Computed Binding of Peptides to Proteins with MELD-Accelerated Molecular Dynamics

MELD in Action: Harnessing Data to Accelerate Molecular Dynamics

We review MELD, an accelerator of Molecular Dynamics simulations of biomolecules. MELD (Modeling Employing Limited Data) integrates molecular dynamics (MD) with a variety of types of structural information through Bayesian inference, generating ensembles of protein and DNA structures having proper Boltzmann populations. MELD minimizes the computational sampling of irrelevant regions of phase space by applying energetic penalties to areas that conflict with the available data. MELD is effective in refining protein structures using NMR or cryo-EM data or predicting protein-ligand binding poses. As a plugin for OpenMM, MELD is interoperable with other enhanced sampling methods, offering a versatile tool for structural determination in computational chemistry and biophysics.

PepBinding: A Workflow for Predicting Peptide Binding Structures by Combining Peptide Docking and Peptide Gaussian Accelerated Molecular Dynamics Simulations

Predicting protein-peptide interactions is crucial for understanding peptide binding processes and designing peptide drugs. However, traditional computational modeling approaches face challenges in accurately predicting peptide-protein binding structures due to the slow dynamics and high flexibility of the peptides. Here, we introduce a new workflow termed "PepBinding" for predicting peptide binding structures, which combines peptide docking, all-atom enhanced sampling simulations using the Peptide Gaussian accelerated Molecular Dynamics (Pep-GaMD) method, and structural clustering. PepBinding has been demonstrated on seven distinct model peptides. In peptide docking using HPEPDOCK, the peptide backbone root-mean-square deviations (RMSDs) of their bound conformations relative to X-ray structures ranged from 3.8 to 16.0 Å, corresponding to the medium to inaccurate quality models according to the Critical Assessment of PRediction of Interactions (CAPRI) criteria. The Pep-GaMD simulations performed for only 200 ns significantly improved the docking models, resulting in five medium and two acceptable quality models. Therefore, PepBinding is an efficient workflow for predicting peptide binding structures and is publicly available at https://github.com/MiaoLab20/PepBinding.

A Computational Pipeline for Accurate Prioritization of Protein-Protein Binding Candidates in High-Throughput Protein Libraries

Identifying the interactome for a protein of interest is challenging due to the large number of possible binders. High-throughput experimental approaches narrow down possible binding partners but often include false positives. Furthermore, they provide no information about what the binding region is (e.g., the binding epitope). We introduce a novel computational pipeline based on an AlphaFold2 (AF) Competitive Binding Assay (AF-CBA) to identify proteins that bind a target of interest from a pull-down experiment and the binding epitope. Our focus is on proteins that bind the Extraterminal (ET) domain of Bromo and Extraterminal domain (BET) proteins, but we also introduce nine additional systems to show transferability to other peptide-protein systems. We describe a series of limitations to the methodology based on intrinsic deficiencies of AF and AF-CBA to help users identify scenarios where the approach will be most useful. Given the method's speed and accuracy, we anticipate its broad applicability to identify binding epitope regions among potential partners, setting the stage for experimental verification.

Fast, accurate ranking of engineered proteins by target-binding propensity using structure modeling

Deep-learning-based methods for protein structure prediction have achieved unprecedented accuracy, yet their utility in the engineering of protein-based binders remains constrained due to a gap between the ability to predict the structures of candidate proteins and the ability toprioritize proteins by their potential to bind to a target. To bridge this gap, we introduce Automated Pairwise Peptide-Receptor Analysis for Screening Engineered proteins (APPRAISE), a method for predicting the target-binding propensity of engineered proteins. After generating structural models of engineered proteins competing for binding to a target using an established structure prediction tool such as AlphaFold-Multimer or ESMFold, APPRAISE performs a rapid (under 1 CPU second per model) scoring analysis that takes into account biophysical and geometrical constraints. As proof-of-concept cases, we demonstrate that APPRAISE can accurately classify receptor-dependent vs. receptor-independent adeno-associated viral vectors and diverse classes of engineered proteins such as miniproteins targeting the severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) spike, nanobodies targeting a G-protein-coupled receptor, and peptides that specifically bind to transferrin receptor or programmed death-ligand 1 (PD-L1). APPRAISE is accessible through a web-based notebook interface using Google Colaboratory (https://tiny.cc/APPRAISE). With its accuracy, interpretability, and generalizability, APPRAISE promises to expand the utility of protein structure prediction and accelerate protein engineering for biomedical applications.

Leveraging machine learning models for peptide-protein interaction prediction

Peptides play a pivotal role in a wide range of biological activities through participating in up to 40% protein-protein interactions in cellular processes. They also demonstrate remarkable specificity and efficacy, making them promising candidates for drug development. However, predicting peptide-protein complexes by traditional computational approaches, such as docking and molecular dynamics simulations, still remains a challenge due to high computational cost, flexible nature of peptides, and limited structural information of peptide-protein complexes. In recent years, the surge of available biological data has given rise to the development of an increasing number of machine learning models for predicting peptide-protein interactions. These models offer efficient solutions to address the challenges associated with traditional computational approaches. Furthermore, they offer enhanced accuracy, robustness, and interpretability in their predictive outcomes. This review presents a comprehensive overview of machine learning and deep learning models that have emerged in recent years for the prediction of peptide-protein interactions.

Design of target specific peptide inhibitors using generative deep learning and molecular dynamics simulations

We introduce a computational approach for the design of target-specific peptides. Our method integrates a Gated Recurrent Unit-based Variational Autoencoder with Rosetta FlexPepDock for peptide sequence generation and binding affinity assessment. Subsequently, molecular dynamics simulations are employed to narrow down the selection of peptides for experimental assays. We apply this computational strategy to design peptide inhibitors that specifically target β-catenin and NF-κB essential modulator. Among the twelve β-catenin inhibitors, six exhibit improved binding affinity compared to the parent peptide. Notably, the best C-terminal peptide binds β-catenin with an IC50 of 0.010 ± 0.06 μM, which is 15-fold better than the parent peptide. For NF-κB essential modulator, two of the four tested peptides display substantially enhanced binding compared to the parent peptide. Collectively, this study underscores the successful integration of deep learning and structure-based modeling and simulation for target specific peptide design.

Molecular Modeling of Self-Assembling Peptides

Peptide epitopes mediate as many as 40% of protein-protein interactions and fulfill signaling, inhibition, and activation roles within the cell. Beyond protein recognition, some peptides can self- or coassemble into stable hydrogels, making them a readily available source of biomaterials. While these 3D assemblies are routinely characterized at the fiber level, there are missing atomistic details about the assembly scaffold. Such atomistic detail can be useful in the rational design of more stable scaffold structures and with improved accessibility to functional motifs. Computational approaches can in principle reduce the experimental cost of such an endeavor by predicting the assembly scaffold and identifying novel sequences that adopt said structure. Yet, inaccuracies in physical models and inefficient sampling have limited atomistic studies to short (two or three amino acid) peptides. Given recent developments in machine learning and advances in sampling strategies, we revisit the suitability of physical models for this task. We use the MELD (Modeling Employing Limited Data) approach to drive self-assembly in combination with generic data in cases where conventional MD is unsuccessful. Finally, despite recent developments in machine learning algorithms for protein structure and sequence predictions, we find the algorithms are not yet suited for studying the assembly of short peptides.

Revolutionizing Peptide-Based Drug Discovery: Advances in the Post-AlphaFold Era

Peptide-based drugs offer high specificity, potency, and selectivity. However, their inherent flexibility and differences in conformational preferences between their free and bound states create unique challenges that have hindered progress in effective drug discovery pipelines. The emergence of AlphaFold (AF) and Artificial Intelligence (AI) presents new opportunities for enhancing peptide-based drug discovery. We explore recent advancements that facilitate a successful peptide drug discovery pipeline, considering peptides' attractive therapeutic properties and strategies to enhance their stability and bioavailability. AF enables efficient and accurate prediction of peptide-protein structures, addressing a critical requirement in computational drug discovery pipelines. In the post-AF era, we are witnessing rapid progress with the potential to revolutionize peptide-based drug discovery such as the ability to rank peptide binders or classify them as binders/non-binders and the ability to design novel peptide sequences. However, AI-based methods are struggling due to the lack of well-curated datasets, for example to accommodate modified amino acids or unconventional cyclization. Thus, physics-based methods, such as docking or molecular dynamics simulations, continue to hold a complementary role in peptide drug discovery pipelines. Moreover, MD-based tools offer valuable insights into binding mechanisms, as well as the thermodynamic and kinetic properties of complexes. As we navigate this evolving landscape, a synergistic integration of AI and physics-based methods holds the promise of reshaping the landscape of peptide-based drug discovery.

Roles of Accelerated Molecular Dynamics Simulations in Predictions of Binding Kinetic Parameters

Rational predictions on binding kinetics parameters of drugs to targets play significant roles in future drug designs. Full conformational samplings of targets are requisite for accurate predictions of binding kinetic parameters. In this review, we mainly focus on the applications of enhanced sampling technologies in calculations of binding kinetics parameters and residence time of drugs. The methods involved in molecular dynamics simulations are applied to not only probe conformational changes of targets but also reveal calculations of residence time that is significant for drug efficiency. For this review, special attention are paid to accelerated molecular dynamics (aMD) and Gaussian aMD (GaMD) simulations that have been adopted to predict the association or disassociation rate constant. We also expect that this review can provide useful information for future drug design.

Markov State Model of Solvent Features Reveals Water Dynamics in Protein-Peptide Binding

In this work, we investigate the role of solvent in the binding reaction of the p53 transactivation domain (TAD) peptide to its receptor MDM2. Previously, our group generated 831 μs of explicit-solvent aggregate molecular simulation trajectory data for the MDM2-p53 peptide binding reaction using large-scale distributed computing and subsequently built a Markov State Model (MSM) of the binding reaction (Zhou et al. 2017). Here, we perform a tICA analysis and construct an MSM with similar hyperparameters while using only solvent-based structural features. We find a remarkably similar landscape but accelerated implied timescales for the slowest motions. The solvent shells contributing most to the first tICA eigenvector are those centered on Lys24 and Thr18 of the p53 TAD peptide in the range of 3-6 Å. Important solvent shells were visualized to reveal solvation and desolvation transitions along the peptide-protein binding trajectories. Our results provide a solvent-centric view of the hydrophobic effect in action for a realistic peptide-protein binding scenario.

When MELD Meets GaMD: Accelerating Biomolecular Landscape Exploration

We introduce Gaussian accelerated MELD (GaMELD) as a new method for exploring the energy landscape of biomolecules. GaMELD combines the strengths of Gaussian accelerated molecular dynamics (GaMD) and modeling employing limited data (MELD) to navigate complex energy landscapes. MELD uses replica-exchange molecular simulations to integrate limited and uncertain data into simulations via Bayesian inference. MELD has been successfully applied to problems of structure prediction like protein folding and complex structure prediction. However, the computational cost for MELD simulations has limited its broader applicability. The synergy of GaMD and MELD surmounts this limitation efficiently sampling the energy landscape at a lower computational cost (reducing the computational cost by a factor of 2 to six). Effectively, GaMD is used to shift energy distributions along replicas to increase the overlap in energy distributions across replicas, facilitating a random walk in replica space. We tested GaMELD on a benchmark set of 12 small proteins that have been previously studied through MELD and conventional MD. GaMELD consistently achieves accurate predictions with fewer replicas. By increasing the efficacy of replica exchange, GaMELD effectively accelerates convergence in the conformational space, enabling improved sampling across a diverse set of systems.

Computing Free Energies of Fold-Switching Proteins Using MELD x MD

Some proteins are conformational switches, able to transition between relatively different conformations. To understand what drives them requires computing the free-energy difference ΔGAB between their stable states, A and B. Molecular dynamics (MD) simulations alone are often slow because they require a reaction coordinate and must sample many transitions in between. Here, we show that modeling employing limited data (MELD) x MD on known endstates A and B is accurate and efficient because it does not require passing over barriers or knowing reaction coordinates. We validate this method on two problems: (1) it gives correct relative populations of α and β conformers for small designed chameleon sequences of protein G; and (2) it correctly predicts the conformations of the C-terminal domain (CTD) of RfaH. Free-energy methods like MELD x MD can often resolve structures that confuse machine-learning (ML) methods.

Binding-and-Folding Recognition of an Intrinsically Disordered Protein Using Online Learning Molecular Dynamics

Intrinsically disordered proteins participate in many biological processes by folding upon binding to other proteins. However, coupled folding and binding processes are not well understood from an atomistic point of view. One of the main questions is whether folding occurs prior to or after binding. Here we use a novel, unbiased, high-throughput adaptive sampling approach to reconstruct the binding and folding between the disordered transactivation domain of c-Myb and the KIX domain of the CREB-binding protein. The reconstructed long-term dynamical process highlights the binding of a short stretch of amino acids on c-Myb as a folded α-helix. Leucine residues, especially Leu298-Leu302, establish initial native contacts that prime the binding and folding of the rest of the peptide, with a mixture of conformational selection on the N-terminal region with an induced fit of the C-terminal.

Computational Study of Driving Forces in ATSP, PDIQ, and P53 Peptide Binding: C═O···C═O Tetrel Bonding Interactions at Work

Understanding the molecular interactions that drive peptide folding is crucial to chemistry and biology. In this study, we analyzed the role of CO···CO tetrel bonding (TtB) interactions in the folding mechanism of three different peptides (ATSP, pDIQ, and p53), which exhibit a different propensity to fold in an α helix motif. To achieve this goal, we used both a recently developed Bayesian inference approach (MELDxMD) and Quantum Mechanics (QM) calculations at the RI-MP2/def2-TZVP level of theory. These techniques allowed us to study the folding process and to evaluate the strength of the CO···CO TtBs as well as the synergies between TtBs and hydrogen-bonding (HB) interactions. We believe that the results derived from our study will be helpful for those scientists working in computational biology, peptide chemistry, and structural biology.

BICePs v2.0: Software for Ensemble Reweighting Using Bayesian Inference of Conformational Populations

Bayesian Inference of Conformational Populations (BICePs) version 2.0 (v2.0) is a free, open-source Python package that reweights theoretical predictions of conformational state populations using sparse and/or noisy experimental measurements. In this article, we describe the implementation and usage of the latest version of BICePs (v2.0), a powerful, user-friendly and extensible package which makes several improvements upon the previous version. The algorithm now supports many experimental NMR observables (NOE distances, chemical shifts, J-coupling constants, and hydrogen-deuterium exchange protection factors), and enables convenient data preparation and processing. BICePs v2.0 can perform automatic analysis of the sampled posterior, including visualization, and evaluation of statistical significance and sampling convergence. We provide specific coding examples for these topics, and present a detailed example illustrating how to use BICePs v2.0 to reweight a theoretical ensemble using experimental measurements.

MELD-Bracket Ranks Binding Affinities of Diverse Sets of Ligands

Affinity ranking of structurally diverse small-molecule ligands is a challenging problem with important applications in structure-based drug discovery. Absolute binding free energy methods can model diverse ligands, but the high computational cost of the current methods limits application to data sets with few ligands. We recently developed MELD-Bracket, a Molecular Dynamics method for efficient affinity ranking of ligands [ JCTC 2022, 18 (1), 374-379]. It utilizes a Bayesian framework to guide sampling to relevant regions of phase space, and it couples this with a bracket-like competition on a pool of ligands. Here we find that 6-competitor MELD-Bracket can rank dozens of diverse ligands that have low structural similarity and different net charges. We benchmark it on four protein systems─PTB1B, Tyk2, BACE, and JAK3─having varied modes of interactions. We also validated 8-competitor and 12-competitor protocols. The MELD-Bracket protocols presented here may have the appropriate balance of accuracy and computational efficiency to be suitable for ranking diverse ligands from typical drug discovery campaigns.

Computational approaches for the design of modulators targeting protein-protein interactions

BACKGROUND

Protein-protein interactions (PPIs) are intriguing targets for designing novel small-molecule inhibitors. The role of PPIs in various infectious and neurodegenerative disorders makes them potential therapeutic targets . Despite being portrayed as undruggable targets, due to their flat surfaces, disorderedness, and lack of grooves. Recent progresses in computational biology have led researchers to reconsider PPIs in drug discovery.

AREAS COVERED

In this review, we introduce in-silico methods used to identify PPI interfaces and present an in-depth overview of various computational methodologies that are successfully applied to annotate the PPIs. We also discuss several successful case studies that use computational tools to understand PPIs modulation and their key roles in various physiological processes.

EXPERT OPINION

Computational methods face challenges due to the inherent flexibility of proteins, which makes them expensive, and result in the use of rigid models. This problem becomes more significant in PPIs due to their flexible and flat interfaces. Computational methods like molecular dynamics (MD) simulation and machine learning can integrate the chemical structure data into biochemical and can be used for target identification and modulation. These computational methodologies have been crucial in understanding the structure of PPIs, designing PPI modulators, discovering new drug targets, and predicting treatment outcomes.

Structural predictions of protein-DNA binding: MELD-DNA

Structural, regulatory and enzymatic proteins interact with DNA to maintain a healthy and functional genome. Yet, our structural understanding of how proteins interact with DNA is limited. We present MELD-DNA, a novel computational approach to predict the structures of protein-DNA complexes. The method combines molecular dynamics simulations with general knowledge or experimental information through Bayesian inference. The physical model is sensitive to sequence-dependent properties and conformational changes required for binding, while information accelerates sampling of bound conformations. MELD-DNA can: (i) sample multiple binding modes; (ii) identify the preferred binding mode from the ensembles; and (iii) provide qualitative binding preferences between DNA sequences. We first assess performance on a dataset of 15 protein-DNA complexes and compare it with state-of-the-art methodologies. Furthermore, for three selected complexes, we show sequence dependence effects of binding in MELD predictions. We expect that the results presented herein, together with the freely available software, will impact structural biology (by complementing DNA structural databases) and molecular recognition (by bringing new insights into aspects governing protein-DNA interactions).

Assessing a computational pipeline to identify binding motifs to the α2β1 integrin

Integrins in the cell surface interact with functional motifs found in the extracellular matrix (ECM) that queue the cell for biological actions such as migration, adhesion, or growth. Multiple fibrous proteins such as collagen or fibronectin compose the ECM. The field of biomechanical engineering often deals with the design of biomaterials compatible with the ECM that will trigger cellular response (e.g., in tissue regeneration). However, there are a relative few number of known integrin binding motifs compared to all the possible peptide epitope sequences available. Computational tools could help identify novel motifs, but have been limited by the challenges in modeling the binding to integrin domains. We revisit a series of traditional and novel computational tools to assess their performance in identifying novel binding motifs for the I-domain of the α2β1 integrin.

Ranking Peptide Binders by Affinity with AlphaFold

AlphaFold has revolutionized structural biology by predicting highly accurate structures of proteins and their complexes with peptides and other proteins. However, for protein-peptide systems, we are also interested in identifying the highest affinity binder among a set of candidate peptides. We present a novel competitive binding assay using AlphaFold to predict structures of the receptor in the presence of two peptides. For systems in which the individual structures of the peptides are well predicted, the assay captures the higher affinity binder in the bound state, and the other peptide in the unbound form with statistical significance. We test the application on six protein receptors for which we have experimental binding affinities to several peptides. We find that the assay is best suited for identifying medium to strong peptide binders that adopt stable secondary structures upon binding.

Towards rational computational peptide design

Peptides are prevalent in biology, mediating as many as 40% of protein-protein interactions, and involved in other cellular functions such as transport and signaling. Their ability to bind with high specificity make them promising therapeutical agents with intermediate properties between small molecules and large biologics. Beyond their biological role, peptides can be programmed to self-assembly, and they are already being used for functions as diverse as oligonuclotide delivery, tissue regeneration or as drugs. However, the transient nature of their interactions has limited the number of structures and knowledge of binding affinities available-and their flexible nature has limited the success of computational pipelines that predict the structures and affinities of these molecules. Fortunately, recent advances in experimental and computational pipelines are creating new opportunities for this field. We are starting to see promising predictions of complex structures, thermodynamic and kinetic properties. We believe in the following years this will lead to robust rational peptide design pipelines with success similar to those applied for small molecule drug discovery.

Accurate Prediction for Protein-Peptide Binding Based on High-Temperature Molecular Dynamics Simulations

The structural characterization of protein-peptide interactions is fundamental to elucidating biological processes and designing peptide drugs. Molecular dynamics (MD) simulations are extensively used to study biomolecular systems. However, simulating the protein-peptide binding process is usually quite expensive. Based on our previous studies, herein, we propose a simple and effective method to predict the binding site and pose of the peptide simultaneously using high-temperature (high-T) MD simulations with the RSFF2C force field. Thousands of binding events (nonspecific or specific) can be sampled during microseconds of high-T MD. From density-based clustering analysis, the structures of all of the 12 complexes (nine with linear peptides and three with cyclic peptides) can be successfully predicted with root-mean-square deviation (RMSD) < 2.5 Å. By directly simulating the process of the ligand binding onto the receptor, our method approaches experimental precision for the first time, significantly surpassing previous protein-peptide docking methods in terms of accuracy.

Searching for Low Probability Opening Events in a DNA Sliding Clamp

The β subunit of E. coli DNA polymererase III is a DNA sliding clamp associated with increasing the processivity of DNA synthesis. In its free form, it is a circular homodimer structure that can accomodate double-stranded DNA in a nonspecific manner. An open state of the clamp must be accessible before loading the DNA. The opening mechanism is still a matter of debate, as is the effect of bound DNA on opening/closing kinetics. We use a combination of atomistic, coarse-grained, and enhanced sampling strategies in both explicit and implicit solvents to identify opening events in the sliding clamp. Such simulations of large nucleic acid and their complexes are becoming available and are being driven by improvements in force fields and the creation of faster computers. Different models support alternative opening mechanisms, either through an in-plane or out-of-plane opening event. We further note some of the current limitations, despite advances, in modeling these highly charged systems with implicit solvent.

Accelerating Molecular Dynamics Enrichments of High-Affinity Ligands for Proteins

Molecular docking algorithms are used to seek the most active compounds from a pool of ligands. In principle, molecular dynamics (MD) simulations with accurate physical potentials and sampling could yield better enrichments, but they are computationally expensive. Here, we describe a method called MELD-Bracket that utilizes biased replica exchange ladders in MD in order to compete different ligands against each other within a fast bracket style "binding tournament". MELD-Bracket finds best-binders rapidly when ligands are well separated in their binding affinities.

CryoFold: determining protein structures and data-guided ensembles from cryo-EM density maps

Cryo-electron microscopy (EM) requires molecular modeling to refine structural details from data. Ensemble models arrive at low free-energy molecular structures, but are computationally expensive and limited to resolving only small proteins that cannot be resolved by cryo-EM. Here, we introduce CryoFold - a pipeline of molecular dynamics simulations that determines ensembles of protein structures directly from sequence by integrating density data of varying sparsity at 3-5 Å resolution with coarse-grained topological knowledge of the protein folds. We present six examples showing its broad applicability for folding proteins between 72 to 2000 residues, including large membrane and multi-domain systems, and results from two EMDB competitions. Driven by data from a single state, CryoFold discovers ensembles of common low-energy models together with rare low-probability structures that capture the equilibrium distribution of proteins constrained by the density maps. Many of these conformations, unseen by traditional methods, are experimentally validated and functionally relevant. We arrive at a set of best practices for data-guided protein folding that are controlled using a Python GUI.

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.

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.

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.

MELD-accelerated molecular dynamics help determine amyloid fibril structures

It is challenging to determine the structures of protein fibrils such as amyloids. In principle, Molecular Dynamics (MD) modeling can aid experiments, but normal MD has been impractical for these large multi-molecules. Here, we show that MELD accelerated MD (MELD x MD) can give amyloid structures from limited data. Five long-chain fibril structures are accurately predicted from NMR and Solid State NMR (SSNMR) data. Ten short-chain fibril structures are accurately predicted from more limited restraints information derived from the knowledge of strand directions. Although the present study only tests against structure predictions - which are the most detailed form of validation currently available - the main promise of this physical approach is ultimately in going beyond structures to also give mechanical properties, conformational ensembles, and relative stabilities.

Computational Modeling as a Tool to Investigate PPI: From Drug Design to Tissue Engineering

Protein-protein interactions (PPIs) mediate a large number of important regulatory pathways. Their modulation represents an important strategy for discovering novel therapeutic agents. However, the features of PPI binding surfaces make the use of structure-based drug discovery methods very challenging. Among the diverse approaches used in the literature to tackle the problem, linear peptides have demonstrated to be a suitable methodology to discover PPI disruptors. Unfortunately, the poor pharmacokinetic properties of linear peptides prevent their direct use as drugs. However, they can be used as models to design enzyme resistant analogs including, cyclic peptides, peptide surrogates or peptidomimetics. Small molecules have a narrower set of targets they can bind to, but the screening technology based on virtual docking is robust and well tested, adding to the computational tools used to disrupt PPI. We review computational approaches used to understand and modulate PPI and highlight applications in a few case studies involved in physiological processes such as cell growth, apoptosis and intercellular communication.

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.

Binding Ensembles of p53-MDM2 Peptide Inhibitors by Combining Bayesian Inference and Atomistic Simulations

Designing peptide inhibitors of the p53-MDM2 interaction against cancer is of wide interest. Computational modeling and virtual screening are a well established step in the rational design of small molecules. But they face challenges for binding flexible peptide molecules that fold upon binding. We look at the ability of five different peptides, three of which are intrinsically disordered, to bind to MDM2 with a new Bayesian inference approach (MELD × MD). The method is able to capture the folding upon binding mechanism and differentiate binding preferences between the five peptides. Processing the ensembles with statistical mechanics tools depicts the most likely bound conformations and hints at differences in the binding mechanism. Finally, the study shows the importance of capturing two driving forces to binding in this system: the ability of peptides to adopt bound conformations (ΔGconformation) and the interaction between interface residues (ΔGinteraction).

An integrated view of p53 dynamics, function, and reactivation

The tumor suppressor p53 plays a vital role in responding to cell stressors such as DNA damage, hypoxia, and tumor formation by inducing cell-cycle arrest, senescence, or apoptosis. Expression level alterations and mutational frequency implicates p53 in most human cancers. In this review, we show how both computational and experimental methods have been used to provide an integrated view of p53 dynamics, function, and reactivation potential. We argue that p53 serves as an exceptional case study for developing methods in modeling intrinsically disordered proteins. We describe how these methods can be leveraged to improve p53 reactivation molecule design and other novel therapeutic modalities, such as PROteolysis TARgeting Chimeras (PROTACs).

Computing Ligands Bound to Proteins Using MELD-Accelerated MD

Predicting the poses of small-molecule ligands in protein binding sites is often done by virtual screening algorithms such as DOCK. In principle, molecular dynamics (MD) using atomistic force fields could give better free-energy-based pose selection, but MD is computationally expensive. Here, we ask if modeling employing limited data (MELD)-accelerated MD (MELD × MD) can pick out the best DOCK poses taken as input. We study 30 different ligand-protein pairs. MELD × MD finds native poses, based on best free energies, in 23 out of the 30 cases, 20 of which were previously known DOCK failures. We conclude that MELD × MD can add value for predicting accurate poses of small molecules bound to proteins.

Modeling beta-sheet peptide-protein interactions: Rosetta FlexPepDock in CAPRI rounds 38-45

Peptide-protein docking is challenging due to the considerable conformational freedom of the peptide. CAPRI rounds 38-45 included two peptide-protein interactions, both characterized by a peptide forming an additional beta strand of a beta sheet in the receptor. Using the Rosetta FlexPepDock peptide docking protocol we generated top-performing, high-accuracy models for targets 134 and 135, involving an interaction between a peptide derived from L-MAG with DLC8. In addition, we were able to generate the only medium-accuracy models for a particularly challenging target, T121. In contrast to the classical peptide-mediated interaction, in which receptor side chains contact both peptide backbone and side chains, beta-sheet complementation involves a major contribution to binding by hydrogen bonds between main chain atoms. To establish how binding affinity and specificity are established in this special class of peptide-protein interactions, we extracted PeptiDBeta, a benchmark of solved structures of different protein domains that are bound by peptides via beta-sheet complementation, and tested our protocol for global peptide-docking PIPER-FlexPepDock on this dataset. We find that the beta-strand part of the peptide is sufficient to generate approximate and even high resolution models of many interactions, but inclusion of adjacent motif residues often provides additional information necessary to achieve high resolution model quality.

Characterization of partially ordered states in the intrinsically disordered N-terminal domain of p53 using millisecond molecular dynamics simulations

The exploration of intrinsically disordered proteins in isolation is a crucial step to understand their complex dynamical behavior. In particular, the emergence of partially ordered states has not been explored in depth. The experimental characterization of such partially ordered states remains elusive due to their transient nature. Molecular dynamics mitigates this limitation thanks to its capability to explore biologically relevant timescales while retaining atomistic resolution. Here, millisecond unbiased molecular dynamics simulations were performed in the exemplar N-terminal region of p53. In combination with state-of-the-art Markov state models, simulations revealed the existence of several partially ordered states accounting for [Formula: see text] 40% of the equilibrium population. Some of the most relevant states feature helical conformations similar to the bound structure of p53 to Mdm2, as well as novel [Formula: see text]-sheet elements. This highlights the potential complexity underlying the energy surface of intrinsically disordered proteins.

Bioinformatics and Biosimulations as Toolbox for Peptides and Peptidomimetics Design: Where Are We?

Peptides and peptidomimetics are strongly re-emerging as amenable candidates in the development of therapeutic strategies against a plethora of pathologies. In particular, these molecules are extremely suitable to treat diseases in which a major role is played by protein-protein interactions (PPIs). Unlike small organic compounds, peptides display both a high degree of specificity avoiding secondary off-targets effects and a relatively low degree of toxicity. Further advantages are provided by the possibility to easily conjugate peptides to functionalized nanoparticles, so improving their delivery and cellular uptake. In many cases, such molecules need to assume a specific three-dimensional conformation that resembles the bioactive one of the endogenous ligand. To this end, chemical modifications are introduced in the polypeptide chain to constrain it in a well-defined conformation, and to improve the drug-like properties. In this context, a successful strategy for peptide/peptidomimetics design and optimization is to combine different computational approaches ranging from structural bioinformatics to atomistic simulations. Here, we review the computational tools for peptide design, highlighting their main features and differences, and discuss selected protocols, among the large number of methods available, used to assess and improve the stability of the functional folding of the peptides. Finally, we introduce the simulation techniques employed to predict the binding affinity of the designed peptides for their targets.

Effect of linker on the binding free energy of stapled p53/HDM2 complex

Inactivation of the tumor suppressor p53 resulting from the binding with a negative regulator HDM2 is among the predominant defects in human cancers. p53-mimicking peptides whose conformational and proteolytic stability is enhanced by an all-hydrocarbon staple are being recognized as promising anticancer agents for disrupting the p53–HDM2 binding and reactivating p53. Herein, we conduct a computational modeling and thermodynamic characterization of stapled p53/HDM2 complex via molecular docking, simulations, and binding free energy analysis. The binding thermodynamics analysis is done based on the end-point calculation of the effective binding energy—a sum of the direct peptide–protein interaction energy and the dehydration penalty—and on its decomposition into contributions from specific groups constituting the complex. This allows us to investigate how individual amino acids in the stapled p53 and HDM2 contribute to the binding affinity. We find that not only the epitope residues (F19, W23 and L26), but also the hydrocarbon linker of the stapled p53 impart significant contributions. Our computational approach will be useful in designing new stapled peptides in which the staple location is also optimized to improve the binding affinity.

Exploring the Ligand Binding/Unbinding Pathway by Selectively Enhanced Sampling of Ligand in a Protein-Ligand Complex

Understanding the protein-ligand binding is of fundamental biological interest and is essential for structure-based drug design. The difficulty in capturing the dynamic process, however, poses a great challenge for current experimental and theoretical simulation techniques. A selective integrated-tempering-sampling molecular dynamics (SITSMD) method offering an option for selectively enhanced sampling of the ligand in a protein-ligand complex was utilized to quantitatively illuminate the binding of benzamidine to the wild-type trypsin protease and its two mutants (S214E and S214K). The SITSMD simulations could produce consistent results as the extensive conventional MD simulation and gave additional insights into the binding pathway for the test protein-ligand complex system using significantly saved computational resource and time, indicating the potential of such a method in investigating protein-ligand binding. Additionally, the simulations identified the different roles of trypsin-benzamidine van der Waals (vdW) and electrostatic interactions in the binding: the former interaction works as the driving force for dragging the benzamidine close to the native binding pocket, and the latter interaction mainly contributes to stabilizing the benzamidine inside the pocket. The S214E mutation introduces more favorable electrostatic interactions, and as a result, both vdW and electrostatic interactions drive the benzamidine binding, lowering the binding and unbinding free energy barrier. In contrast, the S214K mutation prohibits the binding of the benzamidine to the native ligand binding pocket by introducing disliked charge-charge interactions. In summary, these findings suggest that the change in specific residues could modify the protein druggability, including the binding kinetics and thermodynamics.

Predicting Protein Dimer Structures Using MELD × MD

It is challenging to predict the docked conformations of two proteins. Current methods are susceptible to errors from treating proteins as rigid bodies and from an inability to compute relative Boltzmann populations of different docked conformations. Here, we show that by using the ClusPro server as a front end to generate possible protein-protein contacts, and using Modeling Employing Limited Data (MELD) accelerated molecular dynamics (MELD × MD) as a back end for atomistic simulations, we can find 16/20 native dimer structures of small proteins as those having the lowest free energy, starting from good-bound-backbone structures. We show that atomistic MD free energies can be used to identify native protein dimer structures.

Monte Carlo on the manifold and MD refinement for binding pose prediction of protein-ligand complexes: 2017 D3R Grand Challenge

Manifold representations of rotational/translational motion and conformational space of a ligand were previously shown to be effective for local energy optimization. In this paper we report the development of the Monte-Carlo energy minimization approach (MCM), which uses the same manifold representation. The approach was integrated into the docking pipeline developed for the current round of D3R experiment, and according to D3R assessment produced high accuracy poses for Cathepsin S ligands. Additionally, we have shown that (MD) refinement further improves docking quality. The code of the Monte-Carlo minimization is freely available at https://bitbucket.org/abc-group/mcm-demo .

Specific Residue Interactions Regulate the Binding of Dengue Antigens to Broadly Neutralizing EDE Antibodies

Antibodies binding to antigens present on the dengue virus (DENV) represent the main defense mechanism of the host organism against the pathogen. Among the antibodies elicited by DENV and that bind to DII of protein E, EDE1-C8 can bind all DENV serotypes. Our analysis reveals the key residues in this interaction as well as structurally conserved hydrogen bonds located at the binding interface. They stabilize the dengue antigen-antibody complex among the EDE1 group of antibodies (Abs). Combining structural alignments with molecular dynamics simulations in the EDE1 Abs, we identified the critical elements that provide a major energetic contribution to the association of antigens from protein E with Abs. We discuss possible molecular insights into the binding mechanism by using a surrogate molecular entity resembling the protein E that forms native salt bridges and hydrogen bonds, including inferences on the light of high-resolution crystal structures of dengue Fab complexes. Finally, the molecular determinants, the free energy profile, and the binding mechanism provide inspiration for potential strategies in protein engineering to design novel immunogens of protein E against DENV.

Online Optimization of Total Acceptance in Hamiltonian Replica Exchange Simulations

Replica exchange is a widely used sampling strategy in molecular simulation. While a variety of methods exist to optimize parameters for temperature replica exchange, less is known about how to optimize parameters for more general Hamiltonian replica exchange simulations. We present an algorithm for the online optimization of total acceptance for both temperature and Hamiltonian replica exchange simulations using stochastic gradient descent. We optimize the total acceptance, a heuristic objective function capturing the efficiency of replica exchange. Our approach is general and has several desirable properties, including: (1) it makes few assumptions about the system of interest, (2) optimization occurs online without the requirement of presimulation, and (3) most importantly, it readily generalizes to systems where there are multiple control parameters (e.g., temperatures, force constants, etc.) that determine the Hamiltonian of each replica. We explore some general properties of the algorithm on a simple harmonic oscillator system, and demonstrate its effectiveness on a more complex data-guided protein folding simulation.

MELD-Path Efficiently Computes Conformational Transitions, Including Multiple and Diverse Paths

The molecular actions of proteins occur along reaction coordinates. Current computer methods have limited ability to explore them. We describe a fast protocol called MELD-path that (1) efficiently samples relevant conformational states via MELD, an accelerator of Molecular Dynamics (MD), (2) seeds multiple short MD trajectories from MELD states, and then (3) constructs Markov State Models (MSM) that give the routes and kinetics. We tested the method against extensive (multi μs) MD simulations of the right-handed- to left-handed-helix transition of a 9-mer peptide of AIB, the symmetry of which allows us to establish convergence. MELD-path finds all the metastable states, their correct relative populations, and the full ensemble of routes, not just a single assumed route. For this transition, we find a very broad route structure. MELD-path is highly parallelizable and efficient, yielding the full route map in a few days of computation. We believe MELD-path could be a general and rapid way to explore mechanistic processes in biomolecules on the computer.

Computational Exploration of Conformational Transitions in Protein Drug Targets

Protein drug targets vary from highly structured to completely disordered; either way dynamics governs function. Hence, understanding the dynamical aspects of how protein targets function can enable improved interventions with drug molecules. Computational approaches offer highly detailed structural models of protein dynamics which are becoming more predictive as model quality and sampling power improve. However, the most advanced and popular models still have errors owing to imperfect parameter sets and often cannot access longer timescales of many crucial biological processes. Experimental approaches offer more certainty but can struggle to detect and measure lightly populated conformations of target proteins and subtle allostery. An emerging solution is to integrate available experimental data into advanced molecular simulations. In the future, molecular simulation in combination with experimental data may be able to offer detailed models of important drug targets such that improved functional mechanisms or selectivity can be accessed.