Sparsity-weighted outlier FLOODing (OFLOOD) method: Efficient rare event sampling method using sparsity of distribution

Preferential Door for Ligand Binding and Unbinding Pathways in Inhibited Human Acetylcholinesterase

Rising global population and increased food demands have resulted in the increased use of organophosphate pesticides (OPs), leading to toxin accumulation and transmission to humans. Pralidoxime (2-PAM), an FDA-approved drug, serves as an antidote for OP therapy. However, the atomic-level detoxification mechanisms regarding the design of novel antidotes remain unclear. This is the first study to examine the binding and unbinding pathways of 2-PAM to human acetylcholinesterase (HuAChE) through three identified doors using an enhanced sampling method called ligand-binding parallel cascade selection molecular dynamics (LB-PaCS-MD). Remarkably, LB-PaCS-MD could identify a predominant in-line binding mechanism through the acyl door at 63.79% ± 6.83%, also implicating it in a potential unbinding route (90.14% ± 4.22%). Interestingly, crucial conformational shifts in key residues, W86, Y341, and Y449, and the Ω loop significantly affect door dynamics and ligand binding modes. The LB-PaCS-MD technique can study ligand-binding pathways, thereby contributing to the design of antidotes and covalent drugs.

PaCS-Toolkit: Optimized Software Utilities for Parallel Cascade Selection Molecular Dynamics (PaCS-MD) Simulations and Subsequent Analyses

Parallel cascade selection molecular dynamics (PaCS-MD) is an enhanced conformational sampling method conducted as a "repetition of time leaps in parallel worlds", comprising cycles of multiple molecular dynamics (MD) simulations performed in parallel and selection of the initial structures of MDs for the next cycle. We developed PaCS-Toolkit, an optimized software utility enabling the use of different MD software and trajectory analysis tools to facilitate the execution of the PaCS-MD simulation and analyze the obtained trajectories, including the preparation for the subsequent construction of the Markov state model. PaCS-Toolkit is coded with Python, is compatible with various computing environments, and allows for easy customization by editing the configuration file and specifying the MD software and analysis tools to be used. We present the software design of PaCS-Toolkit and demonstrate applications of PaCS-MD variations: original targeted PaCS-MD to peptide folding; rmsdPaCS-MD to protein domain motion; and dissociation PaCS-MD to ligand dissociation from adenosine A2A receptor.

Protein Structure Validation Derives a Smart Conformational Search in a Physically Relevant Configurational Subspace

Since proteins perform biological functions through their dynamic properties, molecular dynamics (MD) simulation is a sophisticated strategy for investigating their functions. Analyses of trajectories provide statistical information about a specific protein as a free-energy landscape (FEL). However, the timescale of normal MD is shorter than that of biological functions, resulting in statistically insufficient conformational sampling, finally leading to unreliable FEL calculation. To search for a broad configurational subspace, an external bias is imposed on a target protein as biased sampling. However, its regulation is challenging because the optimal strength of the perturbation is unknown. Furthermore, a physically irrelevant configurational subspace was searched when imposing an inappropriate external bias. To address this issue, we newly proposed an external biased regulation scheme known as the G-factor external bias limiter (GERBIL). In GERBIL, protein configurations generated by external bias are structurally validated by an indicator (G-factor), enabling the search for a physically relevant subspace. In addition to biased sampling, nonbiased sampling might search for a physically irrelevant configurational subspace because repeating multiple MD simulations from several initial structures tends to search for an overly broad configurational subspace. For this issue, the structural qualities of configurations generated by nonbiased sampling have not been investigated. Therefore, we confirmed whether the G-factor screened the collapsed (low-quality) configurations generated by nonbiased sampling. To address this issue, the outlier flooding method (OFLOOD) was adopted in GERBIL as a nonbiased sampling method, which is referred to as OFLOOD-GERBIL. OFLOOD rapidly expands a configurational subspace by resampling the rarely occurring states of a given protein and tends to search an overly broad subspace. Thus, we considered that GERBIL might improve the excessive conformational search of OFLOOD for a physically irrelevant configurational subspace. As a demonstration, OFLOOD and OFLOOD-GERBIL were applied to a globular protein (T4 lysozyme) and their conformational search qualities were assessed. Based on our assessment, normal OFLOOD without the outlier validation frequently sampled low-quality configurations, whereas OFLOOD-GERBIL with the outlier validation intensively sampled high-quality configurations. In conclusion, OFLOOD-GERBIL derives a smart conformational search in a physically relevant configurational subspace, indicating that protein structure validation works in both nonbiased and biased sampling methods.

The role of ATP in solubilizing RNA-binding protein fused in sarcoma

Intrinsically disordered protein (IDP) plays an important role in liquid-liquid phase separation (LLPS). RNA-binding protein fused in sarcoma (FUS) is a well-studied IDP that induces LLPS since its low-complexity core region (FUS-LC-core) is essential for droplet formation through contacts between FUS-LC-cores. Several experimental studies have reported that adenosine triphosphate (ATP) concentrations modulate LLPS-driven droplet formation through the dissolution of FUS. To elucidate the role of ATP in this dissolution, microsecond-order all-atom molecular dynamics (MD) simulations were performed for a crowded system of FUS-LC-cores in the presence of multiple ATP molecules. Our analysis revealed that the adenine group of ATP frequently contacted the FUS-LC-core, and the phosphoric acid group of ATP was exposed to the external solvent, which promoted both hydration and solubilization of FUS.

Structural Validation by the G-Factor Properly Regulates Boost Potentials Imposed in Conformational Sampling of Proteins

Free energy landscapes (FELs) of proteins are indispensable for evaluating thermodynamic properties. Molecular dynamics (MD) simulation is a computational method for calculating FELs; however, conventional MD simulation frequently fails to search a broad conformational subspace due to its accessible timescale, which results in the calculation of an unreliable FEL. To search a broad subspace, an external bias can be imposed on a protein system, and biased sampling tends to cause a strong perturbation that might collapse the protein structures, indicating that the strength of the external bias should be properly regulated. This regulation can be challenging, and empirical parameters are frequently employed to impose an optimal bias. To address this issue, several methods regulate the external bias by referring to system energies. Herein, we focused on protein structural information for this regulation. In this study, a well-established structural indicator (the G-factor) was used to obtain structural information. Based on the G-factor, we proposed a scheme for regulating biased sampling, which is referred to as a G-factor-based external bias limiter (GERBIL). With GERBIL, the configurations were structurally validated by the G-factor during biased sampling. As an example of biased sampling, an accelerated MD (aMD) simulation was adopted in GERBIL (aMD-GERBIL), whereby the aMD simulation was repeatedly performed by increasing the strength of the boost potential. Furthermore, the configurations sampled by the aMD simulation were structurally validated by their G-factor values, and aMD-GERBIL stopped increasing the strength of the boost potential when the sampled configurations were regarded as low-quality (collapsed) structures. This structural validation is regarded as a "Brake" of the boost potential. For demonstrations, aMD-GERBIL was applied to globular proteins (ribose binding and maltose-binding proteins) to promote their large-amplitude open-closed transitions and successfully identify their domain motions.

Ligand Binding Path Sampling Based on Parallel Cascade Selection Molecular Dynamics: LB-PaCS-MD

Parallel cascade selection molecular dynamics (PaCS-MD) is a rare-event sampling method that generates transition pathways between a reactant and product. To sample the transition pathways, PaCS-MD repeats short-time MD simulations from important configurations as conformational resampling cycles. In this study, PaCS-MD was extended to sample ligand binding pathways toward a target protein, which is referred to as LB-PaCS-MD. In a ligand-concentrated environment, where multiple ligand copies are randomly arranged around the target protein, LB-PaCS-MD allows for the frequent sampling of ligand binding pathways. To select the important configurations, we specified the center of mass (COM) distance between each ligand and the relevant binding site of the target protein, where snapshots generated by the short-time MD simulations were ranked by their COM distance values. From each cycle, snapshots with smaller COM distance values were selected as the important configurations to be resampled using the short-time MD simulations. By repeating conformational resampling cycles, the COM distance values gradually decreased and converged to constants, meaning that a set of ligand binding pathways toward the target protein was sampled by LB-PaCS-MD. To demonstrate relative efficiency, LB-PaCS-MD was applied to several proteins, and their ligand binding pathways were sampled more frequently than conventional MD simulations.

Edge expansion parallel cascade selection molecular dynamics simulation for investigating large-amplitude collective motions of proteins

We propose edge expansion parallel cascade selection molecular dynamics (eePaCS-MD) as an efficient adaptive conformational sampling method to investigate the large-amplitude motions of proteins without prior knowledge of the conformational transitions. In this method, multiple independent MD simulations are iteratively conducted from initial structures randomly selected from the vertices of a multi-dimensional principal component subspace. This subspace is defined by an ensemble of protein conformations sampled during previous cycles of eePaCS-MD. The edges and vertices of the conformational subspace are determined by solving the "convex hull problem." The sampling efficiency of eePaCS-MD is achieved by intensively repeating MD simulations from the vertex structures, which increases the probability of rare event occurrence to explore new large-amplitude collective motions. The conformational sampling efficiency of eePaCS-MD was assessed by investigating the open-close transitions of glutamine binding protein, maltose/maltodextrin binding protein, and adenylate kinase and comparing the results to those obtained using related methods. In all cases, the open-close transitions were simulated in ∼10 ns of simulation time or less, offering 1-3 orders of magnitude shorter simulation time compared to conventional MD. Furthermore, we show that the combination of eePaCS-MD and accelerated MD can further enhance conformational sampling efficiency, which reduced the total computational cost of observing the open-close transitions by at most 36%.

Selection Rules for Outliers in Outlier Flooding Method Regulate Its Conformational Sampling Efficiency

The outlier flooding method (OFLOOD) has been proposed as an enhanced conformational sampling method of proteins. In OFLOOD, rarely occurring states of proteins are detected as sparse conformational distributions (outliers) with a clustering algorithm. The detected outliers are intensively resampled with short-time molecular dynamics (MD) simulations. As a set of cycles, OFLOOD repeats selections of outliers and their conformational resampling. Herein, as an essential issue to be tackled to perform OFLOOD efficiently, a selection rule for outliers should be carefully specified. Generally, many outliers are detected from distributions on conformational subspaces with the clustering. Judging from its computational costs, it is unreasonable to select all the detected outliers upon the conformational resampling. Therefore, it is important to consider which outliers should be selected from the sparse distributions when restarting their short-time MD simulations with limited computational costs. In this sense, we investigated the conformational sampling efficiency of OFLOOD by changing the selection rules for outliers. To address the conformational sampling efficiency of OFLOOD depending on its selection rules, outliers to be resampled were selected by focusing their probability occurrences (populations of outliers). As a comparison, a random selection rule for outliers was also considered. Through the present assessment, the random selection of outliers showed the most efficient conformational sampling efficiency compared to the other OFLOOD trials using the biased selection rules, indicating that a variety of outliers should be selected and resampled during the OFLOOD cycles. In conclusion, the random outlier selection rule is the best strategy to perform OFLOOD efficiently.

How low-resolution structural data predict the conformational changes of a protein: a study on data-driven molecular dynamics simulations

Parallel cascade selection molecular dynamics (PaCS-MD) is a conformational sampling method for generating transition pathways between a given reactant and a product. PaCS-MD repeats the following two steps: (1) selections of initial structures relevant to transitions and (2) their conformational resampling. When selecting the initial structures, several measures are utilized to identify their potential to undergo transitions. In the present study, low-resolution structural data obtained from small angle scattering (SAXS) and cryo-electron microscopy (EM) are adopted as the measures in PaCS-MD to promote the conformational transitions of proteins, which is defined as SAXS-/EM-driven targeted PaCS-MD. By selecting the essential structures that have high correlations with the low-resolution structural data, the SAXS-/EM-driven targeted PaCS-MD identifies a set of transition pathways between the reactant and the product. As a demonstration, the present method successfully predicted the open-closed transition pathway of the lysine-, arginine-, ornithine-binding protein with a ns-order simulation time, indicating that the data-driven PaCS-MD simulation might work to promote the conformational transitions of proteins efficiently.

Hybrid Cascade-Type Molecular Dynamics with a Markov State Model for Efficient Free Energy Calculations

A protocol for calculating free energy landscapes (FELs) is proposed based on a combination of two cascade-type molecular dynamics (MD) methods, parallel cascade selection MD (PaCS-MD) and outlier flooding method (OFLOOD), with the help of a Markov state model (MSM). The former rapidly generates approximated transition paths directly connecting reactants with products, and the latter complementary resamples marginal conformational subspaces. Trajectories obtained by them give reliable microstates in MSM providing accurate FEL with low computational costs. As a demonstration, the present method was applied to a miniprotein (Chignolin and Trp-cage) in explicit water and successfully elucidated multiple folding paths on their free energy landscapes. Our method could be applicable to a wide variety of biological systems to estimate their free energy profiles.

Selection rules on initial structures in parallel cascade selection molecular dynamics affect conformational sampling efficiency

Parallel cascade selection molecular dynamics (PaCS-MD) is a conformational sampling method for generating transition pathways from a given reactant to a product. In PaCS-MD, initial structures relevant to conformational transitions of proteins are selected and resampled by short-time MD simulations. As a general reaction coordinate, a root-mean-square deviation measured from the product (RMSD) is employed to rank the resampled configurations. Quantitatively, n initial structures are randomly selected from among the top X % of highly ranked configurations and resampled again. In PaCS-MD, the selection of initial structures and their conformational resampling are repeated as a cycle to promote the essential conformational transitions. Therefore, rules for selecting the initial structures might affect the conformational sampling efficiency. In the present study, to address the conformational sampling efficiency depending on the selection rule, the open-closed transition of di-ubiquitin was reproduced by PaCS-MD based on the resampling from the top X = 0.1, 1.0, 2.0, 5.0, 10.0, 25.0, 30.0, 40.0, and 50.0% of highly ranked configurations. Judging from broadness of sampled conformational area and required cycles, we conclude that the resampling from the top ∼2.0% of highly ranked configurations might be the most efficient for generating a set of transition pathways in PaCS-MD.

Protein-Ligand Dissociation Simulated by Parallel Cascade Selection Molecular Dynamics

We investigated the dissociation process of tri-N-acetyl-d-glucosamine from hen egg white lysozyme using parallel cascade selection molecular dynamics (PaCS-MD), which comprises cycles of multiple unbiased MD simulations using a selection of MD snapshots as the initial structures for the next cycle. Dissociation was significantly accelerated by PaCS-MD, in which the probability of rare event occurrence toward dissociation was enhanced by the selection and rerandomization of the initial velocities. Although this complex was stable during 1 μs of conventional MD, PaCS-MD easily induced dissociation within 10⁰-10¹ ns. We found that velocity rerandomization enhances the dissociation of triNAG from the bound state, whereas diffusion plays a more important role in the unbound state. We calculated the dissociation free energy by analyzing all PaCS-MD trajectories using the Markov state model (MSM), compared the results to those obtained by combinations of PaCS-MD and umbrella sampling (US), steered MD (SMD) and US, and SMD and the Jarzynski equality, and experimentally determined binding free energy. PaCS-MD/MSM yielded results most comparable to the experimentally determined binding free energy, independent of simulation parameter variations, and also gave the lowest standard errors.

Efficient Conformational Search Based on Structural Dissimilarity Sampling: Applications for Reproducing Structural Transitions of Proteins

Structural Dissimilarity Sampling (SDS) is proposed as an efficient conformational search method to promote structural transitions essential for the biological functions of proteins. In SDS, initial structures are selected based on structural dissimilarity, and conformational resampling is repeated. Conformational resampling is performed as follows: (I) arrangement of initial structures for a diverse distribution at the edge of a conformational subspace and (II) promotion of the structural transitions with multiple short-time molecular dynamics (MD) simulations restarting from the diversely distributed initial structures. Cycles of (I) and (II) are repeated to intensively promote structural transitions because conformational resampling from the initial structures would quickly expand conformational distributions toward unvisited conformational subspaces. As a demonstration, SDS was first applied to maltodextrin binding protein (MBP) in explicit water to reproduce structural transitions between the open and closed states of MBP. Structural transitions of MBP were successfully reproduced with SDS in nanosecond-order simulation times. Starting from both the open and closed forms, SDS successfully reproduced the structural transitions within 25 cycles (a total of 250 ns of simulation time). For reference, a conventional long-time (500 ns) MD simulation under NPT (300 K and 1 bar) starting from the open form failed to reproduce the structural transition. In addition to the open-closed motions of MBP, SDS was applied to folding processes of the fast-folding proteins (chignolin, Trp-cage, and villin) and successfully sampled their native states. To confirm how the selections of initial structures affected conformational sampling efficiency, numbers of base sets for characterizing structural dissimilarity of initial structures were addressed in distinct trials of SDS. The parameter searches showed that the conformational sampling efficiency was relatively insensitive with respect to the numbers of base sets, indicating the robustness of SDS for actual applications.