Biased Molecular Simulations for Free-Energy Mapping: A Comparison on the KcsA Channel as a Test Case

Unraveling of a Strongly Correlated Dynamical Network of Residues Controlling the Permeation of Potassium in KcsA Ion Channel

The complicated patterns of the single-channel currents in potassium ion channel KcsA are governed by the structural variability of the selectivity filter. A comparative analysis of the dynamics of the wild type KcsA channel and several of its mutants showing different conducting patterns was performed. A strongly correlated dynamical network of interacting residues is found to play a key role in regulating the state of the wild type channel. The network is centered on the aspartate D80 which plays the role of a hub by strong interacting via hydrogen bonds with residues E71, R64, R89, and W67. Residue D80 also affects the selectivity filter via its backbones. This network further compromises ions and water molecules located inside the channel that results in the mutual influence: the permeation depends on the configuration of residues in the network, and the dynamics of network's residues depends on locations of ions and water molecules inside the selectivity filter. Some features of the network provide a further understanding of experimental results describing the KcsA activity. In particular, the necessity of anionic lipids to be present for functioning the channel is explained by the interaction between the lipids and the arginine residues R64 and R89 that prevents destabilizing the structure of the selectivity filter.

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.

Mechanistic Insights into the Reaction of Chlorination of Tryptophan Catalyzed by Tryptophan 7-Halogenase

Tryptophan 7-halogenase catalyzes chlorination of free tryptophan to 7-chlorotryptophan, which is the first step in the antibiotic pyrrolnitrin biosynthesis. Many biologically and pharmaceutically active natural products contain chlorine and thus, an understanding of the mechanism of its introduction into organic molecules is important. Whilst enzyme-catalyzed chlorination is accomplished with ease, it remains a difficult task for the chemists. Therefore, utilizing enzymes in the synthesis of chlorinated organic compounds is important, and providing atomistic mechanistic insights about the reaction mechanism of tryptophan 7-halogenase is vital and timely. In this work, we examined a mechanism for the reaction of tryptophan chlorination, performed by tryptophan 7-halogenase, by calculating potential energy and free energy surfaces using two different Combined Quantum Mechanical/Molecular Mechanical (QM/MM) methods both employing Density Functional Theory (DFT) for the QM region. Both computational strategies agree on the nature of the rate-limiting step and provided close results for the reaction barriers of the two reaction steps. The calculations for both the potential energy and the free energy profiles showed very similar geometric features and hydrogen bonding interactions for the characterized stationary points.

Calculating the free energy of transfer of small solutes into a model lipid membrane: Comparison between metadynamics and umbrella sampling

We compare the performance of two well-established computational algorithms for the calculation of free-energy landscapes of biomolecular systems, umbrella sampling and metadynamics. We look at benchmark systems composed of polyethylene and polypropylene oligomers interacting with lipid (phosphatidylcholine) membranes, aiming at the calculation of the oligomer water-membrane free energy of transfer. We model our test systems at two different levels of description, united-atom and coarse-grained. We provide optimized parameters for the two methods at both resolutions. We devote special attention to the analysis of statistical errors in the two different methods and propose a general procedure for the error estimation in metadynamics simulations. Metadynamics and umbrella sampling yield the same estimates for the water-membrane free energy profile, but metadynamics can be more efficient, providing lower statistical uncertainties within the same simulation time.

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.

Adaptive Steered Molecular Dynamics of the Long-Distance Unfolding of Neuropeptide Y

Neuropeptide Y (NPY) has been found to adopt two stable conformations in vivo: (1) a monomeric form called the PP-fold in which a polyproline tail is folded onto an α-helix via a β-turn and (2) a dimeric form of the unfolded proteins in which the α-helices interact with each other via side chains. The transition pathway and rates between the two conformations remain unknown and are important to the nature of the binding of the protein. Toward addressing this question, the present work suggests that the unfolding of the PP-fold is too slow to play a role in NPY monomeric binding unless the receptor catalyzes it to do so. Specifically, the dynamics and structural changes of the unfolding of a monomeric NPY protein have been investigated in this work. Temperature accelerated molecular dynamics (MD) simulations at 500 K under constant (N,V,E) conditions suggests a hinge-like unraveling of the tail rather than a random unfolding. The free energetics of the proposed unfolding pathway have been described using an adaptive steered MD (SMD) approach at various temperatures. This approach generalizes the use of Jarzynski's equality through a series of stages that allows for better convergence along nonlinear and long-distance pathways. Results acquired using this approach provide a potential of mean force (PMF) with narrower error bars and are consistent with some of the earlier reports on the qualitative behavior of NPY binding.

Physical methods to quantify small antibiotic molecules uptake into Gram-negative bacteria

The development of antibiotics against Gram-negative bacteria is a challenge: any active compound must cross the outer cell envelope composed of a hydrophilic highly charged lipopolysaccharide layer followed by a tight hydrophobic layer containing water filled gates called porins to reach the hydrophilic periplasmic space and depending on the target with the further need to cross the hydrophobic inner membrane. In addition to a possible rapid enzymatic deactivation efflux pumps shuffle compounds back outside. The resulting low permeability of cell envelope requires high dose and leads therefore to toxicity problems. Despite its relevance the permeability barrier in Gram-negative bacteria is not well understood partially caused by the lack of appropriate direct assays. Here we give a brief introduction on current available techniques to quantify passive diffusion of small hydrophilic molecules into Gram-negative bacteria.

Theoretical and simulation studies on voltage-gated sodium channels

Voltage-gated sodium (Na_v) channels are indispensable membrane elements for the generation and propagation of electric signals in excitable cells. The successes in the crystallographic studies on prokaryotic Na_v channels in recent years greatly promote the mechanistic investigation of these proteins and their eukaryotic counterparts. In this paper, we mainly review the progress in computational studies, especially the simulation studies, on these proteins in the past years.

Net charge changes in the calculation of relative ligand-binding free energies via classical atomistic molecular dynamics simulation

The calculation of binding free energies of charged species to a target molecule is a frequently encountered problem in molecular dynamics studies of (bio-)chemical thermodynamics. Many important endogenous receptor-binding molecules, enzyme substrates, or drug molecules have a nonzero net charge. Absolute binding free energies, as well as binding free energies relative to another molecule with a different net charge will be affected by artifacts due to the used effective electrostatic interaction function and associated parameters (e.g., size of the computational box). In the present study, charging contributions to binding free energies of small oligoatomic ions to a series of model host cavities functionalized with different chemical groups are calculated with classical atomistic molecular dynamics simulation. Electrostatic interactions are treated using a lattice-summation scheme or a cutoff-truncation scheme with Barker-Watts reaction-field correction, and the simulations are conducted in boxes of different edge lengths. It is illustrated that the charging free energies of the guest molecules in water and in the host strongly depend on the applied methodology and that neglect of correction terms for the artifacts introduced by the finite size of the simulated system and the use of an effective electrostatic interaction function considerably impairs the thermodynamic interpretation of guest-host interactions. Application of correction terms for the various artifacts yields consistent results for the charging contribution to binding free energies and is thus a prerequisite for the valid interpretation or prediction of experimental data via molecular dynamics simulation. Analysis and correction of electrostatic artifacts according to the scheme proposed in the present study should therefore be considered an integral part of careful free-energy calculation studies if changes in the net charge are involved.

Well-tempered metadynamics as a tool for characterizing multi-component, crystalline molecular machines

The well-tempered, smoothly converging form of the metadynamics algorithm has been implemented in classical molecular dynamics simulations and used to obtain an estimate of the free energy surface explored by the molecular rotations in the plastic crystal, octafluoronaphthalene. The biased simulations explore the full energy surface extremely efficiently, more than 4 orders of magnitude faster than unbiased molecular dynamics runs. The metadynamics collective variables used have also been expanded to include the simultaneous orientations of three neighboring octafluoronaphthalene molecules. Analysis of the resultant three-dimensional free energy surface, which is sampled to a very high degree despite its significant complexity, demonstrates that there are strong correlations between the molecular orientations. Although this correlated motion is of limited applicability in terms of exploiting dynamical motion in octafluoronaphthalene, the approach used is extremely well suited to the investigation of the function of crystalline molecular machines.

Membrane binding and insertion of a pHLIP peptide studied by all-atom molecular dynamics simulations

Recent experiments in function mechanism study reported that a pH low-insertion peptide (pHLIP) can insert into a zwitterionic palmitoyloleoylphosphatidylcholine (POPC) lipid bilayer at acidic pH while binding to the bilayer surface at basic pH. However, the atomic details of the pH-dependent interaction of pHLIP with a POPC bilayer are not well understood. In this study, we investigate the detailed interactions of pHLIP with a POPC bilayer at acidic and basic pH conditions as those used in function mechanism study, using all-atom molecular dynamics (MD) simulations. Simulations have been performed by employing the initial configurations, where pHLIP is placed in aqueous solution, parallel to bilayer surface (system S), partially-inserted (system P), or fully-inserted (system F) in POPC bilayers. On the basis of multiple 200-ns MD simulations, we found (1) pHLIP in system S can spontaneously insert into a POPC bilayer at acidic pH, while binding to the membrane surface at basic pH; (2) pHLIP in system P can insert deep into a POPC bilayer at acidic pH, while it has a tendency to exit, and stays at bilayer surface at basic pH; (3) pHLIP in system F keeps in an α-helical structure at acidic pH while partially unfolding at basic pH. This study provides at atomic-level the pH-induced insertion of pHLIP into POPC bilayer.

Using metadynamics and path collective variables to study ligand binding and induced conformational transitions

Large-scale conformational transitions represent both a challenge and an opportunity for computational drug design. Exploring the conformational space of a druggable target with sufficient detail is computationally demanding. However, if it were possible to fully account for target flexibility, one could exploit this knowledge to rationally design more potent and more selective drug candidates. Here, we discuss how molecular dynamics together with free energy algorithms based on Metadynamics and Path Collective Variables can be used to study both large-scale conformational transitions and ligand binding to flexible targets. We show real-life examples of how these methods have been applied in the case of cyclin-dependent kinases, a family of flexible targets that shows promise in cancer therapy.

A permeation theory for single-file ion channels: one- and two-step models

How many steps are required to model permeation through ion channels? This question is investigated by comparing one- and two-step models of permeation with experiment and MD simulation for the first time. In recent MD simulations, the observed permeation mechanism was identified as resembling a Hodgkin and Keynes knock-on mechanism with one voltage-dependent rate-determining step [Jensen et al., PNAS 107, 5833 (2010)]. These previously published simulation data are fitted to a one-step knock-on model that successfully explains the highly non-Ohmic current-voltage curve observed in the simulation. However, these predictions (and the simulations upon which they are based) are not representative of real channel behavior, which is typically Ohmic at low voltages. A two-step association/dissociation (A/D) model is then compared with experiment for the first time. This two-parameter model is shown to be remarkably consistent with previously published permeation experiments through the MaxiK potassium channel over a wide range of concentrations and positive voltages. The A/D model also provides a first-order explanation of permeation through the Shaker potassium channel, but it does not explain the asymmetry observed experimentally. To address this, a new asymmetric variant of the A/D model is developed using the present theoretical framework. It includes a third parameter that represents the value of the "permeation coordinate" (fractional electric potential energy) corresponding to the triply occupied state n of the channel. This asymmetric A/D model is fitted to published permeation data through the Shaker potassium channel at physiological concentrations, and it successfully predicts qualitative changes in the negative current-voltage data (including a transition to super-Ohmic behavior) based solely on a fit to positive-voltage data (that appear linear). The A/D model appears to be qualitatively consistent with a large group of published MD simulations, but no quantitative comparison has yet been made. The A/D model makes a network of predictions for how the elementary steps and the channel occupancy vary with both concentration and voltage. In addition, the proposed theoretical framework suggests a new way of plotting the energetics of the simulated system using a one-dimensional permeation coordinate that uses electric potential energy as a metric for the net fractional progress through the permeation mechanism. This approach has the potential to provide a quantitative connection between atomistic simulations and permeation experiments for the first time.

Biomolecular simulation and modelling: status, progress and prospects

Molecular simulation is increasingly demonstrating its practical value in the investigation of biological systems. Computational modelling of biomolecular systems is an exciting and rapidly developing area, which is expanding significantly in scope. A range of simulation methods has been developed that can be applied to study a wide variety of problems in structural biology and at the interfaces between physics, chemistry and biology. Here, we give an overview of methods and some recent developments in atomistic biomolecular simulation. Some recent applications and theoretical developments are highlighted.