Determining Protein Folding Pathway and Associated Energetics through Partitioned Integrated-Tempering-Sampling Simulation

Deep-Learning-Assisted Enhanced Sampling for Exploring Molecular Conformational Changes

We present a novel strategy to explore conformational changes and identify stable states of molecular objects, eliminating the need for a priori knowledge. The approach applies a deep learning method to extract information about the movement modes of the molecular object from a short, high-dimensional, and parameter-free preliminary enhanced-sampling simulation. The gathered information is described by a small set of deep-learning-based collective variables (dCVs), which steer the production-enhanced-sampling simulation. Considering the challenge of adequately exploring the configurational space using the low-dimensional, suboptimal dCVs, we incorporate a method designed for ergodic sampling, namely, Gaussian-accelerated molecular dynamics (MD), into the framework of CV-based enhanced sampling. MD simulations on both toy models and nontrivial examples demonstrate the remarkable computational efficiency of the strategy in capturing the conformational changes of molecular objects without a priori knowledge. Specifically, we achieved the blind folding of two fast folders, chignolin and villin, within a time scale of hundreds of nanoseconds and successfully reconstructed the free-energy landscapes that characterize their reversible folding. All in all, the presented strategy holds significant promise for investigating conformational changes in macromolecules, and it is anticipated to find extensive applications in the fields of chemistry and biology.

Enhanced sampling without borders: on global biasing functions and how to reweight them

Molecular dynamics (MD) simulations are a powerful tool to follow the time evolution of biomolecular motions in atomistic resolution. However, the high computational demand of these simulations limits the timescales of motions that can be observed. To resolve this issue, so called enhanced sampling techniques are developed, which extend conventional MD algorithms to speed up the simulation process. Here, we focus on techniques that apply global biasing functions. We provide a broad overview of established enhanced sampling methods and promising new advances. As the ultimate goal is to retrieve unbiased information from biased ensembles, we also discuss benefits and limitations of common reweighting schemes. In addition to concisely summarizing critical assumptions and implications, we highlight the general application opportunities as well as uncertainties of global enhanced sampling.

Exploring vibronic coupling in the benzene radical cation and anion with different levels of the GW approximation

The linear vibronic coupling constants of the benzene radical cation and anion have been obtained with different levels of the GW approximation, including G₀W₀, eigenvalue self-consistent GW, and quasiparticle self-consistent GW, as well as DFT with the following exchange-correlation functionals: BLYP, B3LYP, CAM-B3LYP, tuned CAM-B3LYP, and an IP-tuned CAM-B3LYP functional. The vibronic coupling constants were calculated numerically using the gradients of the eigenvalues of the degenerate HOMOs and LUMOs of the neutral benzene molecule for DFT, while the numerical gradients of the quasiparticle energies were used in the case of GW. The results were evaluated against those of high level wave function methods in the literature, and the approximate self-consistent GW methods and G₀W₀ with long-range corrected functionals were found to yield the best results on the whole.

Molecular mechanism concerning conformational changes of CDK2 mediated by binding of inhibitors using molecular dynamics simulations and principal component analysis

Cyclin-dependent kinase 2 (CDK2) has been regarded as a promising drug target for anti-tumour agents. In this study, molecular dynamics (MD) simulations and principal component (PC) analysis were used to explore binding mechanism of three inhibitors 1PU, CDK, 50Z to CDK2 and influences of their bindings on conformational changes of CDK2. The results show that bindings of inhibitors yield obvious impacts on internal dynamics, movement patterns and conformational changes of CDK2. In addition, molecular mechanics generalized Born surface area (MM-GBSA) was applied to calculate binding free energies between three inhibitors and CDK2 and evaluate their binding ability to CDK2. The results show that CDK has the strongest binding to CDK2 among the current three inhibitors. Residue-based free energy decomposition method was further utilized to decode the contributions of a single residue to binding of inhibitors, and it was found that three inhibitors not only produce hydrogen bonding interactions and hydrophobic interactions with key residues of CDK2, which promotes binding of three inhibitors to CDK2, but also share similar binding modes. This work is expected to be helpful for design of efficient drugs targeting CDK2.

Combining Virtual Reality Visualization with Ensemble Molecular Dynamics to Study Complex Protein Conformational Changes

Molecular dynamics (MD) simulations are increasingly used to elucidate relationships between protein structure, dynamics, and their biological function. Currently, it is extremely challenging to perform MD simulations of large-scale structural rearrangements in proteins that occur on millisecond timescales or beyond, as this requires very significant computational resources, or the use of cumbersome "collective variable" enhanced sampling protocols. Here, we describe a framework that combines ensemble MD simulations and virtual reality visualization (eMD-VR) to enable users to interactively generate realistic descriptions of large amplitude, millisecond timescale protein conformational changes in proteins. Detailed tests demonstrate that eMD-VR substantially decreases the computational cost of folding simulations of a WW domain, without the need to define collective variables a priori. We further show that eMD-VR generated pathways can be combined with Markov state models to describe the thermodynamics and kinetics of large-scale loop motions in the enzyme cyclophilin A. Our results suggest eMD-VR is a powerful tool for exploring protein energy landscapes in bioengineering efforts.

Enhanced sampling in molecular dynamics

Although molecular dynamics simulations have become a useful tool in essentially all fields of chemistry, condensed matter physics, materials science, and biology, there is still a large gap between the time scale which can be reached in molecular dynamics simulations and that observed in experiments. To address the problem, many enhanced sampling methods were introduced, which effectively extend the time scale being approached in simulations. In this perspective, we review a variety of enhanced sampling methods. We first discuss collective-variables-based methods including metadynamics and variationally enhanced sampling. Then, collective variable free methods such as parallel tempering and integrated tempering methods are presented. At last, we conclude with a brief introduction of some newly developed combinatory methods. We summarize in this perspective not only the theoretical background and numerical implementation of these methods but also the new challenges and prospects in the field of the enhanced sampling.

Ligand binding effects on the activation of the EGFR extracellular domain

The epidermal growth factor receptor (EGFR) is one of the most common target proteins in anti-cancer therapy. The binding of the EGF ligand to the EGFR extracellular domain (EGFR-ECD) promotes its inactive-to-active conformational transition (activation) but the relevant detailed mechanism remains elusive still. Here, the structural characterization and energetics of the EGFR-ECD conformational transition with and without the binding of the EGF are quantitatively explored using an innovative enhanced sampling MD simulation method. Intriguingly, the EGF offers hydrophobic interactions (e.g., EGF residues of Tyr44 and Leu47) and electrostatic interactions (e.g., the EGF residues of Glu5, Asp11, Asp17, and Arg41) to play a dominant role in dragging domain III to close the ligand binding domain gap. Subsequently, the correlation between domains III and II is enhanced through salt-bridges among Glu376, Arg403, and Arg405 from domain III and Glu293, Glu295, and Arg300 from domain II. Finally, the structural bending of domain II is regulated to facilitate the disengagement of domain II from domain IV. In this regard, the functional conformational transition of EGFR-ECD is a consequence of the cooperative motion of protein domains driven by the EGF ligand binding. The present study shows a detailed scenario of the EGF induced activation of EGFR-ECD and provides valuable information for drug discovery targeting the EGFR.

Decoding molecular mechanism of inhibitor bindings to CDK2 using molecular dynamics simulations and binding free energy calculations

CDK2 can be used as an attractive target for development of efficient inhibitors curing multiple disease relating with CDK2. In this work, molecular dynamics (MD) simulations and binding free energy calculations were coupled to probe conformational changes of CDK2 due to inhibitor associations and binding mechanisms of inhibitors PM1, FMD and X64 to CDK2. The results suggest that the binding strength of FMD and X64 to CDK2 is stronger than that of PM1. Principal component (PC) analysis and cross-correlation map calculations based on the equilibrated MD trajectories demonstrate that the structural difference in inhibitors exerts important impact on motion modes and dynamics behavior of CDK2. Residue-based free energy decomposition method was adopted to estimate the inhibitor-residue spectrum. The results not only efficiently identify the hot interaction spot of inhibitors with CDK2 but also show that the hydrophobic rings R1, R2 and R3 as well as polar groups of three inhibitors play key roles in favorably binding of inhibitors to CDK2. This work is expected to contribute energetic basis and dynamics information to development of promising inhibitors toward CDK2.Communicated by Ramaswamy H. Sarma.

Nonnative contact effects in protein folding

The folding simulations of three ββα-motifs and β-barrel structured proteins (NTL9, NuG2b, and CspA) were performed to determine the important roles of native and nonnative contacts in protein folding.

Assessing AMBER force fields for protein folding in an implicit solvent

Molecular dynamics (MD) simulation implemented with a state-of-the-art protein force field and implicit solvent model is an attractive approach to investigate protein folding, one of the most perplexing problems in molecular biology. But how well can force fields developed independently of implicit solvent models work together in reproducing diverse protein native structures and measuring the corresponding folding thermodynamics is not always clear. In this work, we performed enhanced sampling MD simulations to assess the ability of six AMBER force fields (FF99SBildn, FF99SBnmr, FF12SB, FF14ipq, FF14SB, and FF14SBonlysc) as coupled with a recently improved pair-wise GB-Neck2 model in modeling the folding of two helical and two β-sheet peptides. Whilst most of the tested force fields can yield roughly similar features for equilibrium conformational ensembles and detailed folding free-energy profiles for short α-helical TC10b in an implicit solvent, the measured counterparts are significantly discrepant in the cases of larger or β-structured peptides (HP35, 1E0Q, and GTT). Additionally, the calculated folding/unfolding thermodynamic quantities can only partially match the experimental data. Although a combination of the force fields and GB-Neck2 implicit model able to describe all aspects of the folding transitions towards the native structures of all the considered peptides was not identified, we found that FF14SBonlysc coupled with the GB-Neck2 model seems to be a reasonably balanced combination to predict peptide folding preferences.

Exploring molecular mechanism of allosteric inhibitor to relieve drug resistance of multiple mutations in HIV-1 protease by enhanced conformational sampling

Recently, allosteric regulations of HIV-1 protease (PR) are suggested as a promising approach to relieve drug resistance of mutations toward inhibitors targeting the active site of PR. Replica-exchange molecular dynamics (REMD) simulations and normal mode analysis (NMA) are integrated to enhance conformational sampling of PR. Molecular mechanics generalized Born surface area (MM-GBSA) method was applied to calculate binding free energies of three inhibitors APV, DRV, and NIT to the wild-type (WT) and multidrug resistance (MDR) PRs. The results suggest that binding free energies of APV and DRV are decreased in the MDR PR relative to the WT PR, suggesting drug resistance of mutations on these two inhibitors. However, the binding ability of the allosteric inhibitor NIT is not impaired in the MDR PR. In addition, internal dynamics analysis based on REMD simulations proves that mutations hardly produce obvious effect on the conformation of the MDR PR in comparison to the WT PR. Scanning of hydrophobic contacts and hydrogen bond contacts of inhibitors with residues of PRs on the concatenated trajectories of REMD demonstrates that mutations change the symmetric interaction networks of APV and DRV with PR, but do not generate obvious influence on the asymmetric interaction network of NIT with PR. In summary, allosteric inhibitor NIT can adapt the MDR PR better than those inhibitors toward the active site of PR, thus allosteric inhibitors of PR may be a possible channel to overcome drug resistance of PR.

The effects of implicit modeling of nonpolar solvation on protein folding simulations

Implicit solvent models, in which the polar and nonpolar solvation free-energies of solute molecules are treated separately, have been widely adopted for molecular dynamics simulation of protein folding. While the development of the implicit models is mainly focused on the methodological improvement and key parameter optimization for polar solvation, nonpolar solvation has been either ignored or described by a simplistic surface area (SA) model. In this work, we performed the folding simulations of multiple β-hairpin and α-helical proteins with varied surface tension coefficients embedded in the SA model to clearly demonstrate the effects of nonpolar solvation treated by a popular SA model on protein folding. The results indicate that the change in the surface tension coefficient does not alter the ability of implicit solvent simulations to reproduce a protein native structure but indeed controls the components of the equilibrium conformational ensemble and modifies the energetic characterization of the folding transition pathway. The suitably set surface tension coefficient can yield explicit solvent simulations and/or experimentally suggested folding mechanism of protein. In addition, the implicit treatment of both polar and nonpolar components of solvation free-energy contributes to the overestimation of the secondary structure in implicit solvent simulations.