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

Dissociation process of polyalanine aggregates by free electron laser irradiation

Polyalanine (polyA) disease-causative proteins with an expansion of alanine repeats can be aggregated. Although curative treatments for polyA diseases have not been explored, the dissociation of polyA aggregates likely reduces the cytotoxicity of polyA. Mid-infrared free electron laser (FEL) successfully dissociated multiple aggregates. However, whether the FEL dissociates polyA aggregates like other aggregates has not been tested. Here, we show that FEL at 6.1 μm experimentally weakened the extent of aggregation of a peptide with 13 alanine repeats (13A), and the irradiated 13A exerted lesser cytotoxicity to neuron-like cells than non-irradiated 13A. Then, we applied molecular dynamics (MD) simulation to follow the dissociation process by FEL. We successfully observed how the intermolecular β-sheet of polyA aggregates was dissociated and separated into monomers with helix structures upon FEL irradiation. After the dissociation by FEL, water molecules inhibited the reformation of polyA aggregates. We recently verified the same dissociation process using FEL-treated amyloid-β aggregates. Thus, a common mechanism underlies the dissociation of different protein aggregates that cause different diseases, polyA disease and Alzheimer's disease. However, MD simulation indicated that polyA aggregates are less easily dissociated than amyloid-β aggregates and require longer laser irradiation due to hydrophobic alanine repeats.

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.

State-of-the-Art Molecular Dynamics Simulation Studies of RNA-Dependent RNA Polymerase of SARS-CoV-2

Molecular dynamics (MD) simulations are powerful theoretical methods that can reveal biomolecular properties, such as structure, fluctuations, and ligand binding, at the level of atomic detail. In this review article, recent MD simulation studies on these biomolecular properties of the RNA-dependent RNA polymerase (RdRp), which is a multidomain protein, of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) are presented. Although the tertiary structures of RdRps in SARS-CoV-2 and SARS-CoV are almost identical, the RNA synthesis activity of RdRp of SARS-CoV is higher than SARS-CoV-2. Recent MD simulations observed a difference in the dynamic properties of the two RdRps, which may cause activity differences. RdRp is also a drug target for Coronavirus disease 2019 (COVID-19). Nucleotide analogs, such as remdesivir and favipiravir, are considered to be taken up by RdRp and inhibit RNA replication. Recent MD simulations revealed the recognition mechanism of RdRp for these drug molecules and adenosine triphosphate (ATP). The ligand-recognition ability of RdRp decreases in the order of remdesivir, favipiravir, and ATP. As a typical recognition process, it was found that several lysine residues of RdRp transfer these ligand molecules to the binding site such as a “bucket brigade.” This finding will contribute to understanding the mechanism of the efficient ligand recognition by RdRp. In addition, various simulation studies on the complexes of SARS-CoV-2 RdRp with several nucleotide analogs are reviewed, and the molecular mechanisms by which these compounds inhibit the function of RdRp are discussed. The simulation studies presented in this review will provide useful insights into how nucleotide analogs are recognized by RdRp and inhibit the RNA replication.

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.

Dynamic properties of SARS-CoV and SARS-CoV-2 RNA-dependent RNA polymerases studied by molecular dynamics simulations

One of the promising drug targets against COVID-19 is an RNA-dependent RNA polymerase (RdRp) of SARS-CoV-2. The tertiary structures of the SARS-CoV-2 and SARS-CoV RdRps are almost the same. However, the RNA-synthesizing activity of the SARS-CoV RdRp is higher than that of the SARS-CoV-2 RdRp. We performed molecular dynamics simulations and found differences in their dynamic properties. In the SARS-CoV RdRp, motifs A-G, which form the active site, are up to 63% closer to each other. We also observed cooperative domain motion in the SARS-CoV RdRp. Such dynamic differences may cause the activity differences between the two RdRps.

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.

Energetics and kinetics of substrate analog-coupled staphylococcal nuclease folding revealed by a statistical mechanical approach

Protein conformational changes associated with ligand binding, especially those involving intrinsically disordered proteins, are mediated by tightly coupled intra- and intermolecular events. Such reactions are often discussed in terms of two limiting kinetic mechanisms, conformational selection (CS), where folding precedes binding, and induced fit (IF), where binding precedes folding. It has been shown that coupled folding/binding reactions can proceed along both CS and IF pathways with the flux ratio depending on conditions such as ligand concentration. However, the structural and energetic basis of such complex reactions remains poorly understood. Therefore, we used experimental, theoretical, and computational approaches to explore structural and energetic aspects of the coupled-folding/binding reaction of staphylococcal nuclease in the presence of the substrate analog adenosine-3',5'-diphosphate. Optically monitored equilibrium and kinetic data, combined with a statistical mechanical model, gave deeper insight into the relative importance of specific and Coulombic protein-ligand interactions in governing the reaction mechanism. We also investigated structural aspects of the reaction at the residue level using NMR and all-atom replica-permutation molecular dynamics simulations. Both approaches yielded clear evidence for accumulation of a transient protein-ligand encounter complex early in the reaction under IF-dominant conditions. Quantitative analysis of the equilibrium/kinetic folding revealed that the ligand-dependent CS-to-IF shift resulted from stabilization of the compact transition state primarily by weakly ligand-dependent Coulombic interactions with smaller contributions from specific binding energies. At a more macroscopic level, the CS-to-IF shift was represented as a displacement of the reaction "route" on the free energy surface, which was consistent with a flux analysis.

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.