Origin of the kinetic HDAC2-selectivity of an HDAC inhibitor.

A newly synthesized small molecule, KTT-1, exhibits kinetically selective inhibition of histone deacetylase 2, HDAC2, over its homologous enzyme, HDAC1. KTT-1 is hard to be released from the HDAC2/KTT-1 complex, compared to the HDAC1/KTT-1 complex and the residence time of KTT-1 in HDAC2 is longer than that in HDAC1. To explore the physical origin of this kinetic selectivity, we performed replica-exchange umbrella sampling molecular dynamics simulations for formation of both complexes. The calculated potentials of mean force suggest that KTT-1 is stably bound to HDAC2 and that it is easily disassociated from HDAC1. In the direct vicinity of the KTT-1 binding site in both enzymes, there exists a conserved loop consisting of four consecutive glycine residues (Gly304-307 for HDAC2; Gly299-302 for HDA1). The difference between the two enzymes comes from a single un-conserved residue behind this loop, namely, Ala268 in HDAC2 and Ser263 in HDAC1. The Ala268 contributes to the tight binding of KTT-1 to HDAC2 by the linear orientation of Ala268, Gly306, and one carbon atom in KTT-1. On the other hand, Ser263 cannot stabilize the binding of KTT-1 to HDAC1, because it is relatively further away from the glycine loop and because the directions of the two forces are not in line.

Generalized-ensemble method study: A helix-mimetic compound inhibits protein-protein interaction by long-range and short-range intermolecular interactions.

A heterocyclic compound mS-11 is a helix-mimetic designed to inhibit binding of an intrinsic disordered protein neural restrictive silence factor/repressor element 1 silencing factor (NRSF/REST) to a receptor protein mSin3B. We apply a generalized ensemble method, multi-dimensional virtual-system coupled molecular dynamics developed by ourselves recently, to a system consisting of mS-11 and mSin3B, and obtain a thermally equilibrated distribution, which is comprised of the bound and unbound states extensively. The lowest free-energy position of mS-11 coincides with the NRSF/REST position in the experimentally-determined NRSF/REST-mSin3B complex. Importantly, the molecular orientation of mS-11 is ordering in a wide region around mSin3B. The resultant binding scenario is: When mS-11 is distant from the binding site of mSin3B, mS-11 descends the free-energy slope toward the binding site maintaining the molecular orientation to be advantageous for binding. Then, finally a long and flexible hydrophobic sidechain of mS-11 fits into the binding site, which is the lowest-free-energy complex structure inhibiting NRSF/REST binding to mSin3B.

Determination of the structural ensemble of the molten globule state of a protein by computer simulations.

We have used computer simulations to investigate the structural nature of the molten globule (MG) state of canine milk lysozyme. To sample the conformational space efficiently, we performed replica-exchange umbrella sampling simulations with the radius of gyration as a reaction coordinate. We applied the Weighted Histogram Analysis Method to the trajectory of the simulations to obtain the potential of mean force, from which we identified representative structures corresponding to local minima in the free energy surface. The representative structures obtained in this way are in accord with the characteristics of the MG state reported previously by experimental studies. We conjecture that the MG state comprises a series of partially structured states undergoing relatively fast conformational interchange.

Replica sub-permutation method for molecular dynamics and monte carlo simulations.

We propose an improvement of the replica-exchange and replica-permutation methods, which we call the replica sub-permutation method (RSPM). Instead of considering all permutations, this method uses a new algorithm referred to as sub-permutation to perform parameter transition. The RSPM succeeds in reducing the number of combinations between replicas and parameters without the loss of sampling efficiency. For comparison, we applied the replica sub-permutation, replica-permutation, and replica-exchange methods to a ß-hairpin mini protein, chignolin, in explicit water. We calculated the transition ratio and number of tunneling events in the parameter space, the number of folding-unfolding events, the autocorrelation function, and the autocorrelation time as measures of sampling efficiency. The results indicate that among the three methods, the proposed RSPM is the most efficient in both parameter and conformational spaces. © 2019 Wiley Periodicals, Inc.

Multidimensional virtual-system coupled canonical molecular dynamics to compute free-energy landscapes of peptide multimer assembly.

An enhanced-sampling method termed multidimensional virtual-system coupled canonical molecular dynamics (mD-VcMD) method is developed. In many cases, generalized-ensemble methods realizing enhanced sampling, for example, adaptive umbrella sampling, apply an effective potential, which is derived from temporarily assumed canonical distribution as a function of one or more arbitrarily defined reaction coordinates. However, it is not straightforward to estimate the appropriate canonical distribution, especially for cases applying multiple reaction coordinates. The current method, mD-VcMD, does not rely on the form of the canonical distribution. Therefore, it is practically useful to explore a high-dimensional reaction-coordinate space. In this article, formulation of mD-VcMD and its evaluation with the simple molecular models consisting of three or four alanine peptides are presented. We confirmed that mD-VcMD efficiently searched 2D and 3D reaction-coordinate spaces defined as interpeptide distances. Direct comparisons with results of long-term canonical MD simulations revealed that mD-VcMD produces correct canonical ensembles. © 2019 Wiley Periodicals, Inc.

Molecular dynamics simulations of biological membranes and membrane proteins using enhanced conformational sampling algorithms.

This paper reviews various enhanced conformational sampling methods and explicit/implicit solvent/membrane models, as well as their recent applications to the exploration of the structure and dynamics of membranes and membrane proteins. Molecular dynamics simulations have become an essential tool to investigate biological problems, and their success relies on proper molecular models together with efficient conformational sampling methods. The implicit representation of solvent/membrane environments is reasonable approximation to the explicit all-atom models, considering the balance between computational cost and simulation accuracy. Implicit models can be easily combined with replica-exchange molecular dynamics methods to explore a wider conformational space of a protein. Other molecular models and enhanced conformational sampling methods are also briefly discussed. As application examples, we introduce recent simulation studies of glycophorin A, phospholamban, amyloid precursor protein, and mixed lipid bilayers and discuss the accuracy and efficiency of each simulation model and method. This article is part of a Special Issue entitled: Membrane Proteins edited by J.C. Gumbart and Sergei Noskov.

Conformational changes of ubiquitin under high pressure conditions: A pressure simulated tempering molecular dynamics study.

Molecular dynamics simulations for the system of ubiquitin were performed with pressure simulated tempering to study pressure-induced conformational changes of ubiquitin. The pressure dependence of ubiquitin was analyzed in a wide range of pressure from atmospheric pressure (0.1 MPa) to 1.0 GPa. The fluctuation of the distance between amino-acid residues and the distribution of a largely fluctuating distance were calculated. The large fluctuation of the L8-E34 distance induced by pressure means that the conformation of ubiquitin changes under high pressure conditions. There were more water molecules near the largely fluctuating region at high pressure than at low pressure. The pressure dependence of interaction energies among ubiquitin and water was also calculated to investigate the role of water for the pressure-induced conformational changes of ubiquitin. The protein-water interaction is important when the conformation of ubiquitin changes at high pressure. © 2017 Wiley Periodicals, Inc.

Enhanced conformational sampling to visualize a free-energy landscape of protein complex formation.

We introduce various, recently developed, generalized ensemble methods, which are useful to sample various molecular configurations emerging in the process of protein-protein or protein-ligand binding. The methods introduced here are those that have been or will be applied to biomolecular binding, where the biomolecules are treated as flexible molecules expressed by an all-atom model in an explicit solvent. Sampling produces an ensemble of conformations (snapshots) that are thermodynamically probable at room temperature. Then, projection of those conformations to an abstract low-dimensional space generates a free-energy landscape. As an example, we show a landscape of homo-dimer formation of an endothelin-1-like molecule computed using a generalized ensemble method. The lowest free-energy cluster at room temperature coincided precisely with the experimentally determined complex structure. Two minor clusters were also found in the landscape, which were largely different from the native complex form. Although those clusters were isolated at room temperature, with rising temperature a pathway emerged linking the lowest and second-lowest free-energy clusters, and a further temperature increment connected all the clusters. This exemplifies that the generalized ensemble method is a powerful tool for computing the free-energy landscape, by which one can discuss the thermodynamic stability of clusters and the temperature dependence of the cluster networks.

On the use of mass scaling for stable and efficient simulated tempering with molecular dynamics.

Simulated tempering (ST) is a generalized-ensemble algorithm that employs trajectories exploring a range of temperatures to effectively sample rugged energy landscapes. When implemented using the molecular dynamics method, ST can require the use of short time steps for ensuring the stability of trajectories at high temperatures. To address this shortcoming, a mass-scaling ST (MSST) method is presented in which the particle mass is scaled in proportion to the temperature. Mass scaling in the MSST method leads to velocity distributions that are independent of temperature and eliminates the need for velocity scaling after the accepted temperature updates that are required in conventional ST simulations. The homogeneity in time scales with changing temperature improves the stability of simulations and allows for the use of longer time steps at high temperatures. As a result, the MSST is found to be more efficient than the standard ST method, particularly for cases in which a large temperature range is employed. © 2016 Wiley Periodicals, Inc.

Simulated tempering based on global balance or detailed balance conditions: Suwa-Todo, heat bath, and Metropolis algorithms.

Simulated tempering (ST) is a useful method to enhance sampling of molecular simulations. When ST is used, the Metropolis algorithm, which satisfies the detailed balance condition, is usually applied to calculate the transition probability. Recently, an alternative method that satisfies the global balance condition instead of the detailed balance condition has been proposed by Suwa and Todo. In this study, ST method with the Suwa-Todo algorithm is proposed. Molecular dynamics simulations with ST are performed with three algorithms (the Metropolis, heat bath, and Suwa-Todo algorithms) to calculate the transition probability. Among the three algorithms, the Suwa-Todo algorithm yields the highest acceptance ratio and the shortest autocorrelation time. These suggest that sampling by a ST simulation with the Suwa-Todo algorithm is most efficient. In addition, because the acceptance ratio of the Suwa-Todo algorithm is higher than that of the Metropolis algorithm, the number of temperature states can be reduced by 25% for the Suwa-Todo algorithm when compared with the Metropolis algorithm.

Molecular dynamics of the structural changes of helical peptides induced by pressure.

An AK16 peptide and a C-peptide analog are experimentally known to form more helical structures under high-pressure conditions than those at atmospheric pressure, even though most proteins usually unfold at high pressure. To understand the pressure-induced structural changes of the two peptides, molecular dynamics simulations with the simulated tempering method for the isobaric-isothermal ensemble were performed in a wide pressure range from 0.1 MPa to 1.4 GPa. We found that the fraction of the folded state decreases once and then increases with increasing pressure for both peptides. The partial molar volume change of both peptides from the folded state to the unfolded state increases monotonically from a negative value to a positive value as pressure increases. By calculating the radius of gyration and interatomic distances of the AK16 peptide and the C-peptide analog, we found that these peptides are compressed under high-pressure conditions, which causes the folded state to be more stable at high pressure. Furthermore, we found that the salt bridge of the C-peptide analog is broken under high pressure.

Adaptive lambda square dynamics simulation: an efficient conformational sampling method for biomolecules.

A novel, efficient sampling method for biomolecules is proposed. The partial multicanonical molecular dynamics (McMD) was recently developed as a method that improved generalized ensemble (GE) methods to focus sampling only on a part of a system (GEPS); however, it was not tested well. We found that partial McMD did not work well for polylysine decapeptide and gave significantly worse sampling efficiency than a conventional GE. Herein, we elucidate the fundamental reason for this and propose a novel GEPS, adaptive lambda square dynamics (ALSD), which can resolve the problem faced when using partial McMD. We demonstrate that ALSD greatly increases the sampling efficiency over a conventional GE. We believe that ALSD is an effective method and is applicable to the conformational sampling of larger and more complicated biomolecule systems.

In silico concurrent multisite pH titration in proteins.

The concurrent proton binding at multiple sites in macromolecules such as proteins and nucleic acids is an important yet challenging problem in biochemistry. We develop an efficient generalized Hamiltonian approach to attack this issue. Based on the previously developed generalized-ensemble methods, an effective potential energy is constructed which combines the contributions of all (relevant) protonation states of the molecule. The effective potential preserves important phase regions of all states and, thus, allows efficient sampling of these regions in one simulation. The need for intermediate states in alchemical free energy simulations is greatly reduced. Free energy differences between different protonation states can be determined accurately and enable one to construct the grand canonical partition function. Therefore, the complicated concurrent multisite proton titration process of protein molecules can be satisfactorily simulated. Application of this method to the simulation of the pKa of Glu49, Asp50, and C-terminus of bovine pancreatic trypsin inhibitor shows reasonably good agreement with published experimental work. This method provides an unprecedented vivid picture of how different protonation states change their relative population upon pH titration. We believe that the method will be very useful in deciphering the molecular mechanism of pH-dependent biomolecular processes in terms of a detailed atomistic description.

Why Is Arginine the Only Amino Acid That Inhibits Polyglutamine Monomers from Taking on Toxic Conformations?

Polyglutamine (polyQ) diseases are devastating neurodegenerative disorders characterized by abnormal expansion of glutamine repeats within specific proteins. The aggregation of polyQ proteins is a critical pathological hallmark of these diseases. Arginine was identified as a promising inhibitory compound because it prevents polyQ-protein monomers from forming intra- and intermolecular ß-sheet structures and hinders polyQ proteins from aggregating to form oligomers. Such an aggregation inhibitory effect was not observed in other amino acids. However, the underlying molecular mechanism of the aggregation inhibition and the factors that differentiate arginine from other amino acids, in terms of the inhibition of the polyQ-protein aggregation, remain poorly understood. Here, we performed replica-permutation molecular dynamics simulations to elucidate the molecular mechanism by which arginine inhibits the formation of the intramolecular ß-sheet structure of a polyQ monomer. We found that the intramolecular ß-sheet structure with more than four ß-bridges of the polyQ monomer with arginine is more unstable than without any ligand and with lysine. We also found that arginine has 1.6-2.1 times more contact with polyQ than lysine. In addition, we revealed that arginine forms more hydrogen bonds with the main chain of the polyQ monomer than lysine. More hydrogen bonds formed between arginine and polyQ inhibit polyQ from forming the long intramolecular ß-sheet structure. It is known that intramolecular ß-sheet structure enhances intermolecular ß-sheet structure between proteins. These effects are thought to be the reason for the inhibition of polyQ aggregation. This study provides insights into the molecular events underlying arginine's inhibition of polyQ-protein aggregation.

Binding free-energy landscapes of small molecule binder and non-binder to FMN riboswitch: All-atom molecular dynamics.

A small and flexible molecule, ribocil A (non-binder) or B (binder), binds to the deep pocket of the aptamer domain of the FMN riboswitch, which is an RNA molecule. This binding was studied by mD-VcMD, which is a generalized-ensemble simulation method. Ribocil A and B are structurally similar because they are optical isomers to each other. In the initial conformation of simulation, the ligands and the aptamer were completely dissociated in explicit solvent. The aptamer-ribocil B binding was stronger than the aptamer-ribocil A binding, which agrees with experiments. The computed free-energy landscape for the aptamer-ribocil B binding was funnel-like, whereas that for the aptamer-ribocil A binding was rugged. When passing through the gate (named "front gate") of the binding pocket, each ligand interacted with bases of the riboswitch by non-native π-π stackings, and the stackings restrained the ligand's orientation to be advantageous to reach the binding site smoothly. When the ligands reached the binding site in the pocket, the non-native stackings were replaced by the native stackings. The ligand's orientation restriction is discussed referring to a selection mechanism reported in an earlier work on a drug-GPCR interaction. The present simulation showed another pathway leading the ligands to the binding site. The gate ("rear gate") for this pathway was located completely opposite to the front gate on the aptamer's surface. However, the approach from the rear gate required overcoming a free-energy barrier regarding ligand's rotation before reaching the binding site.

Key Residue for Aggregation of Amyloid-ß Peptides.

It is known that oligomers of amyloid-ß (Aß) peptide are associated with Alzheimer's disease. Aß has two isoforms: Aß40 and Aß42. Although the difference between Aß40 and Aß42 is only two additional C-terminal residues, Aß42 aggregates much faster than Aß40. It is unknown what role the C-terminal two residues play in accelerating aggregation. Since Aß42 is more toxic than Aß40, its oligomerization process needs to be clarified. Moreover, clarifying the differences between the oligomerization processes of Aß40 and Aß42 is essential to elucidate the key factors of oligomerization. Therefore, to investigate the dimerization process, which is the early oligomerization process, Hamiltonian replica-permutation molecular dynamics simulations were performed for Aß40 and Aß42. We identified a key residue, Arg5, for the Aß42 dimerization. The two additional residues in Aß42 allow the C-terminus to form contact with Arg5 because of the electrostatic attraction between them, and this contact stabilizes the ß-hairpin. This ß-hairpin promotes dimer formation through the intermolecular ß-bridges. Thus, we examined the effects of amino acid substitutions of Arg5, thereby confirming that the mutations remarkably suppressed the aggregation of Aß42. Moreover, the mutations of Arg5 suppressed the Aß40 aggregation. It was found by analyzing the simulations that Arg5 is important for Aß40 to form intermolecular contacts. Thus, it was clarified that the role of Arg5 in the oligomerization process varies due to the two additional C-terminal residues.

All-Atom Molecular Dynamics Simulation Methods for the Aggregation of Protein and Peptides: Replica Exchange/Permutation and Nonequilibrium Simulations.

Protein aggregates are associated with more than 40 serious human diseases. To understand the formation mechanism of protein aggregates at atomic level, all-atom molecular dynamics (MD) simulation is a powerful computational tool. In this chapter, we review the all-atom MD simulation methods that are useful for study on the protein aggregation. We first explain conventional MD simulation methods in physical statistical ensembles, such as the canonical and isothermal-isobaric ensembles. We then describe the generalized-ensemble algorithms such as replica-exchange and replica-permutation MD methods. These methods can overcome a difficulty, in which simulations tend to get trapped in local-minimum free-energy states. Finally we explain the nonequilibrium MD method. Some simulation results based on these methods are also presented.

GA-guided mD-VcMD: A genetic-algorithm-guided method for multi-dimensional virtual-system coupled molecular dynamics.

We introduced a conformational sampling method in an earlier report: The multi-dimensional virtual-system coupled molecular dynamics (mD-VcMD) enhances conformational sampling of a biomolecular system by computer simulations. Herein, new sampling method, a subzone-based mD-VcMD, is presented as an extension of mD-VcMD. Then, the subzone-based method is extended further using a genetic algorithm (GA) named the GA-guided mD-VcMD. In these methods, iterative simulation runs are performed to increase the sampled region gradually. The new methods have the following benefits: (1) They are free from a production run: i.e., all snapshots from all iterations are useful for analyses. (2) They are free from fine tuning of a weight function (probability distribution function or potential of mean force). (3) A canonical ensemble (i.e., a thermally equilibrated ensemble) is generated from a simple procedure. A thermodynamic weight is assigned to each snapshot. (4) Selective sampling can be performed for particularly addressing a poorly sampled region without breaking the proportion of the canonical ensemble if the poorly sampled conformational region emerges in sampling. By applying the methods to a simple system that involves an energy barrier between potential-energy minima, we demonstrated that the new methods have considerably higher sampling efficiency than the original mD-VcMD does.

myPresto/omegagene 2020: a molecular dynamics simulation engine for virtual-system coupled sampling.

The molecular dynamics (MD) method is a promising approach for investigating the molecular mechanisms of microscopic phenomena. In particular, generalized ensemble MD methods can efficiently explore the conformational space with a rugged free-energy surface. However, the implementation and acquisition of technical knowledge for each generalized ensemble MD method are not straightforward for end-users. Here, we present a new version of the myPresto/omegagene software, which is an MD simulation engine tailored for a series of generalized ensemble methods, which are virtual-system coupled multicanonical MD (V-McMD), virtual-system coupled adaptive umbrella sampling (V-AUS), and virtual-system coupled canonical MD (VcMD). This program has been applied in several studies analyzing free-energy landscapes of a variety of molecular systems with all-atom simulations. The updated version provides new functionality for coarse-grained simulations powered by the hydrophobicity scale method. The software package includes a step-by-step tutorial document for enhanced conformational sampling of the poly-glutamine (poly-Q) oligomer expressed as a one-bead per residue model. The myPresto/omegagene software is freely available at the following URL: https://github.com/kotakasahara/omegagene under the Apache2 license.

Molecular simulations by generalized-ensemble algorithms in isothermal-isobaric ensemble.

Generalized-ensemble algorithms are powerful techniques for investigating biomolecules such as protein, DNA, lipid membrane, and glycan. The generalized-ensemble algorithms were originally developed in the canonical ensemble. On the other hand, not only temperature but also pressure is controlled in experiments. Additionally, pressure is used as perturbation to study relationship between function and structure of biomolecules. For this reason, it is important to perform efficient conformation sampling based on the isothermal-isobaric ensemble. In this article, we review a series of the generalized-ensemble algorithms in the isothermal-isobaric ensemble: multibaric-multithermal, pressure- and temperature-simulated tempering, replica-exchange, and replica-permutation methods. These methods achieve more efficient simulation than the conventional isothermal-isobaric simulation. Furthermore, the isothermal-isobaric generalized-ensemble simulation samples conformations of biomolecules from wider range of temperature and pressure. Thus, we can estimate physical quantities more accurately at any temperature and pressure values. The applications to the biomolecular system are also presented.