Improving Convergence of Replica-Exchange Simulations through Coupling to a High-Temperature Structure Reservoir

Small-Molecule Inhibitors of Amyloid Beta: Insights from Molecular Dynamics-Part A: Endogenous Compounds and Repurposed Drugs

The amyloid hypothesis is the predominant model of Alzheimer's disease (AD) pathogenesis, suggesting that amyloid beta (Aβ) peptide is the primary driver of neurotoxicity and a cascade of pathological events in the central nervous system. Aβ aggregation into oligomers and deposits triggers various processes, such as vascular damage, inflammation-induced astrocyte and microglia activation, disrupted neuronal ionic homeostasis, oxidative stress, abnormal kinase and phosphatase activity, tau phosphorylation, neurofibrillary tangle formation, cognitive dysfunction, synaptic loss, cell death, and, ultimately, dementia. Molecular dynamics (MD) is a powerful structure-based drug design (SBDD) approach that aids in understanding the properties, functions, and mechanisms of action or inhibition of biomolecules. As the only method capable of simulating atomic-level internal motions, MD provides unique insights that cannot be obtained through other techniques. Integrating experimental data with MD simulations allows for a more comprehensive understanding of biological processes and molecular interactions. This review summarizes and evaluates MD studies from the past decade on small molecules, including endogenous compounds and repurposed drugs, that inhibit amyloid beta. Furthermore, it outlines key considerations for future MD simulations of amyloid inhibitors, offering a potential framework for studies aimed at elucidating the mechanisms of amyloid beta inhibition by small molecules.

CHARMM at 45: Enhancements in Accessibility, Functionality, and Speed

Since its inception nearly a half century ago, CHARMM has been playing a central role in computational biochemistry and biophysics. Commensurate with the developments in experimental research and advances in computer hardware, the range of methods and applicability of CHARMM have also grown. This review summarizes major developments that occurred after 2009 when the last review of CHARMM was published. They include the following: new faster simulation engines, accessible user interfaces for convenient workflows, and a vast array of simulation and analysis methods that encompass quantum mechanical, atomistic, and coarse-grained levels, as well as extensive coverage of force fields. In addition to providing the current snapshot of the CHARMM development, this review may serve as a starting point for exploring relevant theories and computational methods for tackling contemporary and emerging problems in biomolecular systems. CHARMM is freely available for academic and nonprofit research at https://academiccharmm.org/program.

Protein Retrieval via Integrative Molecular Ensembles (PRIME) through Extended Similarity Indices

Molecular dynamics (MD) simulations are ideally suited to describe conformational ensembles of biomolecules such as proteins and nucleic acids. Microsecond-long simulations are now routine, facilitated by the emergence of graphical processing units. Clustering, which groups objects based on structural similarity, is typically used to process ensembles, leading to different states, their populations, and the identification of representative structures. A popular pipeline combines hierarchical clustering for clustering and selecting the cluster centroid as representative of the cluster. Here, we propose to improve on this approach, by developing a module-Protein Retrieval via Integrative Molecular Ensembles (PRIME), that consists of tools to improve the prediction of the representative in the most populated cluster using extended continuous similarity. PRIME is integrated with our Molecular Dynamics Analysis with N-ary Clustering Ensembles (MDANCE) package and can be used as a postprocessing tool for arbitrary clustering algorithms, compatible with several MD suites. PRIME predictions produced structures that when aligned to the experimental structure were better superposed (lower RMSD). A further benefit of PRIME is its linear scaling─rather than the traditional O(N2) traditionally associated with comparisons of elements in a set.

Advanced computational approaches to understand protein aggregation

Protein aggregation is a widespread phenomenon implicated in debilitating diseases like Alzheimer's, Parkinson's, and cataracts, presenting complex hurdles for the field of molecular biology. In this review, we explore the evolving realm of computational methods and bioinformatics tools that have revolutionized our comprehension of protein aggregation. Beginning with a discussion of the multifaceted challenges associated with understanding this process and emphasizing the critical need for precise predictive tools, we highlight how computational techniques have become indispensable for understanding protein aggregation. We focus on molecular simulations, notably molecular dynamics (MD) simulations, spanning from atomistic to coarse-grained levels, which have emerged as pivotal tools in unraveling the complex dynamics governing protein aggregation in diseases such as cataracts, Alzheimer's, and Parkinson's. MD simulations provide microscopic insights into protein interactions and the subtleties of aggregation pathways, with advanced techniques like replica exchange molecular dynamics, Metadynamics (MetaD), and umbrella sampling enhancing our understanding by probing intricate energy landscapes and transition states. We delve into specific applications of MD simulations, elucidating the chaperone mechanism underlying cataract formation using Markov state modeling and the intricate pathways and interactions driving the toxic aggregate formation in Alzheimer's and Parkinson's disease. Transitioning we highlight how computational techniques, including bioinformatics, sequence analysis, structural data, machine learning algorithms, and artificial intelligence have become indispensable for predicting protein aggregation propensity and locating aggregation-prone regions within protein sequences. Throughout our exploration, we underscore the symbiotic relationship between computational approaches and empirical data, which has paved the way for potential therapeutic strategies against protein aggregation-related diseases. In conclusion, this review offers a comprehensive overview of advanced computational methodologies and bioinformatics tools that have catalyzed breakthroughs in unraveling the molecular basis of protein aggregation, with significant implications for clinical interventions, standing at the intersection of computational biology and experimental research.

Formation and Effects of Upstream DNA-RNA Base Pairing in Telomerase

Telomere elongation by telomerase consists of two types of translocation: duplex translocation during each repeat synthesis and template translocation at the end of repeat synthesis. Our replica exchange molecular dynamics simulations show that in addition to the Watson-Crick interactions in the active site, templating RNA can also form base pairs with the upstream regions of DNA, mostly with the second upstream DNA repeat with respect to the 3'-end. At the end of the repeat synthesis, dG10-P442 and dG11-N446 hydrogen bonds form. Then, active-site base pairs dissociate one by one, and the RNA bases reanneal with the complementary base on the upstream DNA repeat. For each dissociating base pair a new one forms, thus conserving the number of base pairs during template translocation.

Rapid Rescoring and Refinement of Ligand-Receptor Complexes Using Replica Exchange Molecular Dynamics with a Monte Carlo Pose Reservoir

Virtual screening (VS) involves generation of poses for a library of ligands and ranking using simplified energy functions and limited flexibility. Top-scored poses are used to rank and prioritize ligands. Here, we adapt the reservoir replica exchange molecular dynamics (res-REMD) method to rerank poses generated through VS. REMD simulations are carried out but with occasional Monte Carlo jumps to alternate VS-generated poses using a Metropolis criterion. The simulations converge within 10 ns for all systems, generating populations of alternate poses in the context of fully flexible ligand and protein side chains. The protocol is applied to four model protein-ligand complexes, where DOCK resulted in two successes and two scoring failures. In all four systems, the most populated cluster from the final ensemble exhibits high similarity to the crystallographic pose with ligand RMSD values under 2.0 Å. Both DOCK failures were rescued. For one DOCK success, the protocol identified the correct pose but also sampled an alternate pose at equal probability. Opportunities for future improvements and extensions are discussed.

Conformational dynamics of RNA G4C2 and G2C4 repeat expansions causing ALS/FTD using NMR and molecular dynamics studies

G4C2 and G2C4 repeat expansions in chromosome 9 open reading frame 72 (C9orf72) are the most common cause of genetically defined amyotrophic lateral sclerosis (ALS) and frontotemporal dementia (FTD), or c9ALS/FTD. The gene is bidirectionally transcribed, producing G4C2 repeats [r(G4C2)exp] and G2C4 repeats [r(G2C4)exp]. The c9ALS/FTD repeat expansions are highly structured, and structural studies showed that r(G4C2)exp predominantly folds into a hairpin with a periodic array of 1 × 1 G/G internal loops and a G-quadruplex. A small molecule probe revealed that r(G4C2)exp also adopts a hairpin structure with 2 × 2 GG/GG internal loops. We studied the conformational dynamics adopted by 2 × 2 GG/GG loops using temperature replica exchange molecular dynamics (T-REMD) and further characterized the structure and underlying dynamics using traditional 2D NMR techniques. These studies showed that the loop's closing base pairs influence both structure and dynamics, particularly the configuration adopted around the glycosidic bond. Interestingly, r(G2C4) repeats, which fold into an array of 2 × 2 CC/CC internal loops, are not as dynamic. Collectively, these studies emphasize the unique sensitivity of r(G4C2)exp to small changes in stacking interactions, which is not observed in r(G2C4)exp, providing important considerations for further principles in structure-based drug design.

Exploring the Transferability of Replica Exchange Structure Reservoirs to Accelerate Generation of Ensembles for Alternate Hamiltonians or Protein Mutations

Generating precise ensembles is commonly a prerequisite to understand the energetics of biological processes using Molecular Dynamics (MD) simulations. Previously, we have shown how unweighted reservoirs built from high temperature MD simulations can accelerate convergence of Boltzmann-weighted ensembles by at least 10× with the Reservoir Replica Exchange MD (RREMD) method. Therefore, in this work, we explore whether an unweighted structure reservoir generated with one Hamiltonian (solute force field plus solvent model) can be reused to quickly generate accurately weighted ensembles for Hamiltonians other than the one that was used to generate the reservoir. We also extended this methodology to rapidly estimate the effects of mutations on peptide stability by using a reservoir of diverse structures obtained from wild-type simulations. These results suggest that structures generated via fast methods such as coarse-grained models or structures predicted by Rosetta or deep learning approaches could be integrated into a reservoir to accelerate generation of ensembles using more accurate representations.

Ensemble Generation for Linear and Cyclic Peptides Using a Reservoir Replica Exchange Molecular Dynamics Implementation in GROMACS

The profile of shapes presented by a cyclic peptide modulates its therapeutic efficacy and is represented by the ensemble of its sampled conformations. Although some algorithms excel at creating a diverse ensemble of cyclic peptide conformations, they seldom address the entropic contribution of flexible conformations and often have significant practical difficulty producing an ensemble with converged and reliable thermodynamic properties. In this study, an accelerated molecular dynamics (MD) method, namely, reservoir replica exchange MD (R-REMD or Res-REMD), was implemented in GROMACS ver. 4.6.7 and benchmarked on two small cyclic peptide model systems: a cyclized furin cleavage site of the severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) spike (cyclo-(CGPRRARSG)) and oxytocin (disulfide-bonded CYIQNCPLG). Additionally, we also benchmarked Res-REMD on alanine dipeptide and Trpzip2 to demonstrate its validity and efficiency over REMD. For Trpzip2, Res-REMD coupled with an umbrella-sampling-derived reservoir generated similar folded fractions as regular REMD but on a much faster time scale. For cyclic peptides, Res-REMD appeared to be marginally faster than REMD in ensemble generation. Finally, Res-REMD was more effective in sampling rare events such as trans to cis peptide bond isomerization. We provide a GitHub page with the modified GROMACS source code for running Res-REMD at https://github.com/PlotkinLab/Reservoir-REMD.

Fundamental Redesign of the TIGER2hs Kernel to Address Severe Parameter Sensitivity

Replica exchange molecular dynamics simulations are one of the most popular approaches to enhance conformational sampling of molecular systems. Applications range from protein folding to protein-protein or other host-guest interactions, as well as binding free energy calculations. While these methods are computationally expensive, highly accurate results can be obtained. We recently developed TIGER2hs, an improved version of the temperature intervals with global exchange of replicas (TIGER2) algorithm. This method combines the replica-based enhanced sampling in an explicit solvent with a hybrid solvent energy evaluation. During the exchange attempts, bulk water is replaced by an implicit solvent model, allowing sampling with significantly less replicas than parallel tempering (REMD). This enables accurate enhanced sampling calculations with only a fraction of computational resources compared to REMD. Our latest results highlight several issues with sampling imbalance and parameter sensitivity within the original TIGER2 exchange algorithms that affect the overall state populations. A high sensitivity on replica number and maximum temperature is eliminated by changing to a pairwise exchange kernel (PE) without additional sorting. Simulations are controlled by adjusting the average temperature change per exchange ⟨ΔT/χ⟩ to below 30 K to mimic a controlled temperature mixing of replicas similar to REMD. Thus, this parameter provides an applicable property for selecting combinations of replica number and maximum temperature to adjust simulations for best accuracy, with flexible resource investment. This increases the robustness of the method and ensures results in excellent agreement with REMD, as demonstrated for three different peptides.

Accelerating the Ensemble Convergence of RNA Hairpin Simulations with a Replica Exchange Structure Reservoir

RNA is a key participant in many biological processes, but studies of RNA using computer simulations lag behind those of proteins, largely due to less-developed force fields and the slow dynamics of RNA. Generating converged RNA ensembles for force field development and other studies remains a challenge. In this study, we explore the ability of replica exchange molecular dynamics to obtain well-converged conformational ensembles for two RNA hairpin systems in an implicit solvent. Even for these small model systems, standard REMD remains computationally costly, but coupling to a pre-generated structure library using the reservoir REMD approach provides a dramatic acceleration of ensemble convergence for both model systems. Such precise ensembles could facilitate RNA force field development and validation and applications of simulation to more complex RNA systems. The advantages and remaining challenges of applying R-REMD to RNA are investigated in detail.

First Principles Calculation of Protein-Protein Dimer Affinities of ALS-Associated SOD1 Mutants

Cu,Zn superoxide dismutase (SOD1) is a 32 kDa homodimer that converts toxic oxygen radicals in neurons to less harmful species. The dimerization of SOD1 is essential to the stability of the protein. Monomerization increases the likelihood of SOD1 misfolding into conformations associated with aggregation, cellular toxicity, and neuronal death in familial amyotrophic lateral sclerosis (fALS). The ubiquity of disease-associated mutations throughout the primary sequence of SOD1 suggests an important role of physicochemical processes, including monomerization of SOD1, in the pathology of the disease. Herein, we use a first-principles statistical mechanics method to systematically calculate the free energy of dimer binding for SOD1 using molecular dynamics, which involves sequentially computing conformational, orientational, and separation distance contributions to the binding free energy. We consider the effects of two ALS-associated mutations in SOD1 protein on dimer stability, A4V and D101N, as well as the role of metal binding and disulfide bond formation. We find that the penalty for dimer formation arising from the conformational entropy of disordered loops in SOD1 is significantly larger than that for other protein-protein interactions previously considered. In the case of the disulfide-reduced protein, this leads to a bound complex whose formation is energetically disfavored. Somewhat surprisingly, the loop free energy penalty upon dimerization is still significant for the holoprotein, despite the increased structural order induced by the bound metal cations. This resulted in a surprisingly modest increase in dimer binding free energy of only about 1.5 kcal/mol upon metalation of the protein, suggesting that the most significant stabilizing effects of metalation are on folding stability rather than dimer binding stability. The mutant A4V has an unstable dimer due to weakened monomer-monomer interactions, which are manifested in the calculation by a separation free energy surface with a lower barrier. The mutant D101N has a stable dimer partially due to an unusually rigid β-barrel in the free monomer. D101N also exhibits anticooperativity in loop folding upon dimerization. These computational calculations are, to our knowledge, the most quantitatively accurate calculations of dimer binding stability in SOD1 to date.

Computational methods for exploring protein conformations

Proteins are dynamic molecules that can transition between a potentially wide range of structures comprising their conformational ensemble. The nature of these conformations and their relative probabilities are described by a high-dimensional free energy landscape. While computer simulation techniques such as molecular dynamics simulations allow characterisation of the metastable conformational states and the transitions between them, and thus free energy landscapes, to be characterised, the barriers between states can be high, precluding efficient sampling without substantial computational resources. Over the past decades, a dizzying array of methods have emerged for enhancing conformational sampling, and for projecting the free energy landscape onto a reduced set of dimensions that allow conformational states to be distinguished, known as collective variables (CVs), along which sampling may be directed. Here, a brief description of what biomolecular simulation entails is followed by a more detailed exposition of the nature of CVs and methods for determining these, and, lastly, an overview of the myriad different approaches for enhancing conformational sampling, most of which rely upon CVs, including new advances in both CV determination and conformational sampling due to machine learning.

Elucidating Solution Structures of Cyclic Peptides Using Molecular Dynamics Simulations

Protein-protein interactions are vital to biological processes, but the shape and size of their interfaces make them hard to target using small molecules. Cyclic peptides have shown promise as protein-protein interaction modulators, as they can bind protein surfaces with high affinity and specificity. Dozens of cyclic peptides are already FDA approved, and many more are in various stages of development as immunosuppressants, antibiotics, antivirals, or anticancer drugs. However, most cyclic peptide drugs so far have been natural products or derivatives thereof, with de novo design having proven challenging. A key obstacle is structural characterization: cyclic peptides frequently adopt multiple conformations in solution, which are difficult to resolve using techniques like NMR spectroscopy. The lack of solution structural information prevents a thorough understanding of cyclic peptides' sequence-structure-function relationship. Here we review recent development and application of molecular dynamics simulations with enhanced sampling to studying the solution structures of cyclic peptides. We describe novel computational methods capable of sampling cyclic peptides' conformational space and provide examples of computational studies that relate peptides' sequence and structure to biological activity. We demonstrate that molecular dynamics simulations have grown from an explanatory technique to a full-fledged tool for systematic studies at the forefront of cyclic peptide therapeutic design.

Accelerating atomistic simulations of proteins using multiscale enhanced sampling with independent tempering

Efficient sampling of the conformational space is essential for quantitative simulations of proteins. The multiscale enhanced sampling (MSES) method accelerates atomistic sampling by coupling it to a coarse-grained (CG) simulation. Bias from coupling to the CG model is removed using Hamiltonian replica exchange, such that one could benefit simultaneously from the high accuracy of atomistic models and fast dynamics of CG ones. Here, we extend MSES to allow independent control of the effective temperatures of atomistic and CG simulations, by directly scaling the atomistic and CG Hamiltonians. The new algorithm, named MSES with independent tempering (MSES-IT), supports more sophisticated Hamiltonian and temperature replica exchange protocols to further improve the sampling efficiency. Using a small but nontrivial β-hairpin, we show that setting the effective temperature of CG model in all conditions to its melting temperature maximizes structural transition rates at the CG level and promotes more efficient replica exchange and diffusion in the condition space. As the result, MSES-IT drive faster reversible transitions at the atomic level and leads to significant improvement in generating converged conformational ensembles compared to the original MSES scheme.

Exploring Protocols to Build Reservoirs to Accelerate Temperature Replica Exchange MD Simulations

Temperature replica exchange molecular dynamics (REMD) is a widely used enhanced sampling method for accelerating biomolecular simulations. During the past 2 decades, several variants of REMD have been developed to further improve the rate of conformational sampling of REMD. One such variant, reservoir REMD (RREMD), was shown to improve the rate of conformational sampling by around 5-20×. Despite the significant increase in the sampling speed, RREMD methods have not been widely used because of the difficulties in building the reservoir and also because of the code not being available on the graphics processing units (GPUs). In this work, we ported the Amber RREMD code onto GPUs making it 20× faster than the central processing unit code. Then, we explored protocols for building Boltzmann-weighted reservoirs as well as non-Boltzmann reservoirs and tested how each choice affects the accuracy of the resulting RREMD simulations. We show that, using the recommended protocols outlined here, RREMD simulations can accurately reproduce Boltzmann-weighted ensembles obtained by much more expensive conventional temperature-based REMD simulations, with at least 15× faster convergence rates even for larger proteins (>50 amino acids) compared to conventional REMD.

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.

Hamiltonian-Reservoir Replica Exchange and Machine Learning Potentials for Computational Organic Chemistry

This work combines a machine learning potential energy function with a modular enhanced sampling scheme to obtain statistically converged thermodynamical properties of flexible medium-size organic molecules at high ab initio level. We offer a modular environment in the python package MORESIM that allows custom design of replica exchange simulations with any level of theory including ML-based potentials. Our specific combination of Hamiltonian and reservoir replica exchange is shown to be a powerful technique to accelerate enhanced sampling simulations and explore free energy landscapes with a quantum chemical accuracy unattainable otherwise (e.g., DLPNO-CCSD(T)/CBS quality). This engine is used to demonstrate the relevance of accessing the ab initio free energy landscapes of molecules whose stability is determined by a subtle interplay between variations in the underlying potential energy and conformational entropy (i.e., a bridged asymmetrically polarized dithiacyclophane and a widely used organocatalyst) both in the gas phase and in solution (implicit solvent).

Enhanced solvation force extrapolation for speeding up molecular dynamics simulations of complex biochemical liquids

We propose an enhanced approach to the extrapolation of mean potential forces acting on atoms of solute macromolecules due to their interactions with solvent atoms in complex biochemical liquids. It improves and extends our previous extrapolation schemes by additionally including new techniques such as an exponential scaling transformation of coordinate space with weights complemented by an automatically adjusted balancing between the least square minimization of force deviations and the norm of expansion coefficients in the approximation. The expensive mean potential forces are treated in terms of the three-dimensional reference interaction site model with Kovalenko-Hirata closure molecular theory of solvation. During the dynamics, they are calculated only after every long (outer) time interval, i.e., quite rarely to reduce the computational costs. At much shorter (inner) time steps, these forces are extrapolated on the basis of their outer values. The equations of motion are then solved using a multiple time step integration within an optimized isokinetic Nosé-Hoover chain thermostat. The new approach is applied to molecular dynamics simulations of various systems consisting of solvated organic and biomolecules of different complexity. For example, we consider hydrated alanine dipeptide, asphaltene in toluene solvent, miniprotein 1L2Y, and protein G in aqueous solution. It is shown that in all these cases, the enhanced extrapolation provides much better accuracy of the solvation force approximation than the existing approaches. As a result, it can be used with much larger outer time steps, leading to a significant speedup of the simulations.

Combining the biased and unbiased sampling strategy into one convenient free energy calculation method

Constructing a free energy landscape for a large molecule is difficult. One has to use either a high temperature or a strong driving force to enhance the sampling on the free energy barriers. In this work, we propose a mixed method that combines these two kinds of acceleration strategies into one simulation. First, it applies an adaptive biasing potential to some replicas of the molecule. These replicas are particularly accelerated in a collective variable space. Second, it places some unbiased and exchangeable replicas at various temperature levels. These replicas generate unbiased sampling data in the canonical ensemble. To improve the sampling efficiency, biased replicas transfer their state variables to the unbiased replicas after equilibrium by Monte Carlo trial moves. In comparison to previous integrated methods, it is more convenient for users. It does not need an initial reference biasing potential to guide the sampling of the molecule. And it is also unnecessary to insert many replicas for the requirement of passing the free energy barriers. The free energy calculation is accomplished in a single stage. It samples the data as fast as a biased simulation and it processes the data as simple as an unbiased simulation. The method provides a minimalist approach to the construction of the free energy landscape. © 2019 Wiley Periodicals, Inc.

Replica-Based Protein Structure Sampling Methods II: Advanced Hybrid Solvent TIGER2hs

In many cases, native states of proteins may be predicted with sufficient accuracy by molecular dynamics simulations (MDSs) with modern force fields. Enhanced sampling methods based on MDS are applied for exploring the phase space of a protein sequence and to overcome barriers on rough conformational energy landscapes. The minimum free energy state is obtained with sampling algorithms providing sufficient convergence and accuracy. A reliable but computationally very expensive method is replica exchange molecular dynamics, with many modifications to this approach presented in the past. Recently, we demonstrated how our temperature intervals with global exchange of replicas hybrid (TIGER2h) solvent sampling algorithm made a good compromise between efficiency and accuracy. There, all states are sampled under full explicit solvent conditions with a freely chosen number of replicas, whereas an implicit solvent is used during the swap decisions. This hybrid method yielded a much better approximation to the agreement with calculations in an explicit solvent than fully implicit solvent simulations. Here, we present an extension of TIGER2h and add a few layers of explicit water molecules around the peptide for the energy calculations, whereas the dynamics in fully explicit water is maintained. We claim that these water layers better reproduce steric effects, the polarization of the solvent, and the resulting reaction field energy than typical implicit solvent models. By investigating the protein-solvent interactions across comprehensive thermodynamic state ensembles, we found a strong conformational dependence of this reaction field energy. All simulations were performed with nanoscale molecular dynamics on two peptides, the α-helical peptide (AAQAA)₃ and the β-hairpin peptide HP7. A production-ready TIGER2hs implementation is supplied, approaching the accuracy of full explicit solvent sampling at a fraction of computational resources.

Massive-Scale Binding Free Energy Simulations of HIV Integrase Complexes Using Asynchronous Replica Exchange Framework Implemented on the IBM WCG Distributed Network

To perform massive-scale replica exchange molecular dynamics (REMD) simulations for calculating binding free energies of protein-ligand complexes, we implemented the asynchronous replica exchange (AsyncRE) framework of the binding energy distribution analysis method (BEDAM) in implicit solvent on the IBM World Community Grid (WCG) and optimized the simulation parameters to reduce the overhead and improve the prediction power of the WCG AsyncRE simulations. We also performed the first massive-scale binding free energy calculations using the WCG distributed computing grid and 301 ligands from the SAMPL4 challenge for large-scale binding free energy predictions of HIV-1 integrase complexes. In total there are ∼10000 simulated complexes, ∼1 million replicas, and ∼2000 μs of aggregated MD simulations. Running AsyncRE MD simulations on the WCG requires accepting a trade-off between the number of replicas that can be run (breadth) and the number of full RE cycles that can be completed per replica (depth). As compared with synchronous Replica Exchange (SyncRE) running on tightly coupled clusters like XSEDE, on the WCG many more replicas can be launched simultaneously on heterogeneous distributed hardware, but each full RE cycle requires more overhead. We compared the WCG results with that from AutoDock and more advanced RE simulations including the use of flattening potentials to accelerate sampling of selected degrees of freedom of ligands and/or receptors related to slow dynamics due to high energy barriers. We propose a suitable strategy of RE simulations to refine high throughput docking results which can be matched to corresponding computing resources: from HPC clusters, to small or medium-size distributed campus grids, and finally to massive-scale computing networks including millions of CPUs like the resources available on the WCG.

Alchemical Free-Energy Calculations by Multiple-Replica λ-Dynamics: The Conveyor Belt Thermodynamic Integration Scheme

A new method is proposed to calculate alchemical free-energy differences based on molecular dynamics (MD) simulations, called the conveyor belt thermodynamic integration (CBTI) scheme. As in thermodynamic integration (TI), K replicas of the system are simulated at different values of the alchemical coupling parameter λ. The number K is taken to be even, and the replicas are equally spaced on a forward-turn-backward-turn path, akin to a conveyor belt (CB) between the two physical end-states; and as in λ-dynamics (λD), the λ-values associated with the individual systems evolve in time along the simulation. However, they do so in a concerted fashion, determined by the evolution of a single dynamical variable Λ of period 2π controlling the advance of the entire CB. Thus, a change of Λ is always associated with K/2 equispaced replicas moving forward and K/2 equispaced replicas moving backward along λ. As a result, the effective free-energy profile of the replica system along Λ is periodic of period 2 πK^-1, and the magnitude of its variations decreases rapidly upon increasing K, at least as K^-1 in the limit of large K. When a sufficient number of replicas is used, these variations become small, which enables a complete and quasi-homogeneous coverage of the λ-range by the replica system, without application of any biasing potential. If desired, a memory-based biasing potential can still be added to further homogenize the sampling, the preoptimization of which is computationally inexpensive. The final free-energy profile along λ is calculated similarly to TI, by binning of the Hamiltonian λ-derivative as a function of λ considering all replicas simultaneously, followed by quadrature integration. The associated quadrature error can be kept very low owing to the continuous and quasi-homogeneous λ-sampling. The CBTI scheme can be viewed as a continuous/deterministic/dynamical analog of the Hamiltonian replica-exchange/permutation (HRE/HRP) schemes or as a correlated multiple-replica analog of the λD or λ-local elevation umbrella sampling (λ-LEUS) schemes. Compared to TI, it shares the advantage of the latter schemes in terms of enhanced orthogonal sampling, i.e. the availability of variable-λ paths to circumvent conformational barriers present at specific λ-values. Compared to HRE/HRP, it permits a deterministic and continuous sampling of the λ-range, is expected to be less sensitive to possible artifacts of the thermo- and barostating schemes, and bypasses the need to carefully preselect a λ-ladder and a swapping-attempt frequency. Compared to λ-LEUS, it eliminates (or drastically reduces) the dead time associated with the preoptimization of a biasing potential. The goal of this article is to provide the mathematical/physical formulation of the proposed CBTI scheme, along with an initial application of the method to the calculation of the hydration free energy of methanol.

CoCo-MD: A Simple and Effective Method for the Enhanced Sampling of Conformational Space

CoCo ("complementary coordinates") is a method for ensemble enrichment based on principal component analysis (PCA) that was developed originally for the investigation of NMR data. Here we investigate the potential of the CoCo method, in combination with molecular dynamics simulations (CoCo-MD), to be used more generally for the enhanced sampling of conformational space. Using the alanine penta-peptide as a model system, we find that an iterative workflow, interleaving short multiple-walker MD simulations with long-range jumps through conformational space informed by CoCo analysis, can increase the rate of sampling of conformational space up to 10 times for the same computational effort (total number of MD timesteps). Combined with the reservoir-REMD method, free energies can be readily calculated. An alternative, approximate but fast and practically useful, alternative approach to unbiasing CoCo-MD generated data is also described. Applied to cyclosporine A, we can achieve far greater conformational sampling than has been reported previously, using a fraction of the computational resource. Simulations of the maltose binding protein, begun from the "open" state, effectively sample the "closed" conformation associated with ligand binding. The PCA-based approach means that optimal collective variables to enhance sampling need not be defined in advance by the user but are identified automatically and are adaptive, responding to the characteristics of the developing ensemble. In addition, the approach does not require any adaptations to the associated MD code and is compatible with any conventional MD package.

Why Computed Protein Folding Landscapes Are Sensitive to the Water Model

We investigate the effect of solvent models on the computed thermodynamics of protein folding. Atomistic folding simulations of a fast-folding mini-protein, CLN025, were employed to compare two commonly used explicit solvent water models, TIP3P and TIP4P/Ew, and one implicit solvent (AMBER generalized Born) model. Although all three solvent models correctly identify the same native folded state (RMSD = 1.5 ± 0.1 Å relative to the experimental structure), the corresponding free energy landscapes vary drastically between water models: almost an order-of-magnitude difference is seen in the predicted fraction of the unfolded state between the two explicit solvent models, with even larger differences between the implicit and the explicit models. Quantitative arguments are presented for why the sensitivity is expected to hold for other proteins, as well as for other conformational transitions involving large changes in solvent exposed areas such as protein-ligand binding. Comparing protein-solvent and solvent-solvent contributions to the folding energy between different water models, water-water electrostatic interactions are identified as the largest contributor to the differences in the predicted folding energy, which helps explain the strong sensitivity of the folding landscape to subtle details of the water model. For the two explicit solvent models, differences in water model parameters also result in the average number of water molecules surrounding the protein being noticeably different. Water models that poorly reproduce certain bulk properties of liquid water such as self-diffusion are likely to misrepresent water-water interactions; we argue that within a pairwise additive energy function this error cannot, in general, be compensated by an adjustment to the solute-solute and solute-solvent parts of the energy.

Reservoir pH replica exchange

We present the reservoir pH replica exchange (R-pH-REM) method for constant pH simulations. The R-pH-REM method consists of a two-step procedure; the first step involves generation of one or more reservoirs of conformations. Each reservoir is obtained from a standard or enhanced molecular dynamics simulation with a constrained (fixed) protonation state. In the second step, fixed charge constraints are relaxed, as the structures from one or more reservoirs are periodically injected into a constant pH or a pH-replica exchange (pH-REM) simulation. The benefit of this two-step process is that the computationally intensive part of conformational search can be decoupled from constant pH simulations, and various techniques for enhanced conformational sampling can be applied without the need to integrate such techniques into the pH-REM framework. Simulations on blocked Lys, KK, and KAAE peptides were used to demonstrate an agreement between pH-REM and R-pH-REM simulations. While the reservoir simulations are not needed for these small test systems, the real need arises in cases when ionizable molecules can sample two or more conformations separated by a large energy barrier, such that adequate sampling is not achieved on a time scale of standard constant pH simulations. Such problems might be encountered in protein systems that exploit conformational transitions for function. A hypothetical case is studied, a small molecule with a large torsional barrier; while results of pH-REM simulations depend on the starting structure, R-pH-REM calculations on this model system are in excellent agreement with a theoretical model.

Replica-Based Protein Structure Sampling Methods: Compromising between Explicit and Implicit Solvents

The structure of a protein is often not completely accessible by experiments. In silico, replica exchange molecular dynamics (REMD) is the standard sampling method for predicting the secondary and tertiary structures from the amino acid sequence, but it is computationally very expensive. Two recent adaptations from REMD, temperature intervals with global exchange of replicas (TIGER2) and TIGER2A, have been tested here in implicit and explicit solvents. Additionally, explicit, implicit, and hybrid solvent REMD are compared. On the basis of the hybrid REMD (REMDh) method, we present a new hybrid TIGER2h algorithm for faster structural sampling, while retaining good accuracy. The implementations of REMDh, TIGER2, TIGER2A, and TIGER2h are provided for nanoscale molecular dynamics (NAMD). All the methods were tested with two model peptides of known structure, (AAQAA)₃ and HP7, with helix and sheet motifs, respectively. The TIGER2 methods and REMDh were also applied to the unknown structure of the collagen type I telopeptides, which represent bigger proteins with some degree of disorder. We present simulations covering more than 180 μs and analyze the performance and convergence of the distributions of states between the particular methods by dihedral principal component and secondary structure analysis.

Assessing Exhaustiveness of Stochastic Sampling for Integrative Modeling of Macromolecular Structures

Modeling of macromolecular structures involves structural sampling guided by a scoring function, resulting in an ensemble of good-scoring models. By necessity, the sampling is often stochastic, and must be exhaustive at a precision sufficient for accurate modeling and assessment of model uncertainty. Therefore, the very first step in analyzing the ensemble is an estimation of the highest precision at which the sampling is exhaustive. Here, we present an objective and automated method for this task. As a proxy for sampling exhaustiveness, we evaluate whether two independently and stochastically generated sets of models are sufficiently similar. The protocol includes testing 1) convergence of the model score, 2) whether model scores for the two samples were drawn from the same parent distribution, 3) whether each structural cluster includes models from each sample proportionally to its size, and 4) whether there is sufficient structural similarity between the two model samples in each cluster. The evaluation also provides the sampling precision, defined as the smallest clustering threshold that satisfies the third, most stringent test. We validate the protocol with the aid of enumerated good-scoring models for five illustrative cases of binary protein complexes. Passing the proposed four tests is necessary, but not sufficient for thorough sampling. The protocol is general in nature and can be applied to the stochastic sampling of any set of models, not just structural models. In addition, the tests can be used to stop stochastic sampling as soon as exhaustiveness at desired precision is reached, thereby improving sampling efficiency; they may also help in selecting a model representation that is sufficiently detailed to be informative, yet also sufficiently coarse for sampling to be exhaustive.

Speed of conformational change: comparing explicit and implicit solvent molecular dynamics simulations

Adequate sampling of conformation space remains challenging in atomistic simulations, especially if the solvent is treated explicitly. Implicit-solvent simulations can speed up conformational sampling significantly. We compare the speed of conformational sampling between two commonly used methods of each class: the explicit-solvent particle mesh Ewald (PME) with TIP3P water model and a popular generalized Born (GB) implicit-solvent model, as implemented in the AMBER package. We systematically investigate small (dihedral angle flips in a protein), large (nucleosome tail collapse and DNA unwrapping), and mixed (folding of a miniprotein) conformational changes, with nominal simulation times ranging from nanoseconds to microseconds depending on system size. The speedups in conformational sampling for GB relative to PME simulations, are highly system- and problem-dependent. Where the simulation temperatures for PME and GB are the same, the corresponding speedups are approximately onefold (small conformational changes), between ∼1- and ∼100-fold (large changes), and approximately sevenfold (mixed case). The effects of temperature on speedup and free-energy landscapes, which may differ substantially between the solvent models, are discussed in detail for the case of miniprotein folding. In addition to speeding up conformational sampling, due to algorithmic differences, the implicit solvent model can be computationally faster for small systems or slower for large systems, depending on the number of solute and solvent atoms. For the conformational changes considered here, the combined speedups are approximately twofold, ∼1- to 60-fold, and ∼50-fold, respectively, in the low solvent viscosity regime afforded by the implicit solvent. For all the systems studied, 1) conformational sampling speedup increases as Langevin collision frequency (effective viscosity) decreases; and 2) conformational sampling speedup is mainly due to reduction in solvent viscosity rather than possible differences in free-energy landscapes between the solvent models.

Adaptive Steered Molecular Dynamics of the Long-Distance Unfolding of Neuropeptide Y

Neuropeptide Y (NPY) has been found to adopt two stable conformations in vivo: (1) a monomeric form called the PP-fold in which a polyproline tail is folded onto an α-helix via a β-turn and (2) a dimeric form of the unfolded proteins in which the α-helices interact with each other via side chains. The transition pathway and rates between the two conformations remain unknown and are important to the nature of the binding of the protein. Toward addressing this question, the present work suggests that the unfolding of the PP-fold is too slow to play a role in NPY monomeric binding unless the receptor catalyzes it to do so. Specifically, the dynamics and structural changes of the unfolding of a monomeric NPY protein have been investigated in this work. Temperature accelerated molecular dynamics (MD) simulations at 500 K under constant (N,V,E) conditions suggests a hinge-like unraveling of the tail rather than a random unfolding. The free energetics of the proposed unfolding pathway have been described using an adaptive steered MD (SMD) approach at various temperatures. This approach generalizes the use of Jarzynski's equality through a series of stages that allows for better convergence along nonlinear and long-distance pathways. Results acquired using this approach provide a potential of mean force (PMF) with narrower error bars and are consistent with some of the earlier reports on the qualitative behavior of NPY binding.

Partial unfolding and refolding for structure refinement: A unified approach of geometric simulations and molecular dynamics

The most successful protein structure prediction methods to date have been template-based modeling (TBM) or homology modeling, which predicts protein structure based on experimental structures. These high accuracy predictions sometimes retain structural errors due to incorrect templates or a lack of accurate templates in the case of low sequence similarity, making these structures inadequate in drug-design studies or molecular dynamics simulations. We have developed a new physics based approach to the protein refinement problem by mimicking the mechanism of chaperons that rehabilitate misfolded proteins. The template structure is unfolded by selectively (targeted) pulling on different portions of the protein using the geometric based technique FRODA, and then refolded using hierarchically restrained replica exchange molecular dynamics simulations (hr-REMD). FRODA unfolding is used to create a diverse set of topologies for surveying near native-like structures from a template and to provide a set of persistent contacts to be employed during re-folding. We have tested our approach on 13 previous CASP targets and observed that this method of folding an ensemble of partially unfolded structures, through the hierarchical addition of contact restraints (that is, first local and then nonlocal interactions), leads to a refolding of the structure along with refinement in most cases (12/13). Although this approach yields refined models through advancement in sampling, the task of blind selection of the best refined models still needs to be solved. Overall, the method can be useful for improved sampling for low resolution models where certain of the portions of the structure are incorrectly modeled.

Large-scale asynchronous and distributed multidimensional replica exchange molecular simulations and efficiency analysis

We describe methods to perform replica exchange molecular dynamics (REMD) simulations asynchronously (ASyncRE). The methods are designed to facilitate large scale REMD simulations on grid computing networks consisting of heterogeneous and distributed computing environments as well as on homogeneous high-performance clusters. We have implemented these methods on NSF (National Science Foundation) XSEDE (Extreme Science and Engineering Discovery Environment) clusters and BOINC (Berkeley Open Infrastructure for Network Computing) distributed computing networks at Temple University and Brooklyn College at CUNY (the City University of New York). They are also being implemented on the IBM World Community Grid. To illustrate the methods, we have performed extensive (more than 60 ms in aggregate) simulations for the beta-cyclodextrin-heptanoate host-guest system in the context of one- and two-dimensional ASyncRE, and we used the results to estimate absolute binding free energies using the binding energy distribution analysis method. We propose ways to improve the efficiency of REMD simulations: these include increasing the number of exchanges attempted after a specified molecular dynamics (MD) period up to the fast exchange limit and/or adjusting the MD period to allow sufficient internal relaxation within each thermodynamic state. Although ASyncRE simulations generally require long MD periods (>picoseconds) per replica exchange cycle to minimize the overhead imposed by heterogeneous computing networks, we found that it is possible to reach an efficiency similar to conventional synchronous REMD, by optimizing the combination of the MD period and the number of exchanges attempted per cycle.

Exploring biomolecular dynamics and interactions using advanced sampling methods

Molecular dynamics (MD) and Monte Carlo (MC) simulations have emerged as a valuable tool to investigate statistical mechanics and kinetics of biomolecules and synthetic soft matter materials. However, major limitations for routine applications are due to the accuracy of the molecular mechanics force field and due to the maximum simulation time that can be achieved in current simulations studies. For improving the sampling a number of advanced sampling approaches have been designed in recent years. In particular, variants of the parallel tempering replica-exchange methodology are widely used in many simulation studies. Recent methodological advancements and a discussion of specific aims and advantages are given. This includes improved free energy simulation approaches and conformational search applications.

Parameterization of an effective potential for protein-ligand binding from host-guest affinity data

Force field accuracy is still one of the "stalemates" in biomolecular modeling. Model systems with high quality experimental data are valuable instruments for the validation and improvement of effective potentials. With respect to protein-ligand binding, organic host-guest complexes have long served as models for both experimental and computational studies because of the abundance of binding affinity data available for such systems. Binding affinity data collected for cyclodextrin (CD) inclusion complexes, a popular model for molecular recognition, is potentially a more reliable resource for tuning energy parameters than hydration free energy measurements. Convergence of binding free energy calculations on CD host-guest systems can also be obtained rapidly, thus offering the opportunity to assess the robustness of these parameters. In this work, we demonstrate how implicit solvent parameters can be developed using binding affinity experimental data and the binding energy distribution analysis method (BEDAM) and validated using the Grid Inhomogeneous Solvation Theory analysis. These new solvation parameters were used to study protein-ligand binding in two drug targets against the HIV-1 virus and improved the agreement between the calculated and the experimental binding affinities. This work illustrates how benchmark sets of high quality experimental binding affinity data and physics-based binding free energy models can be used to evaluate and optimize force fields for protein-ligand systems. Copyright © 2015 John Wiley & Sons, Ltd.

Enhancing constant-pH simulation in explicit solvent with a two-dimensional replica exchange method

We present a new method for enhanced sampling for constant-pH simulations in explicit water based on a two-dimensional (2D) replica exchange scheme. The new method is a significant extension of our previously developed constant-pH simulation method, which is based on enveloping distribution sampling (EDS) coupled with a one-dimensional (1D) Hamiltonian exchange method (HREM). EDS constructs a hybrid Hamiltonian from multiple discrete end state Hamiltonians that, in this case, represent different protonation states of the system. The ruggedness and heights of the hybrid Hamiltonian's energy barriers can be tuned by the smoothness parameter. Within the context of the 1D EDS-HREM method, exchanges are performed between replicas with different smoothness parameters, allowing frequent protonation-state transitions and sampling of conformations that are favored by the end-state Hamiltonians. In this work, the 1D method is extended to 2D with an additional dimension, external pH. Within the context of the 2D method (2D EDS-HREM), exchanges are performed on a lattice of Hamiltonians with different pH conditions and smoothness parameters. We demonstrate that both the 1D and 2D methods exactly reproduce the thermodynamic properties of the semigrand canonical (SGC) ensemble of a system at a given pH. We have tested our new 2D method on aspartic acid, glutamic acid, lysine, a four residue peptide (sequence KAAE), and snake cardiotoxin. In all cases, the 2D method converges faster and without loss of precision; the only limitation is a loss of flexibility in how CPU time is employed. The results for snake cardiotoxin demonstrate that the 2D method enhances protonation-state transitions, samples a wider conformational space with the same amount of computational resources, and converges significantly faster overall than the original 1D method.

Disordered structural ensembles of vasopressin and oxytocin and their mutants

Vasopressin and oxytocin are intrinsically disordered cyclic nonapeptides belonging to a family of neurohypophysial hormones. Although unique in their functions, these peptides differ only by two residues and both feature a tocin ring formed by the disulfide bridge between first and sixth cysteine residues. This sequence and structural similarity are experimentally linked to oxytocin agonism at vasopressin receptors and vasopressin antagonism at oxytocin receptors. Yet single- or double-residue mutations in both peptides have been shown to have drastic impacts on their activities at either receptor, and possibly the ability to bind to their neurophysin carrier protein. In this study we perform molecular dynamics simulations of the unbound native and mutant sequences of the oxytocin and vasopressin hormones to characterize their structural ensembles. We classify the subpopulations of these structural ensembles on the basis of the distributions of radius of gyration and secondary structure and hydrogen-bonding features of the canonical tocin ring and disordered tail region. We then relate the structural changes observed in the unbound form of the different hormone sequences to experimental information about peptide receptor binding, and more indirectly, carrier protein binding affinity, receptor activity, and protease degradation. This study supports the hypothesis that the structural characteristics of the unbound form of an IDP can be used to predict structural or functional preferences of its functional bound form.

Evaluation of enhanced sampling provided by accelerated molecular dynamics with Hamiltonian replica exchange methods

Many problems studied via molecular dynamics require accurate estimates of various thermodynamic properties, such as the free energies of different states of a system, which in turn requires well-converged sampling of the ensemble of possible structures. Enhanced sampling techniques are often applied to provide faster convergence than is possible with traditional molecular dynamics simulations. Hamiltonian replica exchange molecular dynamics (H-REMD) is a particularly attractive method, as it allows the incorporation of a variety of enhanced sampling techniques through modifications to the various Hamiltonians. In this work, we study the enhanced sampling of the RNA tetranucleotide r(GACC) provided by H-REMD combined with accelerated molecular dynamics (aMD), where a boosting potential is applied to torsions, and compare this to the enhanced sampling provided by H-REMD in which torsion potential barrier heights are scaled down to lower force constants. We show that H-REMD and multidimensional REMD (M-REMD) combined with aMD does indeed enhance sampling for r(GACC), and that the addition of the temperature dimension in the M-REMD simulations is necessary to efficiently sample rare conformations. Interestingly, we find that the rate of convergence can be improved in a single H-REMD dimension by simply increasing the number of replicas from 8 to 24 without increasing the maximum level of bias. The results also indicate that factors beyond replica spacing, such as round trip times and time spent at each replica, must be considered in order to achieve optimal sampling efficiency.

Multidimensional Replica Exchange Molecular Dynamics Yields a Converged Ensemble of an RNA Tetranucleotide

A necessary step to properly assess and validate the performance of force fields for biomolecules is to exhaustively sample the accessible conformational space, which is challenging for large RNA structures. Given questions regarding the reliability of modeling RNA structure and dynamics with current methods, we have begun to use RNA tetranucleotides to evaluate force fields. These systems, though small, display considerable conformational variability and complete sampling with standard simulation methods remains challenging. Here we compare and discuss the performance of known variations of replica exchange molecular dynamics (REMD) methods, specifically temperature REMD (T-REMD), Hamiltonian REMD (H-REMD), and multidimensional REMD (M-REMD) methods, which have been implemented in Amber’s accelerated GPU code. Using two independent simulations, we show that M-REMD not only makes very efficient use of emerging large-scale GPU clusters, like Blue Waters at the University of Illinois, but also is critically important in generating the converged ensemble more efficiently than either T-REMD or H-REMD. With 57.6 μs aggregate sampling of a conformational ensemble with M-REMD methods, the populations can be compared to NMR data to evaluate force field reliability and further understand how putative changes to the force field may alter populations to be in more consistent agreement with experiment.

Optimization of Umbrella Sampling Replica Exchange Molecular Dynamics by Replica Positioning

The positioning of sampling windows in an umbrella sampling simulation has an effect on the rate of convergence and computational efficiency. When such simulation is coupled with a Hamiltonian replica exchange setup, we show that such positioning can be optimized for maximal convergence of the results. We present a method for estimating the exchange acceptance ratio (EAR) between two arbitrary positions on a reaction coordinate in umbrella sampling replica exchange (USRE) molecular dynamics (MD). We designed a scoring function to optimize the position of the set of replicas (windows). By maximizing the scoring function, we make EAR the same for all neighbor replica pairs, increasing the efficiency of the method. We tested our algorithm by sampling a torsion for butane in implicit solvent and by studying a salt bridge in explicit solvent. We found that the optimized set of replicas recovers the correct free energy profile much faster than for equally spaced umbrellas.

Large scale affinity calculations of cyclodextrin host-guest complexes: Understanding the role of reorganization in the molecular recognition process

Host-guest inclusion complexes are useful models for understanding the structural and energetic aspects of molecular recognition. Due to their small size relative to much larger protein-ligand complexes, converged results can be obtained rapidly for these systems thus offering the opportunity to more reliably study fundamental aspects of the thermodynamics of binding. In this work, we have performed a large scale binding affinity survey of 57 β-cyclodextrin (CD) host guest systems using the binding energy distribution analysis method (BEDAM) with implicit solvation (OPLS-AA/AGBNP2). Converged estimates of the standard binding free energies are obtained for these systems by employing techniques such as parallel Hamitionian replica exchange molecular dynamics, conformational reservoirs and multistate free energy estimators. Good agreement with experimental measurements is obtained in terms of both numerical accuracy and affinity rankings. Overall, average effective binding energies reproduce affinity rank ordering better than the calculated binding affinities, even though calculated binding free energies, which account for effects such as conformational strain and entropy loss upon binding, provide lower root mean square errors when compared to measurements. Interestingly, we find that binding free energies are superior rank order predictors for a large subset containing the most flexible guests. The results indicate that, while challenging, accurate modeling of reorganization effects can lead to ligand design models of superior predictive power for rank ordering relative to models based only on ligand-receptor interaction energies.

Combining coarse-grained protein models with replica-exchange all-atom molecular dynamics

We describe a combination of all-atom simulations with CABS, a well-established coarse-grained protein modeling tool, into a single multiscale protocol. The simulation method has been tested on the C-terminal beta hairpin of protein G, a model system of protein folding. After reconstructing atomistic details, conformations derived from the CABS simulation were subjected to replica-exchange molecular dynamics simulations with OPLS-AA and AMBER99sb force fields in explicit solvent. Such a combination accelerates system convergence several times in comparison with all-atom simulations starting from the extended chain conformation, demonstrated by the analysis of melting curves, the number of native-like conformations as a function of time and secondary structure propagation. The results strongly suggest that the proposed multiscale method could be an efficient and accurate tool for high-resolution studies of protein folding dynamics in larger systems.

Reliable oligonucleotide conformational ensemble generation in explicit solvent for force field assessment using reservoir replica exchange molecular dynamics simulations

Molecular dynamics force field development and assessment requires a reliable means for obtaining a well-converged conformational ensemble of a molecule in both a time-efficient and cost-effective manner. This remains a challenge for RNA because its rugged energy landscape results in slow conformational sampling and accurate results typically require explicit solvent which increases computational cost. To address this, we performed both traditional and modified replica exchange molecular dynamics simulations on a test system (alanine dipeptide) and an RNA tetramer known to populate A-form-like conformations in solution (single-stranded rGACC). A key focus is on providing the means to demonstrate that convergence is obtained, for example, by investigating replica RMSD profiles and/or detailed ensemble analysis through clustering. We found that traditional replica exchange simulations still require prohibitive time and resource expenditures, even when using GPU accelerated hardware, and our results are not well converged even at 2 μs of simulation time per replica. In contrast, a modified version of replica exchange, reservoir replica exchange in explicit solvent, showed much better convergence and proved to be both a cost-effective and reliable alternative to the traditional approach. We expect this method will be attractive for future research that requires quantitative conformational analysis from explicitly solvated simulations.

Generating reservoir conformations for replica exchange through the use of the conformational space annealing method

Temperature replica exchange molecular dynamics (T-REM) has been successfully used to improve the conformational search for model peptides and small proteins. However, for larger and more complicated systems, the use of T-REM is computationally intensive since the complexity of the free energy landscape and number of replicas required increase with system size. Achieving convergence of systems with slow transition kinetics is often difficult. Several methods have been proposed to overcome the size and convergence speed issues of standard T-REM. One of these is the Reservoir Replica Exchange Method (R-REM), in which the conformational search and temperature equilibration are separated by exchanging with a pre-existing reservoir of structures. This approach allows the integration of computationally efficient search algorithms with replica exchange. The Conformational Space Annealing (CSA) method has been shown to be able to determine the global energy minimum of proteins efficiently and has been used in structure prediction successfully. CSA uses a genetic algorithm to generate a diverse set of conformations to determine the minimum energy structure. We combine these methods by using conformations generated by the CSA method to build a reservoir. R-REM is then used to seed the top replica with the structures from the reservoir; fast convergence at every temperature is observed. The efficiency of this method is then demonstrated with model peptides and small proteins, and significant improvement of efficiency is observed while maintaining the overall shape of the free energy landscape.

Advanced replica-exchange sampling to study the flexibility and plasticity of peptides and proteins

Molecular dynamics (MD) simulations are ideally suited to investigate protein and peptide plasticity and flexibility simultaneously at high spatial (atomic) and high time resolution. However, the applicability is still limited by the force field accuracy and by the maximum simulation time that can be routinely achieved in current MD simulations. In order to improve the sampling the replica-exchange (REMD) methodology has become popular and is now the most widely applied advanced sampling approach. Many variants of the REMD method have been designed to reduce the computational demand or to enhance sampling along specific sets of conformational variables. An overview on recent methodological advances and discussion of specific aims and advantages of the approaches will be given. Applications in the area of free energy simulations and advanced sampling of intrinsically disordered peptides and proteins will also be discussed. This article is part of a Special Issue entitled: The emerging dynamic view of proteins: Protein plasticity in allostery, evolution and self-assembly.

Conformational flexibility of N-glycans in solution studied by REMD simulations

Protein-glycan recognition regulates a wide range of biological and pathogenic processes. Conformational diversity of glycans in solution is apparently incompatible with specific binding to their receptor proteins. One possibility is that among the different conformational states of a glycan, only one conformer is utilized for specific binding to a protein. However, the labile nature of glycans makes characterizing their conformational states a challenging issue. All-atom molecular dynamics (MD) simulations provide the atomic details of glycan structures in solution, but fairly extensive sampling is required for simulating the transitions between rotameric states. This difficulty limits application of conventional MD simulations to small fragments like di- and tri-saccharides. Replica-exchange molecular dynamics (REMD) simulation, with extensive sampling of structures in solution, provides a valuable way to identify a family of glycan conformers. This article reviews recent REMD simulations of glycans carried out by us or other research groups and provides new insights into the conformational equilibria of N-glycans and their alteration by chemical modification. We also emphasize the importance of statistical averaging over the multiple conformers of glycans for comparing simulation results with experimental observables. The results support the concept of "conformer selection" in protein-glycan recognition.