Parallel Cascade Selection Molecular Dynamics (PaCS-MD) to generate conformational transition pathway

Machine learning-based QSAR and LB-PaCS-MD guided design of SARS-CoV-2 main protease inhibitors

The global outbreak of the COVID-19 pandemic caused by the SARS-CoV-2 virus had led to profound respiratory health implications. This study focused on designing organoselenium-based inhibitors targeting the SARS-CoV-2 main protease (Mpro). The ligand-binding pathway sampling method based on parallel cascade selection molecular dynamics (LB-PaCS-MD) simulations was employed to elucidate plausible paths and conformations of ebselen, a synthetic organoselenium drug, within the Mpro catalytic site. Ebselen effectively engaged the active site, adopting proximity to H41 and interacting through the benzoisoselenazole ring in a π-π T-shaped arrangement, with an additional π-sulfur interaction with C145. In addition, the ligand-based drug design using the QSAR with GFA-MLR, RF, and ANN models were employed for biological activity prediction. The QSAR-ANN model showed robust statistical performance, with an r2training exceeding 0.98 and an RMSEtest of 0.21, indicating its suitability for predicting biological activities. Integration the ANN model with the LB-PaCS-MD insights enabled the rational design of novel compounds anchored in the ebselen core structure, identifying promising candidates with favorable predicted IC50 values. The designed compounds exhibited suitable drug-like characteristics and adopted an active conformation similar to ebselen, inhibiting Mpro function. These findings represent a synergistic approach merging ligand and structure-based drug design; with the potential to guide experimental synthesis and enzyme assay testing.

Balancing G protein selectivity and efficacy in the adenosine A2A receptor

The adenosine A2A receptor (A2AR) engages several G proteins, notably Go and its cognate Gs protein. This coupling promiscuity is facilitated by a dynamic ensemble, revealed by 19F nuclear magnetic resonance imaging of A2AR and G protein. Two transmembrane helix 6 (TM6) activation states, formerly associated with partial and full agonism, accommodate the differing volumes of Gs and Go. While nucleotide depletion biases TM7 toward a fully active state in A2AR-Gs, A2AR-Go is characterized by a dynamic inactive/intermediate fraction. Molecular dynamics simulations reveal that the NPxxY motif, a highly conserved switch, establishes a unique configuration in the A2AR-Go complex, failing to stabilize the helix-8 interface with Gs, and adoption of the active state. The resulting TM7 dynamics hamper G protein coupling, suggesting kinetic gating may be responsible for reduced efficacy in the noncognate G protein complex. Thus, dual TM6 activation states enable greater diversity of coupling partners while TM7 dynamics dictate coupling efficacy.

Evaluating solubility, stability, and inclusion complexation of oxyresveratrol with various β-cyclodextrin derivatives using advanced computational techniques and experimental validation

Oxyresveratrol (OXY), a natural stilbenoid in mulberry fruits, is known for its diverse pharmacological properties. However, its clinical use is hindered by low water solubility and limited bioavailability. In the present study, the inclusion complexes of OXY with β-cyclodextrin (βCD) and its three analogs, dimethyl-β-cyclodextrin (DMβCD), hydroxypropyl-β-cyclodextrin (HPβCD) and sulfobutylether-β-cyclodextrin (SBEβCD), were investigated using in silico and in vitro studies. Molecular docking revealed two binding orientations of OXY, namely, 4',6'-dihydroxyphenyl (A-form) and 5,7-benzenediol ring (B-form). Molecular Dynamics simulations suggested the formation of inclusion complexes with βCDs through two distinct orientations, with OXY/SBEβCD exhibiting maximum atom contacts and the lowest solvent-exposed area in the hydrophobic cavity. These results corresponded well with the highest binding affinity observed in OXY/SBEβCD when assessed using the MM/GBSA method. Beyond traditional simulation methods, Ligand-binding Parallel Cascade Selection Molecular Dynamics method was employed to investigate how the drug enters and accommodates within the hydrophobic cavity. The in silico results aligned with stability constants: SBEβCD (2060 M-1), HPβCD (1860 M-1), DMβCD (1700 M-1), and βCD (1420 M-1). All complexes exhibited a 1:1 binding mode (AL type), with SBEβCD enhancing OXY solubility (25-fold). SEM micrographs, DSC thermograms, FT-IR and 1H NMR spectra confirm the inclusion complex formation, revealing novel surface morphologies, distinctive thermal behaviors, and new peaks. Notably, the inhibitory impact on the proliferation of breast cancer cell lines, MCF-7, exhibited by inclusion complexes particularly OXY/DMβCD, OXY/HPβCD, and OXY/SBEβCD were markedly superior compared to that of OXY alone.

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.

HIV-1 capsid shape, orientation, and entropic elasticity regulate translocation into the nuclear pore complex

Nuclear import and uncoating of the viral capsid are critical steps in the HIV-1 life cycle that serve to transport and release genomic material into the nucleus. Viral core import involves translocating the HIV-1 capsid at the nuclear pore complex (NPC). Notably, the central channel of the NPC appears to often accommodate and allow passage of intact HIV-1 capsid, though mechanistic details of the process remain to be fully understood. Here, we investigate the molecular interactions that operate in concert between the HIV-1 capsid and the NPC that regulate capsid translocation through the central channel. To this end, we develop a "bottom-up" coarse-grained (CG) model of the human NPC from recently released cryo-electron tomography structure and then construct composite membrane-embedded CG NPC models. We find that successful translocation from the cytoplasmic side to the NPC central channel is contingent on the compatibility of the capsid morphology and channel dimension and the proper orientation of the capsid approach to the channel from the cytoplasmic side. The translocation dynamics is driven by maximizing the contacts between phenylalanine-glycine nucleoporins at the central channel and the capsid. For the docked intact capsids, structural analysis reveals correlated striated patterns of lattice disorder likely related to the intrinsic capsid elasticity. Uncondensed genomic material inside the docked capsid augments the overall lattice disorder of the capsid. Our results suggest that the intrinsic "elasticity" can also aid the capsid to adapt to the stress and remain structurally intact during translocation.

[Development of Membrane Permeability Coefficient by Means of Novel Molecular Dynamics Methods]

The membrane permeability, and its evaluation, is crucial factor in the process of uptake of compounds from outside to inside the cell and in the inhibition of the activity of disease-causing target proteins. Although molecular dynamics (MD) simulations have been shown to be able to reproduce the conformational changes of compounds occurring during membrane permeation, it is still challenging to extract the membrane permeability at an affordable computational workload solely by conventional MD. Indeed, the time scale accessible by MD is far below the one characterizing the actual permeation process. Phenomena occurring in living organisms escaping the reach of standard MD are generally referred to as biological rare events, and the membrane permeation process is one of them. To overcome this time-scale problem, several enhanced sampling methods have been proposed over the years to improve conformational sampling. In this review, a hybrid sampling method that combines the parallel cascade selection MD (PaCS-MD) and the outlier flooding method (OFLOOD), introduced and developed by our group, is proposed as a tool to study the membrane permeation from structural sampling (rare-event sampling). The obtained trajectories are used to estimate the free energy profiles for the membrane permeation and to compute the membrane permeation coefficients. Moreover, we present an example of application of the free energy reaction network method as a versatile way for incorporating explicitly into reaction coordinates the degrees of freedom related to internal motion.

Design of electron-donating group substituted 2-PAM analogs as antidotes for organophosphate insecticide poisoning

The use of organophosphate (OPs) pesticides is widespread in agriculture and horticulture, but these chemicals can be lethal to humans, causing fatalities and deaths each year. The inhibition of acetylcholinesterase (AChE) by OPs leads to the overstimulation of cholinergic receptors, ultimately resulting in respiratory arrest, seizures, and death. Although 2-pralidoxime (2-PAM) is the FDA-approved drug for treating OP poisoning, there is difficulty in blood-brain barrier permeation. To address this issue, we designed and evaluated a series of 2-PAM analogs by substituting electron-donating groups on the para and/or ortho positions of the pyridinium core using in silico techniques. Our PCM-ONIOM2 (MP2/6-31G*:PM7//B3LYP/6-31G*:UFF) binding energy results demonstrated that 13 compounds exhibited higher binding energy than 2-PAM. The analog with phenyl and methyl groups substituted on the para and ortho positions, respectively, showed the most favorable binding characteristics, with aromatic residues in the active site (Y124, W286, F297, W338, and Y341) and the catalytic residue S203 covalently bonding with paraoxon. The results of DS-MD simulation revealed a highly favorable apical conformation of the potent analog, which has the potential to enhance reactivation of AChE. Importantly, newly designed compound demonstrated appropriate drug-likeness properties and blood-brain barrier penetration. These results provide a rational guide for developing new antidotes to treat organophosphate insecticide toxicity.

Free Energy Simulations of Receptor-Binding Domain Opening of the SARS-CoV-2 Spike Indicate a Barrierless Transition with Slow Conformational Motions

Infection by sarbecoviruses begins with the attachment of the homotrimeric viral "spike" protein to the angiotensin-converting enzyme 2 receptor on the surface of mammalian cells. This requires one or more receptor-binding domains (RBDs) to be in the open (up) position. Here, we present the results of long molecular dynamics simulations with umbrella sampling (US) to compute a one-dimensional free energy profile of RBD opening/closing and the associated transition times. After ≃3.58μs of simulation time per US window (∼229 μs in total), which was required to approach trajectory decorrelation, the computed free energy profile was found to be without large barriers. This suggests that the RBD diffuses between the open and closed positions without significant energetic hindrance. This interpretation appears consistent with experiments but is at odds with some previous simulations. Modeling the RBD motion as diffusive dynamics along the computed free energy profile, we find that the overall time required for the transition is only about 2 μs, which is 5 orders of magnitude shorter than experimentally measured transition times. We speculate that the most likely reason for the transition time mismatch is our use of very short glycans, which was required to make the simulations performed here feasible. Despite the long simulation times, the final free energy profile is not fully converged with statistical errors of ≃1.16 kcal/mol, which were found to be consistent with the slow time decay in the autocorrelation of the conformational motions of the protein. The simulation lengths that would be required to obtain fully converged results remain unknown, but the present calculations would benefit from at least an order-of-magnitude extension.

Elucidating protein-ligand binding kinetics based on returning probability theory

The returning probability (RP) theory, a rigorous diffusion-influenced reaction theory, enables us to analyze the binding process systematically in terms of thermodynamics and kinetics using molecular dynamics (MD) simulations. Recently, the theory was extended to atomistically describe binding processes by adopting the host-guest interaction energy as the reaction coordinate. The binding rate constants can be estimated by computing the thermodynamic and kinetic properties of the reactive state existing in the binding processes. Here, we propose a methodology based on the RP theory in conjunction with the energy representation theory of solution, applicable to complex binding phenomena, such as protein-ligand binding. The derived scheme of calculating the equilibrium constant between the reactive and dissociate states, required in the RP theory, can be used for arbitrary types of reactive states. We apply the present method to the bindings of small fragment molecules [4-hydroxy-2-butanone (BUT) and methyl methylthiomethyl sulphoxide (DSS)] to FK506 binding protein (FKBP) in an aqueous solution. Estimated binding rate constants are consistent with those obtained from long-timescale MD simulations. Furthermore, by decomposing the rate constants to the thermodynamic and kinetic contributions, we clarify that the higher thermodynamic stability of the reactive state for DSS causes the faster binding kinetics compared with BUT.

Energetic and Kinetic Origins of CALB Interfacial Activation Revealed by PaCS-MD/MSM

The conformational dynamics of Candida antarctica lipase B (CALB) was investigated by molecular dynamics (MD) simulation, parallel cascade selection MD (PaCS-MD), and the Markov state model (MSM) and mainly focused on the lid-opening motion closely related to substrate binding. All-atom MD simulation of CALB was conducted in water and on the interface of water and tricaprylin. CALB initially situated in water and separated by layers of water from the interface is spontaneously adsorbed onto the tricaprylin surface during MD simulation. The opening and closing motions of the lid are simulated by PaCS-MD, and subsequent MSM analysis provided the free-energy landscape and time scale of the conformational transitions among the closed, semiopen, and open states. The closed state is the most stable in the water system, but the stable conformation in the interface system shifts to the semiopen state. These effects could explain the energetics and kinetics origin of the previously reported interfacial activation of CALB. These findings could help expand the application of CALB toward a wide variety of substrates.

Neutralizing Carbapenem Resistance by Co-Administering Meropenem with Novel β-Lactam-Metallo-β-Lactamase Inhibitors

Virulent Enterobacterale strains expressing serine and metallo-β-lactamases (MBL) genes have emerged responsible for conferring resistance to hard-to-treat infectious diseases. One strategy that exists is to develop β-lactamase inhibitors to counter this resistance. Currently, serine β-lactamase inhibitors (SBLIs) are in therapeutic use. However, an urgent global need for clinical metallo-β-lactamase inhibitors (MBLIs) has become dire. To address this problem, this study evaluated BP2, a novel beta-lactam-derived β-lactamase inhibitor, co-administered with meropenem. According to the antimicrobial susceptibility results, BP2 potentiates the synergistic activity of meropenem to a minimum inhibitory concentration (MIC) of ≤1 mg/L. In addition, BP2 is bactericidal over 24 h and safe to administer at the selected concentrations. Enzyme inhibition kinetics showed that BP2 had an apparent inhibitory constant (K_iapp) of 35.3 µM and 30.9 µM against New Delhi Metallo-β-lactamase (NDM-1) and Verona Integron-encoded Metallo-β-lactamase (VIM-2), respectively. BP2 did not interact with glyoxylase II enzyme up to 500 µM, indicating specific (MBL) binding. In a murine infection model, BP2 co-administered with meropenem was efficacious, observed by the >3 log₁₀ reduction in K. pneumoniae NDM cfu/thigh. Given the promising pre-clinical results, BP2 is a suitable candidate for further research and development as an (MBLI).

In Vitro and In Vivo Development of a β-Lactam-Metallo-β-Lactamase Inhibitor: Targeting Carbapenem-Resistant Enterobacterales

β-lactams are the most prescribed class of antibiotics due to their potent, broad-spectrum antimicrobial activities. However, alarming rates of antimicrobial resistance now threaten the clinical relevance of these drugs, especially for the carbapenem-resistant Enterobacterales expressing metallo-β-lactamases (MBLs). Antimicrobial agents that specifically target these enzymes to restore the efficacy of last resort β-lactam drugs, that is, carbapenems, are therefore desperately needed. Herein, we present a cyclic zinc chelator covalently attached to a β-lactam scaffold (cephalosporin), that is, BP1. Observations from in vitro assays (with seven MBL expressing bacteria from different geographies) have indicated that BP1 restored the efficacy of meropenem to ≤ 0.5 mg/L, with sterilizing activity occurring from 8 h postinoculation. Furthermore, BP1 was nontoxic against human hepatocarcinoma cells (IC₅₀ > 1000 mg/L) and exhibited a potency of (K_iapp) 24.8 and 97.4 μM against Verona integron-encoded MBL (VIM-2) and New Delhi metallo β-lactamase (NDM-1), respectively. There was no inhibition observed from BP1 with the human zinc-containing enzyme glyoxylase II up to 500 μM. Preliminary molecular docking of BP1 with NDM-1 and VIM-2 sheds light on BP1's mode of action. In Klebsiella pneumoniae NDM infected mice, BP1 coadministered with meropenem was efficacious in reducing the bacterial load by >3 log₁₀ units' postinfection. The findings herein propose a favorable therapeutic combination strategy that restores the activity of the carbapenem antibiotic class and complements the few MBL inhibitors under development, with the ultimate goal of curbing antimicrobial resistance.

Molecular Simulation to Investigate Open-Close Motion of a Flagellar Export Apparatus Protein FlhAC

Molecular dynamics (MD) simulation and parallel cascade selection molecular dynamics (PaCS-MD) are widely used to investigate large-amplitude motions of proteins. PaCS-MD is an enhanced conformational sampling method consisting of cycles of parallel unbiased MD simulations combined with a selection of MD snapshots as the initial structures for the next cycle. In addition, free energy calculation can be achieved by the combination of PaCS-MD and the Markov state model (MSM). In this chapter, the protocols to investigate the open-close motion of a flagellar export apparatus protein, FlhA_C, by MD and the combination of PaCS-MD and MSM are described.

Free-Energy Profiles for Membrane Permeation of Compounds Calculated Using Rare-Event Sampling Methods

The free-energy profile of a compound is an essential measurement in evaluating the membrane permeation process by means of theoretical methods. Computationally, molecular dynamics (MD) simulation allows the free-energy profile calculation. However, MD simulations frequently fail to sample membrane permeation because they are rare events induced in longer timescales than the accessible timescale of MD, leading to an insufficient conformational search to calculate an incorrect free-energy profile. To achieve a sufficient conformational search, several enhanced sampling methods have been developed and elucidated the membrane permeation process. In addition to these enhanced sampling methods, we proposed a simple yet powerful free-energy calculation of a compound for the membrane permeation process based on originally rare-event sampling methods developed by us. Our methods have a weak dependency on external biases and their optimizations to promote the membrane permeation process. Based on distributed computing, our methods only require the selection of initial structures and their conformational resampling, whereas the enhanced sampling methods may be required to adjust external biases. Furthermore, our methods efficiently search membrane permeation processes with simple scripts without modifying any MD program. As demonstrations, we calculated the free-energy profiles of seven linear compounds for their membrane permeation based on a hybrid conformational search using two rare-event sampling methods, that is, (1) parallel cascade selection MD (PaCS-MD) and (2) outlier flooding method (OFLOOD), combined with a Markov state model (MSM) construction. In the first step, PaCS-MD generated initial membrane permeation paths of a compound. In the second step, OFLOOD expanded the unsearched conformational area around the initial paths, allowing for a broad conformational search. Finally, the trajectories were employed to construct reliable MSMs, enabling correct free-energy profile calculations. Furthermore, we estimated the membrane permeability coefficients of all compounds by constructing the reliable MSMs for their membrane permeation. In conclusion, the calculated coefficients were qualitatively correlated with the experimental measurements (correlation coefficient (R²) = 0.8689), indicating that the hybrid conformational search successfully calculated the free-energy profiles and membrane permeability coefficients of the seven compounds.

LAST: Latent Space-Assisted Adaptive Sampling for Protein Trajectories

Molecular dynamics (MD) simulation is widely used to study protein conformations and dynamics. However, conventional simulation suffers from being trapped in some local energy minima that are hard to escape. Thus, most of the computational time is spent sampling in the already visited regions. This leads to an inefficient sampling process and further hinders the exploration of protein movements in affordable simulation time. The advancement of deep learning provides new opportunities for protein sampling. Variational autoencoders are a class of deep learning models to learn a low-dimensional representation (referred to as the latent space) that can capture the key features of the input data. Based on this characteristic, we proposed a new adaptive sampling method, latent space-assisted adaptive sampling for protein trajectories (LAST), to accelerate the exploration of protein conformational space. This method comprises cycles of (i) variational autoencoder training, (ii) seed structure selection on the latent space, and (iii) conformational sampling through additional MD simulations. The proposed approach is validated through the sampling of four structures of two protein systems: two metastable states of Escherichia coli adenosine kinase (ADK) and two native states of Vivid (VVD). In all four conformations, seed structures were shown to lie on the boundary of conformation distributions. Moreover, large conformational changes were observed in a shorter simulation time when compared with structural dissimilarity sampling (SDS) and conventional MD (cMD) simulations in both systems. In metastable ADK simulations, LAST explored two transition paths toward two stable states, while SDS explored only one and cMD neither. In VVD light state simulations, LAST was three times faster than cMD simulation with a similar conformational space. Overall, LAST is comparable to SDS and is a promising tool in adaptive sampling. The LAST method is publicly available at https://github.com/smu-tao-group/LAST to facilitate related research.

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.

Promising SARS-CoV-2 main protease inhibitor ligand-binding modes evaluated using LB-PaCS-MD/FMO

Parallel cascade selection molecular dynamics-based ligand binding-path sampling (LB-PaCS-MD) was combined with fragment molecular orbital (FMO) calculations to reveal the ligand path from an aqueous solution to the SARS-CoV-2 main protease (M^pro) active site and to customise a ligand-binding pocket suitable for delivering a potent inhibitor. Rubraxanthone exhibited mixed-inhibition antiviral activity against SARS-CoV-2 M^pro, relatively low cytotoxicity, and high cellular inhibition. However, the atomic inhibition mechanism remains ambiguous. LB-PaCS-MD/FMO is a hybrid ligand-binding evaluation method elucidating how rubraxanthone interacts with SARS-CoV-2 M^pro. In the first step, LB-PaCS-MD, which is regarded as a flexible docking, efficiently samples a set of ligand-binding pathways. After that, a reasonable docking pose of LB-PaCS-MD is evaluated by the FMO calculation to elucidate a set of protein-ligand interactions, enabling one to know the binding affinity of a specified ligand with respect to a target protein. A possible conformation was proposed for rubraxanthone binding to the SARS-CoV-2 M^pro active site, and allosteric inhibition was elucidated by combining blind docking with k-means clustering. The interaction profile, key binding residues, and considerable interaction were elucidated for rubraxanthone binding to both M^pro sites. Integrated LB-PaCS-MD/FMO provided a more reasonable complex structure for ligand binding at the SARS-CoV-2 M^pro active site, which is vital for discovering and designing antiviral drugs.

Role of Repeated Conformational Transitions in Substrate Binding of Adenylate Kinase

The catalytic cycle of the enzyme adenylate kinase involves large conformational motions between open and closed states. A previous single-molecule experiment showed that substrate binding tends to accelerate both the opening and the closing rates and that a single turnover event often involves multiple rounds of conformational switching. In this work, we showed that the repeated conformational transitions of adenylate kinase are essential for the relaxation of incorrectly bound substrates into the catalytically competent conformation by combining all-atom and coarse-grained molecular simulations. In addition, free energy calculations based on all-atom and coarse-grained models demonstrated that the enzyme with incorrectly bound substrates has much a lower free energy barrier for domain opening compared to that with the correct substrate conformation, which may explain the the acceleration of the domain opening rate by substrate binding. The results of this work provide mechanistic understanding to previous experimental observations and shed light onto the interplay between conformational dynamics and enzyme catalysis.

Multiagent Reinforcement Learning-Based Adaptive Sampling for Conformational Dynamics of Proteins

Machine learning is increasingly applied to improve the efficiency and accuracy of molecular dynamics (MD) simulations. Although the growth of distributed computer clusters has allowed researchers to obtain higher amounts of data, unbiased MD simulations have difficulty sampling rare states, even under massively parallel adaptive sampling schemes. To address this issue, several algorithms inspired by reinforcement learning (RL) have arisen to promote exploration of the slow collective variables (CVs) of complex systems. Nonetheless, most of these algorithms are not well-suited to leverage the information gained by simultaneously sampling a system from different initial states (e.g., a protein in different conformations associated with distinct functional states). To fill this gap, we propose two algorithms inspired by multiagent RL that extend the functionality of closely related techniques (REAP and TSLC) to situations where the sampling can be accelerated by learning from different regions of the energy landscape through coordinated agents. Essentially, the algorithms work by remembering which agent discovered each conformation and sharing this information with others at the action-space discretization step. A stakes function is introduced to modulate how different agents sense rewards from discovered states of the system. The consequences are three-fold: (i) agents learn to prioritize CVs using only relevant data, (ii) redundant exploration is reduced, and (iii) agents that obtain higher stakes are assigned more actions. We compare our algorithm with other adaptive sampling techniques (least counts, REAP, TSLC, and AdaptiveBandit) to show and rationalize the gain in performance.

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.

Inositol Hexakisphosphate (IP6) Accelerates Immature HIV-1 Gag Protein Assembly toward Kinetically Trapped Morphologies

During the late stages of the HIV-1 lifecycle, immature virions are produced by the concerted activity of Gag polyproteins, primarily mediated by the capsid (CA) and spacer peptide 1 (SP1) domains, which assemble into a spherical lattice, package viral genomic RNA, and deform the plasma membrane. Recently, inositol hexakisphosphate (IP6) has been identified as an essential assembly cofactor that efficiently produces both immature virions in vivo and immature virus-like particles in vitro. To date, however, several distinct mechanistic roles for IP6 have been proposed on the basis of independent functional, structural, and kinetic studies. In this work, we investigate the molecular influence of IP6 on the structural outcomes and dynamics of CA/SP1 assembly using coarse-grained (CG) molecular dynamics (MD) simulations and free energy calculations. Here, we derive a bottom-up, low-resolution, and implicit-solvent CG model of CA/SP1 and IP6, and simulate their assembly under conditions that emulate both in vitro and in vivo systems. Our analysis identifies IP6 as an assembly accelerant that promotes curvature generation and fissure-like defects throughout the lattice. Our findings suggest that IP6 induces kinetically trapped immature morphologies, which may be physiologically important for later stages of viral morphogenesis and potentially useful for virus-like particle technologies.

Inhibition of the hexamerization of SARS-CoV-2 endoribonuclease and modeling of RNA structures bound to the hexamer

Non-structural protein 15 (Nsp15) of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) forms a homo hexamer and functions as an endoribonuclease. Here, we propose that Nsp15 activity may be inhibited by preventing its hexamerization through drug binding. We first explored the stable conformation of the Nsp15 monomer as the global free energy minimum conformation in the free energy landscape using a combination of parallel cascade selection molecular dynamics (PaCS-MD) and the Markov state model (MSM), and found that the Nsp15 monomer forms a more open conformation with larger druggable pockets on the surface. Targeting the pockets with high druggability scores, we conducted ligand docking and identified compounds that tightly bind to the Nsp15 monomer. The top poses with Nsp15 were subjected to binding free energy calculations by dissociation PaCS-MD and MSM (dPaCS-MD/MSM), indicating the stability of the complexes. One of the identified pockets, which is distinctively bound by inosine analogues, may be an alternative binding site to stabilize viral RNA binding and/or an alternative catalytic site. We constructed a stable RNA structure model bound to both UTP and alternative binding sites, providing a reasonable proposed model of the Nsp15/RNA complex.

Dissociation Pathways of the p53 DNA Binding Domain from DNA and Critical Roles of Key Residues Elucidated by dPaCS-MD/MSM

p53 is a transcriptional factor that regulates cell response to a variety of stresses. About a half of all human tumors contain p53 mutations, and the accumulation of mutations in the DNA binding domain of p53 (p53-DBD) can cause destabilization of p53 and its complex with DNA. To identify the key residues of the p53-DBD/DNA binding and to understand the dissociation mechanisms of the p53-DBD/DNA complex, the dissociation process of p53-DBD from a DNA duplex that contains the consensus sequence (the specific target of p53-DBD) was investigated by a combination of dissociation parallel cascade selection molecular dynamics (dPaCS-MD) and the Markov state model (MSM). This combination (dPaCS-MD/MSM) enabled us to simulate dissociation of the two large molecules based on an all-atom model with a short simulation time (11.2 ± 2.2 ns per trial) and to analyze dissociation pathways, free energy landscape (FEL), and binding free energy. Among 75 trials of dPaCS-MD, p53-DBD dissociated first from the major groove and then detached from the minor groove in 93% of the cases, while 7% of the cases unbinding from the minor groove occurred first. Minor groove binding is mainly stabilized by R248, identified as the most important residue that tightly binds deep inside the minor groove. The standard binding free energy calculated from the FEL was -10.9 ± 0.4 kcal/mol, which agrees with an experimental value of -11.1 kcal/mol. These results indicate that the dPaCS-MD/MSM combination can be a powerful tool to investigate dissociation mechanisms of two large molecules. Analysis of the p53 key residues for DNA binding indicates high correlations with cancer-related mutations, confirming that impairment of the interactions between p53-DBD and DNA can be frequently related to cancer.

Binding free energy of protein/ligand complexes calculated using dissociation Parallel Cascade Selection Molecular Dynamics and Markov state model

We recently proposed a computational procedure to simulate the dissociation of protein/ligand complexes using the dissociation Parallel Cascade Selection Molecular Dynamics simulation (dPaCS-MD) method and to analyze the generated trajectories using the Markov state model (MSM). This procedure, called dPaCS-MD/MSM, enables calculation of the dissociation free energy profile and the standard binding free energy. To examine whether this method can reproduce experimentally determined binding free energies for a variety of systems, we used it to investigate the dissociation of three protein/ligand complexes: trypsin/benzamine, FKBP/FK506, and adenosine A_2A receptor/T4E. First, dPaCS-MD generated multiple dissociation pathways within a reasonable computational time for all the complexes, although the complexes differed significantly in the size of the molecules and in intermolecular interactions. Subsequent MSM analyses produced free energy profiles for the dissociations, which provided insights into how each ligand dissociates from the protein. The standard binding free energies obtained by dPaCS-MD/MSM are in good agreement with experimental values for all the complexes. We conclude that dPaCS-MD/MSM can accurately calculate the binding free energies of these complexes.

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.

Atomistic description of molecular binding processes based on returning probability theory

The efficiency of molecular binding such as host-guest binding is commonly evaluated in terms of kinetics, such as rate coefficients. In general, to compute the coefficient of the overall binding process, we need to consider both the diffusion of reactants and barrier crossing to reach the bound state. Here, we develop a methodology of quantifying the rate coefficient of binding based on molecular dynamics simulation and returning probability (RP) theory proposed by Kim and Lee [J. Chem. Phys. 131, 014503 (2009)]. RP theory provides a tractable formula of the rate coefficient in terms of the thermodynamic stability and kinetics of the intermediate state on a predefined reaction coordinate. In this study, the interaction energy between reactants is utilized as the reaction coordinate, enabling us to effectively describe the reactants' relative position and orientation on one-dimensional space. Application of this method to the host-guest binding systems, which consist of β-cyclodextrin and small guest molecules, yields the rate coefficients consistent with the experimental results.

Independent Nontargeted Parallel Cascade Selection Molecular Dynamics (Ino-PaCS-MD) to Enhance the Conformational Sampling of Proteins

Biological functions are related to long-time protein dynamics (rare events) that are induced over microseconds. Such protein dynamics can be investigated using molecular dynamics (MD) simulations. However, the detection of rare events remains challenging using conventional MD (cMD) since the accessible timescales of cMD are shorter than those of the biological functions. Recently, the parallel cascade selection MD (PaCS-MD) has been proposed to detect such rare events, wherein transition paths are generated between a given reactant and product. As an extension, the nontargeted PaCS-MD (nt-PaCS-MD) has been proposed to predict the transition paths without requiring reference to any product. Thus, as a further extension, we herein propose independent nt-PaCS-MD, namely, Ino-PaCS-MD, wherein multiple walkers are launched from a set of different starting configurations. Each walker repeats a cycle of restarting short-time MD simulations from configurations with high potentials for making transitions to neighboring metastable states. To further enhance the sampling ability, Ino-PaCS-MD temporarily stops the conformational search and periodically resets the starting configurations so that they are uniformly distributed in a conformational subspace, thereby preventing a given protein from being trapped in one of the metastable states. As a demonstration, Ino-PaCS-MD successfully detects rare events of a maltose-binding protein as open-close transitions with a nanosecond-order simulation time, although a microsecond-order cMD simulation failed to detect these rare events, showing the high sampling efficiency of Ino-PaCS-MD.

Activation Pathways and Free Energy Landscapes of the SARS-CoV-2 Spike Protein

Severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) uses a spike protein (S-protein) to recognize the receptor protein ACE2 of human cells and initiate infection, during which the conformational transition of the S-protein from inactive (down) state to active (up) state is one of the key molecular events determining the infectivity but the underlying mechanism remains poorly understood. In this work, we investigated the activation pathways and free energy landscape of the S-protein of SARS-CoV-2 and compared with those of the closely related counterpart SARS-CoV using molecular dynamics simulations. Our results revealed a large difference between the activation pathways of the two S-proteins. The transition from inactive to an active state for the S-protein of SARS-CoV-2 is more cooperative, involving simultaneous disruptions of several key interfacial hydrogen bonds, and the transition encounters a much higher free energy barrier. In addition, the conformational equilibrium of the SARS-CoV-2 S-protein is more biased to the inactive state compared to that of the SARS-CoV S-protein, suggesting the transient feature of the active state before binding to the receptor protein of the host cell. The key interactions contributing to the difference of the activation pathways and free energy landscapes were discussed. The results provide insights into the molecular mechanism involved in the initial stage of the SARS-CoV-2 infection.

Reduced efficacy of a Src kinase inhibitor in crowded protein solution

The inside of a cell is highly crowded with proteins and other biomolecules. How proteins express their specific functions together with many off-target proteins in crowded cellular environments is largely unknown. Here, we investigate an inhibitor binding with c-Src kinase using atomistic molecular dynamics (MD) simulations in dilute as well as crowded protein solution. The populations of the inhibitor, 4-amino-5-(4-methylphenyl)-7-(t-butyl)pyrazolo[3,4-d]pyrimidine (PP1), in bulk solution and on the surface of c-Src kinase are reduced as the concentration of crowder bovine serum albumins (BSAs) increases. This observation is consistent with the reduced PP1 inhibitor efficacy in experimental c-Src kinase assays in addition with BSAs. The crowded environment changes the major binding pathway of PP1 toward c-Src kinase compared to that in dilute solution. This change is explained based on the population shift mechanism of local conformations near the inhibitor binding site in c-Src kinase.

Enhanced sampling protocol to elucidate fusion peptide opening of SARS-CoV-2 spike protein

Large-scale conformational transitions in the spike protein S2 domain are required during host-cell infection of the severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) virus. Although conventional molecular dynamics simulations have been extensively used to study therapeutic targets of SARS-CoV-2, it is still challenging to gain molecular insight into the key conformational changes because of the size of the spike protein and the long timescale required to capture these transitions. In this work, we have developed an efficient simulation protocol that leverages many short simulations, a dynamic selection algorithm, and Markov state models to interrogate the structural changes of the S2 domain. We discovered that the conformational flexibility of the dynamic region upstream of the fusion peptide in S2 is coupled to the proteolytic cleavage state of the spike protein. These results suggest that opening of the fusion peptide likely occurs on a submicrosecond timescale after cleavage at the S2' site. Building on the structural and dynamical information gained to date about S2 domain dynamics, we provide proof of principle that a small molecule bound to a seam neighboring the fusion peptide can slow the opening of the fusion peptide, leading to a new inhibition strategy for experiments to confirm. In aggregate, these results will aid the development of drug cocktails to inhibit infections caused by SARS-CoV-2 and other coronaviruses.

DESP: Deep Enhanced Sampling of Proteins' Conformation Spaces Using AI-Inspired Biasing Forces

The molecular structures (i.e., conformation spaces, CS) of bio-macromolecules and the dynamics that molecules exhibit are crucial to the understanding of the basis of many diseases and in the continuous attempts to retarget known drugs/medications, improve the efficacy of existing drugs, or develop novel drugs. These make a better understanding and the exploration of the CS of molecules a research hotspot. While it is generally easy to computationally explore the CS of small molecules (such as peptides and ligands), the exploration of the CS of a larger biomolecule beyond the local energy well and beyond the initial equilibrium structure of the molecule is generally nontrivial and can often be computationally prohibitive for molecules of considerable size. Therefore, research efforts in this area focus on the development of ways that systematically favor the sampling of new conformations while penalizing the resampling of previously sampled conformations. In this work, we present Deep Enhanced Sampling of Proteins’ Conformation Spaces Using AI-Inspired Biasing Forces (DESP), a technique for enhanced sampling that combines molecular dynamics (MD) simulations and deep neural networks (DNNs), in which biasing potentials for guiding the MD simulations are derived from the KL divergence between the DNN-learned latent space vectors of [a] the most recently sampled conformation and those of [b] the previously sampled conformations. Overall, DESP efficiently samples wide CS and outperforms conventional MD simulations as well as accelerated MD simulations. We acknowledge that this is an actively evolving research area, and we continue to further develop the techniques presented here and their derivatives tailored at achieving DNN-enhanced steered MD simulations and DNN-enhanced targeted MD simulations.

Integrating an Enhanced Sampling Method and Small-Angle X-Ray Scattering to Study Intrinsically Disordered Proteins

Intrinsically disordered proteins (IDPs) have been paid more and more attention over the past decades because they are involved in a multitude of crucial biological functions. Despite their functional importance, IDPs are generally difficult to investigate because they are very flexible and lack stable structures. Computer simulation may serve as a useful tool in studying IDPs. With the development of computer software and hardware, computational methods, such as molecular dynamics (MD) simulations, are popularly used. However, there is a sampling problem in MD simulations. In this work, this issue is investigated using an IDP called unique long region 11 (UL11), which is the conserved outer tegument component from herpes simplex virus 1. After choosing a proper force field and water model that is suitable for simulating IDPs, integrative modeling by combining an enhanced sampling method and experimental data like small-angle X-ray scattering (SAXS) is utilized to efficiently sample the conformations of UL11. The simulation results are in good agreement with experimental data. This work may provide a general protocol to study structural ensembles of IDPs.

Recent Force Field Strategies for Intrinsically Disordered Proteins

Intrinsically disordered proteins (IDPs) are widely distributed across eukaryotic cells, playing important roles in molecular recognition, molecular assembly, post-translational modification, and other biological processes. IDPs are also associated with many diseases such as cancers, cardiovascular diseases, and neurodegenerative diseases. Due to their structural flexibility, conventional experimental methods cannot reliably capture their heterogeneous structures. Molecular dynamics simulation becomes an important complementary tool to quantify IDP structures. This review covers recent force field strategies proposed for more accurate molecular dynamics simulations of IDPs. The strategies include adjusting dihedral parameters, adding grid-based energy correction map (CMAP) parameters, refining protein-water interactions, and others. Different force fields were found to perform well on specific observables of specific IDPs but also are limited in reproducing all available experimental observables consistently for all tested IDPs. We conclude the review with perspective areas for improvements for future force fields for IDPs.

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%.

Enhanced Conformational Sampling Method Based on Anomaly Detection Parallel Cascade Selection Molecular Dynamics: ad-PaCS-MD

In the present study, we propose a rare-event sampling method called anomaly detection parallel cascade selection molecular dynamics (ad-PaCS-MD). The original PaCS-MD was designed to generate conformational transition pathways from a given reactant to a product when the latter is known a priori. As an extension of the original method, ad-PaCS-MD has been designed to efficiently search transition pathways from a given reactant without referring to a given product. In ad-PaCS-MD, rarely occurring but essential states (configurations) of proteins for the transitions are identified based on the degrees of an anomaly. In more detail, ad-PaCS-MD adopts an algorithm called an anomaly detection generative adversarial network (anoGAN) as a measure for detecting rarely occurring states to be resampled. Here, the essential configurations with higher degrees of the anomaly are selected with anoGAN and intensively resampled by restarting short-time MD simulations from the selected configurations. By repeating the detections and resampling of configurations with the higher degrees of the anomaly, ad-PaCS-MD automatically and efficiently promotes the rare events and gives a wide range of the free energy landscape by combining with the Markov state model construction. As demonstrations, open-closed transitions of two globular proteins (T4 lysozyme and maltose-binding protein) were promoted with ad-PaCS-MD by referring only to the given starting configurations. In each demonstration, ad-PaCS-MD promoted the large-amplitude open-closed transitions with nanosecond-order simulation times. In conclusion, our demonstrations showed a higher conformational sampling efficiency for ad-PaCS-MD than conventional MD (CMD) because CMD required computational costs of more than microsecond-order simulation times to promote the rare events.

Efficient Conformational Sampling of Collective Motions of Proteins with Principal Component Analysis-Based Parallel Cascade Selection Molecular Dynamics

Molecular dynamics (MD) simulation has become a powerful tool because it provides a time series of protein dynamics at high temporal-spatial resolution. However, the accessible timescales of MD simulation are shorter than those of the biologically rare events. Generally, long-time MD simulations over microseconds are required to detect the rare events. Therefore, it is desirable to develop rare-event-sampling methods. For a rare-event-sampling method, we have developed parallel cascade selection MD (PaCS-MD). PaCS-MD generates transition pathways from a given source structure to a target structure by repeating short-time MD simulations. The key point in PaCS-MD is how to select reasonable candidates (protein configurations) with high potentials to make transitions toward the target structure. In the present study, based on principal component analysis (PCA), we propose PCA-based PaCS-MD to detect rare events of collective motions of a given protein. Here, the PCA-based PaCS-MD is composed of the following two steps. At first, as a preliminary run, PCA is performed using an MD trajectory from the target structure to define a principal coordinate (PC) subspace for describing the collective motions of interest. PCA provides principal modes as eigenvectors to project a protein configuration onto the PC subspace. Then, as a production run, all the snapshots of short-time MD simulations are ranked by inner products (IPs), where an IP is defined between a snapshot and the target structure. Then, snapshots with higher values of the IP are selected as reasonable candidates, and short-time MD simulations are independently restarted from them. By referring to the values of the IP, the PCA-based PaCS-MD repeats the short-time MD simulations from the reasonable candidates that are highly correlated with the target structure. As a demonstration, we applied the PCA-based PaCS-MD to adenylate kinase and detected its large-amplitude (open-closed) transition with a nanosecond-order computational cost.

Frontier Expansion Sampling: A Method to Accelerate Conformational Search by Identifying Novel Seed Structures for Restart

Traditional molecular dynamics (MD) simulations have difficulties in tracking the slow molecular motions, at least partially due to the waste of sampling in already sampled regions. Here, we proposed a new enhanced sampling method, frontier expansion sampling (FEXS), to improve the sampling efficiency of molecular simulations by iteratively selecting seed structures diversely distributed at the "frontier" of an already sampled region to initiate new simulations. Different from other enhanced sampling methods, FEXS identifies the "frontier" seeds by integrating the Gaussian mixture model and the convex hull algorithm, which effectively improves the structural variation among the selected seeds and thus the descendant simulations. Validation in three protein systems, including the folding of chignolin, open-to-closed transition of maltodextrin binding protein, and internal conformational change of bovine pancreatic trypsin inhibitor, confirmed the effectiveness of this novel method in enhancing the sampling of conventional MD simulations to observe the large-scale protein conformational changes. When compared with other enhanced sampling methods like the structural dissimilarity sampling (SDS), FEXS reached at least the same level of sampling efficiency but was capable of providing complementary information in the three tested protein systems.

Role of substrate-product frustration on enzyme functional dynamics

Natural enzymes often have enormous catalytic power developed by evolution. Revealing the underlying physical strategy used by enzymes to achieve high catalysis efficiency is one of the central focuses in the field of biological physics. Our recent work demonstrated that multisubstrate enzymes can utilize steric frustration encountered in the substrate-product cobound complex to overcome the bottleneck of the enzymatic cycle [W. Li et al., Phys. Rev. Lett. 122, 238102 (2019)10.1103/PhysRevLett.122.238102]. However, the key atomic-level interactions by which the steric frustration contributes to the enzymatic cycle remain elusive. In this work we study the microscopic mechanism for the role of the substrate-product frustration on the key physical steps in the enzymatic cycle of adenylate kinase (AdK), a multisubstrate enzyme catalyzing the reversible phosphoryl transfer reaction ATP+AMP⇋ADP+ADP. By using atomistic molecular dynamics simulations with enhanced sampling, we showed that the competitive interactions from the phosphate groups of the substrate ATP and product ADP in the ATP-ADP cobound complex of the AdK lead to local frustration in the binding pockets. Such local frustration disrupts the hydrogen bond network around the binding pockets, which causes lowered barrier height for the opening of the enzyme conformations and expedited release of the bottleneck product ADP. Our results directly demonstrated from the atomistic level that the local frustration in the active sites of the enzyme can be utilized to facilitate the key physical steps of the enzymatic cycle, providing numerical evidence to the predictions of the previous theoretical work.

A Two-Ended Data-Driven Accelerated Sampling Method for Exploring the Transition Pathways between Two Known States of Protein

Conformational transitions of protein between different states are often associated with their biological functions. These dynamic processes, however, are usually not easy to be well characterized by experimental measurements, mainly because of inadequate temporal and spatial resolution. Meantime, sampling of configuration space with molecular dynamics (MD) simulations is still a challenge. Here we proposed a robust two-ended data-driven accelerated (teDA2) conformational sampling method, which drives the structural change in an adaptively updated feature space without introducing a bias potential. teDA2 was applied to explore adenylate kinase (ADK), a model with well characterized "open" and "closed" states. A single conformational transition event of ADK could be achieved within only a few or tens of nanoseconds sampled with teDA2. By analyzing hundreds of transition events, we reproduced different mechanisms and the associated pathways for domain motion of ADK reported in the literature. The multiroute characteristic of ADK was confirmed by the fact that some metastable states identified with teDA2 resemble available crystal structures determined at different conditions. This feature was further validated with Markov state modeling with independent MD simulations. Therefore, our work provides strong evidence for the conformational plasticity of protein, which is mainly due to the inherent degree of flexibility. As a reliable and efficient enhanced sampling protocol, teDA2 could be used to study the dynamics between functional states of various biomolecular machines.

Protein Dynamics and the Folding Degree

The analysis of folding trajectories for proteins is an open challenge. One of the problems is how to describe the amount of folded secondary structure in a protein. We extend the use of Estradas' folding degree (Bioinformatics 2002, 18, 697) for the analysis of the evolution of the folding stage during molecular dynamics (MD) simulation. It is shown that residue contribution to the total folding degree is a predominantly local property, well-defined by the backbone dihedral angles at the given residue, without significant contribution from the backbone conformation of other residues. Moreover, the magnitude of this residue contribution can be quite easily associated with characteristic motifs of secondary protein structures such as the α-helix, β-sheet (hairpin), and so on by means of a Ramachandran-like plot as a function of backbone dihedral angles φ,ψ. Additionally, the understanding of the free energy profile associated with the folding process becomes much simpler. Often a 1D profile is sufficient to locate global minima and the corresponding structure for short peptides.

High pressure inhibits signaling protein binding to the flagellar motor and bacterial chemotaxis through enhanced hydration

High pressure below 100 MPa interferes inter-molecular interactions without causing pressure denaturation of proteins. In Escherichia coli, the binding of the chemotaxis signaling protein CheY to the flagellar motor protein FliM induces reversal of the motor rotation. Using molecular dynamics (MD) simulations and parallel cascade selection MD (PaCS-MD), we show that high pressure increases the water density in the first hydration shell of CheY and considerably induces water penetration into the CheY-FliM interface. PaCS-MD enabled us to observe pressure-induced dissociation of the CheY-FliM complex at atomic resolution. Pressure dependence of binding free energy indicates that the increase of pressure from 0.1 to 100 MPa significantly weakens the binding. Using high-pressure microscopy, we observed that high hydrostatic pressure fixes the motor rotation to the counter-clockwise direction. In conclusion, the application of pressure enhances hydration of the proteins and weakens the binding of CheY to FliM, preventing reversal of the flagellar motor.