Enhanced sampling techniques in biomolecular simulations

Increased throughput in methods for simulating protein ligand binding and unbinding

By incorporating full flexibility and enabling the quantification of crucial parameters such as binding free energies and residence times, methods for investigating protein-ligand binding and unbinding via molecular dynamics provide details on the involved mechanisms at the molecular level. While these advancements hold promise for impacting drug discovery, a notable drawback persists: their relatively time-consuming nature limits throughput. Herein, we survey recent implementations which, employing a blend of enhanced sampling techniques, a clever choice of collective variables, and often machine learning, strive to enhance the efficiency of new and previously reported methods without compromising accuracy. Particularly noteworthy is the validation of these methods that was often performed on systems mirroring real-world drug discovery scenarios.

Mechanism of Ligand Binding to Theophylline RNA Aptamer

Studying RNA-ligand interactions and quantifying their binding thermodynamics and kinetics are of particular relevance in the field of drug discovery. Here, we combined biochemical binding assays and accelerated molecular simulations to investigate ligand binding and dissociation in RNA using the theophylline-binding RNA as a model system. All-atom simulations using a Ligand Gaussian accelerated Molecular Dynamics method (LiGaMD) have captured repetitive binding and dissociation of theophylline and caffeine to RNA. Theophylline's binding free energy and kinetic rate constants align with our experimental data, while caffeine's binding affinity is over 10,000 times weaker, and its kinetics could not be determined. LiGaMD simulations allowed us to identify distinct low-energy conformations and multiple ligand binding pathways to RNA. Simulations revealed a "conformational selection" mechanism for ligand binding to the flexible RNA aptamer, which provides important mechanistic insights into ligand binding to the theophylline-binding model. Our findings suggest that compound docking using a structural ensemble of representative RNA conformations would be necessary for structure-based drug design of flexible RNA.

Phanto-IDP: compact model for precise intrinsically disordered protein backbone generation and enhanced sampling

The biological function of proteins is determined not only by their static structures but also by the dynamic properties of their conformational ensembles. Numerous high-accuracy static structure prediction tools have been recently developed based on deep learning; however, there remains a lack of efficient and accurate methods for exploring protein dynamic conformations. Traditionally, studies concerning protein dynamics have relied on molecular dynamics (MD) simulations, which incur significant computational costs for all-atom precision and struggle to adequately sample conformational spaces with high energy barriers. To overcome these limitations, various enhanced sampling techniques have been developed to accelerate sampling in MD. Traditional enhanced sampling approaches like replica exchange molecular dynamics (REMD) and frontier expansion sampling (FEXS) often follow the MD simulation approach and still cost a lot of computational resources and time. Variational autoencoders (VAEs), as a classic deep generative model, are not restricted by potential energy landscapes and can explore conformational spaces more efficiently than traditional methods. However, VAEs often face challenges in generating reasonable conformations for complex proteins, especially intrinsically disordered proteins (IDPs), which limits their application as an enhanced sampling method. In this study, we presented a novel deep learning model (named Phanto-IDP) that utilizes a graph-based encoder to extract protein features and a transformer-based decoder combined with variational sampling to generate highly accurate protein backbones. Ten IDPs and four structured proteins were used to evaluate the sampling ability of Phanto-IDP. The results demonstrate that Phanto-IDP has high fidelity and diversity in the generated conformation ensembles, making it a suitable tool for enhancing the efficiency of MD simulation, generating broader protein conformational space and a continuous protein transition path.

Deep Boosted Molecular Dynamics (DBMD): Accelerating molecular simulations with Gaussian boost potentials generated using probabilistic Bayesian deep neural network

We have developed a new Deep Boosted Molecular Dynamics (DBMD) method. Probabilistic Bayesian neural network models were implemented to construct boost potentials that exhibit Gaussian distribution with minimized anharmonicity, thereby allowing for accurate energetic reweighting and enhanced sampling of molecular simulations. DBMD was demonstrated on model systems of alanine dipeptide and the fast-folding protein and RNA structures. For alanine dipeptide, 30ns DBMD simulations captured up to 83-125 times more backbone dihedral transitions than 1μs conventional molecular dynamics (cMD) simulations and were able to accurately reproduce the original free energy profiles. Moreover, DBMD sampled multiple folding and unfolding events within 300ns simulations of the chignolin model protein and identified low-energy conformational states comparable to previous simulation findings. Finally, DBMD captured a general folding pathway of three hairpin RNAs with the GCAA, GAAA, and UUCG tetraloops. Based on Deep Learning neural network, DBMD provides a powerful and generally applicable approach to boosting biomolecular simulations. DBMD is available with open source in OpenMM at https://github.com/MiaoLab20/DBMD/.

Molecular Modeling Insights into the Structure and Behavior of Integrins: A Review

Integrins are heterodimeric glycoproteins crucial to the physiology and pathology of many biological functions. As adhesion molecules, they mediate immune cell trafficking, migration, and immunological synapse formation during inflammation and cancer. The recognition of the vital roles of integrins in various diseases revealed their therapeutic potential. Despite the great effort in the last thirty years, up to now, only seven integrin-based drugs have entered the market. Recent progress in deciphering integrin functions, signaling, and interactions with ligands, along with advancement in rational drug design strategies, provide an opportunity to exploit their therapeutic potential and discover novel agents. This review will discuss the molecular modeling methods used in determining integrins' dynamic properties and in providing information toward understanding their properties and function at the atomic level. Then, we will survey the relevant contributions and the current understanding of integrin structure, activation, the binding of essential ligands, and the role of molecular modeling methods in the rational design of antagonists. We will emphasize the role played by molecular modeling methods in progress in these areas and the designing of integrin antagonists.

Significance of an Electrochemical Sensor and Nanocomposites: Toward the Electrocatalytic Detection of Neurotransmitters and Their Importance within the Physiological System

A prominent neurotransmitter (NT), dopamine (DA), is a chemical messenger that transmits signals between one neuron to the next to pass on a signal to and from the central nervous system (CNS). The imbalanced concentration of DA may cause numerous neurological sicknesses and syndromes, for example, Parkinson's disease (PD) and schizophrenia. There are many types of NTs in the brain, including epinephrine, norepinephrine (NE), serotonin, and glutamate. Electrochemical sensors have offered a creative direction to biomedical analysis and testing. Researches are in progress to improve the performance of sensors and develop new protocols for sensor design. This review article focuses on the area of sensor growth to discover the applicability of polymers and metallic particles and composite materials as tools in electrochemical sensor surface incorporation. Electrochemical sensors have attracted the attention of researchers as they possess high sensitivity, quick reaction rate, good controllability, and instantaneous detection. Efficient complex materials provide considerable benefits for biological detection as they have exclusive chemical and physical properties. Due to distinctive electrocatalytic characteristics, metallic nanoparticles add fascinating traits to materials that depend on the material's morphology and size. Herein, we have collected much information on NTs and their importance within the physiological system. Furthermore, the electrochemical sensors and corresponding techniques (such as voltammetric, amperometry, impedance, and chronoamperometry) and the different types of electrodes' roles in the analysis of NTs are discussed. Furthermore, other methods for detecting NTs include optical and microdialysis methods. Finally, we show the advantages and disadvantages of different techniques and conclude remarks with future perspectives.

Solvent paramagnetic relaxation enhancement as a versatile method for studying structure and dynamics of biomolecular systems

Solvent paramagnetic relaxation enhancement (sPRE) is a versatile nuclear magnetic resonance (NMR)-based method that allows characterization of the structure and dynamics of biomolecular systems through providing quantitative experimental information on solvent accessibility of NMR-active nuclei. Addition of soluble paramagnetic probes to the solution of a biomolecule leads to paramagnetic relaxation enhancement in a concentration-dependent manner. Here we review recent progress in the sPRE-based characterization of structural and dynamic properties of biomolecules and their complexes, and aim to deliver a comprehensive illustration of a growing number of applications of the method to various biological systems. We discuss the physical principles of sPRE measurements and provide an overview of available co-solute paramagnetic probes. We then explore how sPRE, in combination with complementary biophysical techniques, can further advance biomolecular structure determination, identification of interaction surfaces within protein complexes, and probing of conformational changes and low-population transient states, as well as deliver insights into weak, nonspecific, and transient interactions between proteins and co-solutes. In addition, we present examples of how the incorporation of solvent paramagnetic probes can improve the sensitivity of NMR experiments and discuss the prospects of applying sPRE to NMR metabolomics, drug discovery, and the study of intrinsically disordered proteins.

From free-energy profiles to activation free energies

Given a chemical reaction going from reactant (R) to the product (P) on a potential energy surface (PES) and a collective variable (CV) discriminating between R and P, we define the free-energy profile (FEP) as the logarithm of the marginal Boltzmann distribution of the CV. This FEP is not a true free energy. Nevertheless, it is common to treat the FEP as the “free-energy” analog of the minimum potential energy path and to take the activation free energy, [Formula: see text], as the difference between the maximum at the transition state and the minimum at R. We show that this approximation can result in large errors. The FEP depends on the CV and is, therefore, not unique. For the same reaction, different discriminating CVs can yield different [Formula: see text]. We derive an exact expression for the activation free energy that avoids this ambiguity. We find [Formula: see text] to be a combination of the probability of the system being in the reactant state, the probability density on the dividing surface, and the thermal de Broglie wavelength associated with the transition. We apply our formalism to simple analytic models and realistic chemical systems and show that the FEP-based approximation applies only at low temperatures for CVs with a small effective mass. Most chemical reactions occur on complex, high-dimensional PES that cannot be treated analytically and pose the added challenge of choosing a good CV. We study the influence of that choice and find that, while the reaction free energy is largely unaffected, [Formula: see text] is quite sensitive.

Gaussian Accelerated Molecular Dynamics in OpenMM

Gaussian accelerated molecular dynamics (GaMD) is a computational technique that provides both unconstrained enhanced sampling and free energy calculations of biomolecules. Here, we present the implementation of GaMD in the OpenMM simulation package and validate it on model systems of alanine dipeptide and RNA folding. For alanine dipeptide, 30 ns GaMD production simulations reproduced free energy profiles of 1000 ns conventional molecular dynamics (cMD) simulations. In addition, GaMD simulations captured the folding pathways of three hyperstable RNA tetraloops (UUCG, GCAA, and CUUG) and binding of the rbt203 ligand to the HIV-1 Tar RNA, both of which involved critical electrostatic interactions such as hydrogen bonding and base stacking. Together with previous implementations, GaMD in OpenMM will allow for wider applications in simulations of proteins, RNA, and other biomolecules.

A plausible contributor to multiple sclerosis; presentation of antigenic myelin protein epitopes by major histocompatibility complexes

BACKGROUND

Multiple sclerosis (MS) can be induced upon successful presentation of myelin antigens by MHC I/II. Antigenic similarity between the myelin and viral proteins may worsen the immunological responses.

METHODOLOGY

Antigenic regions within myelin proteins; PLP1, MBP, MOG, and MAG were analyzed using SVMTrip and EMBOSS. Homology search identified sequence similarity between the predicted host epitopes and viral proteins. NetMHCpan predicted MHC I/II binding followed by peptide-protein docking through the HPEPDOCK server. Thereafter we analyzed conformational flexibility and stability of 15 protein-peptide complexes based on high docking scores. The binding free energy was calculated using conventional (MD) and Gaussian accelerated molecular dynamics simulation.

RESULTS

PLP1, MBP, MAG and MOG contained numerous antigenic epitopes. MBP and MOG epitopes had sequence similarity to HHV-6 BALF5; EBNA1 and CMV glycoprotein M (gM), and EBV LMP2B, gp350/220; HHV-8 ORFs respectively. Many herpes virus proteins like tegument, envelope glycoproteins, and ORFs of EBV, CMV, HHV-6, and HHV-8 demonstrated sequence similarity with MAG and PLP1. Some antigenic peptides were also linear B-cell epitopes and influenced cytokine production by T-cell. MHC I allele HLA-B*57:01 bound to PLP1 peptide and HLA-A*68:02 bound to a MAG peptide strongly. MHC II alleles HLA-DRB1*04:05 and HLA-DR1*01:01 associated with MAG- and MOG-derived peptides, respectively, demonstrating high HPEPDOCK scores. MD simulations established stable binding of certain peptides with the MHC namely HLA-B*51:01-MBP(DYKSAHKGFKGVDAQGTLSKIFKL), HLA-B*57:01-PLP1(PDKFVGITYALTVVWLLVFACSAVPVYIYF), HLA-DR1*01:01-MOG(VEDPFYWVSPGVLVLLAVLPVLLLQITVGLVFLCLQYR) and HLA-DRB1*04:05-MAG(TWVQVSLLHFVPTREA).

CONCLUSIONS

Cross-reactivity between self-antigens and pathogen derived immunodominant epitopes may induce MS. Our study supported the role of specific MHC alleles as a contributing MS risk factor.

Statistically optimal analysis of the extended-system adaptive biasing force (eABF) method

The extended-system adaptive biasing force (eABF) method and its newer variants offer rapid exploration of the configuration space of chemical systems. Instead of directly applying the ABF bias to collective variables, they are harmonically coupled to fictitious particles, which separates the problem of enhanced sampling from that of free energy estimation. The prevalent analysis method to obtain the potential of mean force (PMF) from eABF is thermodynamic integration. However, besides the PMF, most information is lost as the unbiased probability of visited configurations is never recovered. In this contribution, we show how statistical weights of individual frames can be computed using the Multistate Bennett's Acceptance Ratio (MBAR), putting the post-processing of eABF on one level with other frequently used sampling methods. In addition, we apply this formalism to the prediction of nuclear magnetic resonance shieldings, which are very sensitive to molecular geometries and often require extensive sampling. The results show that the combination of enhanced sampling by means of extended-system dynamics with the MBAR estimator is a highly useful tool for the calculation of ensemble properties. Furthermore, the extension of the presented scheme to the recently published Gaussian-accelerated molecular dynamics eABF hybrid is straightforward and approximation free.

Learning Efficient, Collective Monte Carlo Moves with Variational Autoencoders

Discovering meaningful collective variables for enhancing sampling, via applied biasing potentials or tailored MC move sets, remains a major challenge within molecular simulation. While recent studies identifying collective variables with variational autoencoders (VAEs) have focused on the encoding and latent space discovered by a VAE, the impact of the decoding and its ability to act as a generative model remains unexplored. We demonstrate how VAEs may be used to learn (on-the-fly and with minimal human intervention) highly efficient, collective Monte Carlo moves that accelerate sampling along the learned collective variable. In contrast to many machine learning-based efforts to bias sampling and generate novel configurations, our methods result in exact sampling in the ensemble of interest and do not require reweighting. In fact, we show that the acceptance rates of our moves approach unity for a perfect VAE model. While this is never observed in practice, VAE-based Monte Carlo moves still enhance sampling of new configurations. We demonstrate, however, that the form of the encoding and decoding distributions, in particular the extent to which the decoder reflects the underlying physics, greatly impacts the performance of the trained VAE.

Collective Variable for Metadynamics Derived From AlphaFold Output

AlphaFold is a neural network–based tool for the prediction of 3D structures of proteins. In CASP14, a blind structure prediction challenge, it performed significantly better than other competitors, making it the best available structure prediction tool. One of the outputs of AlphaFold is the probability profile of residue–residue distances. This makes it possible to score any conformation of the studied protein to express its compliance with the AlphaFold model. Here, we show how this score can be used to drive protein folding simulation by metadynamics and parallel tempering metadynamics. Using parallel tempering metadynamics, we simulated the folding of a mini-protein Trp-cage and β hairpin and predicted their folding equilibria. We observe the potential of the AlphaFold-based collective variable in applications beyond structure prediction, such as in structure refinement or prediction of the outcome of a mutation.

Molecular Simulations and Drug Discovery of Adenosine Receptors

G protein-coupled receptors (GPCRs) represent the largest family of human membrane proteins. Four subtypes of adenosine receptors (ARs), the A1AR, A2AAR, A2BAR and A3AR, each with a unique pharmacological profile and distribution within the tissues in the human body, mediate many physiological functions and serve as critical drug targets for treating numerous human diseases including cancer, neuropathic pain, cardiac ischemia, stroke and diabetes. The A1AR and A3AR preferentially couple to the Gi/o proteins, while the A2AAR and A2BAR prefer coupling to the Gs proteins. Adenosine receptors were the first subclass of GPCRs that had experimental structures determined in complex with distinct G proteins. Here, we will review recent studies in molecular simulations and computer-aided drug discovery of the adenosine receptors and also highlight their future research opportunities.

Mechanism of Peptide Agonist Binding in CXCR4 Chemokine Receptor

Chemokine receptors are key G-protein-coupled receptors (GPCRs) that control cell migration in immune system responses, development of cardiovascular and central nervous systems, and numerous diseases. In particular, the CXCR4 chemokine receptor promotes metastasis, tumor growth and angiogenesis in cancers. CXCR4 is also used as one of the two co-receptors for T-tropic HIV-1 entry into host cells. Therefore, CXCR4 serves as an important therapeutic target for treating cancers and HIV infection. Apart from the CXCL12 endogenous peptide agonist, previous studies suggested that the first 17 amino acids of CXCL12 are sufficient to activate CXCR4. Two 17-residue peptides with positions 1-4 mutated to RSVM and ASLW functioned as super and partial agonists of CXCR4, respectively. However, the mechanism of peptide agonist binding in CXCR4 remains unclear. Here, we have investigated this mechanism through all-atom simulations using a novel Peptide Gaussian accelerated molecular dynamics (Pep-GaMD) method. The Pep-GaMD simulations have allowed us to explore representative binding conformations of each peptide and identify critical low-energy states of CXCR4 activated by the super versus partial peptide agonists. Our simulations have provided important mechanistic insights into peptide agonist binding in CXCR4, which are expected to facilitate rational design of new peptide modulators of CXCR4 and other chemokine receptors.

Protein-Protein Interaction-Gaussian Accelerated Molecular Dynamics (PPI-GaMD): Characterization of Protein Binding Thermodynamics and Kinetics

Protein-protein interactions (PPIs) play key roles in many fundamental biological processes such as cellular signaling and immune responses. However, it has proven challenging to simulate repetitive protein association and dissociation in order to calculate binding free energies and kinetics of PPIs due to long biological timescales and complex protein dynamics. To address this challenge, we have developed a new computational approach to all-atom simulations of PPIs based on a robust Gaussian accelerated molecular dynamics (GaMD) technique. The method, termed "PPI-GaMD", selectively boosts interaction potential energy between protein partners to facilitate their slow dissociation. Meanwhile, another boost potential is applied to the remaining potential energy of the entire system to effectively model the protein's flexibility and rebinding. PPI-GaMD has been demonstrated on a model system of the ribonuclease barnase interactions with its inhibitor barstar. Six independent 2 μs PPI-GaMD simulations have captured repetitive barstar dissociation and rebinding events, which enable calculations of the protein binding thermodynamics and kinetics simultaneously. The calculated binding free energies and kinetic rate constants agree well with the experimental data. Furthermore, PPI-GaMD simulations have provided mechanistic insights into barstar binding to barnase, which involves long-range electrostatic interactions and multiple binding pathways, being consistent with previous experimental and computational findings of this model system. In summary, PPI-GaMD provides a highly efficient and easy-to-use approach for binding free energy and kinetics calculations of PPIs.

GLOW: A Workflow Integrating Gaussian-Accelerated Molecular Dynamics and Deep Learning for Free Energy Profiling

We introduce a Gaussian-accelerated molecular dynamics (GaMD), deep learning (DL), and free energy profiling workflow (GLOW) to predict molecular determinants and map free energy landscapes of biomolecules. All-atom GaMD-enhanced sampling simulations are first performed on biomolecules of interest. Structural contact maps are then calculated from GaMD simulation frames and transformed into images for building DL models using a convolutional neural network. Important structural contacts are further determined from DL models of attention maps of the structural contact gradients, which allow us to identify the system reaction coordinates. Finally, free energy profiles are calculated for the selected reaction coordinates through energetic reweighting of the GaMD simulations. We have also successfully demonstrated GLOW for the characterization of activation and allosteric modulation of a G protein-coupled receptor, using the adenosine A₁ receptor (A₁AR) as a model system. GLOW findings are highly consistent with previous experimental and computational studies of the A₁AR, while also providing further mechanistic insights into the receptor function. In summary, GLOW provides a systematic approach to mapping free energy landscapes of biomolecules. The GLOW workflow and its user manual can be downloaded at http://miaolab.org/GLOW.

Accelerated Ligand-Mapping Molecular Dynamics Simulations for the Detection of Recalcitrant Cryptic Pockets and Occluded Binding Sites

The identification and characterization of binding sites is a critical component of structure-based drug design (SBDD). Probe-based/cosolvent molecular dynamics (MD) methods that allow for protein flexibility have been developed to predict ligand binding sites. However, cryptic pockets that appear only upon ligand binding and occluded binding sites with no access to the solvent pose significant challenges to these methods. Here, we report the development of accelerated ligand-mapping MD (aLMMD), which combines accelerated MD with LMMD, for the detection of these challenging binding sites. The method was validated on five proteins with what we term "recalcitrant" cryptic pockets, which are deeply buried pockets that require extensive movement of the protein backbone to expose, and three proteins with occluded binding sites. In all the cases, aLMMD was able to detect and sample the binding sites. Our results suggest that aLMMD could be used as a general approach for the detection of such elusive binding sites in protein targets, thus providing valuable information for SBDD.

Mechanism of RNA recognition by a Musashi RNA-binding protein

The Musashi RNA-binding proteins (RBPs) regulate translation of target mRNAs and maintenance of cell stemness and tumorigenesis. Musashi-1 (MSI1), long considered as an intestinal and neural stem cell marker, has been more recently found to be over expressed in many cancers. It has served as an important drug target for treating acute myeloid leukemia and solid tumors such as ovarian, colorectal and bladder cancer. One of the reported binding targets of MSI1 is Numb, a negative regulator of the Notch signaling. However, the dynamic mechanism of Numb RNA binding to MSI1 remains unknown, largely hindering effective drug design targeting this critical interaction. Here, we have performed extensive all-atom microsecond-timescale simulations using a robust Gaussian accelerated molecular dynamics (GaMD) method, which successfully captured multiple times of spontaneous and highly accurate binding of the Numb RNA from bulk solvent to the MSI1 protein target site. GaMD simulations revealed that Numb RNA binding to MSI1 involved largely induced fit in both the RNA and protein. The simulations also identified important low-energy intermediate conformational states during RNA binding, in which Numb interacted mainly with the β2-β3 loop and C terminus of MSI1. The mechanistic understanding of RNA binding obtained from our GaMD simulations is expected to facilitate rational structure-based drug design targeting MSI1 and other RBPs.

Gaussian accelerated molecular dynamics (GaMD): principles and applications

Gaussian accelerated molecular dynamics (GaMD) is a robust computational method for simultaneous unconstrained enhanced sampling and free energy calculations of biomolecules. It works by adding a harmonic boost potential to smooth biomolecular potential energy surface and reduce energy barriers. GaMD greatly accelerates biomolecular simulations by orders of magnitude. Without the need to set predefined reaction coordinates or collective variables, GaMD provides unconstrained enhanced sampling and is advantageous for simulating complex biological processes. The GaMD boost potential exhibits a Gaussian distribution, thereby allowing for energetic reweighting via cumulant expansion to the second order (i.e., "Gaussian approximation"). This leads to accurate reconstruction of free energy landscapes of biomolecules. Hybrid schemes with other enhanced sampling methods, such as the replica exchange GaMD (rex-GaMD) and replica exchange umbrella sampling GaMD (GaREUS), have also been introduced, further improving sampling and free energy calculations. Recently, new "selective GaMD" algorithms including the ligand GaMD (LiGaMD) and peptide GaMD (Pep-GaMD) enabled microsecond simulations to capture repetitive dissociation and binding of small-molecule ligands and highly flexible peptides. The simulations then allowed highly efficient quantitative characterization of the ligand/peptide binding thermodynamics and kinetics. Taken together, GaMD and its innovative variants are applicable to simulate a wide variety of biomolecular dynamics, including protein folding, conformational changes and allostery, ligand binding, peptide binding, protein-protein/nucleic acid/carbohydrate interactions, and carbohydrate/nucleic acid interactions. In this review, we present principles of the GaMD algorithms and recent applications in biomolecular simulations and drug design.

Overcoming Free-Energy Barriers with a Seamless Combination of a Biasing Force and a Collective Variable-Independent Boost Potential

Amid collective-variable (CV)-based importance-sampling algorithms, a hybrid of the extended adaptive biasing force and the well-tempered metadynamics algorithms (WTM-eABF) has proven particularly cost-effective for exploring the rugged free-energy landscapes that underlie biological processes. However, as an inherently CV-based algorithm, this hybrid scheme does not explicitly accelerate sampling in the space orthogonal to the chosen CVs, thereby limiting its efficiency and accuracy, most notably in those cases where the slow degrees of freedom of the process at hand are not accounted for in the model transition coordinate. Here, inspired by Gaussian-accelerated molecular dynamics (GaMD), we introduce the same CV-independent harmonic boost potential into WTM-eABF, yielding a hybrid algorithm coined GaWTM-eABF. This algorithm leans on WTM-eABF to explore the transition coordinate with a GaMD-mollified potential and recovers the unbiased free-energy landscape through thermodynamic integration followed by proper reweighting. As illustrated in our numerical tests, GaWTM-eABF effectively overcomes the free-energy barriers in orthogonal space and correctly recovers the unbiased potential of mean force (PMF). Furthermore, applying both GaWTM-eABF and WTM-eABF to two biologically relevant processes, namely, the reversible folding of (i) deca-alanine and (ii) chignolin, our results indicate that GaWTM-eABF reduces the uncertainty in the PMF calculation and converges appreciably faster than WTM-eABF. Obviating the need of multiple-copy strategies, GaWTM-eABF is a robust, computationally efficient algorithm to surmount the free-energy barriers in orthogonal space and maps with utmost fidelity the free-energy landscape along selections of CVs. Moreover, our strategy that combines WTM-eABF with GaMD can be easily extended to other biasing-force algorithms.

Ubiquitin Interacting Motifs: Duality Between Structured and Disordered Motifs

Ubiquitin is a small protein at the heart of many cellular processes, and several different protein domains are known to recognize and bind ubiquitin. A common motif for interaction with ubiquitin is the Ubiquitin Interacting Motif (UIM), characterized by a conserved sequence signature and often found in multi-domain proteins. Multi-domain proteins with intrinsically disordered regions mediate interactions with multiple partners, orchestrating diverse pathways. Short linear motifs for binding are often embedded in these disordered regions and play crucial roles in modulating protein function. In this work, we investigated the structural propensities of UIMs using molecular dynamics simulations and NMR chemical shifts. Despite the structural portrait depicted by X-crystallography of stable helical structures, we show that UIMs feature both helical and intrinsically disordered conformations. Our results shed light on a new class of disordered UIMs. This group is here exemplified by the C-terminal domain of one isoform of ataxin-3 and a group of ubiquitin-specific proteases. Intriguingly, UIMs not only bind ubiquitin. They can be a recruitment point for other interactors, such as parkin and the heat shock protein Hsc70-4. Disordered UIMs can provide versatility and new functions to the client proteins, opening new directions for research on their interactome.

Structure-based in silico approaches for drug discovery against Mycobacterium tuberculosis

Mycobacterium tuberculosis is the causative agent of TB and was estimated to cause 1.4 million death in 2019, alongside 10 million new infections. Drug resistance is a growing issue, with multi-drug resistant infections representing 3.3% of all new infections, hence novel antimycobacterial drugs are urgently required to combat this growing health emergency. Alongside this, increased knowledge of gene essentiality in the pathogenic organism and larger compound databases can aid in the discovery of new drug compounds. The number of protein structures, X-ray based and modelled, is increasing and now accounts for greater than > 80% of all predicted M. tuberculosis proteins; allowing novel targets to be investigated. This review will focus on structure-based in silico approaches for drug discovery, covering a range of complexities and computational demands, with associated antimycobacterial examples. This includes molecular docking, molecular dynamic simulations, ensemble docking and free energy calculations. Applications of machine learning onto each of these approaches will be discussed. The need for experimental validation of computational hits is an essential component, which is unfortunately missing from many current studies. The future outlooks of these approaches will also be discussed.

How to Determine Accurate Conformational Ensembles by Metadynamics Metainference: A Chignolin Study Case

The reliability and usefulness of molecular dynamics simulations of equilibrium processes rests on their statistical precision and their capability to generate conformational ensembles in agreement with available experimental knowledge. Metadynamics Metainference (M&M), coupling molecular dynamics with the enhanced sampling ability of Metadynamics and with the ability to integrate experimental information of Metainference, can in principle achieve both goals. Here we show that three different Metadynamics setups provide converged estimate of the populations of the three-states populated by a model peptide. Errors are estimated correctly by block averaging, but higher precision is obtained by performing independent replicates. One effect of Metadynamics is that of dramatically decreasing the number of effective frames resulting from the simulations and this is relevant for M&M where the number of replicas should be large enough to capture the conformational heterogeneity behind the experimental data. Our simulations allow also us to propose that monitoring the relative error associated with conformational averaging can help to determine the minimum number of replicas to be simulated in the context of M&M simulations. Altogether our data provides useful indication on how to generate sound conformational ensemble in agreement with experimental data.

Peptide Gaussian accelerated molecular dynamics (Pep-GaMD): Enhanced sampling and free energy and kinetics calculations of peptide binding

Peptides mediate up to 40% of known protein-protein interactions in higher eukaryotes and play an important role in cellular signaling. However, it is challenging to simulate both binding and unbinding of peptides and calculate peptide binding free energies through conventional molecular dynamics, due to long biological timescales and extremely high flexibility of the peptides. Based on the Gaussian accelerated molecular dynamics (GaMD) enhanced sampling technique, we have developed a new computational method "Pep-GaMD," which selectively boosts essential potential energy of the peptide in order to effectively model its high flexibility. In addition, another boost potential is applied to the remaining potential energy of the entire system in a dual-boost algorithm. Pep-GaMD has been demonstrated on binding of three model peptides to the SH3 domains. Independent 1 µs dual-boost Pep-GaMD simulations have captured repetitive peptide dissociation and binding events, which enable us to calculate peptide binding thermodynamics and kinetics. The calculated binding free energies and kinetic rate constants agreed very well with available experimental data. Furthermore, the all-atom Pep-GaMD simulations have provided important insights into the mechanism of peptide binding to proteins that involves long-range electrostatic interactions and mainly conformational selection. In summary, Pep-GaMD provides a highly efficient, easy-to-use approach for unconstrained enhanced sampling and calculations of peptide binding free energies and kinetics.

New Perspectives of CYP1B1 Inhibitors in the Light of Molecular Studies

Human cytochrome P450 1B1 (CYP1B1) is an extrahepatic heme-containing monooxygenase. CYP1B1 contributes to the oxidative metabolism of xenobiotics, drugs, and endogenous substrates like melatonin, fatty acids, steroid hormones, and retinoids, which are involved in diverse critical cellular functions. CYP1B1 plays an important role in the pathogenesis of cardiovascular diseases, hormone-related cancers and is responsible for anti-cancer drug resistance. Inhibition of CYP1B1 activity is considered as an approach in cancer chemoprevention and cancer chemotherapy. CYP1B1 can activate anti-cancer prodrugs in tumor cells which display overexpression of CYP1B1 in comparison to normal cells. CYP1B1 involvement in carcinogenesis and cancer progression encourages investigation of CYP1B1 interactions with its ligands: substrates and inhibitors. Computational methods, with a simulation of molecular dynamics (MD), allow the observation of molecular interactions at the binding site of CYP1B1, which are essential in relation to the enzyme’s functions.

Computational design of enzymes for biotechnological applications

Enzymes are the natural catalysts that execute biochemical reactions upholding life. Their natural effectiveness has been fine-tuned as a result of millions of years of natural evolution. Such catalytic effectiveness has prompted the use of biocatalysts from multiple sources on different applications, including the industrial production of goods (food and beverages, detergents, textile, and pharmaceutics), environmental protection, and biomedical applications. Natural enzymes often need to be improved by protein engineering to optimize their function in non-native environments. Recent technological advances have greatly facilitated this process by providing the experimental approaches of directed evolution or by enabling computer-assisted applications. Directed evolution mimics the natural selection process in a highly accelerated fashion at the expense of arduous laboratory work and economic resources. Theoretical methods provide predictions and represent an attractive complement to such experiments by waiving their inherent costs. Computational techniques can be used to engineer enzymatic reactivity, substrate specificity and ligand binding, access pathways and ligand transport, and global properties like protein stability, solubility, and flexibility. Theoretical approaches can also identify hotspots on the protein sequence for mutagenesis and predict suitable alternatives for selected positions with expected outcomes. This review covers the latest advances in computational methods for enzyme engineering and presents many successful case studies.

Assessment of software methods for estimating protein-protein relative binding affinities

A growing number of computational tools have been developed to accurately and rapidly predict the impact of amino acid mutations on protein-protein relative binding affinities. Such tools have many applications, for example, designing new drugs and studying evolutionary mechanisms. In the search for accuracy, many of these methods employ expensive yet rigorous molecular dynamics simulations. By contrast, non-rigorous methods use less exhaustive statistical mechanics, allowing for more efficient calculations. However, it is unclear if such methods retain enough accuracy to replace rigorous methods in binding affinity calculations. This trade-off between accuracy and computational expense makes it difficult to determine the best method for a particular system or study. Here, eight non-rigorous computational methods were assessed using eight antibody-antigen and eight non-antibody-antigen complexes for their ability to accurately predict relative binding affinities (ΔΔG) for 654 single mutations. In addition to assessing accuracy, we analyzed the CPU cost and performance for each method using a variety of physico-chemical structural features. This allowed us to posit scenarios in which each method may be best utilized. Most methods performed worse when applied to antibody-antigen complexes compared to non-antibody-antigen complexes. Rosetta-based JayZ and EasyE methods classified mutations as destabilizing (ΔΔG < -0.5 kcal/mol) with high (83-98%) accuracy and a relatively low computational cost for non-antibody-antigen complexes. Some of the most accurate results for antibody-antigen systems came from combining molecular dynamics with FoldX with a correlation coefficient (r) of 0.46, but this was also the most computationally expensive method. Overall, our results suggest these methods can be used to quickly and accurately predict stabilizing versus destabilizing mutations but are less accurate at predicting actual binding affinities. This study highlights the need for continued development of reliable, accessible, and reproducible methods for predicting binding affinities in antibody-antigen proteins and provides a recipe for using current methods.

Extrapolation and interpolation strategies for efficiently estimating structural observables as a function of temperature and density

Thermodynamic extrapolation has previously been used to predict arbitrary structural observables in molecular simulations at temperatures (or relative chemical potentials in open-system mixtures) different from those at which the simulation was performed. This greatly reduces the computational cost in mapping out phase and structural transitions. In this work, we explore the limitations and accuracy of thermodynamic extrapolation applied to water, where qualitative shifts from anomalous to simple-fluid-like behavior are manifested through shifts in the liquid structure that occur as a function of both temperature and density. We present formulas for extrapolating in volume for canonical ensembles and demonstrate that linear extrapolations of water's structural properties are only accurate over a limited density range. On the other hand, linear extrapolation in temperature can be accurate across the entire liquid state. We contrast these extrapolations with classical perturbation theory techniques, which are more conservative and slowly converging. Indeed, we show that such behavior is expected by demonstrating exact relationships between extrapolation of free energies and well-known techniques to predict free energy differences. An ideal gas in an external field is also studied to more clearly explain these results for a toy system with fully analytical solutions. We also present a recursive interpolation strategy for predicting arbitrary structural properties of molecular fluids over a predefined range of state conditions, demonstrating its success in mapping qualitative shifts in water structure with density.

Structure and Dynamics in the ATG8 Family From Experimental to Computational Techniques

Autophagy is a conserved and essential intracellular mechanism for the removal of damaged components. Since autophagy deregulation is linked to different kinds of pathologies, it is fundamental to gain knowledge on the fine molecular and structural details related to the core proteins of the autophagy machinery. Among these, the family of human ATG8 proteins plays a central role in recruiting other proteins to the different membrane structures involved in the autophagic pathway. Several experimental structures are available for the members of the ATG8 family alone or in complex with their different biological partners, including disordered regions of proteins containing a short linear motif called LC3 interacting motif. Recently, the first structural details of the interaction of ATG8 proteins with biological membranes came into light. The availability of structural data for human ATG8 proteins has been paving the way for studies on their structure-function-dynamic relationship using biomolecular simulations. Experimental and computational structural biology can help to address several outstanding questions on the mechanism of human ATG8 proteins, including their specificity toward different interactors, their association with membranes, the heterogeneity of their conformational ensemble, and their regulation by post-translational modifications. We here summarize the main results collected so far and discuss the future perspectives within the field and the knowledge gaps. Our review can serve as a roadmap for future structural and dynamics studies of the ATG8 family members in health and disease.

Modelling flexible protein–ligand binding in p38α MAP kinase using the QUBE force field

The accuracy of quantum mechanical bespoke (QUBE) force fields for protein–ligand binding free energy calculations are benchmarked against experiment.

Improved Modeling of Peptide-Protein Binding Through Global Docking and Accelerated Molecular Dynamics Simulations

Peptides mediate up to 40% of known protein-protein interactions in higher eukaryotes and play a key role in cellular signaling, protein trafficking, immunology, and oncology. However, it is challenging to predict peptide-protein binding with conventional computational modeling approaches, due to slow dynamics and high peptide flexibility. Here, we present a prototype of the approach which combines global peptide docking using ClusPro PeptiDock and all-atom enhanced simulations using Gaussian accelerated molecular dynamics (GaMD). For three distinct model peptides, the lowest backbone root-mean-square deviations (RMSDs) of their bound conformations relative to X-ray structures obtained from PeptiDock were 3.3–4.8 Å, being medium quality predictions according to the Critical Assessment of PRediction of Interactions (CAPRI) criteria. GaMD simulations refined the peptide-protein complex structures with significantly reduced peptide backbone RMSDs of 0.6–2.7 Å, yielding two high quality (sub-angstrom) and one medium quality models. Furthermore, the GaMD simulations identified important low-energy conformational states and revealed the mechanism of peptide binding to the target proteins. Therefore, PeptiDock+GaMD is a promising approach for exploring peptide-protein interactions.

The effect of dimerization on the activation and conformational dynamics of adenosine A1 receptor

The adenosine A1 receptor (A1R) is one of four adenosine receptors in humans, which are involved in the function of the cardiovascular, respiratory and central nervous systems. Experimental results indicate that A1R can form a homodimer and that the protomer-protomer interaction in the A1R dimer is related to certain pharmacological characteristics of A1R activation. In this work, we performed docking, metadynamics simulation, conventional molecular dynamics simulations, Gaussian-accelerated molecular dynamics simulations, potential of mean force calculations, dynamic cross-correlation motions analysis and community network analysis to study the binding mode of 5'-N-ethylcarboxamidoadenosine (NECA) to A1R and the effect of dimerization on the activation of A1R. Our results show that NECA binds to A1R in a similar mode to adenosine in the A1R crystal structure and NECA in the A2AR crystal structure. The A1R homodimer can be activated by one or two agonists with NECA occupying its orthosteric pockets in one (which we call the NECA-A1R system) or both protomers (which we call the dNECA-A1R system). In the NECA-A1R system, activation is predicated in the protomer without NECA bound. In the dNECA-A1R system, only one protomer achieves the active state. These findings suggest an asymmetrical activation mechanism of the homodimer and a negative cooperativity between the two protomers. We envision that our results may further facilitate the drug development of A1R.

Anncolvar: Approximation of Complex Collective Variables by Artificial Neural Networks for Analysis and Biasing of Molecular Simulations

The state of a molecular system can be described in terms of collective variables. These low-dimensional descriptors of molecular structure can be used to monitor the state of the simulation, to calculate free energy profiles or to accelerate rare events by a bias potential or a bias force. Frequent calculation of some complex collective variables may slow down the simulation or analysis of trajectories. Moreover, many collective variables cannot be explicitly calculated for newly sampled structures. In order to address this problem, we developed a new package called anncolvar. This package makes it possible to build and train an artificial neural network model that approximates a collective variable. It can be used to generate an input for the open-source enhanced sampling simulation PLUMED package, so the collective variable can be monitored and biased by methods available in this program. The computational efficiency and the accuracy of anncolvar are demonstrated on selected molecular systems (cyclooctane derivative, Trp-cage miniprotein) and selected collective variables (Isomap, molecular surface area).

Use of Computational Biochemistry for Elucidating Molecular Mechanisms of Nitric Oxide Synthase

Nitric oxide (NO) is an essential signaling molecule in the regulation of multiple cellular processes. It is endogenously synthesized by NO synthase (NOS) as the product of L-arginine oxidation to L-citrulline, requiring NADPH, molecular oxygen, and a pterin cofactor. Two NOS isoforms are constitutively present in cells, nNOS and eNOS, and a third is inducible (iNOS). Despite their biological relevance, the details of their complex structural features and reactivity mechanisms are still unclear. In this review, we summarized the contribution of computational biochemistry to research on NOS molecular mechanisms. We described in detail its use in studying aspects of structure, dynamics and reactivity. We also focus on the numerous outstanding questions in the field that could benefit from more extensive computational investigations.

Multiscale Simulations of Biological Membranes: The Challenge To Understand Biological Phenomena in a Living Substance

Biological membranes are tricky to investigate. They are complex in terms of molecular composition and structure, functional over a wide range of time scales, and characterized by nonequilibrium conditions. Because of all of these features, simulations are a great technique to study biomembrane behavior. A significant part of the functional processes in biological membranes takes place at the molecular level; thus computer simulations are the method of choice to explore how their properties emerge from specific molecular features and how the interplay among the numerous molecules gives rise to function over spatial and time scales larger than the molecular ones. In this review, we focus on this broad theme. We discuss the current state-of-the-art of biomembrane simulations that, until now, have largely focused on a rather narrow picture of the complexity of the membranes. Given this, we also discuss the challenges that we should unravel in the foreseeable future. Numerous features such as the actin-cytoskeleton network, the glycocalyx network, and nonequilibrium transport under ATP-driven conditions have so far received very little attention; however, the potential of simulations to solve them would be exceptionally high. A major milestone for this research would be that one day we could say that computer simulations genuinely research biological membranes, not just lipid bilayers.

Recent advances in computational studies of GPCR-G protein interactions

Protein-protein interactions are key in cellular signaling. G protein-coupled receptors (GPCRs), the largest superfamily of human membrane proteins, are able to transduce extracellular signals (e.g., hormones and neurotransmitters) to intracellular proteins, in particular the G proteins. Since GPCRs serve as primary targets of ~1/3 of currently marketed drugs, it is important to understand mechanisms of GPCR signaling in order to design selective and potent drug molecules. This chapter focuses on recent advances in computational studies of the GPCR-G protein interactions using bioinformatics, protein-protein docking and molecular dynamics simulation approaches.

Analyzing Biomolecular Ensembles

Several techniques are available to generate conformational ensembles of proteins and other biomolecules either experimentally or computationally. These methods produce a large amount of data that need to be analyzed to identify structure-dynamics-function relationship. In this chapter, we will cover different tools to unveil the information hidden in conformational ensemble data and to guide toward the rationalization of the data. We included routinely used approaches such as dimensionality reduction, as well as new methods inspired by high-order statistics and graph theory.

Structural Basis for Binding of Allosteric Drug Leads in the Adenosine A1 Receptor

Despite intense interest in designing positive allosteric modulators (PAMs) as selective drugs of the adenosine A₁ receptor (A₁AR), structural binding modes of the receptor PAMs remain unknown. Using the first X-ray structure of the A₁AR, we have performed all-atom simulations using a robust Gaussian accelerated molecular dynamics (GaMD) technique to determine binding modes of the A₁AR allosteric drug leads. Two prototypical PAMs, PD81723 and VCP171, were selected. Each PAM was initially placed at least 20 Å away from the receptor. Extensive GaMD simulations using the AMBER and NAMD simulation packages at different acceleration levels captured spontaneous binding of PAMs to the A₁AR. The simulations allowed us to identify low-energy binding modes of the PAMs at an allosteric site formed by the receptor extracellular loop 2 (ECL2), which are highly consistent with mutagenesis experimental data. Furthermore, the PAMs stabilized agonist binding in the receptor. In the absence of PAMs at the ECL2 allosteric site, the agonist sampled a significantly larger conformational space and even dissociated from the A₁AR alone. In summary, the GaMD simulations elucidated structural binding modes of the PAMs and provided important insights into allostery in the A₁AR, which will greatly facilitate the receptor structure-based drug design.

Gaussian accelerated molecular dynamics for elucidation of drug pathways

INTRODUCTION

Understanding pathways and mechanisms of drug binding to receptors is important for rational drug design. Remarkable advances in supercomputing and methodological developments have opened a new era for application of computer simulations in predicting drug-receptor interactions at an atomistic level. Gaussian accelerated molecular dynamics (GaMD) is a computational enhanced sampling technique that works by adding a harmonic boost potential to reduce energy barriers. GaMD enables free energy calculations without the requirement of predefined collective variables. GaMD has proven useful in biomolecular simulations, in particular, the prediction of drug-receptor interactions. Areas covered: Herein, the authors review recent GaMD simulation studies that elucidated pathways of drug binding to proteins including the G-protein-coupled receptors and HIV protease. Expert opinion: GaMD is advantageous for enhanced simulations of, amongst many biological processes, drug binding to target receptors. Compared with conventional molecular dynamics, GaMD speeds up biomolecular simulations by orders of magnitude. GaMD enables routine drug binding simulations using personal computers with GPUs or common computing clusters. GaMD and, more broadly, enhanced sampling simulations are expected to dramatically increase our capabilities to determine the mechanisms of drug binding to a wide range of receptors in the near future. This will greatly facilitate computer-aided drug design.

Acceleration of biomolecular kinetics in Gaussian accelerated molecular dynamics

Recent studies demonstrated that Gaussian accelerated molecular dynamics (GaMD) is a robust computational technique, which provides simultaneous unconstrained enhanced sampling and free energy calculations of biomolecules. However, the exact acceleration of biomolecular dynamics or speedup of kinetic rates in GaMD simulations and, more broadly, in enhanced sampling methods, remains a challenging task to be determined. Here, the GaMD acceleration is examined using alanine dipeptide in explicit solvent as a biomolecular model system. Relative to long conventional molecular dynamics simulation, GaMD simulations exhibited ∼36-67 times speedup for sampling of the backbone dihedral transitions. The acceleration depended on level of the GaMD boost potential. Furthermore, Kramers' rate theory was applied to estimate GaMD acceleration using simulation-derived diffusion coefficients, curvatures and barriers of free energy profiles. In most cases, the calculations also showed significant speedup of dihedral transitions in GaMD, although the GaMD acceleration factors tended to be underestimated by ∼3-96 fold. Because greater boost potential can be applied in GaMD simulations of systems with increased sizes, which potentially leads to higher acceleration, it is subject to future studies on accelerating the dynamics and recovering kinetic rates of larger biomolecules such as proteins and protein-protein/nucleic acid complexes.

Atomistic-Level Investigation of a LL37-Conjugated Gold Nanoparticle By Well-Tempered Metadynamics

LL37 is a cathelicidin-derived antimicrobial peptide (AMP) with a broad spectrum of antimicrobial activity and wound-healing potential. The enhancement of these characteristics was recently demonstrated for a cysteine (CYS)-modified cathelicidin-derived LL37-SH conjugated with gold nanoparticles (AuNPs). Considering the potential of this peptide, we hereby report a computational study in which well-tempered metadynamics was applied to unveil the interaction of LL37-SH and LL37 with a AuNP with atomistic detail. A structural analysis combined with the free energy surface (FES) characterization allowed the assessment of the role of CYS residue during the formation of the conjugate, as well as to understand how the AuNP improves the antimicrobial activity of the peptide. It was found that CYS promotes a lower conformational entropy (before and after adsorption onto the AuNP) and a faster adsorption process when compared to the LL37 without CYS. The FES for LL37-SH is characterized by one global minimum, while for LL37 a potential metastable state was found. The presence of the AuNP leads to an elongation of the peptides along with the adsorption, which translates into the increase of the solvent-accessible surface area. This elongation combined with the greater availability of positively charged residues upon adsorption rationalizes the observed enhancement of the activity of the LL37-SH/AuNP conjugate.