Influence of protein flexibility on the electrostatic energy landscape in gramicidin A

Site-specific ion occupation in the selectivity filter causes voltage-dependent gating in a viral K+ channel

Many potassium channels show voltage-dependent gating without a dedicated voltage sensor domain. This is not fully understood yet, but often explained by voltage-induced changes of ion occupation in the five distinct K+ binding sites in the selectivity filter. To better understand this mechanism of filter gating we measured the single-channel current and the rate constant of sub-millisecond channel closure of the viral K+ channel KcvNTS for a wide range of voltages and symmetric and asymmetric K+ concentrations in planar lipid membranes. A model-based analysis employed a global fit of all experimental data, i.e., using a common set of parameters for current and channel closure under all conditions. Three different established models of ion permeation and various relationships between ion occupation and gating were tested. Only one of the models described the data adequately. It revealed that the most extracellular binding site (S0) in the selectivity filter functions as the voltage sensor for the rate constant of channel closure. The ion occupation outside of S0 modulates its dependence on K+ concentration. The analysis uncovers an important role of changes in protein flexibility in mediating the effect from the sensor to the gate.

Dual mechanism of ion permeation through VDAC revealed with inorganic phosphate ions and phosphate metabolites

In the exchange of metabolites and ions between the mitochondrion and the cytosol, the voltage-dependent anion channel (VDAC) is a key element, as it forms the major transport pathway for these compounds through the mitochondrial outer membrane. Numerous experimental studies have promoted the idea that VDAC acts as a regulator of essential mitochondrial functions. In this study, using a combination of molecular dynamics simulations, free-energy calculations, and electrophysiological measurements, we investigated the transport of ions through VDAC, with a focus on phosphate ions and metabolites. We showed that selectivity of VDAC towards small anions including monovalent phosphates arises from short-lived interactions with positively charged residues scattered throughout the pore. In dramatic contrast, permeation of divalent phosphate ions and phosphate metabolites (AMP and ATP) involves binding sites along a specific translocation pathway. This permeation mechanism offers an explanation for the decrease in VDAC conductance measured in the presence of ATP or AMP at physiological salt concentration. The binding sites occur at similar locations for the divalent phosphate ions, AMP and ATP, and contain identical basic residues. ATP features a marked affinity for a central region of the pore lined by two lysines and one arginine of the N-terminal helix. This cluster of residues together with a few other basic amino acids forms a "charged brush" which facilitates the passage of the anionic metabolites through the pore. All of this reveals that VDAC controls the transport of the inorganic phosphates and phosphate metabolites studied here through two different mechanisms.

A High-Throughput Steered Molecular Dynamics Study on the Free Energy Profile of Ion Permeation through Gramicidin A

Steered molecular dynamics (SMD) simulations for the calculation of free energies are well suited for high-throughput molecular simulations on a distributed infrastructure due to the simplicity of the setup and parallel granularity of the runs. However, so far, the computational cost limited the estimation of the free energy typically over just a few pullings, thus impeding the evaluation of statistical uncertainties involved. In this work, we performed two thousand pulls for the permeation of a potassium ion in the gramicidin A pore by all-atom molecular dynamics in order to assess the bidirectional SMD protocol with a proper amount of sampling. The estimated free energy profile still shows a statistical error of several kcal/mol, while the work distributions are estimated to be non-Gaussian at pulling speeds of 10 Å/ns. We discuss the methodology and the confidence intervals in relation to increasing amounts of computed trajectories and how different permeation pathways for the potassium ion, knock-on and sideways, affect the sampling and the free energy estimation.

Multiple Scales in the Simulation of Ion Channels and Proteins

Computation of living processes creates great promise for the everyday life of mankind and great challenges for physical scientists. Simulations molecular dynamics have great appeal to biologists as a natural extension of structural biology. Once a biologist sees a structure, she/he wants to see it move. Molecular biology has shown that a small number of atoms, sometimes even one messenger ion, like Ca(2+), can control biological function on the scale of cells, organs, tissues, and organisms. Enormously concentrated ions-at number densities of ~20 M-in protein channels and enzymes are responsible for many of the characteristics of living systems, just as highly concentrated ions near electrodes are responsible for many of the characteristics of electrochemical systems. Here we confront the reality of the scale differences of ions. We show that the scale differences needed to simulate all the atoms of biological cells are 10(7) in linear dimension, 10(21) in three dimensions, 10(9) in resolution, 10(11) in time, and 10(13) in particle number (to deal with concentrations of Ca(2+)). These scales must be dealt with simultaneously if the simulation is to deal with most biological functions. Biological function extends across all of them, all at once in most cases. We suggest a computational approach using explicit multiscale analysis instead of implicit simulation of all scales. The approach is based on an energy variational principle EnVarA introduced by Chun Liu to deal with complex fluids. Variational methods deal automatically with multiple interacting components and scales. When an additional component is added to the system, the resulting Euler Lagrange field equations change form automatically-by algebra alone-without additional unknown parameters. Multifaceted interactions are solutions of the resulting equations. We suggest that ionic solutions should be viewed as complex fluids with simple components. Highly concentrated solutions-dominated by interactions of components-are easily computed by EnVarA. Successful computation of ions concentrated in special places may be a significant step to understanding the defining characteristics of biological and electrochemical systems. Indeed, computing ions near proteins and nucleic acids may prove as important to molecular biology and chemical technology as computing holes and electrons has been to our semiconductor and digital technology.

Calculating free-energy profiles in biomolecular systems from fast nonequilibrium processes

Often gaining insight into the functioning of biomolecular systems requires to follow their dynamics along a microscopic reaction coordinate (RC) on a macroscopic time scale, which is beyond the reach of current all atom molecular dynamics (MD) simulations. A practical approach to this inherently multiscale problem is to model the system as a fictitious overdamped Brownian particle that diffuses along the RC in the presence of an effective potential of mean force (PMF) due to the rest of the system. By employing the recently proposed FR method [I. Kosztin, J. Chem. Phys. 124, 064106 (2006)], which requires only a small number of fast nonequilibrium MD simulations of the system in both forward and time reversed directions along the RC, we reconstruct the PMF: (1) of deca-alanine as a function of its end-to-end distance, and (2) that guides the motion of potassium ions through the gramicidin A channel. In both cases the computed PMFs are found to be in good agreement with previous results obtained by different methods. Our approach appears to be about one order of magnitude faster than the other PMF calculation methods and, in addition, it also provides the position-dependent diffusion coefficient along the RC. Thus, the obtained PMF and diffusion coefficient can be used in an overdamped Brownian model to estimate important characteristics of the studied systems, e.g., the mean folding time of the stretched deca-alanine and the mean diffusion time of the potassium ion through gramicidin A.

Conduction properties of KcsA measured using brownian dynamics with flexible carbonyl groups in the selectivity filter

In the narrow segment of an ion conducting pathway, it is likely that a permeating ion influences the positions of the nearby atoms that carry partial or full electronic charges. Here we introduce a method of incorporating the motion of charged atoms lining the pore into Brownian dynamics simulations of ion conduction. The movements of the carbonyl groups in the selectivity filter of the KcsA channel are calculated explicitly, allowing their bond lengths, bond angles, and dihedral angels to change in response to the forces acting upon them. By systematically changing the coefficients of bond stretching and of angle bending, the carbon and oxygen atoms can be made to fluctuate from their fixed positions by varying mean distances. We show that incorporating carbonyl motion in this way does not alter the mechanism of ion conduction and only has a small influence on the computed current. The slope conductance of the channel increases by approximately 25% when the root mean-square fluctuations of the carbonyl groups are increased from 0.01 to 0.61 A. The energy profiles and the number of resident ions in the channel remain unchanged. The method we utilized here can be extended to allow the movement of glutamate or aspartate side chains lining the selectivity filters of other ionic channels.

Ion permeation through a narrow channel: using gramicidin to ascertain all-atom molecular dynamics potential of mean force methodology and biomolecular force fields

We investigate methods for extracting the potential of mean force (PMF) governing ion permeation from molecular dynamics simulations (MD) using gramicidin A as a prototypical narrow ion channel. It is possible to obtain well-converged meaningful PMFs using all-atom MD, which predict experimental observables within order-of-magnitude agreement with experimental results. This was possible by careful attention to issues of statistical convergence of the PMF, finite size effects, and lipid hydrocarbon chain polarizability. When comparing the modern all-atom force fields of CHARMM27 and AMBER94, we found that a fairly consistent picture emerges, and that both AMBER94 and CHARMM27 predict observables that are in semiquantitative agreement with both the experimental conductance and dissociation coefficient. Even small changes in the force field, however, result in significant changes in permeation energetics. Furthermore, the full two-dimensional free-energy surface describing permeation reveals the location and magnitude of the central barrier and the location of two binding sites for K(+) ion permeation near the channel entrance--i.e., an inner site on-axis and an outer site off-axis. We conclude that the MD-PMF approach is a powerful tool for understanding and predicting the function of narrow ion channels in a manner that is consistent with the atomic and thermally fluctuating nature of proteins.

Role of protein flexibility in ion permeation: a case study in gramicidin A

Proteins have a flexible structure, and their atoms exhibit considerable fluctuations under normal operating conditions. However, apart from some enzyme reactions involving ligand binding, our understanding of the role of flexibility in protein function remains mostly incomplete. Here we investigate this question in the realm of membrane proteins that form ion channels. Specifically, we consider ion permeation in the gramicidin A channel, and study how the energetics of ion conduction changes as the channel structure is progressively changed from completely flexible to a fixed one. For each channel structure, the potential of mean force for a permeating potassium ion is determined from molecular dynamics (MD) simulations. Using the same molecular dynamics data for completely flexible gramicidin A, we also calculate the average densities and fluctuations of the peptide atoms and investigate the correlations between these fluctuations and the motion of a permeating ion. Our results show conclusively that peptide flexibility plays an important role in ion permeation in the gramicidin A channel, thus providing another reason--besides the well-known problem with the description of single file pore water--why this channel cannot be modeled using continuum electrostatics with a fixed structure. The new method developed here for studying the role of protein flexibility on its function clarifies the contributions of the fluctuations to energy and entropy, and places limits on the level of detail required in a coarse-grained model.

Molecular dynamics simulations of proteins in lipid bilayers

With recent advances in X-ray crystallography of membrane proteins promising many new high-resolution structures, molecular dynamics simulations will become increasingly valuable for understanding membrane protein function, as they can reveal the dynamic behavior concealed in the static structures. Dramatic increases in computational power, in synergy with more efficient computational methodologies, now allow us to carry out molecular dynamics simulations of any structurally known membrane protein in its native environment, covering timescales of up to 0.1 micros. At the frontiers of membrane protein simulations are ion channels, aquaporins, passive and active transporters, and bioenergetic proteins.

Three computational methods for studying permeation, selectivity and dynamics in biological ion channels

The cell membrane, confining some ions and molecules on one side and exchanging others with the other side, is the ultimate unit of the physiology of life. The delicate task of regulating the transport of ions across the membrane is carried out by biological nanotubes called 'ion channels'. Recently, there have been enormous strides in our understanding of the structure-function relationships of biological ion channels. The molecular structures of several ion channels have been determined from crystallographic analysis, including potassium channels, mechanosensitive channels, a chloride channel, as well as gramicidin channels and porins. It is expected that the X-ray structures of other ion channels will soon follow these discoveries, ushering in a new era of ion channel studies in which predicting the function of channels from their atomic structures will become the main quest. In parallel to these experimental findings, there have been important advances in computational biophysics. Here we summarize three theoretical approaches that have been utilized to understand the dynamics of ion permeation across bio-nanotubes, highlighting their advantages and shortcomings, and briefly describe some of the salient properties of ion channels uncovered through computational studies.