A kinetic model of trp-cage folding from multiple biased molecular dynamics simulations

Robust and predictive 3D-QSAR models for predicting the activities of novel oxadiazole derivatives as multifunctional anti-Alzheimer agents

In recent years, Alzheimer disease (AD) as a neurodegenerative disorder has been increasing annually with the aging of the global population, therefore, development of novel anti-AD drugs is imperative. Studies have proven that glycogen synthase kinase-3β (GSK-3β) is a pivotal factor in the development of AD. Therefore, GSK-3β inhibitors would provide powerful means to treat the disorders, such as AD. To in-depth study the structure-activity relationship of a series of oxadiazole derivatives as multifunctional anti-Alzheimer agents, computational three dimensional quantitative structure-activity relationship (3D-QSAR) studies, molecular docking and molecular dynamics were conducted. The comparative molecular field analysis (CoMFA) and comparative molecular similarity indices analysis (CoMSIA) methods were conducted to build up the 3D-QSAR models, and exhibited significant results (R cv 2 = 0.692, R pred 2 = 0.6885/CoMFA, R cv 2 = 0.696, R pred 2 = 0.6887/CoMSIA). The accuracy of the 3D-QSAR models was validated by external validation and applicability domain analysis. The derived contour maps provided structural information for designing novel compounds to improve the inhibitory activities. Additionally, molecular docking and molecular dynamics were also employed to investigate the bonding interactions and stability of this series of inhibitors in the active site of GSK-3β, and the results revealed that the importance of residues Ile62, Asn64 Val70, Tyr128, Val129 and Leu182 for ligand binding to the receptor GSK-3β. All the results would be of great help for the discovery of new GSK-3β agents that can solve the problem of AD.

Coarse-Grained Molecular Dynamics with Normalizing Flows

We propose a sampling algorithm relying on a collective variable (CV) of midsize dimension modeled by a normalizing flow and using nonequilibrium dynamics to propose full configurational moves from the proposition of a refreshed value of the CV made by the flow. The algorithm takes the form of a Markov chain with nonlocal updates, allowing jumps through energy barriers across metastable states. The flow is trained throughout the algorithm to reproduce the free energy landscape of the CV. The output of the algorithm is a sample of thermalized configurations and the trained network that can be used to efficiently produce more configurations. We show the functioning of the algorithm first in a test case with a mixture of Gaussians. Then, we successfully tested it on a higher-dimensional system consisting of a polymer in solution with a compact state and an extended stable state separated by a high free energy barrier.

Quantifying Unbiased Conformational Ensembles from Biased Simulations Using ShapeGMM

Quantifying the conformational ensembles of biomolecules is fundamental to describing mechanisms of processes such as protein folding, interconversion between folded states, ligand binding, and allosteric regulation. Accurate quantification of these ensembles remains a challenge for conventional molecular simulations of all but the simplest molecules due to insufficient sampling. Enhanced sampling approaches, such as metadynamics, were designed to overcome this challenge; however, the nonuniform frame weights that result from many of these approaches present an additional challenge to ensemble quantification techniques such as Markov State Modeling or structural clustering. Here, we present rigorous inclusion of nonuniform frame weights into a structural clustering method entitled shapeGMM. The result of frame-weighted shapeGMM is a high dimensional probability density and generative model for the unbiased system from which we can compute important thermodynamic properties such as relative free energies and configurational entropy. The accuracy of this approach is demonstrated by the quantitative agreement between GMMs computed by Hamiltonian reweighting and direct simulation of a coarse-grained helix model system. Furthermore, the relative free energy computed from a shapeGMM probability density of alanine dipeptide reweighted from a metadynamics simulation quantitatively reproduces the underlying free energy in the basins. Finally, the method identifies hidden structures along the actin globular to filamentous-like structural transition from a metadynamics simulation on a linear discriminant analysis coordinate trained on GMM states, illustrating how structural clustering of biased data can lead to biophysical insight. Combined, these results demonstrate that frame-weighted shapeGMM is a powerful approach to quantifying biomolecular ensembles from biased simulations.

Harmonization Risks and Rewards: Nano-QSAR for Agricultural Nanomaterials

This comprehensive review explores the emerging landscape of Nano-QSAR (quantitative structure-activity relationship) for assessing the risk and potency of nanomaterials in agricultural settings. The paper begins with an introduction to Nano-QSAR, providing background and rationale, and explicitly states the hypotheses guiding the review. The study navigates through various dimensions of nanomaterial applications in agriculture, encompassing their diverse properties, types, and associated challenges. Delving into the principles of QSAR in nanotoxicology, this article elucidates its application in evaluating the safety of nanomaterials, while addressing the unique limitations posed by these materials. The narrative then transitions to the progression of Nano-QSAR in the context of agricultural nanomaterials, exemplified by insightful case studies that highlight both the strengths and the limitations inherent in this methodology. Emerging prospects and hurdles tied to Nano-QSAR in agriculture are rigorously examined, casting light on important pathways forward, existing constraints, and avenues for research enhancement. Culminating in a synthesis of key insights, the review underscores the significance of Nano-QSAR in shaping the future of nanoenabled agriculture. It provides strategic guidance to steer forthcoming research endeavors in this dynamic field.

Effect of Main and Side Chains on the Folding Mechanism of the Trp-Cage Miniprotein

Proteins that do not fold into their functional native state have been linked to diseases. In this study, the influence of the main and side chains of individual amino acids on the folding of the tryptophan cage (Trp-cage), a designed 20-residue miniprotein, was analyzed. For this purpose, we calculated the solvation free energy (SFE) contributions of individual atoms by using the 3D-reference interaction site model with the atomic decomposition method. The mechanism by which the Trp-cage is stabilized during the folding process was examined by calculating the total energy, which is the sum of the conformational energy and SFE. The folding process of the Trp-cage resulted in a stable native state, with a total energy that was 62.4 kcal/mol lower than that of the unfolded state. The solvation entropy, which is considered to be responsible for the hydrophobic effect, contributed 31.3 kcal/mol to structural stabilization. In other words, the contribution of the solvation entropy accounted for approximately half of the total contribution to Trp-cage folding. The hydrophobic core centered on Trp6 contributed 15.6 kcal/mol to the total energy, whereas the solvation entropy contribution was 6.3 kcal/mol. The salt bridge formed by the hydrophilic side chains of Asp9 and Arg16 contributed 10.9 and 5.0 kcal/mol, respectively. This indicates that not only the hydrophobic core but also the salt bridge of the hydrophilic side chains gain solvation entropy and contribute to stabilizing the native structure of the Trp-cage.

An interoperable implementation of collective-variable based enhanced sampling methods in extended phase space within the OpenMM package

Collective variable (CV)-based enhanced sampling techniques are widely used today for accelerating barrier-crossing events in molecular simulations. A class of these methods, which includes temperature accelerated molecular dynamics (TAMD)/driven-adiabatic free energy dynamics (d-AFED), unified free energy dynamics (UFED), and temperature accelerated sliced sampling (TASS), uses an extended variable formalism to achieve quick exploration of conformational space. These techniques are powerful, as they enhance the sampling of a large number of CVs simultaneously compared to other techniques. Extended variables are kept at a much higher temperature than the physical temperature by ensuring adiabatic separation between the extended and physical subsystems and employing rigorous thermostatting. In this work, we present a computational platform to perform extended phase space enhanced sampling simulations using the open-source molecular dynamics engine OpenMM. The implementation allows users to have interoperability of sampling techniques, as well as employ state-of-the-art thermostats and multiple time-stepping. This work also presents protocols for determining the critical parameters and procedures for reconstructing high-dimensional free energy surfaces. As a demonstration, we present simulation results on the high dimensional conformational landscapes of the alanine tripeptide in vacuo, tetra-N-methylglycine (tetra-sarcosine) peptoid in implicit solvent, and the Trp-cage mini protein in explicit water.

The "Beacon" Structural Model of Protein Folding: Application for Trp-Cage in Water

Protein folding is a process in which a polypeptide must undergo folding process to obtain its three-dimensional structure. Thermodynamically, it is a process of enthalpy to overcome the loss of conformational entropy in folding. Folding is primarily related to hydrophobic interactions and intramolecular hydrogen bondings. During folding, hydrophobic interactions are regarded to be the driving forces, especially in the initial structural collapse of a protein. Additionally, folding is guided by the strong interactions within proteins, such as intramolecular hydrogen bondings related to the α-helices and β-sheets of proteins. Therefore, a protein is divided into the folding key (FK) regions related to intramolecular hydrogen bondings and the non-folding key (non-FK) regions. Various conformations are expected for FK and non-FK regions. Different from non-FK regions, it is necessary for FK regions to form the specific conformations in folding, which are regarded as the necessary folding pathways (or "beacons"). Additionally, sequential folding is expected for the FK regions, and the intermediate state is found during folding. They are reflected on the local basins in the free energy landscape (FEL) of folding. To demonstrate the structural model, molecular dynamics (MD) simulations are conducted on the folding pathway of the TRP-cage in water.

The Conformational Transitions and Dynamics of Burkholderia cepacia Lipase Regulated by Water-Oil Interfaces

Structural dynamics and conformational transitions are crucial for the activities of enzymes. As one of the most widely used industrial biocatalysts, lipase could be activated by the water-oil interfaces. The interface activations were believed to be dominated by the close-to-open transitions of the lid subdomains. However, the detailed mechanism and the roles of structure transitions are still under debate. In this study, the dynamic structures and conformational transitions of Burkholderia cepacia lipase (LipA) were investigated by combining all-atom molecular dynamics simulations, enhanced sampling simulation, and spectrophotometric assay experiments. The conformational transitions between the lid-open and lid-closed states of LipA in aqueous solution are directly observed by the computational simulation methods. The interactions between the hydrophobic residues on the two lid-subdomains are the driven forces for the LipA closing. Meanwhile, the hydrophobic environment provided by the oil interfaces would separate the interactions between the lid-subdomains and promote the structure opening of LipA. Moreover, our studies demonstrate the opening of the lids structure is insufficient to initiate the interfacial activation, providing explanations for the inability of interfacial activation of many lipases with lid structures.

Folding-unfolding asymmetry and a RetroFold computational algorithm

We treat protein folding as molecular self-assembly, while unfolding is viewed as disassembly. Fracture is typically a much faster process than self-assembly. Self-assembly is often an exponentially decaying process, since energy relaxes due to dissipation, while fracture is a constant-rate process as the driving force is opposed by damping. Protein folding takes two orders of magnitude longer than unfolding. We suggest a mathematical transformation of variables, which makes it possible to view self-assembly as time-reversed disassembly, thus folding can be studied as reversed unfolding. We investigate the molecular dynamics modelling of folding and unfolding of the short Trp-cage protein. Folding time constitutes about 800 ns, while unfolding (denaturation) takes only about 5.0 ns and, therefore, fewer computational resources are needed for its simulation. This RetroFold approach can be used for the design of a novel computation algorithm, which, while approximate, is less time-consuming than traditional folding algorithms.

Analysis of Protein Folding Simulation with Moving Root Mean Square Deviation

We apply moving root-mean-square deviation (mRMSD), which does not require a reference structure, as a method for analyzing protein dynamics. This method can be used to calculate the root-mean-square deviation (RMSD) of structure between two specified time points and to analyze protein dynamics behavior through time series analysis. We applied this method to the Trp-cage trajectory calculated by the Anton supercomputer and found that it shows regions of stable states as well as the conventional RMSD. In addition, we extracted a characteristic structure in which the side chains of Asp1 and Arg16 form hydrogen bonds near the most stable structure of the Trp-cage. We also determined that ≥20 ns is an appropriate time interval to investigate protein dynamics using mRMSD. Applying this method to NuG2 protein, we found that mRMSD can be used to detect regions of metastable states in addition to the stable state. This method can be applied to molecular dynamics simulations of proteins whose stable structures are unknown.

The Role of Transient Intermediate Structures in the Unfolding of the Trp-Cage Fast-Folding Protein: Generating Ensembles from Time-Resolved X-ray Solution Scattering with Genetic Algorithms

The Trp-cage miniprotein is one of the smallest systems to exhibit a stable secondary structure and fast-folding dynamics, serving as an apt model system to study transient intermediates with both experimental and computational analyses. Previous spectroscopic characterizations that have been done on Trp-cage have inferred a single stable intermediate on a pathway from folded to unfolded basins. We aim to bridge the understanding of Trp-cage structural folding dynamics on microsecond-time scales, by utilizing time-resolved X-ray solution scattering to probe the temperature-induced unfolding pathway. Our results indicate the formation of a conformationally extended intermediate on the time scale of 1 μs, which undergoes complete unfolding within 5 μs. We further investigated the atomistic structural details of the unfolding pathway using a genetic algorithm to generate ensemble model fits to the scattering profiles. This analysis paves the way for direct benchmarking of theoretical models of protein folding ensembles produced with molecular dynamics simulations.

Identification of the structural features of quinazoline derivatives as EGFR inhibitors using 3D-QSAR modeling, molecular docking, molecular dynamics simulations and free energy calculations

Epidermal growth factor receptor (EGFR) is a promising target for the treatment of different types of malignant tumors. Therefore, a combined molecular modeling study was performed on a series of quinazoline derivatives as EGFR inhibitors. The optimum ligand-based CoMFA and CoMSIA models showed reliable and satisfactory predictability (with R²_cv=0.681, R²_ncv=0.844, R²_pred=0.8702 and R²_cv=0.643, R²_ncv=0.874, R²_pred=0.6423). The derived contour maps provide structural features to improve inhibitory activity. Furthermore, the contour maps, molecular docking, and molecular dynamics (MD) simulations have good consistency, illustrating that the derived models are reliable. In addition, MD simulations and binding free energy calculations were also carried out to understand the conformational fluctuations at the binding pocket of the receptor. The results indicate that hydrogen bond, hydrophobic and electrostatic interactions play significant roles on activity and selectivity. Furthermore, amino acids Val31, Lys50, Thr95, Leu149 and Asp160 are considered as essential residues to participate in the ligand-receptor interactions. Overall, this work would offer reliable theoretical basis for future structural modification, design and synthesis of novel EGFR inhibitors with good potency.Communicated by Ramaswamy H. Sarma.

Characterization of the Conformations of Amyloid Beta 42 in Solution That May Mediate Its Initial Hydrophobic Aggregation

Intrinsically disordered peptides, such as amyloid β42 (Aβ42), lack a well-defined structure in solution. Aβ42 can undergo abnormal aggregation and amyloidogenesis in the brain, forming fibrillar plaques, a hallmark of Alzheimer's disease. The insoluble fibrillar forms of Aβ42 exhibit well-defined, cross β-sheet structures at the molecular level and are less toxic than the soluble, intermediate disordered oligomeric forms. However, the mechanism of initial interaction of monomers and subsequent oligomerization is not well understood. The structural disorder of Aβ42 adds to the challenges of determining the structural properties of its monomers, making it difficult to understand the underlying molecular mechanism of pathogenic aggregation. Certain regions of Aβ42 are known to exhibit helical propensity in different physiological conditions. NMR spectroscopy has shown that the Aβ42 monomer at lower pH can adopt an α-helical conformation and as the pH is increased, the peptide switches to β-sheet conformation and aggregation occurs. CD spectroscopy studies of aggregation have shown the presence of an initial spike in the amount of α-helical content at the start of aggregation. Such an increase in α-helical content suggests a mechanism wherein the peptide can expose critical non-polar residues for interaction, leading to hydrophobic aggregation with other interacting peptides. We have used molecular dynamics simulations to characterize in detail the conformational landscape of monomeric Aβ42 in solution to identify molecular properties that may mediate the early stages of oligomerization. We hypothesized that conformations with α-helical structure have a higher probability of initiating aggregation because they increase the hydrophobicity of the peptide. Although random coil conformations were found to be the most dominant, as expected, α-helical conformations are thermodynamically accessible, more so than β-sheet conformations. Importantly, for the first time α-helical conformations are observed to increase the exposure of aromatic and hydrophobic residues to the aqueous solvent, favoring their hydrophobically driven interaction with other monomers to initiate aggregation. These findings constitute a first step toward characterizing the mechanism of formation of disordered, low-order oligomers of Aβ42.

Transition Rates and Efficiency of Collective Variables from Time-Dependent Biased Simulations

Simulations with adaptive time-dependent bias enable an efficient exploration of the conformational space of a system. However, the dynamic information is altered by the bias. Infrequent metadynamics recovers the transition rate of crossing a barrier, if the collective variables are ideal and there is no bias deposition near the transition state. Unfortunately, these conditions are not always fulfilled. To overcome these limitations, and inspired by single-molecule force spectroscopy, we use Kramers' theory for calculating the barrier-crossing rate when a time-dependent bias is added to the system. We assess the efficiency of collective variables parameter by measuring how efficiently the bias accelerates the transitions. We present approximate analytical expressions of the survival probability, reproducing the barrier-crossing time statistics and enabling the extraction of the unbiased transition rate even for challenging cases. We explore the limits of our method and provide convergence criteria to assess its validity.

Topological bio-scaling analysis as a universal measure of protein folding

Scaling relationships for polymeric molecules establish power law dependencies between the number of molecular segments and linear dimensions, such as the radius of gyration. They also establish spatial topological properties of the chains, such as their dimensionality. In the spatial domain, power exponents α = 1 (linear stretched molecule), α = 0.5 (the ideal chain) and α = 0.333 (compact globule) are significant. During folding, the molecule undergoes the transition from the one-dimensional linear to the three-dimensional globular state within a very short time. However, intermediate states with fractional dimensions can be stabilized by modifying the solubility (e.g. by changing the solution temperature). Topological properties, such as dimension, correlate with the interaction energy, and thus by tuning the solubility one can control molecular interaction. We investigate these correlations using the example of a well-studied short model of Trp-cage protein. The radius of gyration is used to estimate the fractal dimension of the chain at different stages of folding. It is expected that the same principle is applicable to much larger molecules and that topological (dimensional) characteristics can provide insights into molecular folding and interactions.

A Transfer Free Energy Based Implicit Solvent Model for Protein Simulations in Solvent Mixtures: Urea-Induced Denaturation as a Case Study

We developed a method for implicit solvent molecular dynamics simulations of proteins in solvent mixtures (model with implicit solvation thermodynamics, MIST). The MIST method introduces experimental group transfer free energies to the generalized Born formulation for generating molecular trajectories without the need for developing rigorous explicit-solvent force fields for multicomponent solutions. As a test case, we studied the urea-induced denaturation of the Trp-cage miniprotein in water. We demonstrate that our method allows efficient exploration of the conformational space of the protein in only a few hundreds of nanoseconds of all-atom unbiased simulations. Furthermore, selective implementation of the transfer free energies of specific peptide groups, backbone, and side chains enables us to decouple their specific energetic contributions to the conformational changes of the protein. The approach herein developed can readily be extended to the investigation of complex matrices as well as to the characterization of protein aggregation. The MIST method is implemented in Plumed (ver. 2.8) as a separate module called SASA.

Differential ion dehydration energetics explains selectivity in the non-canonical lysosomal K+ channel TMEM175

Structures of the human lysosomal K⁺ channel transmembrane protein 175 (TMEM175) in open and closed states revealed a novel architecture lacking the canonical K⁺ selectivity filter motif present in previously known K⁺ channel structures. A hydrophobic constriction composed of four isoleucine residues was resolved in the pore and proposed to serve as the gate in the closed state, and to confer ion selectivity in the open state. Here, we achieve higher-resolution structures of the open and closed states and employ molecular dynamics simulations to analyze the conducting properties of the putative open state, demonstrating that it is permeable to K⁺ and, to a lesser degree, also Na⁺. Both cations must dehydrate significantly to penetrate the narrow hydrophobic constriction, but ion flow is assisted by a favorable electrostatic field generated by the protein that spans the length of the pore. The balance of these opposing energetic factors explains why permeation is feasible, and why TMEM175 is selective for K⁺ over Na⁺, despite the absence of the canonical selectivity filter. Accordingly, mutagenesis experiments reveal an exquisite sensitivity of the channel to perturbations that mitigate the constriction. Together, these data reveal a novel mechanism for selective permeation of ions by TMEM175 that is unlike that of other K⁺ channels.

Integrative structure determination reveals functional global flexibility for an ultra-multimodular arabinanase

AbnA is an extracellular GH43 α-L-arabinanase from Geobacillus stearothermophilus, a key bacterial enzyme in the degradation and utilization of arabinan. We present herein its full-length crystal structure, revealing the only ultra-multimodular architecture and the largest structure to be reported so far within the GH43 family. Additionally, the structure of AbnA appears to contain two domains belonging to new uncharacterized carbohydrate-binding module (CBM) families. Three crystallographic conformational states are determined for AbnA, and this conformational flexibility is thoroughly investigated further using the "integrative structure determination" approach, integrating molecular dynamics, metadynamics, normal mode analysis, small angle X-ray scattering, dynamic light scattering, cross-linking, and kinetic experiments to reveal large functional conformational changes for AbnA, involving up to ~100 Å movement in the relative positions of its domains. The integrative structure determination approach demonstrated here may apply also to the conformational study of other ultra-multimodular proteins of diverse functions and structures.

Exploration of high dimensional free energy landscapes by a combination of temperature-accelerated sliced sampling and parallel biasing

Temperature-accelerated sliced sampling (TASS) is an enhanced sampling method for achieving accelerated and controlled exploration of high-dimensional free energy landscapes in molecular dynamics simulations. With the aid of umbrella bias potentials, the TASS method realizes a controlled exploration and divide-and-conquer strategy for computing high-dimensional free energy surfaces. In TASS, diffusion of the system in the collective variable (CV) space is enhanced with the help of metadynamics bias and elevated-temperature of the auxiliary degrees of freedom (DOF) that are coupled to the CVs. Usually, a low-dimensional metadynamics bias is applied in TASS. In order to further improve the performance of TASS, we propose here to use a highdimensional metadynamics bias, in the same form as in a parallel bias metadynamics scheme. Here, a modified reweighting scheme, in combination with artificial neural network is used for computing unbiased probability distribution of CVs and projections of high-dimensional free energy surfaces. We first validate the accuracy and efficiency of our method in computing the four-dimensional free energy landscape for alanine tripeptide in vacuo. Subsequently, we employ the approach to calculate the eight-dimensional free energy landscape of alanine pentapeptide in vacuo. Finally, the method is applied to a more realistic problem wherein we compute the broad four-dimensional free energy surface corresponding to the deacylation of a drug molecule which is covalently complexed with a β-lactamase enzyme. We demonstrate that using parallel bias in TASS improves the efficiency of exploration of high-dimensional free energy landscapes.

Determination of Equilibrium Adsorbed Morphologies of Surfactants at Metal-Water Interfaces Using a Modified Umbrella Sampling-Based Methodology

Surfactants adsorb to metal-water interfaces in various morphologies, including self-assembled monolayers (SAMs), cylindrical and spherical micelles, or hemimicelles. Current molecular simulation methods are unable to efficiently sample the formation of these morphologies because of the large diffusive/energetic barriers. We introduce a modified umbrella sampling-based methodology that allows sampling of these morphologies from any initial configuration and provides free energy differences between them. Using this methodology, we have studied adsorption behavior of cationic [quaternary ammonium (quat) of 4 and 12 carbon long alkyl tails], uncharged [decanethiol], and anionic [phosphate monoester] surfactants and their mixtures at a gold-water interface. We find that while Coulombic repulsion between the charged head groups of quat-4 limits their adsorption to a sparse layer, stronger hydrophobic interactions between the alkyl tails of quat-12 promote adsorption resulting in a morphology with adsorbed hemispherical micelles sitting atop a monolayer. Decanethiol molecules adsorb in a densely packed bilayer with the molecules standing-up on the surface in the first layer and lying parallel to the surface in the second layer. Cationic and anionic surfactant mixtures display a synergistic adsorption behavior. These results elucidate the role of molecular characteristics in dictating the nature of adsorbed morphologies of surfactants at metal-water interfaces.

The auto-inhibition mechanism of transcription factor Ets-1 induced by phosphorylation on the intrinsically disordered region

As the most abundant post-translation modifications (PTMs), the phosphorylation usually occurred on the intrinsically disordered regions (IDRs). The regulation on the structures and interactions of IDRs induced by phosphorylation is critical to the function performing. The eukaryotic transcription factor 1 (Ets-1) is a member of transcription factor family, which participates in many important biological processes. The DNA-binding ability of Ets-1 is auto-inhibited by a disordered serine-rich region (SRR) on the Ets-1. The inhibition ability of SRR is greatly enhanced by the phosphorylation of the serine on the SRR. Nevertheless, the molecular mechanisms of the phosphorylation regulation on the structure and activity of Ets-1 are still unclear and under debates. By using both of the molecular simulations and biochemical experiments, we studied the molecule mechanism of phosphorylation regulation on the auto-inhibition of the Ets-1. The reasons of stabilization of Ets-1 core by phosphorylation on SRR region were elucidated. More important, the free energy landscapes (FEL) show that both of the steric hindrance and allosteric regulation are responsible for the DNA-binding inhibitory induced by phosphorylation, but the steric effects contribute greater than the allosteric regulation. The phosphorylation not only enhances the electrostatic interactions to facilitate the steric impedance, but also promotes the formation of hydrophobic residue clusters, which provide major driven force for the allosteric regulation. The structural basis of auto-inhibition of Ets-1 induced by the phosphorylation revealed in this study would great help the developing of inhibitor for the cancer therapy.

Mechanistic Insights into the Ligand-Induced Unfolding of an RNA G-Quadruplex

The cationic porphyrin TMPyP4 is a well-established DNA G-quadruplex (G4) binding ligand that can stabilize different topologies via multiple binding modes. However, TMPyP4 can have both a stabilizing and destabilizing effect on RNA G4 structures. The structural mechanisms that mediate RNA G4 unfolding remain unknown. Here, we report on the TMPyP4-induced RNA G4 unfolding mechanism studied by well-tempered metadynamics (WT-MetaD) with supporting biophysical experiments. The simulations predict a two-state mechanism of TMPyP4 interaction via a groove-bound and a top-face-bound conformation. The dynamics of TMPyP4 stacking on the top tetrad disrupts Hoogsteen H-bonds between guanine bases, resulting in the consecutive TMPyP4 intercalation from top-to-bottom G-tetrads. The results reveal a striking correlation between computational and experimental approaches and validate WT-MetaD simulations as a powerful tool for studying RNA G4-ligand interactions.

Boosting the conformational sampling by combining replica exchange with solute tempering and well-sliced metadynamics

Methods that combine collective variable (CV) based enhanced sampling and global tempering approaches are used in speeding-up the conformational sampling and free energy calculation of large and soft systems with a plethora of energy minima. In this paper, a new method of this kind is proposed in which the well-sliced metadynamics approach (WSMTD) is united with replica exchange with solute tempering (REST2) method. WSMTD employs a divide-and-conquer strategy wherein high-dimensional slices of a free energy surface are independently sampled and combined. The method enables one to accomplish a controlled exploration of the CV-space with a restraining bias as in umbrella sampling, and enhance-sampling of one or more orthogonal CVs using a metadynamics like bias. The new hybrid method proposed here enables boosting the sampling of more slow degrees of freedom in WSMTD simulations, without the need to specify associated CVs, through a replica exchange scheme within the framework of REST2. The high-dimensional slices of the probability distributions of CVs computed from the united WSMTD and REST2 simulations are subsequently combined using the weighted histogram analysis method to obtain the free energy surface. We show that the new method proposed here is accurate, improves the conformational sampling, and achieves quick convergence in free energy estimates. We demonstrate this by computing the conformational free energy landscapes of solvated alanine tripeptide and Trp-cage mini protein in explicit water.

Resolving Dynamics in the Ensemble: Finding Paths through Intermediate States and Disordered Protein Structures

Proteins have been found to inhabit a diverse set of three-dimensional structures. The dynamics that govern protein interconversion between structures happen over a wide range of time scales─picoseconds to seconds. Our understanding of protein functions and dynamics is largely reliant upon our ability to elucidate physically populated structures. From an experimental structural characterization perspective, we are often limited to measuring the ensemble-averaged structure both in the steady-state and time-resolved regimes. Generating kinetic models and understanding protein structure-function relationships require atomistic knowledge of the populated states in the ensemble. In this Perspective, we present ensemble refinement methodologies that integrate time-resolved experimental signals with molecular dynamics models. We first discuss integration of experimental structural restraints to molecular models in disordered protein systems that adhere to the principle of maximum entropy for creating a complete set of ensemble structures. We then propose strategies to find kinetic pathways between the refined structures, using time-resolved inputs to guide molecular dynamics trajectories and the use of inference to generate tailored stimuli to prepare a desired ensemble of protein states.

Force-Correction Analysis Method for Derivation of Multidimensional Free-Energy Landscapes from Adaptively Biased Replica Simulations

A methodology is proposed for the calculation of multidimensional free-energy landscapes of molecular systems, based on analysis of multiple molecular dynamics trajectories wherein adaptive biases have been applied to enhance the sampling of different collective variables. In this approach, which we refer to as the Force-Correction Analysis Method (FCAM), local averages of the total and biasing forces are evaluated post hoc, and the latter are subtracted from the former to obtain unbiased estimates of the mean force across collective-variable space. Multidimensional free-energy surfaces and minimum free-energy pathways are then derived by integrating the mean-force landscape with a kinetic Monte Carlo algorithm. To evaluate the proposed method, a series of numerical tests and comparisons with existing approaches were carried out for small molecules, peptides, and proteins, based on all-atom trajectories generated with standard, concurrent, and replica-exchange metadynamics in collective-variable spaces ranging from one to six dimensional. The tests confirm the correctness of the FCAM formulation and demonstrate that calculated mean forces and free energies converge rapidly and accurately, outperforming other methods used to unbias this kind of simulation data.

CORE-MD II: A fast, adaptive, and accurate enhanced sampling method

In this paper, we present a fast and adaptive correlation guided enhanced sampling method (CORE-MD II). The CORE-MD II technique relies, in part, on partitioning of the entire pathway into short trajectories that we refer to as instances. The sampling within each instance is accelerated by adaptive path-dependent metadynamics simulations. The second part of this approach involves kinetic Monte Carlo (kMC) sampling between the different states that have been accessed during each instance. Through the combination of the partition of the total simulation into short non-equilibrium simulations and the kMC sampling, the CORE-MD II method is capable of sampling protein folding without any a priori definitions of reaction pathways and additional parameters. In the validation simulations, we applied the CORE-MD II on the dialanine peptide and the folding of two peptides: TrpCage and TrpZip2. In a comparison with long time equilibrium Molecular Dynamics (MD), 1 µs replica exchange MD (REMD), and CORE-MD I simulations, we find that the level of convergence of the CORE-MD II method is improved by a factor of 8.8, while the CORE-MD II method reaches acceleration factors of ∼120. In the CORE-MD II simulation of TrpZip2, we observe the formation of the native state in contrast to the REMD and the CORE-MD I simulations. The method is broadly applicable for MD simulations and is not restricted to simulations of protein folding or even biomolecules but also applicable to simulations of protein aggregation, protein signaling, or even materials science simulations.

Unsupervised Learning Methods for Molecular Simulation Data

Unsupervised learning is becoming an essential tool to analyze the increasingly large amounts of data produced by atomistic and molecular simulations, in material science, solid state physics, biophysics, and biochemistry. In this Review, we provide a comprehensive overview of the methods of unsupervised learning that have been most commonly used to investigate simulation data and indicate likely directions for further developments in the field. In particular, we discuss feature representation of molecular systems and present state-of-the-art algorithms of dimensionality reduction, density estimation, and clustering, and kinetic models. We divide our discussion into self-contained sections, each discussing a specific method. In each section, we briefly touch upon the mathematical and algorithmic foundations of the method, highlight its strengths and limitations, and describe the specific ways in which it has been used-or can be used-to analyze molecular simulation data.

Long-Time-Scale Predictions from Short-Trajectory Data: A Benchmark Analysis of the Trp-Cage Miniprotein

Elucidating physical mechanisms with statistical confidence from molecular dynamics simulations can be challenging owing to the many degrees of freedom that contribute to collective motions. To address this issue, we recently introduced a dynamical Galerkin approximation (DGA) [Thiede, E. H. J. Chem. Phys., 150, 2019, 244111], in which chemical kinetic statistics that satisfy equations of dynamical operators are represented by a basis expansion. Here, we reformulate this approach, clarifying (and reducing) the dependence on the choice of lag time. We present a new projection of the reactive current onto collective variables and provide improved estimators for rates and committors. We also present simple procedures for constructing suitable smoothly varying basis functions from arbitrary molecular features. To evaluate estimators and basis sets numerically, we generate and carefully validate a data set of short trajectories for the unfolding and folding of the trp-cage miniprotein, a well-studied system. Our analysis demonstrates a comprehensive strategy for characterizing reaction pathways quantitatively.

Predicting the aptamer SYL3C-EpCAM complex's structure with the Martini-based simulation protocol

Aptamers (small single strand DNA/RNAs) such as SYL3C are considered as ideal alternatives to antibodies in cancer related research studies. However, 3D structure predictions for aptamers and aptamer-protein complexes are scarce due to the high cost of experimental measurements and unreliable computer-based methods. Thus aptamers' diagnostic and therapeutic applications are severely restricted. To meet the challenge, we proposed a Martini-based aptamer-protein complex prediction protocol. By combining the base-base contact map from simulation and secondary structure prediction from various tools, improved secondary structure predictions can be obtained. This method reduced the risk of providing incorrect or incomplete base pairs in secondary structure prediction. Thus 3D structure modeling based on the secondary structure can be more reliable. We introduced the soft elastic network to the hairpin folded regions of the Martini ssDNAs to preserve their canonical structure. Using our protocol, we predicted the first 3D structure of the aptamer SYL3C and the SYL3C-EpCAM complex. We believe that our work could contribute to the future aptamer-related research studies and medical implications.

Molecular-level understanding of the hTAS2R1 receptor-bitter tasting tetra-peptide binding: a structural biology study based on computational approaches

Effective computational approaches for bitter-tasting peptides have been developed and analyzed in the present work.

Enhanced sampling molecular dynamics simulations correctly predict the diverse activities of a series of stiff-stilbene G-quadruplex DNA ligands

Ligands with the capability to bind G-quadruplexes (G4s) specifically, and to control G4 structure and behaviour, offer great potential in the development of novel therapies, technologies and functional materials. Most known ligands bind to a pre-formed topology, but G4s are highly dynamic and a small number of ligands have been discovered that influence these folding equilibria. Such ligands may be useful as probes to understand the dynamic nature of G4 in vivo, or to exploit the polymorphism of G4 in the development of molecular devices. To date, these fascinating molecules have been discovered serendipitously. There is a need for tools to predict such effects to drive ligand design and development, and for molecular-level understanding of ligand binding mechanisms and associated topological perturbation of G4 structures. Here we study the G4 binding mechanisms of a family of stiff-stilbene G4 ligands to human telomeric DNA using molecular dynamics (MD) and enhanced sampling (metadynamics) MD simulations. The simulations predict a variety of binding mechanisms and effects on G4 structure for the different ligands in the series. In parallel, we characterize the binding of the ligands to the G4 target experimentally using NMR and CD spectroscopy. The results show good agreement between the simulated and experimentally observed binding modes, binding affinities and ligand-induced perturbation of the G4 structure. The simulations correctly predict ligands that perturb G4 topology. Metadynamics simulations are shown to be a powerful tool to aid development of molecules to influence G4 structure, both in interpreting experiments and to help in the design of these chemotypes.

Validation of DBFOLD: An efficient algorithm for computing folding pathways of complex proteins

Atomistic simulations can provide valuable, experimentally-verifiable insights into protein folding mechanisms, but existing ab initio simulation methods are restricted to only the smallest proteins due to severe computational speed limits. The folding of larger proteins has been studied using native-centric potential functions, but such models omit the potentially crucial role of non-native interactions. Here, we present an algorithm, entitled DBFOLD, which can predict folding pathways for a wide range of proteins while accounting for the effects of non-native contacts. In addition, DBFOLD can predict the relative rates of different transitions within a protein’s folding pathway. To accomplish this, rather than directly simulating folding, our method combines equilibrium Monte-Carlo simulations, which deploy enhanced sampling, with unfolding simulations at high temperatures. We show that under certain conditions, trajectories from these two types of simulations can be jointly analyzed to compute unknown folding rates from detailed balance. This requires inferring free energies from the equilibrium simulations, and extrapolating transition rates from the unfolding simulations to lower, physiologically-reasonable temperatures at which the native state is marginally stable. As a proof of principle, we show that our method can accurately predict folding pathways and Monte-Carlo rates for the well-characterized Streptococcal protein G. We then show that our method significantly reduces the amount of computation time required to compute the folding pathways of large, misfolding-prone proteins that lie beyond the reach of existing direct simulation. Our algorithm, which is available online, can generate detailed atomistic models of protein folding mechanisms while shedding light on the role of non-native intermediates which may crucially affect organismal fitness and are frequently implicated in disease.

Many proteins must adopt a specific structure in order to function. Computational simulations have been used to shed light on the mechanisms of protein folding, but unfortunately, realistic simulations can typically only be run for small proteins, due to severe limits in computational speed. Here, we present a method to solve this problem, whereby instead of directly simulating folding from an unfolded state, we run simulations that allow for computation of equilibrium folding free energies, alongside high temperature simulations to compute unfolding rates. From these quantities, folding rates can be computed using detailed balance. Importantly, our method can account for the effects of nonnative contacts which transiently form during folding and must be broken prior to adoption of the native state. Such contacts, which are often excluded from simple models of folding, may crucially affect real protein folding pathways and are often observed in folding intermediates implicated in disease.

Free-energy landscape of polymer-crystal polymorphism

Polymorphism rationalizes how processing can control the final structure of a material. The rugged free-energy landscape and exceedingly slow kinetics in the solid state have so far hampered computational investigations. We report for the first time the free-energy landscape of a polymorphic crystalline polymer, syndiotactic polystyrene. Coarse-grained metadynamics simulations allow us to efficiently sample the landscape at large. The free-energy difference between the two main polymorphs, α and β, is further investigated by quantum-chemical calculations. The results of the two methods are in line with experimental observations: they predict β as the more stable polymorph under standard conditions. Critically, the free-energy landscape suggests how the α polymorph may lead to experimentally observed kinetic traps. The combination of multiscale modeling, enhanced sampling, and quantum-chemical calculations offers an appealing strategy to uncover complex free-energy landscapes with polymorphic behavior.

Examination of Interactions of Hexafluoro-2-propanol with Trp-Cage in Hexafluoro-2-propanol-Water by MD Simulations and Intermolecular Nuclear Overhauser Effects

All-atom molecular dynamic simulations of the peptide Trp-cage in 30% hexafluoro-2-propanol- water (V/V) at 278 K have been carried out with the goal of exploring peptide hydrogen-solvent fluorine nuclear spin cross relaxation. Force field parameters for HFIP reported by Fioroni et al. along with the fluorine parameters of the TFE5 model reported by this lab were used. Water was represented by the TIP5P-Ew model. Peptide modeling used the AMBER99SB-ILDN force field. Translational diffusion coefficients of solution components at 278 K were predicted to within 35% of experimental values using these parameter sets. The simulations indicate that the solvent mixture is not homogeneous, with HFIP molecules clustered into aggregates as large as 53 fluoroalcohol molecules. The solvent environment of surface atoms of Trp-cage fluctuates between being HFIP-rich and more water-rich about every 10 ns. In accord with previous studies by other groups, the average concentration of HFIP near the surface of the peptide is significantly enhanced over the concentration of HFIP in the bulk solvent. In the simulations, ∼7% of the initial contacts between HFIP molecules and Trp-cage develop into peptide-fluoroalcohol interactions that persist for times as long as 8 ns. Most of the available experimental nuclear spin cross-relaxation rates (Σ_HF) for hydrogens of the Trp-cage in 30% HFIP-water are reproduced from the MD trajectories to within uncertainties of the experimental data and the simulations. However, a few calculated Σ_HF values for hydrogens of the Trp-cage do not agree with experiment. These tend to be situations where long-lived peptide-HFIP interactions are predicted. The disagreements between observed and calculated Σ_HF in these instances signal defects in the modeling parameters and procedures that are presently unrecognized.

Phosphorylation regulates the binding of intrinsically disordered proteins via a flexible conformation selection mechanism

Phosphorylation is one of the most common post-translational modifications. The phosphorylation of the kinase-inducible domain (KID), which is an intrinsically disordered protein (IDP), promotes the folding of KID and binding with the KID-interacting domain (KIX). However, the regulation mechanism of the phosphorylation on KID is still elusive. In this study, the structural ensembles and binding process of pKID and KIX are studied by all-atom enhanced sampling technologies. The results show that more hydrophobic interactions are formed in pKID, which promote the formation of the special hydrophobic residue cluster (HRC). The pre-formed HRC promotes binding to the correct sites of KIX and further lead the folding of pKID. Consequently, a flexible conformational selection model is proposed to describe the binding and folding process of intrinsically disordered proteins. The binding mechanism revealed in this work provides new insights into the dynamic interactions and phosphorylation regulation of proteins.

Data Reweighting in Metadynamics Simulations

The data collected along a metadynamics simulation can be used to recover information about the underlying unbiased system by means of a reweighting procedure. Here, we analyze the behavior of several reweighting techniques in terms of the quality of the reconstruction of the underlying unbiased free energy landscape in the early stages of the simulation and propose a simple reweighting scheme that we relate to the other techniques. We then show that the free energy landscape reconstructed from reweighted data can be more accurate than the negative bias potential depending on the reweighting technique, the stage of the simulation, and the adoption of well-tempered or standard metadynamics. While none of the tested reweighting techniques from the literature provides the most accurate results in all the analyzed situations, the one proposed here, in addition to helping simplifying the reweighting procedure, converges quickly and precisely to the underlying free energy surface in all the considered cases, thus allowing for an efficient use of limited simulation data.

Unperturbed Detection of the Dynamic Structure in the Hydrophobic Core of Trp-Cage via Two-Dimensional Infrared Spectroscopy

The tyrosine ring mode is an intrinsic non-perturbing site-specific infrared reporter for conformational dynamics within protein systems. This transition is influenced by direct and indirect interactions associated with the electron-donating ability and the hydrophobicity of the surrounding molecules. Utilizing an intrinsic tyrosine moiety, two-dimensional infrared spectra of Trp-cage, often called the "hydrogen atom" of protein folding, were measured in the folded and denatured states to uncover the dynamics of the hydrophobic core. The vibrational lifetimes and the correlation decays of the tyrosine ring mode showed significant changes upon both temperature and chemical denaturation of the Trp-cage miniprotein, indicating important structural features of the hydrophobic core and its dynamics. The observed Trp6-Tyr3 interactions are in good agreement with the prior studies of the folded state, but they reach beyond the static structure. These stacking interactions and orientations fluctuate on the picosecond time scale as measured through the spectral dephasing within a dehydrated environment.

Ligand-Binding Calculations with Metadynamics

All-atom molecular dynamics simulations can capture the dynamic degrees of freedom that characterize molecular recognition, the knowledge of which constitutes the cornerstone of rational approaches to drug design and optimization. In particular, enhanced sampling algorithms, such as metadynamics, are powerful tools to dramatically reduce the computational cost required for a mechanistic description of the binding process. Here, we describe the essential details characterizing these simulation strategies, focusing on the critical step of identifying suitable reaction coordinates, as well as on the different analysis algorithms to estimate binding affinity and residence times. We conclude with a survey of published applications that provides explicit examples of successful simulations for several targets.

Metadynamics to Enhance Sampling in Biomolecular Simulations

Molecular dynamics is a powerful simulation method to provide detailed atomic-scale insight into a range of biological processes including protein folding, biochemical reactions, ligand binding, and many others. Over the last several decades, enhanced sampling methods have been developed to address the large separation in time scales between a molecular dynamics simulation (usually microseconds or shorter) and the time scales of biological processes (often orders of magnitude longer). This chapter specifically focuses on the metadynamics family of methods, which achieves enhanced sampling through the introduction of a history-dependent bias potential that is based on one or more slow degrees of freedom, called collective variables. We introduce the method and its recent variants related to biomolecular studies and then discuss frontier areas of the method. A large part of this chapter is devoted to helping new users of the method understand how to choose metadynamics parameters properly and apply the method to their system of interest.