Electronic Effects in Biomolecular Simulations: Investigation of the KcsA Potassium Ion Channel

Ion conduction through the hERG potassium channel

The inward rectifier voltage-gated potassium channel hERG is of primary importance for the regulation of the membrane potential of cardiomyocytes. Unlike most voltage-gated K⁺-channels, hERG shows a low elementary conductance at physiological voltage and potassium concentration. To investigate the molecular features underlying this unusual behavior, we simulated the ion conduction through the selectivity filter at a fully atomistic level by means of molecular dynamics-based methods, using a homology-derived model. According to our calculations, permeation of potassium ions can occur along two pathways, one involving site vacancies inside the filter (showing an energy barrier of about 6 kcal mol⁻¹), and the other characterized by the presence of a knock-on intermediate (about 8 kcal mol⁻¹). These barriers are indeed in accordance with a low conductance behavior, and can be explained in terms of a series of distinctive structural features displayed by the hERG ion permeation pathway.

Determination of the charge profile in the KcsA selectivity filter using ab initio calculations and molecular dynamics simulations

The charge profile of K+ and Na+ ions moving in a single file across the filter of the KcsA channel is determined using both molecular dynamics simulations and ab initio calculations. We show a strong correlation between the charge variation and the ion location resulting in a saw-tooth profile, which provides additional information on the influence of charge transfer on the permeation and selectivity of the channel.

Many-body effects and simulations of potassium channels

The electronic polarizability of an ion or a molecule is a measure of the relative tendency of its electron cloud to be distorted from its normal shape by an electric field. On the molecular scale, in a condensed phase, any species sits in an electric field due to its neighbours, and the resulting polarization is an important contribution to the total interaction energy. Electrostatic interactions are crucial for determining the majority of chemical–physical properties of the system and electronic polarization is a fundamental component of these interactions. Thus, polarization effects should be taken into account if accurate descriptions are desired. In classical computer simulations, the forces required to drive the system are typically based on interatomic interaction potentials derived in part from electronic structure calculations or from experimental data. Owing to the difficulties in including polarization effects in classical force fields, most of them are based just on pairwise additive interaction potentials. At present, major efforts are underway to develop polarizable interaction potentials for biomolecular simulations. In this review, various ways of introducing explicit polarizability into biomolecular models and force fields are reviewed, and the progress that might be achieved in applying such methods to study potassium channels is described.

Molecular dynamics simulations of potassium channels

Despite the complexity of ion-channels, MD simulations based on realistic all-atom models have become a powerful technique for providing accurate descriptions of the structure and dynamics of these systems, complementing and reinforcing experimental work. Successful multidisciplinary collaborations, progress in the experimental determination of three-dimensional structures of membrane proteins together with new algorithms for molecular simulations and the increasing speed and availability of supercomputers, have made possible a considerable progress in this area of biophysics. This review aims at highlighting some of the work in the area of potassium channels and molecular dynamics simulations where numerous fundamental questions about the structure, function, folding and dynamics of these systems remain as yet unresolved challenges.

A Linear Scaling Study of Solvent−Solute Interaction Energy of Drug Molecules in Aqua Solution

Solvent-solute interaction energies for three well-known drug molecules in water solution are computed at the Hartree-Fock and B3LYP density functional theory levels using a linear scaling technique, which allows one to explicitly include in the model water molecules up to 14 A away from the solute molecule. The dependence of calculated interaction energies on the amount of included solvent has been examined. It is found that it is necessary to account for water molecules within an 8 A radius around the drug molecule to reach the saturated solvent interaction level. Effects of electron correlation and basis set on solvent-solute interaction energies are discussed.

Ion conductance vs. pore gating and selectivity in KcsA channel: Modeling achievements and perspectives

KcsA potassium channel belongs to a wide family of allosteric proteins that switch between closed and open states conformations in response to a stimulus, and act as a regulator of cation activity in living cells. The gating mechanism and cation selectivity of such channels have been extensively studied in the literature, with a revival emphasis these latter years, due to the publication of the crystallized structure of KcsA. Despite the increasing number of research and review papers on these topics, quantitative interpretation of these processes at the atomic scale is far from achieved. On the basis of available experimental and theoretical data, and by including our recent results, we review the progresses in this field of activity and discuss the weaknesses that should be corrected. In this spirit, we partition the channel into the filter, cavity, extra and intracellular media, in order to analyze separately the specificity of each region. Special emphasis is brought to the study of an open state for the channel and to the different properties generated by the opening. The influence of water as a structural and dynamical component of the channel properties in closed and open states, as well as in the sequential motions of the cations, is analyzed using molecular dynamics simulations and ab initio calculations. The polarization and charge transfer effects on the ions' dynamics and kinetics are discussed in terms of partial charge models.

Quantum mechanical calculations of charge effects on gating the KcsA channel

A series of ab initio (density functional) calculations were carried out on side chains of a set of amino acids, plus water, from the (intracellular) gating region of the KcsA K(+) channel. Their atomic coordinates, except hydrogen, are known from X-ray structures [D.A. Doyle, J.M. Cabral, R.A. Pfuetzner, A. Kuo, J.M. Gulbis, S.L. Cohen, B.T. Chait, R. MacKinnon, The structure of the potassium channel: molecular basis of K(+) conduction and selectivity, Science 280 (1998) 69-77; R. MacKinnon, S.L. Cohen, A. Kuo, A. Lee, B.T. Chait, Structural conservation in prokaryotic and eukaryotic potassium channels, Science 280 (1998) 106-109; Y. Jiang, A. Lee, J. Chen, M. Cadene, B.T. Chait, R. MacKinnon, The open pore conformation of potassium channels. Nature 417 (2001) 523-526], as are the coordinates of some water oxygen atoms. The 1k4c structure is used for the starting coordinates. Quantum mechanical optimization, in spite of the starting configuration, places the atoms in positions much closer to the 1j95, more tightly closed, configuration. This state shows four water molecules forming a "basket" under the Q119 side chains, blocking the channel. When a hydrated K(+) approaches this "basket", the optimized system shows a strong set of hydrogen bonds with the K(+) at defined positions, preventing further approach of the K(+) to the basket. This optimized structure with hydrated K(+) added shows an ice-like 12 molecule nanocrystal of water. If the water molecules exchange, unless they do it as a group, the channel will remain blocked. The "basket" itself appears to be very stable, although it is possible that the K(+) with its hydrating water molecules may be more mobile, capable of withdrawing from the gate. It is also not surprising that water essentially freezes, or forms a kind of glue, in a nanometer space; this agrees with experimental results on a rather different, but similarly sized (nm dimensions) system [K.B. Jinesh, J.W.M. Frenken, Capillary condensation in atomic scale friction: how water acts like a glue, Phys. Rev. Lett. 96 (2006) 166103/1-4]. It also agrees qualitatively with simulations on channels [A. Anishkin, S. Sukharev, Water dynamics and dewetting transitions in the small mechanosensitive channel MscS, Biophys. J. 86 (2004) 2883-2895; O. Beckstein, M.S.P. Sansom, Liquid-vapor oscillations of water in hydrophobic nanopores, Proc. Natl Acad. Sci. U. S. A. 100 (2003) 7063-7068] and on featureless channel-like systems [J. Lu, M.E. Green, Simulation of water in a pore with charges: application to a gating mechanism for ion channels, Prog. Colloid Polym. Sci. 103 (1997) 121-129], in that it forms a boundary on water that is not obvious from the liquid state. The idea that a structure is stable, even if individual molecules exchange, is well known, for example from the hydration shell of ions. We show that when charges are added in the form of protons to the domains (one proton per domain), the optimized structure is open. No stable water hydrogen bonds hold it together; an opening of 11.0 A appears, measured diagonally between non-neighboring domains as glutamine 119 carbonyl O-O distance. This is comparable to the opening in the MthK potassium channel structure that is generally agreed to be open. The appearance of the opening is in rather good agreement with that found by Perozo and coworkers. In contrast, in the uncharged structure this diagonal distance is 6.5 A, and the water "basket" constricts the uncharged opening still further, with the ice-like structure that couples the K(+) ion to the gating region freezing the entrance to the channel. Comparison with our earlier model for voltage gated channels suggests that a similar mechanism may apply in those channels.

Protein grabs a ligand by extending anchor residues: molecular simulation for Ca2+ binding to calmodulin loop

The structural difference in proteins between unbound and bound forms directly suggests the importance of the conformational plasticity of proteins. However, pathways that connect two-end structures and how they are coupled to the binding reaction are not well understood at atomic resolution. Here, we analyzed the free-energy landscape, explicitly taking into account coupling between binding and conformational change by performing atomistic molecular dynamics simulations for Ca2+ binding to a calmodulin loop. Using the AMBER force field with explicit water solvent, we conducted umbrella sampling for the free-energy surface and steered molecular dynamics for the pathway search. We found that, at an early stage of binding, some key residue side chains extend their "arms" to catch Ca2+ and, after catching, they carry the Ca2+ to the center of the binding pocket. This grabbing motion resulted in smooth and stepwise exchange in coordination partners of Ca2+ from water oxygen to atoms in the calmodulin loop. The key residue that first caught the ion was one of the two acidic residues, which are highly conserved. In the pathway simulations, different pathways were observed between binding and dissociation reactions: The former was more diverse than the latter.

Incidence of partial charges on ion selectivity in potassium channels

Potassium channels are membrane proteins known to select potassium over sodium ions at a high diffusion rate. We conducted ab initio calculations on a filter model of KcsA of about 300 atoms at the Hartree-Fock level of theory. Partial charges were derived from the quantum mechanically determined electrostatic potential either with Merz-Kollman or Hinsen-Roux schemes. Large polarization and/or charge transfer occur on potassium ions located in the filter, while the charges on sodium ions remain closer to unity. As a result, a weaker binding is obtained for K(+) ions. Using a simplified version of a permeation model based on the concerted-motion mechanism for ion translocation within the single-file ion channel [P. H. Nelson, J. Chem. Phys. 117, 11396 (2002)], we discuss how differences in polarization effects in the adducts with K(+) and Na(+) can play a role as for ionic selectivity and conductance.

Combining docking and molecular dynamic simulations in drug design

A rational approach is needed to maximize the chances of finding new drugs, and to exploit the opportunities of potential new drug targets emerging from genomic and proteomic initiatives, and from the large libraries of small compounds now readily available through combinatorial chemistry. Despite a shaky early history, computer-aided drug design techniques can now be effective in reducing costs and speeding up drug discovery. This happy outcome results from development of more accurate and reliable algorithms, use of more thoughtfully planned strategies to apply them, and greatly increased computer power to allow studies with the necessary reliability to be performed. Our review focuses on applications and protocols, with the main emphasis on critical analysis of recent studies where docking calculations and molecular dynamics (MD) simulations were combined to dock small molecules into protein receptors. We highlight successes to demonstrate what is possible now, but also point out drawbacks and future directions. The review is structured to lead the reader from the simpler to more compute-intensive methods. Thus, while inexpensive and fast docking algorithms can be used to scan large compound libraries and reduce their size, more accurate but expensive MD simulations can be applied when a few selected ligand candidates remain. MD simulations can be used: during the preparation of the protein receptor before docking, to optimize its structure and account for protein flexibility; for the refinement of docked complexes, to include solvent effects and account for induced fit; to calculate binding free energies, to provide an accurate ranking of the potential ligands; and in the latest developments, during the docking process itself to find the binding site and correctly dock the ligand a priori.

Non-Michaelis-Menten kinetics model for conductance of low-conductance potassium ion channels

A reduced kinetics model is proposed for ion permeation in low-conductance potassium ion channels with zero net electrical charge in the selectivity filter region. The selectivity filter is assumed to be the only conductance-determining part of the channel. Ion entry and exit rate constants depend on the occupancy of the filter due to ion-ion interactions. The corresponding rates are assumed slow relative to the rates of ion motion between binding sites inside the filter, allowing a reduction of the kinetics model of the filter by averaging the entry and exit rate constants over the states with a particular occupancy number. The reduced kinetics model for low-conductance channels is described by only three states and two sets of effective rate constants characterizing transitions between these states. An explicit expression for the channel conductance as a function of symmetrical external ion concentration is derived under the assumption that the average electrical mobility of ions in the selectivity filter region in a limited range of ion concentrations does not depend on these concentrations. The simplified conductance model is shown to provide a good description of the experimentally observed conductance-concentration curve for the low-conductance potassium channel Kir2.1, and also predicts the mean occupancy of the selectivity filter of this channel. We find that at physiological external ion concentrations this occupancy is much lower than the value of two ions observed for one of the high-conductance potassium channels, KcsA.