Computational Studies on Polarization Effects and Selectivity in K+ Channels

Histone tail electrostatics modulate E2-E3 enzyme dynamics: a gateway to regulate ubiquitination machinery

BRCA1 (Breast Cancer-Associated Protein 1) is a human tumor suppressor that functions as an ubiquitin (Ub) ligase enzyme (E3) and plays a key role in genomic stability and DNA repair. Heterodimerization of BRCA1 with BARD1 (BRCA1-associated RING domain protein 1) is known to increase its Ub ligase activity and is important for its stability, and cooperative activation of UbcH5c (Ub conjugating enzyme (E2)). Recent studies demonstrate the importance of ubiquitination of the nucleosomal H2A C-terminal tail by BRCA1/BARD1-UbcH5c in which its mutations inhibit ubiquitination, predispose cells to chromosomal instability and greatly increase the likelihood of breast and ovarian cancer development. Due to the lack of molecular-level insight on the flexible and dis-ordered H2A C-tail, its ubiquitination mechanism by BRCA1/BARD1-UbcH5c and its function and relationship to cancer susceptibility remain elusive. Here, we use molecular dynamics simulations to provide molecular-level insights into the dynamics of the less-studied H2A C-tail and BRCA1/BARD1-UbcH5c on the nucleosome surface and their effect on ubiquitination. Our results precisely identify the key interactions and residues that trigger conformational transitions of BRCA1/BARD1-UbcH5c, and characterize the important role of histone electrostatics in their dynamics. We provide a mechanistic basis for the H2A C-tail lysine approach to UbcH5c and show the role of H2A C-tail and UbcH5c dynamics in lysine ubiquitination. Furthermore, our data demonstrate the potential for ubiquitination based on the lysine position of the C-tail. Altogether, the findings of this study provide unrevealed insights into the mechanism of H2A C-tail ubiquitination and help us understand the communication between Ub ligase/Ub conjugating enzymes (E3/E2) and nucleosome to regulate ubiquitination machinery, paving the way for the development of effective treatments for cancer and chronic pain.

Induced Polarization in Molecular Dynamics Simulations of the 5-HT3 Receptor Channel

Ion channel proteins form water-filled nanoscale pores within lipid bilayers, and their properties are dependent on the complex behavior of water in a nanoconfined environment. Using a simplified model of the pore of the 5-HT3 receptor (5HT3R) which restrains the backbone structure to that of the parent channel protein from which it is derived, we compare additive with polarizable models in describing the behavior of water in nanopores. Molecular dynamics simulations were performed with four conformations of the channel: two closed state structures, an intermediate state, and an open state, each embedded in a phosphatidylcholine bilayer. Water density profiles revealed that for all water models, the closed and intermediate states exhibited strong dewetting within the central hydrophobic gate region of the pore. However, the open state conformation exhibited varying degrees of hydration, ranging from partial wetting for the TIP4P/2005 water model to complete wetting for the polarizable AMOEBA14 model. Water dipole moments calculated using polarizable force fields also revealed that water molecules remaining within dewetted sections of the pore resemble gas phase water. Free energy profiles for Na+ and for Cl- ions within the open state pore revealed more rugged energy landscapes using polarizable force fields, and the hydration number profiles of these ions were also sensitive to induced polarization resulting in a substantive reduction of the number of waters within the first hydration shell of Cl- while it permeates the pore. These results demonstrate that induced polarization can influence the complex behavior of water and ions within nanoscale pores and provides important new insights into their chemical properties.

Many-body effect determines the selectivity for Ca2+ and Mg2+ in proteins

Calcium ion is a versatile messenger in many cell-signaling processes. To achieve their functions, calcium-binding proteins selectively bind Ca2+ against a background of competing ions such as Mg2+ The high specificity of calcium-binding proteins has been intriguing since Mg2+ has a higher charge density than Ca2+ and is expected to bind more tightly to the carboxylate groups in calcium-binding pockets. Here, we showed that the specificity for Ca2+ is dictated by the many-body polarization effect, which is an energetic cost arising from the dense packing of multiple residues around the metal ion. Since polarization has stronger distance dependence compared with permanent electrostatics, the cost associated with the smaller Mg2+ is much higher than that with Ca2+ and outweighs the electrostatic attraction favorable for Mg2+ With the AMOEBA (atomic multipole optimized energetics for biomolecular simulation) polarizable force field, our simulations captured the relative binding free energy between Ca2+ and Mg2+ for proteins with various types of binding pockets and explained the nonmonotonic size dependence of the binding free energy in EF-hand proteins. Without electronic polarization, the smaller ions are always favored over larger ions and the relative binding free energy is roughly proportional to the net charge of the pocket. The many-body effect depends on both the number and the arrangement of charged residues. Fine-tuning of the ion selectivity could be achieved by combining the many-body effect and geometric constraint.

Umbrella sampling molecular dynamics simulations reveal concerted ion movement through G-quadruplex DNA channels

We have applied the umbrella sampling (US) method in all-atom molecular dynamics (MD) simulations to obtain potential of mean force (PMF) profiles for ion transport through three representative G-quadruplex DNA channels: [d(TG₄T)]₄, [d(G₃T₄G₄)]₂, and d[G₄(T₄G₄)₃]. The US MD results are in excellent agreement with those obtained previously with the adaptive biasing force (ABF) method. We then utilized the unique features in the US MD method to investigate multi-ion effects in [d(G₃T₄G₄)]₂ and discovered that the concerted ion movement is crucial for fully explaining the unusual experimental results on ion movement in this particular G-quadruplex system. We anticipate that these modern free-energy methods will be useful tools in evaluating ion transport properties of other G-quadruplex DNA channels.

Chloride Ion Transport by the E. coli CLC Cl-/H+ Antiporter: A Combined Quantum-Mechanical and Molecular-Mechanical Study

We performed steered molecular dynamics (SMD) and umbrella sampling simulations of Cl^- ion migration through the transmembrane domain of a prototypical E. coli CLC Cl^-/H⁺ antiporter by employing combined quantum-mechanical (QM) and molecular-mechanical (MM) calculations. The SMD simulations revealed interesting conformational changes of the protein. While no large-amplitude motions of the protein were observed during pore opening, the side chain rotation of the protonated external gating residue Glu148 was found to be critical for full access of the channel entrance by Cl^-. Moving the anion into the external binding site (S_ext) induced small-amplitude shifting of the protein backbone at the N-terminal end of helix F. As Cl^- traveled through the pore, rigid-body swinging motions of helix R separated it from helix D. Helix R returned to its original position once Cl^- exited the channel. Population analysis based on polarized wavefunction from QM/MM calculations discovered significant (up to 20%) charge loss for Cl^- along the ion translocation pathway inside the pore. The delocalized charge was redistributed onto the pore residues, especially the functional groups containing π bonds (e.g., the Tyr445 side chain), while the charges of the H atoms coordinating Cl^- changed almost negligibly. Potentials of mean force computed from umbrella sampling at the QM/MM and MM levels both displayed barriers at the same locations near the pore entrance and exit. However, the QM/MM PMF showed higher barriers (~10 kcal/mol) than the MM PMF (~2 kcal/mol). Binding energy calculations indicated that the interactions between Cl^- and certain pore residues were overestimated by the semi-empirical PM3 Hamiltonian and underestimated by the CHARMM36 force fields, both of which were employed in the umbrella sampling simulations. In particular, CHARMM36 underestimated binding interactions for the functional groups containing π bonds, missing the stabilizations of the Cl^- ion due to electron delocalization. The results suggested that it is important to explore these quantum effects for accurate descriptions of the Cl^- transport.

Computational studies of transport in ion channels using metadynamics

Molecular dynamics simulations have played a fundamental role in numerous fields of science by providing insights into the structure and dynamics of complex systems at the atomistic level. However, exhaustive sampling by standard molecular dynamics is in most cases computationally prohibitive, and the time scales accessible remain significantly shorter than many biological processes of interest. In particular, in the study of ion channels, realistic models to describe permeation and gating require accounting for large numbers of particles and accurate interaction potentials, which severely limits the length of the simulations. To overcome such limitations, several advanced methods have been proposed among which is metadynamics. In this algorithm, an external bias potential to accelerate sampling along selected collective variables is introduced. This bias potential discourages visiting regions of the configurational space already explored. In addition, the bias potential provides an estimate of the free energy as a function of the collective variables chosen once the simulation has converged. In this review, recent contributions of metadynamics to the field of ion channels are discussed, including how metadynamics has been used to search for transition states, predict permeation pathways, treat conformational flexibility that underlies the coupling between gating and permeation, or compute free energy of permeation profiles. This article is part of a Special Issue entitled: Membrane Proteins edited by J.C. Gumbart and Sergei Noskov.

Effects of the protonation state of the EEEE motif of a bacterial Na(+)-channel on conduction and pore structure

A distinctive feature of prokaryotic Na(+)-channels is the presence of four glutamate residues in their selectivity filter. In this study, how the structure of the selectivity filter, and the free-energy profile of permeating Na(+) ions are altered by the protonation state of Glu177 are analyzed. It was found that protonation of a single glutamate residue was enough to modify the conformation of the selectivity filter and its conduction properties. Molecular dynamics simulations revealed that Glu177 residues may adopt two conformations, with the side chain directed toward the extracellular entrance of the channel or the intracellular cavity. The likelihood of the inwardly directed arrangement increases when Glu177 residues are protonated. The presence of one glutamate residue with its chain directed toward the intracellular cavity increases the energy barrier for translocation of Na(+) ions. These higher-energy barriers preclude Na(+) ions to permeate the selectivity filter of prokaryotic Na(+)-channels when one or more Glu177 residues are protonated.

Permeation and dynamics of an open-activated TRPV1 channel

Transient receptor potential (TRP) ion channels constitute a large and diverse protein family, found in yeast and widespread in the animal kingdom. TRP channels work as sensors for a wide range of cellular and environmental signals. Understanding how these channels respond to physical and chemical stimuli has been hindered by the limited structural information available until now. The three-dimensional structure of the vanilloid receptor 1 (TRPV1) was recently determined by single particle electron cryo-microscopy, offering for the first time the opportunity to explore ionic conduction in TRP channels at atomic detail. In this study, we present molecular dynamics simulations of the open-activated pore domain of TRPV1 in the presence of three cationic species: Na(+), Ca(2+) and K(+). The dynamics of these ions while interacting with the channel pore allowed us to rationalize their permeation mechanism in terms of a pathway involving three binding sites at the intracellular cavity, as well as the extracellular and intracellular entrance of the selectivity filter. Furthermore, conformational analysis of the pore in the presence of these ions reveals specific ion-mediated structural changes in the selectivity filter, which influences the permeability properties of the TRPV1 channel.

K(+) and Na(+) conduction in selective and nonselective ion channels via molecular dynamics simulations

Generations of scientists have been captivated by ion channels and how they control the workings of the cell by admitting ions from one side of the cell membrane to the other. Elucidating the molecular determinants of ion conduction and selectivity are two of the most fundamental issues in the field of biophysics. Combined with ongoing progress in structural studies, modeling and simulation have been an integral part of the development of the field. As of this writing, the relentless growth in computational power, the development of new algorithms to tackle the so-called rare events, improved force-field parameters, and the concomitant increasing availability of membrane protein structures, allow simulations to contribute even further, providing more-complete models of ion conduction and selectivity in ion channels. In this report, we give an overview of the recent progress made by simulation studies on the understanding of ion permeation in selective and nonselective ion channels.

Molecular strategies to achieve selective conductance in NaK channel variants

A recent crystallization of several ion channels has provided strong impetus for efforts aimed at understanding the different strategies employed by nature for selective ion transport. In this work, we used two variants of the selectivity filter of NaK channel to explore molecular mechanisms that give rise to K(+)-selectivity. We computed one-dimensional (1D) and two-dimensional (2D) potentials of mean force (PMFs) for ion permeation across the channel. The results indicate that the energies for Na(+) and K(+) permeation across the selectivity filter display significant differences in positions of the binding sites and barriers. One characteristic signature of a K(+)-selective channel is the apparent preservation of the site analogous to that of S2 in KcsA. The S2-bound ion can be almost ideally dehydrated and coordinated by 6 to 8 carbonyls. In a striking contrast, the PMFs controlling transport of ions in a nonselective variant show almost identical profiles for either K(+) or Na(+) and significant involvement of water molecules in ion coordination across the entire selectivity filter. An analysis of differences in 1D PMFs for Na(+) and K(+) suggests that coordination number alone is an insufficient predictor of site selectivity, while chemical composition (ratio of carbonyls and water molecules) correlates well with preference for K(+). Multi-ion effects such as dependence of the barriers and wells for permeant ion on the type of copermeant ion were found to play a significant role in the selectivity signature of the channel as well.

Nonselective conduction in a mutated NaK channel with three cation-binding sites

The NaK channel is a cation-selective protein with similar permeability for K(+) and Na(+) ions. Crystallographic structures are available for the wild-type and mutated NaK channels with different numbers of cation-binding sites. We have performed a comparison between the potentials of mean force governing the translocation of K(+) ions and mixtures of one Na(+) and three K(+) ions in a mutated NaK channel with only three cation-binding sites (NaK-CNG). Since NaK-CNG is not selective for K(+) over Na(+), analysis of its multi-ion potential energy surfaces can provide clues about how selectivity originates. Comparison of the potentials of mean force of NaK-CNG and K(+)-selective channels yields observations that strongly suggest that the number of contiguous ion binding sites in a single-file mechanism is the key determinant of the channel's selectivity properties, as already proposed by experimental studies. We conclude that the presence of four binding sites in K(+)-selective channels is essential for highly selective and efficient permeation of K(+) ions, and that a key difference between K(+)-selective and nonselective channels is the absence/presence of a binding site for Na(+) ions at the boundary between S2 and S3 in the context of multi-ion permeation events.

On conduction in a bacterial sodium channel

Voltage-gated Na⁺-channels are transmembrane proteins that are responsible for the fast depolarizing phase of the action potential in nerve and muscular cells. Selective permeability of Na⁺ over Ca²⁺ or K⁺ ions is essential for the biological function of Na⁺-channels. After the emergence of the first high-resolution structure of a Na⁺-channel, an anionic coordination site was proposed to confer Na⁺ selectivity through partial dehydration of Na⁺ via its direct interaction with conserved glutamate side chains. By combining molecular dynamics simulations and free-energy calculations, a low-energy permeation pathway for Na⁺ ion translocation through the selectivity filter of the recently determined crystal structure of a prokaryotic sodium channel from Arcobacter butzleri is characterised. The picture that emerges is that of a pore preferentially occupied by two ions, which can switch between different configurations by crossing low free-energy barriers. In contrast to K⁺-channels, the movements of the ions appear to be weakly coupled in Na⁺-channels. When the free-energy maps for Na⁺ and K⁺ ions are compared, a selective site is characterised in the narrowest region of the filter, where a hydrated Na⁺ ion, and not a hydrated K⁺ ion, is energetically stable.

Ion channels are integral membrane proteins that control the passive diffusion of ions down their electrochemical gradient. According to the most permeating ion species, ion channels are classified in three categories: K⁺-channels, Na⁺-channels, and Ca²⁺-channels. The atomic structure of a K⁺-channel was the first to be solved experimentally more than 10 years ago. This structure inspired numerous computational studies, which revealed the mechanisms of conduction and selectivity in K⁺-channels. Recently, the first atomic structure of a Na⁺ selective channel has been solved. Here, molecular dynamics simulations and free-energy calculations are described and a possible mechanism for Na⁺ conduction is identified. In contrast to what it is observed in K⁺-channels, ion movements through Na⁺-channels appeared highly uncorrelated.

Molecular dynamics simulations of the TrkH membrane protein

TrkH is a transmembrane protein that mediates uptake of K(+) through the cell membrane. Despite the recent determination of its crystallographic structure, the nature of the permeation mechanism is still unknown, that is, whether K(+) ions move across TrkH by active transport or passive diffusion. Here, molecular dynamics simulations and the umbrella sampling technique have been employed to shed light on this question. The existence of binding site S3 and two alternative binding sites have been characterized. Analysis of the coordination number renders values that are almost constant, with a full contribution from the carbonyls of the protein only at S3. This observation contrasts with observations of K(+) channels, where the contribution of the protein to the coordination number is roughly constant in all four binding sites. An intramembrane loop is found immediately after the selectivity filter at the intracellular side of the protein, which obstructs the permeation pathway, and this is reflected in the magnitude of the energy barriers.

Gating at the selectivity filter of ion channels that conduct Na+ and K+ ions

The NaK channel is a cation selective channel with similar permeability for K(+) and Na(+). The available crystallographic structure of wild-type (WT) NaK is usually associated with a conductive state of the channel. Here, potential of mean force for complete conduction events of Na(+) and K(+) ions through NaK show that: i), large energy barriers prevent the passage of ions through the WT NaK structure, ii), the barriers are correlated to the presence of a hydrogen bond between Asp-66 and Asn-68, and iii), the structure of NaK mutated to mimic cyclic nucleotide-gated channels conducts Na(+) and K(+). These results support the hypothesis that the filter of cation selective channels can adopt at least two different structures: a conductive one, represented by the x-ray structures of the NaK-CNG chimeras, and a closed one, represented by the x-ray structures of the WT NaK.

Physics-based scoring of protein–ligand interactions: explicit polarizability, quantum mechanics and free energies

The ability to accurately predict the interaction of a ligand with its receptor is a key limitation in computer-aided drug design approaches such as virtual screening and de novo design. In this article, we examine current strategies for a physics-based approach to scoring of protein–ligand affinity, as well as outlining recent developments in force fields and quantum chemical techniques. We also consider advances in the development and application of simulation-based free energy methods to study protein–ligand interactions. Fuelled by recent advances in computational algorithms and hardware, there is the opportunity for increased integration of physics-based scoring approaches at earlier stages in computationally guided drug discovery. Specifically, we envisage increased use of implicit solvent models and simulation-based scoring methods as tools for computing the affinities of large virtual ligand libraries. Approaches based on end point simulations and reference potentials allow the application of more advanced potential energy functions to prediction of protein–ligand binding affinities. Comprehensive evaluation of polarizable force fields and quantum mechanical (QM)/molecular mechanical and QM methods in scoring of protein–ligand interactions is required, particularly in their ability to address challenging targets such as metalloproteins and other proteins that make highly polar interactions. Finally, we anticipate increasingly quantitative free energy perturbation and thermodynamic integration methods that are practical for optimization of hits obtained from screened ligand libraries