extracellular ion is examined in the presence of two additional K(+) in the pore, and the three-ion potential of mean force is computed using extensive all-atom umbrella sampling molecular dynamics simulations. A comparison of the potentials of mean force yields a number of important results. First, the free energy minima corresponding to configurations with extracellular K(+) or Na(+) in binding site S(0) or S(1) are similar in depth, suggesting that the thermodynamic selectivity governed by the free energy minima for those two binding sites is insignificant. Second, the free energy barriers between stable multi-ion configurations are generally higher for Na(+) than for K(+), implying that the kinetics of ion conduction is slower when a Na(+) enters the pore. Third, the region corresponding to binding site S(2) near the center of the narrow pore emerges as the most selective for K(+) over Na(+). In particular, while there is a stable minimum for K(+) in site S(2), Na(+) faces a steep free energy increase with no local free energy well in this region. Lastly, analysis shows that selectivity is not correlated with the overall coordination number of the ion entering the pore, but is predominantly affected by changes in the type of coordinating ligands (carbonyls versus water molecules). These results further highlight the importance of the central region near binding site S(2) in the selectivity filter of K(+) channels.

Ion selectivity of alpha-hemolysin with beta-cyclodextrin adapter. II. Multi-ion effects studied with grand canonical Monte Carlo/Brownian dynamics simulations.

In a previous study of ion selectivity of alpha-hemolysin (alphaHL) in complex with beta-cyclodextrin (betaCD) adapter, we calculated the potential of mean force (PMF) and characterized the self-diffusion coefficients of isolated K(+) and Cl(-) ions using molecular dynamics simulations (Y. Luo et al., "Ion Selectivity of alpha-Hemolysin with beta-Cyclodextrin Adapter: I. Single Ion Potential of Mean Force and Diffusion Coefficient"). In the present effort, these results pertaining to single isolated ions in the wide aqueous pore are extended to take into account multi-ion effects. The grand canonical Monte Carlo/Brownian dynamics (GCMC/BD) algorithm is used to simulate ion currents through the wild-type alphaHL ion channel, as well as two engineered alphaHL mutants, with and without the cyclic oligosaccaride betaCD lodged in the lumen of the pore. The GCMC/BD current-voltage curves agree well with experimental results and show that betaCD increases the anion selectivity of alphaHL. Comparisons between multi-ion PMFs from GCMC/BD simulations and single-ion PMFs demonstrate that multi-ion effects and pore shape are crucial for explaining this behavior. It is concluded that the narrow betaCD adapter increases the anion selectivity of alphaHL because it reduces the pore radius locally, which decreases the ionic screening and the dielectric shielding of the strong electrostatic field induced by a nearby ring of positively charged alphaHL side chains.

Ion selectivity of alpha-hemolysin with a beta-cyclodextrin adapter. I. Single ion potential of mean force and diffusion coefficient.

The alpha-hemolysin (alphaHL) is a self-assembling exotoxin that binds to the membrane of a susceptible host cell and causes its death. Experimental studies show that electrically neutral beta-cyclodextrin (betaCD) can insert into the alphaHL channel and significantly increase its anion selectivity. To understand how betaCD can affect ion selectivity, molecular dynamics simulations and potential of mean force (PMF) calculations are carried out for different alphaHL channels with and without the betaCD adapter. A multiscale approach based on the generalized solvent boundary potential is used to reduce the size of the simulated system. The PMF profiles reveal that betaCD has no anion selectivity by itself but can increase the Cl(-) selectivity of the alphaHL channel when lodged into the pore lumen. Analysis shows that betaCD causes a partial desolvation of ions and affects the orientation of nearby charged residues. The ion selectivity appears to result from increased electrostatic interaction between the ion and the channel due to a reduction in dielectric shielding by the solvent. These observations suggest a reasonable explanation of the ion selectivity and provide important information for further ion channel modification.

Continuum description of ionic and dielectric shielding for molecular-dynamics simulations of proteins in solution.

We extend our continuum description of solvent dielectrics in molecular-dynamics (MD) simulations, which has provided an efficient and accurate solution of the Poisson equation, to ionic solvents as described by the linearized Poisson-Boltzmann (LPB) equation. We start with the formulation of a general theory for the electrostatics of an arbitrarily shaped molecular system, which consists of partially charged atoms and is embedded in a LPB continuum. This theory represents the reaction field induced by the continuum in terms of charge and dipole densities localized within the molecular system. Because these densities cannot be calculated analytically for systems of arbitrary shape, we introduce an atom-based discretization and a set of carefully designed approximations. This allows us to represent the densities by charges and dipoles located at the atoms. Coupled systems of linear equations determine these multipoles and can be rapidly solved by iteration during a MD simulation. The multipoles yield the reaction field forces and energies. Finally, we scrutinize the quality of our approach by comparisons with an analytical solution restricted to perfectly spherical systems and with results of a finite difference method.