Multicanonical Molecular Dynamics Simulation Research Articles

Cyclosporin A: Conformational Complexity and Chameleonicity.

The chameleonic behavior of cyclosporin A (CsA) was investigated through conformational ensembles employing multicanonical molecular dynamics simulations that could sample the cis and trans isomers of N-methylated amino acids; these assessments were conducted in explicit water, dimethyl sulfoxide, acetonitrile, methanol, chloroform, cyclohexane (CHX), and n-hexane (HEX) using AMBER ff03, AMBER10:EHT, AMBER12:EHT, and AMBER14:EHT force fields. The conformational details were discussed employing the free-energy landscapes (FELs) at T = 300 K; it was observed that the experimentally determined structures of CsA were only a part of the conformational space. Comparing the ROESY measurements in CHX-d12 and HEX-d14, the major conformations in those apolar solvents were essentially the same as that in CDCl3 except for the observation of some sidechain rotamers. The effects of the metal ions on the conformations, including the cis/trans isomerization, were also investigated. Based on the analysis of FELs, it was concluded that the AMBER ff03 force field best described the experimentally derived conformations, indicating that CsA intrinsically formed membrane-permeable conformations and that the metal ions might be the key to the cis/trans isomerization of N-methylated amino acids before binding a partner protein.

Effects of number of parallel runs and frequency of bias-strength replacement in generalized ensemble molecular dynamics simulations

Background The generalized ensemble approach with the molecular dynamics (MD) method has been widely utilized. This approach usually has two features. (i) A bias potential, whose strength is replaced during a simulation, is applied. (ii) Sampling can be performed by many parallel runs of simulations. Although the frequency of the bias-strength replacement and the number of parallel runs can be adjusted, the effects of these settings on the resultant ensemble remain unclear. Method In this study, we performed multicanonical MD simulations for a foldable mini-protein (Trp-cage) and two unstructured peptides (8- and 20-residue poly-glutamic acids) with various settings. Results As a result, running many short simulations yielded robust results for the Trp-cage model. Regarding the frequency of the bias-potential replacement, although using a high frequency enhanced the traversals in the potential energy space, it did not promote conformational changes in all the systems.

Conformation and Permeability: Cyclic Hexapeptide Diastereomers.

Conformational ensembles of eight cyclic hexapeptide diastereomers in explicit cyclohexane, chloroform, and water were analyzed by multicanonical molecular dynamics (McMD) simulations. Free-energy landscapes (FELs) for each compound and solvent were obtained from the molecular shapes and principal component analysis at T = 300 K; detailed analysis of the conformational ensembles and flexibility of the FELs revealed that permeable compounds have different structural profiles even for a single stereoisomeric change. The average solvent-accessible surface area (SASA) in cyclohexane showed excellent correlation with the cell permeability, whereas this correlation was weaker in chloroform. The average SASA in water correlated with the aqueous solubility. The average polar surface area did not correlate with cell permeability in these solvents. A possible strategy for designing permeable cyclic peptides from FELs obtained from McMD simulations is proposed.

Dynamic Docking of a Medium-Sized Molecule to Its Receptor by Multicanonical MD Simulations.

A medium-sized and highly flexible inhibitor to the enzyme β-secretase 1 (BACE), which produces the amyloid β-peptide by cleavage of its precursor protein, was dynamically docked into the large and wide catalytic cleft of BACE that binds to the amyloid-precursor by employing multicanonical molecular dynamics (McMD) simulations. We applied our method to predict the native binding configuration and sample the intermediary structures connecting this natively bound state to the unbound one. Representative structures located at free energy minima obtained from McMD were taken and subjected to canonical simulations to refine and validate them, reproducing the native complex structure in agreement with the experimental data in the most stable structure, i.e., the one at the global minimum. In addition, the binding free energy was estimated by umbrella sampling (US) simulations along representative pathways obtained from the McMD ensemble, followed by weighted histogram analysis to estimate the affinity, which also reproduced the experimental inhibitory affinity. Interestingly, the loss of interactions between the two molecules along the pathway was clearly shown in the free energy landscape, reiterating the fundamental importance of atomistic interactions to the binding affinity between receptor and drug compound. The sampled ensemble by the US simulations smoothly connected the bound and unbound states, refining the binding pathway while staying true to the McMD ensemble.

Accurate Prediction of Complex Structure and Affinity for a Flexible Protein Receptor and Its Inhibitor.

In order to predict the accurate binding configuration as well as the binding affinity for a flexible protein receptor and its inhibitor drug, enhanced sampling with multicanonical molecular dynamics (McMD) simulation and thermodynamic integration (TI) were combined as a general drug docking method. CDK2, cyclin-dependent kinase 2, is involved in the cell cycle regulation. Malfunctions in CDK2 can cause tumorigenesis, and thus it is a potential drug target. Here, we performed a long McMD simulation for docking the inhibitor CS3 to CDK2 starting from the unbound structure. Subsequently, a potential binding/unbinding pathway was given from the multicanonical ensemble, and the binding free energy was readily computed by TI along the pathway. Using this combination, the correct binding configuration of CS3 to CDK2 was obtained, and its affinity coincided well with the experimental value.

Enhanced sampling simulations to construct free-energy landscape of protein-partner substrate interaction.

Molecular dynamics (MD) simulations using all-atom and explicit solvent models provide valuable information on the detailed behavior of protein-partner substrate binding at the atomic level. As the power of computational resources increase, MD simulations are being used more widely and easily. However, it is still difficult to investigate the thermodynamic properties of protein-partner substrate binding and protein folding with conventional MD simulations. Enhanced sampling methods have been developed to sample conformations that reflect equilibrium conditions in a more efficient manner than conventional MD simulations, thereby allowing the construction of accurate free-energy landscapes. In this review, we discuss these enhanced sampling methods using a series of case-by-case examples. In particular, we review enhanced sampling methods conforming to trivial trajectory parallelization, virtual-system coupled multicanonical MD, and adaptive lambda square dynamics. These methods have been recently developed based on the existing method of multicanonical MD simulation. Their applications are reviewed with an emphasis on describing their practical implementation. In our concluding remarks we explore extensions of the enhanced sampling methods that may allow for even more efficient sampling.

Density of states estimation for soft core system

The density of states (DOSs) for the soft core system is calculated by the multicanonical molecular dynamics simulation. We found the DOS of this system has a concavity. Owing to this concavity, the probability distribution has double peaks near the temperature where the system undergoes the solid–fluid phase transition.

Multicanonical molecular dynamics simulations of the N-terminal domain of protein L9

We describe multicanonical molecular dynamic simulations of the N-terminal domain of the protein L9. Analyzing free energy landscapes and thermal ordering, we propose a possible folding mechanism for the protein. By comparing our results with that of molecular dynamics runs of the protein at constant temperature, we find that multicanonical molecular dynamics leads to orders of magnitude higher sampling of folding transitions.

3P276 Multicanonical Go モデル分子動力学によるタンパク質の自由エネルギーの網羅的解析(24. 数理生物学,ポスター,第52回日本生物物理学会年会(2014年度))

3P276 Multicanonical Go モデル分子動力学によるタンパク質の自由エネルギーの網羅的解析(24. 数理生物学,ポスター,第52回日本生物物理学会年会(2014年度))

A virtual-system coupled multicanonical molecular dynamics simulation: Principles and applications to free-energy landscape of protein–protein interaction with an all-atom model in explicit solvent

We propose a novel generalized ensemble method, a virtual-system coupled multicanonical molecular dynamics (V-McMD), to enhance conformational sampling of biomolecules expressed by an all-atom model in an explicit solvent. In this method, a virtual system, of which physical quantities can be set arbitrarily, is coupled with the biomolecular system, which is the target to be studied. This method was applied to a system of an Endothelin-1 derivative, KR-CSH-ET1, known to form an antisymmetric homodimer at room temperature. V-McMD was performed starting from a configuration in which two KR-CSH-ET1 molecules were mutually distant in an explicit solvent. The lowest free-energy state (the most thermally stable state) at room temperature coincides with the experimentally determined native complex structure. This state was separated to other non-native minor clusters by a free-energy barrier, although the barrier disappeared with elevated temperature. V-McMD produced a canonical ensemble faster than a conventional McMD method.

Conformational Ensembles of an Intrinsically Disordered Protein pKID with and without a KIX Domain in Explicit Solvent Investigated by All-Atom Multicanonical Molecular Dynamics.

The phosphorylated kinase-inducible activation domain (pKID) adopts a helix–loop–helix structure upon binding to its partner KIX, although it is unstructured in the unbound state. The N-terminal and C-terminal regions of pKID, which adopt helices in the complex, are called, respectively, αA and αB. We performed all-atom multicanonical molecular dynamics simulations of pKID with and without KIX in explicit solvents to generate conformational ensembles. Although the unbound pKID was disordered overall, αA and αB exhibited a nascent helix propensity; the propensity of αA was stronger than that of αB, which agrees with experimental results. In the bound state, the free-energy landscape of αB involved two low free-energy fractions: native-like and non-native fractions. This result suggests that αB folds according to the induced-fit mechanism. The αB-helix direction was well aligned as in the NMR complex structure, although the αA helix exhibited high flexibility. These results also agree quantitatively with experimental observations. We have detected that the αB helix can bind to another site of KIX, to which another protein MLL also binds with the adopting helix. Consequently, MLL can facilitate pKID binding to the pKID-binding site by blocking the MLL-binding site. This also supports experimentally obtained results.

Enhanced and effective conformational sampling of protein molecular systems for their free energy landscapes.

Protein folding and protein–ligand docking have long persisted as important subjects in biophysics. Using multicanonical molecular dynamics (McMD) simulations with realistic expressions, i.e., all-atom protein models and an explicit solvent, free-energy landscapes have been computed for several systems, such as the folding of peptides/proteins composed of a few amino acids up to nearly 60 amino-acid residues, protein–ligand interactions, and coupled folding and binding of intrinsically disordered proteins. Recent progress in conformational sampling and its applications to biophysical systems are reviewed in this report, including descriptions of several outstanding studies. In addition, an algorithm and detailed procedures used for multicanonical sampling are presented along with the methodology of adaptive umbrella sampling. Both methods control the simulation so that low-probability regions along a reaction coordinate are sampled frequently. The reaction coordinate is the potential energy for multicanonical sampling and is a structural identifier for adaptive umbrella sampling. One might imagine that this probability control invariably enhances conformational transitions among distinct stable states, but this study examines the enhanced conformational sampling of a simple system and shows that reasonably well-controlled sampling slows the transitions. This slowing is induced by a rapid change of entropy along the reaction coordinate. We then provide a recipe to speed up the sampling by loosening the rapid change of entropy. Finally, we report all-atom McMD simulation results of various biophysical systems in an explicit solvent.

Communication: Conformation state diagram of polypeptides: A chain length induced α-β transition

By using a generic coarse grained polypeptide model, we perform multicanonical molecular dynamics simulations for determining the equilibrium conformation state diagram of a single homopolypeptide chain as a function of the chain length and temperature. The state diagram highlights the thermal regimes of stability for various conformational patterns in polypeptides, including swollen, random and collapsed coils, globular structures, extended and bended α helices, and compact β bundles. Remarkably, at low temperatures we observe a sharp transition from extended α helix to compact β bundles as the chain length increases. This finding indicates that the chain length is one of the intrisic factors that can trigger α-β transformations in a broad class of polypeptides.

Free Energy Landscapes of Alanine Dipeptide in Explicit Water Reproduced by the Force-Switching Wolf Method.

Precise and rapid calculation of long-range interactions is of crucial importance for molecular dynamics (MD) and Monte Carlo simulations. Instead of the Ewald method or its high speed variant, PME, we applied our novel method, called the force-switching Wolf method, to computation of the free energy landscapes of a short peptide in explicit water. Wolf and co-workers showed that long-range electrostatic energy under a periodic boundary condition can be well reproduced even by truncating the contribution from the distant charges, when the charge neutrality is taken into account. We recently applied the procedure proposed by Wolf and co-workers to a mathematically consistent MD theory by means of a force-switching scheme, and we show that the total electrostatic energy for sodium chloride liquid was well conserved and stable during the MD simulation with the force-switching Wolf method. Our current results for an aqueous peptide solution with a series of canonical and multicanonical molecular dynamics simulations show that the force-switching Wolf method is not only in good accordance with the energies and forces calculated by the conventional PME method but also properly reproduces the solvation and the free energy landscapes of the peptide at 300 K.

Simple and effective application of the Wang–Landau method for multicanonical molecular dynamics simulation

We propose a novel application of the Wang-Landau method (WLM) for multicanonical molecular dynamics (McMD) simulations. Originally, WLM was developed for Monte Carlo (MC) simulations. Fundamentally, WLM remarkably reduces simulation efforts because it estimates the optimal multicanonical energy function automatically. When WLM is applied to McMD, not only the multicanonical energy but also energy gradient must be estimated adequately. However, because of the rugged multicanonical energy function at the early simulation stage, applications of WLM for MD simulations are difficult and require a smoothing procedure: simulation efforts such as cubic-spline extrapolation and gathering multiple preruns are utilized for smoothing. We propose a simple and effective smoothing method that requires only one additional equation and two time-dependent parameters. As a result, our method produced the correct multicanonical energy function and succeeded in the flat sampling of a small biomolecule with reduced simulation effort.

3G1358 マルチカノニカル分子動力学シミュレーションによる抗原-抗体間のフレキシブル・ドッキング・シミュレーション(3G 蛋白質_構造4,日本生物物理学会第49回年会)

3G1358 マルチカノニカル分子動力学シミュレーションによる抗原-抗体間のフレキシブル・ドッキング・シミュレーション(3G 蛋白質_構造4,日本生物物理学会第49回年会)

Optimization of partial multicanonical molecular dynamics simulations applied to an alaninedipeptide in explicit water solvent

The partial multicanonical algorithm for molecular dynamics and Monte Carlo simulations samples a wide range of an important part of the potential energy. Although it is a strong technique for structure prediction of biomolecules, the choice of the partial potential energy has not been optimized. In order to find the best choice, partial multicanonical molecular dynamics simulations of an alanine dipeptide in explicit water solvent were performed with 15 trial choices for the partial potential energy. The best choice was found to be the sum of the electrostatic, Lennard-Jones, and torsion-angle potential energies between solute atoms. In this case, the partial multicanonical simulation sampled all of the local-minimum free-energy states of the P(II), C(5), α(R), α(P), α(L), and C states and visited these states most frequently. Furthermore, backbone dihedral angles ϕ and ψ rotated very well. It is also found that the most important term among these three terms is the electrostatic potential energy and that the Lennard-Jones term also helps the simulation to overcome the steric restrictions. On the other hand, multicanonical simulation sampled all of the six states, but visited these states fewer times. Conventional canonical simulation sampled only four of the six states: The P(II), C(5), α(R), and α(P) states.

Multicanonical molecular dynamics simulations combined with Metadynamics for the free energy landscape of a biomolecular system with high energy barriers

Multicanonical molecular-dynamics (McMD) simulation and Metadynamics (MetaD) are useful for obtaining the free-energies, and can be mutually complementary. We combined McMD with MetaD, and applied it to the conformational free energy calculations of a proline dipeptide. First, MetaD was performed along the dihedral angle at the prolyl bond and we obtained a coarse biasing potential. After adding the biasing potential to the dihedral angle potential energy, we conducted McMD with the modified potential energy. Enhanced sampling was achieved for all degrees-of-freedom, and the sampling of the dihedral angle space was facilitated. After reweighting, we obtained an accurate free energy landscape.

Coupled Folding and Binding of pKID with KIX Domain Investigated by Multicanonical Molecular Dynamics Simulation in Explicit Solvent

Intrinsically disordered proteins (IDPs) do not form any rigid tertiary structures alone. Most of them bind corresponding proteins and fold into an ordered structure to play important roles in biological functions such as signal transduction cascades. The phosphorylated kinase induced domain (pKID) is one of IDPs. The pKID adapts an ordered helical structure while binds to the KIX domain. This structural property of pKID is called “coupled folding and binding”. From nuclear magnetic resonance (NMR) studies a kinetics model of the coupled folding and binding has been proposed: there are four states of pKID (disordered, encounter complex, intermediate, and ordered helical structure). However, the details of these states at atomic level were still unclear.In order to obtain the free energy landscapes and the stable complex structures at various temperatures for the system, where pKID, the KIX domain, water and ions are included and they can interact with each other, multicanonical molecular dynamics (McMD) simulation was performed with the all-atom model in explicit solvent. McMD simulation is one of generalized ensemble methods, which can search conformational space much wider than a conventional molecular dynamics simulation, as well as the replica-exchange molecular dynamics (REMD). In this study, starting from completely disordered and unbound states of pKID, the helices of pKID were reproduced as approaching to the KIX domain at adequate low temperature. Additionally, we found a different binding mode from the NMR model. Interestingly, this binding mode is similar to that of the activation domain of the mixed lineage leukemia (MLL) transcription factor upon binding to the KIX domain.

Verifying trivial parallelization of multicanonical molecular dynamics for conformational sampling of a polypeptide in explicit water

Multicanonical molecular dynamics (McMD) simulation is an enhanced conformational sampling method. For more accelerated sampling, we examined a trajectory-parallelization method, which trivially integrates multiple McMD trajectories into one. This method decreases communications between computing nodes largely. We applied this method to conformational sampling of a seven-residue peptide in explicit water. Physical quantities converged well with those from a long McMD simulation in a wide temperature range. Thus, the integration can generate a canonical ensemble without performing the long simulation. The current method is useful for folding study of long polypeptides (proteins) in explicit water with massive parallelism.