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

Ingenuity in performing replica permutation: How to order the state labels for improving sampling efficiency

In the replica-permutation method, an advanced version of the replica-exchange method, all combinations of replicas and parameters are considered for parameter permutation, and a list of all the combinations is prepared. Here, we report that the temperature transition probability depends on how the list is created, especially in replica permutation with solute tempering (RPST). We found that the transition probabilities decrease at large replica indices when the combinations are sequentially assigned to the state labels as in the originally proposed list. To solve this problem, we propose to modify the list by randomly assigning the combinations to the state labels. We performed molecular dynamics simulations of amyloid-β(16-22) peptides using RPST with the "randomly assigned" list (RPST-RA) and RPST with the "sequentially assigned" list (RPST-SA). The results show the decreases in the transition probabilities in RPST-SA are eliminated, and the sampling efficiency is improved in RPST-RA.

Molecular Dynamics Simulation Studies on the Aggregation of Amyloid-β Peptides and Their Disaggregation by Ultrasonic Wave and Infrared Laser Irradiation

Alzheimer’s disease is understood to be caused by amyloid fibrils and oligomers formed by aggregated amyloid-β (Aβ) peptides. This review article presents molecular dynamics (MD) simulation studies of Aβ peptides and Aβ fragments on their aggregation, aggregation inhibition, amyloid fibril conformations in equilibrium, and disruption of the amyloid fibril by ultrasonic wave and infrared laser irradiation. In the aggregation of Aβ, a β-hairpin structure promotes the formation of intermolecular β-sheet structures. Aβ peptides tend to exist at hydrophilic/hydrophobic interfaces and form more β-hairpin structures than in bulk water. These facts are the reasons why the aggregation is accelerated at the interface. We also explain how polyphenols, which are attracting attention as aggregation inhibitors of Aβ peptides, interact with Aβ. An MD simulation study of the Aβ amyloid fibrils in equilibrium is also presented: the Aβ amyloid fibril has a different structure at one end from that at the other end. The amyloid fibrils can be destroyed by ultrasonic wave and infrared laser irradiation. The molecular mechanisms of these amyloid fibril disruptions are also explained, particularly focusing on the function of water molecules. Finally, we discuss the prospects for developing treatments for Alzheimer’s disease using MD simulations.

Replica permutation with solute tempering for molecular dynamics simulation and its application to the dimerization of amyloid-β fragments

We propose the replica permutation with solute tempering (RPST) by combining the replica-permutation method (RPM) and the replica exchange with solute tempering (REST). Temperature permutations are performed among more than two replicas in RPM, whereas temperature exchanges are performed between two replicas in the replica-exchange method (REM). The temperature transition in RPM occurs more efficiently than in REM. In REST, only the temperatures of the solute region, the solute temperatures, are exchanged to reduce the number of replicas compared to REM. Therefore, RPST is expected to be an improved method taking advantage of these methods. For comparison, we applied RPST, REST, RPM, and REM to two amyloid-β(16–22) peptides in explicit water. We calculated the transition ratio and the number of tunneling events in the temperature space and the number of dimerization events of amyloid-β(16–22) peptides. The results indicate that, in RPST, the number of replicas necessary for frequent random walks in the temperature and conformational spaces is reduced compared to the other three methods. In addition, we focused on the dimerization process of amyloid-β(16–22) peptides. The RPST simulation with a relatively small number of replicas shows that the two amyloid-β(16–22) peptides form the intermolecular antiparallel β-bridges due to the hydrophilic side-chain contact between Lys and Glu and hydrophobic side-chain contact between Leu, Val, and Phe, which stabilizes the dimer of the peptides.

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.

Molecular dynamics simulations of amyloid-β(16-22) peptide aggregation at air-water interfaces

Oligomers of amyloid-β (Aβ) peptides are known to be related to Alzheimer's disease, and their formation is accelerated at hydrophilic-hydrophobic interfaces, such as the cell membrane surface and air-water interface. Here, we report molecular dynamics simulations of aggregation of Aβ(16-22) peptides at air-water interfaces. First, 100 randomly distributed Aβ(16-22) peptides moved to the interface. The high concentration of peptides then accelerated their aggregation and formation of antiparallel β-sheets. Two layers of oligomers were observed near the interface. In the first layer from the interface, the oligomer with less β-bridges exposed the hydrophobic residues to the air. The second layer consisted of oligomers with more β-bridges that protruded into water. They are more soluble in water because the hydrophobic residues are covered by N- and C-terminal hydrophilic residues that are aligned well along the oligomer edge. These results indicate that amyloid protofibril formation mainly occurs in the second layer.

Role of Water Molecules and Helix Structure Stabilization in the Laser-Induced Disruption of Amyloid Fibrils Observed by Nonequilibrium Molecular Dynamics Simulations

Water plays a crucial role in the formation and destruction of biomolecular structures. The mechanism for destroying biomolecular structures was thought to be an active breaking of hydrogen bonds by water molecules. However, using nonequilibrium molecular dynamics simulations, in which an amyloid-β amyloid fibril was destroyed via infrared free-electron laser (IR-FEL) irradiation, we discovered a new mechanism, in which water molecules disrupt protein aggregates. The intermolecular hydrogen bonds formed by C═O and N-H in the fibril are broken at each pulse of laser irradiation. These bonds spontaneously re-form after the irradiation in many cases. However, when a water molecule happens to enter the gap between C═O and N-H, it inhibits the re-formation of the hydrogen bonds. Such sites become defects in the regularly aligned hydrogen bonds, from which all hydrogen bonds in the intermolecular β-sheet are broken as the fraying spreads. This role of water molecules is entirely different from other known mechanisms. This new mechanism can explain the recent experiments showing that the amyloid fibrils are not destroyed by laser irradiation under dry conditions. Additionally, we found that helix structures form more after the amyloid disruption; this is because the resonance frequency is different in a helix structure. Our findings provide a theoretical basis for the application of IR-FEL to the future treatment of amyloidosis.

Dimerization of α-Synuclein Fragments Studied by Isothermal-Isobaric Replica-Permutation Molecular Dynamics Simulation

Aggregates and fibrils of intrinsically disordered α-synuclein are associated with Parkinson's disease. Within a non-amyloid β component (NAC) spanning from the 61st to the 95th residue of α-synuclein, an 11-residue segment called NACore (₆₈GAVVTGVTAVA₇₈) is an essential region for both fibril formation and cytotoxicity. Although NACore peptides alone are known to form aggregates and amyloid fibrils, the mechanisms of aggregation and fibrillation remain unknown. This study investigated the dimerization process of NACore peptides as the initial stage of the aggregation and fibrillation processes. We performed an isothermal-isobaric replica-permutation molecular dynamics simulation, which is one of the efficient sampling methods, for the two NACore peptides in explicit water over 96 μs. The simulation succeeded in sampling a variety of dimer structures. An analysis of secondary structure revealed that most of the NACore dimers form intermolecular β-bridges. In particular, more antiparallel β-bridges were observed than parallel β-bridges. We also found that intramolecular secondary structures such as α-helix and antiparallel β-bridge are stabilized in the pre-dimer state. However, we identified that the intermolecular β-bridges tend to form directly between residues with no specific structure rather than via the intramolecular β-bridges. This is because the NACore peptides still have a low propensity to form the intramolecular secondary structures even though they are stabilized in the pre-dimer state.

Promotion and Inhibition of Amyloid-β Peptide Aggregation: Molecular Dynamics Studies

Aggregates of amyloid-β (Aβ) peptides are known to be related to Alzheimer’s disease. Their aggregation is enhanced at hydrophilic–hydrophobic interfaces, such as a cell membrane surface and air-water interface, and is inhibited by polyphenols, such as myricetin and rosmarinic acid. We review molecular dynamics (MD) simulation approaches of a full-length Aβ peptide, Aβ40, and Aβ(16–22) fragments in these environments. Since these peptides have both hydrophilic and hydrophobic amino acid residues, they tend to exist at the interfaces. The high concentration of the peptides accelerates the aggregation there. In addition, Aβ40 forms a β-hairpin structure, and this structure accelerates the aggregation. We also describe the inhibition mechanism of the Aβ(16–22) aggregation by polyphenols. The aggregation of Aβ(16–22) fragments is caused mainly by the electrostatic attraction between charged amino acid residues known as Lys16 and Glu22. Since polyphenols form hydrogen bonds between their hydroxy and carboxyl groups and these charged amino acid residues, they inhibit the aggregation.

Spatially-Decomposed Free Energy of Solvation Based on the Endpoint Density-Functional Method

A spatially resolved version of the density-functional method for solvation thermodynamics is presented by extending the free-energy functional previously established in the one-dimensional, energy representation and formulating a new expression in a mixed four-dimensional representation (three dimensions for position and one dimension for energy). The space was further divided into a set of discrete regions with respect to the relative position of a solvent molecule from the solute, and the spatially decomposed energetics of solvation were analyzed for small molecules with a methyl, amine, or hydroxyl group and alanine dipeptide in solvent water. It was observed that the density of the solvation free energy is weakly dependent on the solute site in the excluded-volume region and is distinctively favorable in the first shells of the solute atoms that can readily form hydrogen bonds with water. The solvent-reorganization term reduces faster with the separation from the solute than the direct interaction between the solute and solvent, and the latter governs the energetics in the second shell and outer regions. The sum of the contributions to the free energy from the excluded volume and first shell was found to deviate significantly from the total sum over all the regions, implying that the solvation free energy is not spatially localized near the solute in a quantitative sense. Still, a local description was shown to be valid as confirmed by the correlation of the total value of free energy with the corresponding value obtained by integrating the free-energy density to the second shell. The theoretical framework developed in the present work to spatially decompose the solvation free energy can thus be useful to identify stabilizing or destabilizing regions of solvent proximate to a solute and to analyze the role that the displacement of interfacial water plays in the thermodynamics of molecular association.

Understanding the conformational behaviour of Ac-Ala-NHMe in different media. A joint NMR and DFT study

The conformational behaviour of Ac-Ala-NHMe was studied in the gas-phase and in solution by theoretical calculations (B3LYP-D3/aug-cc-pVDZ level) and experimental (1)H NMR. The conformational preferences of this compound were shown to result from a complex interplay between the strengths of possible intramolecular hydrogen bonds, steric interactions, hyperconjugation, entropy effects and the overall dipole moments. The Ac-Ala-N(Me)2 derivative was studied in addition, to design a system akin to Ac-Ala-NHMe, but with disrupted intramolecular hydrogen bonds involving the -NHMe group, mimicking the effect of polar protic solvents.

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.

Transformation of a design peptide between the α-helix and β-hairpin structures using a helix-strand replica-exchange molecular dynamics simulation

We investigated the transformation between the α-helix and β-hairpin structures of an 18-residue design peptide, whose sequence is INYWLAHAKAGYIVHWTA. This peptide has both α-helix and β-hairpin structures in aqueous solution. For this purpose, we proposed the helix-strand replica-exchange method. This is one of the Hamiltonian replica-exchange methods in which we exchange parameters for umbrella potentials to enhance the α-helix or β-strand structure formation. We performed an all-atom helix-strand replica-exchange molecular dynamics (MD) simulation of this peptide in explicit water solvent with five replicas. Because the suitable umbrella potential was applied, the helix-strand replica-exchange MD simulation reproduced conformations closer to experimental conformations than a temperature replica-exchange MD simulation when the same numbers of the replicas were used, while the temperature replica-exchange MD simulation does not require bias along any specific order parameter. We calculated its free-energy landscape and revealed the transformation pathways between the α-helix and β-hairpin structures and the folding pathways from an extended structure. Although the fractions of the α-helix and β-hairpin structures are less than those obtained by the experiment, the free-energy difference between the two structures is calculated to be almost zero, which agrees with the experimental results.

Replica-Permutation Method with the Suwa-Todo Algorithm beyond the Replica-Exchange Method

We propose a new method for molecular dynamics and Monte Carlo simulations, which is referred to as the replica-permutation method (RPM), to realize more efficient sampling than the replica-exchange method (REM). In RPM, not only exchanges between two replicas but also permutations among more than two replicas are performed. Furthermore, instead of the Metropolis algorithm, the Suwa-Todo algorithm is employed for replica-permutation trials to minimize its rejection ratio. We applied RPM to particles in a double-well potential energy, Met-enkephalin in a vacuum, and a C-peptide analog of ribonuclease A in explicit water. For comparison purposes, replica-exchange molecular dynamics simulations were also performed. As a result, RPM sampled not only the temperature space but also the conformational space more efficiently than REM for all systems. From our simulations of C-peptide, we obtained the α-helix structure with salt bridges between Gly2 and Arg10, which is known in experiments. Calculating its free-energy landscape, the folding pathway was revealed from an extended structure to the α-helix structure with the salt bridges. We found that the folding pathway consists of the two steps: The first step is the "salt-bridge formation step," and the second step is the "α-helix formation step."

Coulomb replica-exchange method: handling electrostatic attractive and repulsive forces for biomolecules

We propose a new type of the Hamiltonian replica-exchange method (REM) for molecular dynamics (MD) and Monte Carlo simulations, which we refer to as the Coulomb REM (CREM). In this method, electrostatic charge parameters in the Coulomb interactions are exchanged among replicas while temperatures are exchanged in the usual REM. By varying the atom charges, the CREM overcomes free-energy barriers and realizes more efficient sampling in the conformational space than the REM. Furthermore, this method requires only a smaller number of replicas because only the atom charges of solute molecules are used as exchanged parameters. We performed Coulomb replica-exchange MD simulations of an alanine dipeptide in explicit water solvent and compared the results with those of the conventional canonical, replica exchange, and van der Waals REMs. Two force fields of AMBER parm99 and AMBER parm99SB were used. As a result, the CREM sampled all local-minimum free-energy states more frequently than the other methods for both force fields. Moreover, the Coulomb, van der Waals, and usual REMs were applied to a fragment of an amyloid-β peptide (Aβ) in explicit water solvent to compare the sampling efficiency of these methods for a larger system. The CREM sampled structures of the Aβ fragment more efficiently than the other methods. We obtained β-helix, α-helix, 3(10)-helix, β-hairpin, and β-sheet structures as stable structures and deduced pathways of conformational transitions among these structures from a free-energy landscape.

Generalized essential energy space random walks to more effectively accelerate solute sampling in aqueous environment

Molecular dynamics sampling can be enhanced via the promoting of potential energy fluctuations, for instance, based on a Hamiltonian modified with the addition of a potential-energy-dependent biasing term. To overcome the diffusion sampling issue, which reveals the fact that enlargement of event-irrelevant energy fluctuations may abolish sampling efficiency, the essential energy space random walk (EESRW) approach was proposed earlier. To more effectively accelerate the sampling of solute conformations in aqueous environment, in the current work, we generalized the EESRW method to a two-dimension-EESRW (2D-EESRW) strategy. Specifically, the essential internal energy component of a focused region and the essential interaction energy component between the focused region and the environmental region are employed to define the two-dimensional essential energy space. This proposal is motivated by the general observation that in different conformational events, the two essential energy components have distinctive interplays. Model studies on the alanine dipeptide and the aspartate-arginine peptide demonstrate sampling improvement over the original one-dimension-EESRW strategy; with the same biasing level, the present generalization allows more effective acceleration of the sampling of conformational transitions in aqueous solution. The 2D-EESRW generalization is readily extended to higher dimension schemes and employed in more advanced enhanced-sampling schemes, such as the recent orthogonal space random walk method.