Convergence and sampling efficiency in replica exchange simulations of peptide folding in explicit solvent

Development of Self-Assembled Biomimetic Nanoscale Collagen-like Peptide-Based Scaffolds for Tissue Engineering: An In Silico and Laboratory Study

Development of biocomposite scaffolds has gained tremendous attention due to their potential for tissue regeneration. However, most scaffolds often contain animal-derived collagen that may elicit an immunological response, necessitating the development of new biomaterials. Herein, we developed a new collagen-like peptide,(Pro-Ala-His)10 (PAH)10, and explored its ability to be utilized as a functional biomaterial by incorporating it with a newly synthesized peptide-based self-assembled gel. The gel was prepared by conjugating a pectin derivative, galataric acid, with a pro-angiogenic peptide (LHYQDLLQLQY) and further functionalized with a cortistatin-derived peptide, (Phe-Trp-Lys-Thr)4 (FWKT)4, and the bio-ionic liquid choline acetate. The self-assembly of (PAH)10 and its interactions with the galactarate-peptide conjugates were examined using replica exchange molecular dynamics (REMD) simulations. Results revealed the formation of a multi-layered scaffold, with enhanced stability at higher temperatures. We then synthesized the scaffold and examined its physicochemical properties and its ability to integrate with aortic smooth muscle cells. The scaffold was further utilized as a bioink for bioprinting to form three-dimensional cell-scaffold matrices. Furthermore, the formation of actin filaments and elongated cell morphology was observed. These results indicate that the (PAH)10 hybrid scaffold provides a suitable environment for cell adhesion, proliferation and growth, making it a potentially valuable biomaterial for tissue engineering.

Classification of PTEN missense VUS through exascale simulations

Phosphatase and tensin homolog (PTEN), a tumor suppressor with dual phosphatase properties, is a key factor in PI3K/AKT signaling pathway. Pathogenic germline variation in PTEN can abrogate its ability to dephosphorylate, causing high cancer risk. Lack of functional evidence lets numerous PTEN variants be classified as variants of uncertain significance (VUS). Utilizing Molecular Dynamics (MD) simulations, we performed a thorough evaluation for 147 PTEN missense VUS, sorting them into 66 deleterious and 81 tolerated variants. Utilizing replica exchange molecular dynamic (REMD) simulations, we further assessed the variants situated in the catalytic core of PTEN's phosphatase domain and uncovered conformational alterations influencing the structural stability of the phosphatase domain. There was a high degree of agreement between our results and the variants classified by Variant Abundance by Massively Parallel Sequencing, saturation mutagenesis, multiplexed functional data and experimental assays. Our extensive analysis of PTEN missense VUS should benefit their clinical applications in PTEN-related cancer.

SIGNIFICANCE STATEMENT

Classification of PTEN variants affecting its lipid phosphatase activity is important for understanding the roles of PTEN variation in the pathogenesis of hereditary and sporadic malignancies. Of the 3000 variants identified in PTEN, 1296 (43%) were assigned as VUS. Here, we applied MD and REMD simulations to investigate the effects of PTEN missense VUS on the structural integrity of the PTEN phosphatase domain consisting the WPD, P and TI active sites. We classified a total of 147 missense VUS into 66 deleterious and 81 tolerated variants by referring to the control group comprising 54 pathogenic and 12 benign variants. The classification was largely in concordance with these classified by experimental approaches.

The role of conformational change and key glutamic acid residues in the ClC-ec1 antiporter

The triple glutamine (Q) mutant (QQQ) structure of a Cl-/H+ antiporter from Escherichia coli (ClC-ec1) displaying a novel backbone arrangement has been used to challenge the long-held notion that Cl-/H+ antiporters do not operate through large conformational motions. The QQQ mutant substitutes the glutamine residue for an external glutamate E148, an internal glutamate E203, and a third glutamate E113 that hydrogen-bonds with E203. However, it is unknown if QQQ represents a physiologically relevant state, as well as how the protonation of the wild-type glutamates relates to the global dynamics. We herein apply continuous constant-pH molecular dynamics to investigate the H+-coupled dynamics of ClC-ec1. Although any large-scale conformational rearrangement upon acidification would be due to the accumulation of excess charge within the protein, protonation of the glutamates significantly impacts mainly the local structure and dynamics. Despite the fact that the extracellular pore enlarges at acidic pHs, an occluded ClC-ec1 within the active pH range of 3.5-7.5 requires a protonated E148 to facilitate extracellular Cl- release. E203 is also involved in the intracellular H+ transfer as an H+ acceptor. The water wire connection of E148 with the intracellular solution is regulated by the charge states of the E113/E203 dyad with coupled proton titration. However, the dynamics extracted from our simulations are not QQQ-like, indicating that the QQQ mutant does not represent the behavior of the wild-type ClC-ec1. These findings reinforce the necessity of having a protonatable residue at the E203 position in ClC-ec1 and suggest that a higher level of complexity exists for the intracellular H+ transfer in Cl-/H+ antiporters.

Re-Balancing Replica Exchange with Solute Tempering for Sampling Dynamic Protein Conformations

Replica exchange with solute tempering (REST) is a highly effective variant of replica exchange for enhanced sampling in explicit solvent simulations of biomolecules. By scaling the Hamiltonian for a selected "solute" region of the system, REST effectively applies tempering only to the degrees of freedom of interest but not the rest of the system ("solvent"), allowing fewer replicas for covering the same temperature range. A key consideration of REST is how the solute-solvent interactions are scaled together with the solute-solute interactions. Here, we critically evaluate the performance of the latest REST2 protocol for sampling large-scale conformation fluctuations of intrinsically disordered proteins (IDPs). The results show that REST2 promotes artificial protein conformational collapse at high effective temperatures, which seems to be a designed feature originally to promote the sampling of reversible folding of small proteins. The collapse is particularly severe with larger IDPs, leading to replica segregation in the effective temperature space and hindering effective sampling of large-scale conformational changes. We propose that the scaling of the solute-solvent interactions can be treated as free parameters in REST, which can be tuned to control the solute conformational properties (e.g., chain expansion) at different effective temperatures and achieve more effective sampling. To this end, we derive a new REST3 protocol, where the strengths of the solute-solvent van der Waals interactions are recalibrated to reproduce the levels of protein chain expansion at high effective temperatures. The efficiency of REST3 is examined using two IDPs with nontrivial local and long-range structural features, including the p53 N-terminal domain and the kinase inducible transactivation domain of transcription factor CREB. The results suggest that REST3 leads to a much more efficient temperature random walk and improved sampling efficiency, which also further reduces the number of replicas required. Nonetheless, our analysis also reveals significant challenges of relying on tempering alone for sampling large-scale conformational fluctuations of disordered proteins. It is likely that more efficient sampling protocols will require incorporating more sophisticated Hamiltonian replica exchange schemes in addition to tempering.

Structure-Thermodynamic Relationship of a Polysaccharide Gel (Alginate) as a Function of Water Content and Counterion Type (Na vs Ca)

Biofilms are the predominant mode of microbial life on Earth, and so a deep understanding of microbial communities─and their impacts on environmental processes─requires a firm understanding of biofilm properties. Because of the importance of biofilms to their microbial inhabitants, microbes have evolved different ways of engineering and reconfiguring the matrix of extracellular polymeric substances (EPS) that constitute the main non-living component of biofilms. This ability makes it difficult to distinguish between the biotic and abiotic origins of biofilm properties. An important route toward establishing this distinction has been the study of simplified models of the EPS matrix. This study builds on such efforts by using atomistic simulations to predict the nanoscale (≤10 nm scale) structure of a model EPS matrix and the sensitivity of this structure to interpolymer interactions and water content. To accomplish this, we use replica exchange molecular dynamics (REMD) simulations to generate all-atom configurations of ten 3.4 kDa alginate polymers at a range of water contents and Ca-Na ratios. Simulated systems are solvated with explicitly modeled water molecules, which allows us to capture the discrete structure of the hydrating water and to examine the thermodynamic stability of water in the gels as they are progressively dehydrated. Our primary findings are that (i) the structure of the hydrogels is highly sensitive to the identity of the charge-compensating cations, (ii) the thermodynamics of water within the gels (specific enthalpy and free energy) are, surprisingly, only weakly sensitive to cation identity, and (iii) predictions of the differential enthalpy and free energy of hydration include a short-ranged enthalpic term that promotes hydration and a longer-ranged (presumably entropic) term that promotes dehydration, where short and long ranges refer to distances shorter or longer than ∼0.6 nm between alginate strands.

Amyloid fibrillation of the glaucoma associated myocilin protein is inhibited by epicatechin gallate (ECG)

Inherited glaucoma is a recent addition to the inventory of diseases arising due to protein misfolding. Mutations in the olfactomedin (OLF) domain of myocilin are the most common genetic cause behind this disease. Disease associated variants of m-OLF are predisposed to misfold and aggregate in the trabecular meshwork (TM) tissue of the eye. In recent years, the nature of these aggregates was revealed to exhibit the hallmarks of amyloids. Amyloid aggregates are highly stable structures that are formed, often with toxic consequences in a number of debilitating diseases. In spite of its clinical relevance the amyloidogenic nature of m-OLF has not been studied adequately. Here we have studied the amyloid fibrillation of m-OLF and report ECG as an inhibitor against it. Using biophysical and biochemical assays, coupled with advanced microscopic evaluations we show that ECG binds and stabilizes native m-OLF and thus prevents its aggregation into amyloid fibrils. Furthermore, we have used REMD simulations to delineate the stabilizing effects of ECG on the structure of m-OLF. Collectively, we report ECG as a molecular scaffold for designing and testing of novel inhibitors against m-OLF amyloid fibrillation.

Molecular dynamics simulations of the flexibility and inhibition of SARS-CoV-2 NSP 13 helicase

The helicase protein of the Severe Acute Respiratory Syndrome Coronavirus 2 (SARS-CoV-2) is both a good potential drug target and very flexible. The flexibility, and therefore its function, could be reduced through knowledge of these motions and identification of allosteric pockets. Using molecular dynamics simulations with enhanced sampling, we determined key modes of motion and sites on the protein that are at the interface between flexible domains of the proteins. We developed an approach to map the principal components of motion onto the surface of a potential binding pocket to help in the identification of allosteric sites.

Conformational Fluctuations in GTP-Bound K-Ras: A Metadynamics Perspective with Harmonic Linear Discriminant Analysis

Biomacromolecules often undergo significant conformational rearrangements during function. In proteins, these motions typically consist in nontrivial, concerted rearrangement of multiple flexible regions. Mechanistic, thermodynamics, and kinetic predictions can be obtained via molecular dynamics simulations, provided that the simulation time is at least comparable to the relevant time scale of the process of interest. Because of the substantial computational cost, however, plain MD simulations often have difficulty in obtaining sufficient statistics for converged estimates, requiring the use of more-advanced techniques. Central in many enhanced sampling methods is the definition of a small set of relevant degrees of freedom (collective variables) that are able to describe the transitions between different metastable states of the system. The harmonic linear discriminant analysis (HLDA) has been shown to be useful for constructing low-dimensional collective variables in various complex systems. Here, we apply HLDA to study the free-energy landscape of a monomeric protein around its native state. More precisely, we study the K-Ras protein bound to GTP, focusing on two flexible loops and on the region associated with oncogenic mutations. We perform microsecond-long biased simulations on the wild type and on G12C, G12D, G12 V mutants, describe the resulting free-energy landscapes, and compare our predictions with previous experimental and computational studies. The fast interconversion between open and closed macroscopic states and their similar thermodynamic stabilities are observed. The mutation-induced effects include the alternations of the relative stabilities of different conformational states and the introduction of many microscopic metastable states. Together, our results demonstrate the applicability of the HLDA-based protocol for the conformational sampling of multiple flexible regions in folded proteins.

Using a Coarse-Grained Modeling Framework to Identify Oligomeric Motifs with Tunable Secondary Structure

Coarse-grained modeling can be used to explore general theories that are independent of specific chemical detail. In this paper, we present cg_openmm, a Python-based simulation framework for modeling coarse-grained hetero-oligomers and screening them for structural and thermodynamic characteristics of cooperative secondary structures. cg_openmm facilitates the building of coarse-grained topology and random starting configurations, setup of GPU-accelerated replica exchange molecular dynamics simulations with the OpenMM software package, and features a suite of postprocessing thermodynamic and structural analysis tools. In particular, native contact analysis, heat capacity calculations, and free energy of folding calculations are used to identify and characterize cooperative folding transitions and stable secondary structures. In this work, we demonstrate the capabilities of cg_openmm on a simple 1-1 Lennard-Jones coarse-grained model, in which each residue contains 1 backbone and 1 side-chain bead. By scanning both nonbonded and bonded force-field parameter spaces at the coarse-grained level, we identify and characterize sets of parameters which result in the formation of stable helices through cooperative folding transitions. Moreover, we show that the geometries and stabilities of these helices can be tuned by manipulating the force-field parameters.

Molecular dynamics simulations of bacterial outer membrane lipid extraction: Adequate sampling?

The outer membrane of Gram-negative bacteria is almost exclusively composed of lipopolysaccharide in its outer leaflet, whereas the inner leaflet contains a mixture of phospholipids. Lipopolysaccharide diffuses at least an order of magnitude slower than phospholipids, which can cause issues for molecular dynamics simulations in terms of adequate sampling. Here, we test a number of simulation protocols for their ability to achieve convergence with reasonable computational effort using the MARTINI coarse-grained force-field. This is tested in the context both of potential of mean force (PMF) calculations for lipid extraction from membranes and of lateral mixing within the membrane phase. We find that decoupling the cations that cross-link the lipopolysaccharide headgroups from the extracted lipid during PMF calculations is the best approach to achieve convergence comparable to that for phospholipid extraction. We also show that lateral lipopolysaccharide mixing/sorting is very slow and not readily addressable even with Hamiltonian replica exchange. We discuss why more sorting may be unrealistic for the short (microseconds) timescales we simulate and provide an outlook for future studies of lipopolysaccharide-containing membranes.

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.

An Implementation of Replica Exchange with Dynamical Scaling for Efficient Large-Scale Simulations

An implementation of the replica exchange with dynamical scaling (REDS) method in the commonly used molecular dynamics program GROMACS is presented. REDS is a replica exchange method that requires fewer replicas than conventional replica exchange while still providing data over a range of temperatures and can be used in either constant volume or constant pressure ensembles. Details for running REDS simulations are given, and an application to the human islet amyloid polypeptide (hIAPP) 11-25 fragment shows that the model efficiently samples conformational space.

Computational Assessment of the Three-Dimensional Configuration of Dissolved Organic Matter Chromophores and Influence on Absorption Spectra

The three-dimensional configuration of dissolved organic matter (DOM) is an important factor in determining the role of DOM in natural and engineered systems, yet there is still considerable uncertainty regarding the formation and potential stability of molecular aggregates within DOM. In this paper, we describe a computational assessment of the three-dimensional configuration of DOM. Specifically, we were interested in evaluating the hypothesis that DOM forms thermodynamically stable molecular aggregates that as a result were potentially shielded from water solvent molecules. Molecular dynamics simulations of DOM model compounds carefully selected based on ultrahigh-resolution mass spectrometry data revealed that, while DOM does indeed form molecular aggregates, the large majority of molecules (especially, O-atom bearing molecules) are solvent accessible. Additionally, these computations revealed that molecular aggregates are weak and dissociate when placed in organic solvents (tetrahydrofuran, methyl tert-butyl ether). Time-dependent density functional theory calculations demonstrated long-wavelength absorbance for both model DOM chromophores and their molecular aggregates. This study has important implications for determining the origin of DOM optical properties and for enhancing our collective understanding of DOM three-dimensional structures.

myPresto/omegagene 2020: a molecular dynamics simulation engine for virtual-system coupled sampling

The molecular dynamics (MD) method is a promising approach for investigating the molecular mechanisms of microscopic phenomena. In particular, generalized ensemble MD methods can efficiently explore the conformational space with a rugged free-energy surface. However, the implementation and acquisition of technical knowledge for each generalized ensemble MD method are not straightforward for end-users. Here, we present a new version of the myPresto/omegagene software, which is an MD simulation engine tailored for a series of generalized ensemble methods, which are virtual-system coupled multicanonical MD (V-McMD), virtual-system coupled adaptive umbrella sampling (V-AUS), and virtual-system coupled canonical MD (VcMD). This program has been applied in several studies analyzing free-energy landscapes of a variety of molecular systems with all-atom simulations. The updated version provides new functionality for coarse-grained simulations powered by the hydrophobicity scale method. The software package includes a step-by-step tutorial document for enhanced conformational sampling of the poly-glutamine (poly-Q) oligomer expressed as a one-bead per residue model. The myPresto/omegagene software is freely available at the following URL: https://github.com/kotakasahara/omegagene under the Apache2 license.

Structural dynamics and susceptibility of anti-HIV drugs against HBV reverse transcriptase

Hepatitis B virus (HBV), a small enveloped DNA virus, attacks the human liver causing both acute and chronic diseases. Current therapeutic drugs use the nucleos(t)ide analogues (NAs) as a competitive inhibitor against HBV reverse transcriptase (HBV-RT), an essential enzyme pivotally involved in viral replication. Unfortunately, this treatment still causes the development of resistant variants of HBV against NAs. As HBV-RT is homologous to the human immunodeficiency virus reverse transcriptase (HIV-RT), it is reasonable to treat HBV-RT with anti-HIV drugs. In the present study, we aimed to investigate the structural dynamics and susceptibility of the known anti-HIV drugs (stavudine [d4T], didanosine [DDI], and zidovudine [ZDV]) against HBV-RT enzyme in comparison to the anti-HBV drug lamivudine (3TC) and deoxythymidine triphosphate (dTTP) substrate using several computational approaches. The ΔGbindresidue calculations revealed that seven polar residues (K32, R41, D83, S85, D205, N236, and K239) and three hydrophobic residues (A86, A87, and F88) of HBV-RT as well as the adjacent DNA strands play an important role in the ligand binding. In addition, the H-bond pattern of d4T is similar to that of 3TC, especially at the residues A86 and A87. Such interactions promote the favorable conformation of ligand in the HBV-RT binding pocket, while the several different conformations of ligand are found in the unbound state. The predicted binding free energy results based on QM/MM-GBSA and MM/GB(PB)SA methods suggested that the susceptibility towards HBV-RT of d4T and ZDV is higher than that of 3TC and dTTP. Altogether, this work sheds light on the potentiality of d4T and ZDV as a promising drug for HBV-infected patients harboring 3TC resistance.Communicated by Ramaswamy H. Sarma.

Effects of number of parallel runs and frequency of bias-strength replacement in generalized ensemble molecular dynamics simulations

Background

The generalized ensemble approach with the molecular dynamics (MD) method has been widely utilized. This approach usually has two features. (i) A bias potential, whose strength is replaced during a simulation, is applied. (ii) Sampling can be performed by many parallel runs of simulations. Although the frequency of the bias-strength replacement and the number of parallel runs can be adjusted, the effects of these settings on the resultant ensemble remain unclear.

Method

In this study, we performed multicanonical MD simulations for a foldable mini-protein (Trp-cage) and two unstructured peptides (8- and 20-residue poly-glutamic acids) with various settings.

Results

As a result, running many short simulations yielded robust results for the Trp-cage model. Regarding the frequency of the bias-potential replacement, although using a high frequency enhanced the traversals in the potential energy space, it did not promote conformational changes in all the systems.

Large-scale, dynamin-like motions of the human guanylate binding protein 1 revealed by multi-resolution simulations

Guanylate binding proteins (GBPs) belong to the dynamin-related superfamily and exhibit various functions in the fight against infections. The functions of the human guanylate binding protein 1 (hGBP1) are tightly coupled to GTP hydrolysis and dimerization. Despite known crystal structures of the hGBP1 monomer and GTPase domain dimer, little is known about the dynamics of hGBP1. To gain a mechanistic understanding of hGBP1, we performed sub-millisecond multi-resolution molecular dynamics simulations of both the hGBP1 monomer and dimer. We found that hGBP1 is a highly flexible protein that undergoes a hinge motion similar to the movements observed for other dynamin-like proteins. Another large-scale motion was observed for the C-terminal helix α13, providing a molecular view for the α13-α13 distances previously reported for the hGBP1 dimer. Most of the loops of the GTPase domain were found to be flexible, revealing why GTP binding is needed for hGBP1 dimerization to occur.

Studies on Molecular Dynamics of Intrinsically Disordered Proteins and Their Fuzzy Complexes: A Mini-Review

The molecular dynamics (MD) method is a promising approach toward elucidating the molecular mechanisms of intrinsically disordered regions (IDRs) of proteins and their fuzzy complexes. This mini-review introduces recent studies that apply MD simulations to investigate the molecular recognition of IDRs. Firstly, methodological issues by which MD simulations treat IDRs, such as developing force fields, treating periodic boundary conditions, and enhanced sampling approaches, are discussed. Then, several examples of the applications of MD to investigate molecular interactions of IDRs in terms of the two kinds of complex formations; coupled-folding and binding and fuzzy complex. MD simulations provide insight into the molecular mechanisms of these binding processes by sampling conformational ensembles of flexible IDRs. In particular, we focused on all-atom explicit-solvent MD simulations except for studies of higher-order assembly of IDRs. Recent advances in MD methods, and computational power make it possible to dissect the molecular details of realistic molecular systems involving the dynamic behavior of IDRs.

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.

Influence of various parameters in the replica-exchange molecular dynamics method: Number of replicas, replica-exchange frequency, and thermostat coupling time constant

The replica-exchange molecular dynamics (REMD) method has been used for conformational sampling of various biomolecular systems. To maximize sampling efficiency, some adjustable parameters must be optimized. Although it is agreed that shorter intervals between the replica-exchange attempts enhance traversals in the temperature space, details regarding the artifacts caused by these short intervals are controversial. In this study, we revisit this problem by performing REMD simulations on an alanine octapeptide in an implicit solvent. Fifty different sets of conditions, which are a combination of five replica-exchange periods, five different numbers of replicas, and two thermostat coupling time constants, were investigated. As a result, although short replica-exchange intervals enhanced the traversals in the temperature space, they led to artifacts in the ensemble average of the temperature, potential energy, and helix content. With extremely short replica-exchange intervals, i.e., attempted at every time step, the ensemble average of the temperature deviated from the thermostat temperature by ca. 7 K. Differences in the ensembles were observed even for larger replica-exchange intervals (between 100 and 1,000 steps). In addition, the shorter thermostat coupling time constant reduced the artifacts found when short replica-exchange intervals were used, implying that these artifacts are caused by insufficient thermal relaxation between the replica-exchange events. Our results will be useful to reduce the artifacts found in REMD simulations by adjusting some key parameters.

Folding a viral peptide in different membrane environments: pathway and sampling analyses

Flock House virus (FHV) is a well-characterized model system to study infection mechanisms in non-enveloped viruses. A key stage of the infection cycle is the disruption of the endosomal membrane by a component of the FHV capsid, the membrane active γ peptide. In this study, we perform all-atom molecular dynamics simulations of the 21 N-terminal residues of the γ peptide interacting with membranes of differing compositions. We carry out umbrella sampling calculations to study the folding of the peptide to a helical state in homogenous and heterogeneous membranes consisting of neutral and anionic lipids. From the trajectory data, we evaluate folding energetics and dissect the mechanism of folding in the different membrane environments. We conclude the study by analyzing the extent of configurational sampling by performing time-lagged independent component analysis.

Dimer Interface of the Human Serotonin Transporter and Effect of the Membrane Composition

The oligomeric state of membrane proteins has recently emerged in many cases as having an effect on their function. However, the intrinsic dynamics of their spatial organization in cells and model systems makes it challenging to characterize. Here we use molecular dynamics (MD) simulations at multiple resolutions to determine the dimer conformation of the human serotonin transporter (hSERT). From self-assembly simulations we predict dimer candidates and subsequently quantify their relative strength. We use umbrella sampling (US) replica exchange MD simulations for which we present extensive analysis of their efficiency and improved sampling compared to regular US MD simulations. The data shows that the most stable hSERT dimer interface is symmetrical and involves transmembrane helix 12 (TM12), similar to the crystal structure of the bacterial homologue LeuT, but with a slightly different orientation. We also describe the supramolecular organization of hSERT from a 250 μs self-assembly simulation. Finally, the effects of the presence of phosphatidylinositol bisphosphate or cholesterol in the membrane model has been quantified for the TM12-TM12 predicted interface. Collectively, the presented data bring new insight to the area of protein and lipid interplay in biological membranes.

Mycolyltransferase from Mycobacterium tuberculosis in covalent complex with tetrahydrolipstatin provides insights into antigen 85 catalysis

Mycobacterium tuberculosis antigen 85 (Ag85) enzymes catalyze the transfer of mycolic acid (MA) from trehalose monomycolate to produce the mycolyl arabinogalactan (mAG) or trehalose dimycolate (TDM). These lipids define the protective mycomembrane of mycobacteria. The current model of substrate binding within the active sites of Ag85s for the production of TDM is not sterically and geometrically feasible; additionally, this model does not account for the production of mAG. Furthermore, this model does not address how Ag85s limit the hydrolysis of the acyl-enzyme intermediate while catalyzing acyl transfer. To inform an updated model, we obtained an Ag85 acyl-enzyme intermediate structure that resembles the mycolated form. Here, we present a 1.45-Å X-ray crystal structure of M. tuberculosis Ag85C covalently modified by tetrahydrolipstatin (THL), an esterase inhibitor that suppresses M. tuberculosis growth and mimics structural attributes of MAs. The mode of covalent inhibition differs from that observed in the reversible inhibition of the human fatty-acid synthase by THL. Similarities between the Ag85-THL structure and previously determined Ag85C structures suggest that the enzyme undergoes structural changes upon acylation, and positioning of the peptidyl arm of THL limits hydrolysis of the acyl-enzyme adduct. Molecular dynamics simulations of the modeled mycolated-enzyme form corroborate the structural analysis. From these findings, we propose an alternative arrangement of substrates that rectifies issues with the previous model and suggest a direct role for the β-hydroxy of MA in the second half-reaction of Ag85 catalysis. This information affords the visualization of a complete mycolyltransferase catalytic cycle.

Aqueous ionic liquids influence the disulfide bond isoform equilibrium in conotoxin AuIB: a consequence of the Hofmeister effect?

The appearance of several disulfide bond isoforms in multiple cysteine containing venom peptides poses a significant challenge in their synthesis and purification under laboratory conditions. Recent experiments suggest that careful tuning of solvent and temperature conditions can propel the disulfide bond isoform equilibrium in favor of the most potent, native form. Certain aqueous ionic liquids (ILs) have proven significantly useful as solvents for this purpose, while exceptions have also been noted. To elucidate the molecular level origin behind such a preference, we report a detailed explicit solvent replica exchange molecular dynamics study of a conotoxin, AuIB, in pure water and four different aqueous IL solutions (~45-60% v/v). The ILs studied here are comprised of cations like 1-ethyl-3-methyl-imidazolium (Im₂₁⁺) or 1-butyl-3-methyl-imidazolium (Im₄₁⁺) coupled with either acetate (OAc^-) or chloride (Cl^-) as the counter anion. Our simulations unfold interesting features of the conformational spaces sampled by the peptide and its solvation in pure water and aqueous IL solutions. Detailed investigation into populations of the globular disulfide bond isoform of AuIB in aqueous IL solutions reveal distinct trends which might be related to the Hofmeister effect of the cation and anion of the IL and of specific interactions of the aqueous IL solutions with the peptide. In accordance with experimental observations, the aqueous [Im₂₁][OAc] solution is found to promote the highest globular isoform population in AuIB.

Replica Exchange Molecular Dynamics: A Practical Application Protocol with Solutions to Common Problems and a Peptide Aggregation and Self-Assembly Example

Protein aggregation is associated with many human diseases such as Alzheimer's disease (AD), Parkinson's disease (PD), and type II diabetes (T2D). Understanding the molecular mechanism of protein aggregation is essential for therapy development. Molecular dynamics (MD) simulations have been shown as powerful tools to study protein aggregation. However, conventional MD simulations can hardly sample the whole conformational space of complex protein systems within acceptable simulation time as it can be easily trapped in local minimum-energy states. Many enhanced sampling methods have been developed. Among these, the replica exchange molecular dynamics (REMD) method has gained great popularity. By combining MD simulation with the Monte Carlo algorithm, the REMD method is capable of overcoming high energy-barriers easily and of sampling sufficiently the conformational space of proteins. In this chapter, we present a brief introduction to REMD method and a practical application protocol with a case study of the dimerization of the 11-25 fragment of human islet amyloid polypeptide (hIAPP(11-25)), using the GROMACS software. We also provide solutions to problems that are often encountered in practical use, and provide some useful scripts/commands from our research that can be easily adapted to other systems.

Inference of Calmodulin's Ca2+-Dependent Free Energy Landscapes via Gaussian Mixture Model Validation

A free energy landscape estimation method based on the well-known Gaussian mixture model (GMM) is used to compare the efficiencies of thermally enhanced sampling methods with respect to regular molecular dynamics. The simulations are carried out on two binding states of calmodulin, and the free energy estimation method is compared with other estimators using a toy model. We show that GMM with cross-validation provides a robust estimate that is not subject to overfitting. The continuous nature of Gaussians provides better estimates on sparse data than canonical histogramming. We find that diffusion properties determine the sampling method effectiveness, such that diffusion-dominated apo calmodulin is most efficiently sampled by regular molecular dynamics, while holo calmodulin, with its rugged free energy landscape, is better sampled by enhanced sampling methods.

Constant pH Molecular Dynamics Reveals How Proton Release Drives the Conformational Transition of a Transmembrane Efflux Pump

AcrB is the inner-membrane transporter of an E. coli AcrAB-TolC tripartite efflux complex, which plays a major role in the intrinsic resistance to clinically important antibiotics. AcrB pumps a wide range of toxic substrates by utilizing the proton gradient between periplasm and cytoplasm. Crystal structures of AcrB revealed three distinct conformational states of the transport cycle, substrate access, binding, and extrusion or loose (L), tight (T), and open (O) states. However, the specific residue(s) responsible for proton binding/release and the mechanism of proton-coupled conformational cycling remain controversial. Here we use the newly developed membrane hybrid-solvent continuous constant pH molecular dynamics technique to explore the protonation states and conformational dynamics of the transmembrane domain of AcrB. Simulations show that both Asp407 and Asp408 are deprotonated in the L/T states, while only Asp408 is protonated in the O state. Remarkably, release of a proton from Asp408 in the O state results in large conformational changes, such as the lateral and vertical movement of transmembrane helices as well as the salt-bridge formation between Asp408 and Lys940 and other side chain rearrangements among essential residues. Consistent with the crystallographic differences between the O and L protomers, simulations offer dynamic details of how proton release drives the O-to-L transition in AcrB and address the controversy regarding the proton/drug stoichiometry. This work offers a significant step toward characterizing the complete cycle of proton-coupled drug transport in AcrB and further validates the membrane hybrid-solvent CpHMD technique for studies of proton-coupled transmembrane proteins which are currently poorly understood.

Efficacy of independence sampling in replica exchange simulations of ordered and disordered proteins

Recasting temperature replica exchange (T-RE) as a special case of Gibbs sampling has led to a simple and efficient scheme for enhanced mixing (Chodera and Shirts, J. Chem. Phys., 2011, 135, 194110). To critically examine if T-RE with independence sampling (T-REis) improves conformational sampling, we performed T-RE and T-REis simulations of ordered and disordered proteins using coarse-grained and atomistic models. The results demonstrate that T-REis effectively increase the replica mobility in temperatures space with minimal computational overhead, especially for folded proteins. However, enhanced mixing does not translate well into improved conformational sampling. The convergences of thermodynamic properties interested are similar, with slight improvements for T-REis of ordered systems. The study re-affirms the efficiency of T-RE does not appear to be limited by temperature diffusion, but by the inherent rates of spontaneous large-scale conformational re-arrangements. Due to its simplicity and efficacy of enhanced mixing, T-REis is expected to be more effective when incorporated with various Hamiltonian-RE protocols. © 2017 Wiley Periodicals, Inc.

Computational membrane biophysics: From ion channel interactions with drugs to cellular function

The rapid development of experimental and computational techniques has changed fundamentally our understanding of cellular-membrane transport. The advent of powerful computers and refined force-fields for proteins, ions, and lipids has expanded the applicability of Molecular Dynamics (MD) simulations. A myriad of cellular responses is modulated through the binding of endogenous and exogenous ligands (e.g. neurotransmitters and drugs, respectively) to ion channels. Deciphering the thermodynamics and kinetics of the ligand binding processes to these membrane proteins is at the heart of modern drug development. The ever-increasing computational power has already provided insightful data on the thermodynamics and kinetics of drug-target interactions, free energies of solvation, and partitioning into lipid bilayers for drugs. This review aims to provide a brief summary about modeling approaches to map out crucial binding pathways with intermediate conformations and free-energy surfaces for drug-ion channel binding mechanisms that are responsible for multiple effects on cellular functions. We will discuss post-processing analysis of simulation-generated data, which are then transformed to kinetic models to better understand the molecular underpinning of the experimental observables under the influence of drugs or mutations in ion channels. This review highlights crucial mathematical frameworks and perspectives on bridging different well-established computational techniques to connect the dynamics and timescales from all-atom MD and free energy simulations of ion channels to the physiology of action potentials in cellular models. This article is part of a Special Issue entitled: Biophysics in Canada, edited by Lewis Kay, John Baenziger, Albert Berghuis and Peter Tieleman.

A tendril perversion in a helical oligomer: trapping and characterizing a mobile screw-sense reversal

Helical oligomers of achiral monomers adopt domains of uniform screw sense, which are occasionally interrupted by screw-sense reversals. These rare, elusive, and fast-moving features have eluded detailed characterization. We now describe the structure and habits of a screw-sense reversal trapped within a fragment of a helical oligoamide foldamer of the achiral quaternary amino acid 2-aminoisobutyric acid (Aib). The reversal was enforced by compelling the amide oligomer to adopt a right-handed screw sense at one end and a left-handed screw sense at the other. The trapped reversal was characterized by X-ray crystallography, and its dynamic properties were monitored by NMR and circular dichroism, and modelled computationally. Raman spectroscopy indicated that a predominantly helical architecture was maintained despite the reversal. NMR and computational results indicated a stepwise shift from one screw sense to another on moving along the helical chain, indicating that in solution the reversal is not localised at a specific location, but is free to migrate across a number of residues. Analogous unconstrained screw-sense reversals that are free to move within a helical structure are likely to provide the mechanism by which comparable helical polymers and foldamers undergo screw-sense inversion.

Induced polarization restricts the conformational distribution of a light-harvesting molecular triad in the ground state

Free energy surface of the light-harvesting triad employing a non-polarizable force field (NFF) and a polarizable force field (PFF) shows that induced polarization limits the motion of rotation about chemical bonds as well as bending at the porphyrin, which are prominent using the NFF, thus limiting the conformational space of the triad.

Comparing generalized ensemble methods for sampling of systems with many degrees of freedom

We compare two standard replica exchange methods using temperature and dielectric constant as the scaling variables for independent replicas against two new corresponding enhanced sampling methods based on non-equilibrium statistical cooling (temperature) or descreening (dielectric). We test the four methods on a rough 1D potential as well as for alanine dipeptide in water, for which their relatively small phase space allows for the ability to define quantitative convergence metrics. We show that both dielectric methods are inferior to the temperature enhanced sampling methods, and in turn show that temperature cool walking (TCW) systematically outperforms the standard temperature replica exchange (TREx) method. We extend our comparisons of the TCW and TREx methods to the 5 residue met-enkephalin peptide, in which we evaluate the Kullback-Leibler divergence metric to show that the rate of convergence between two independent trajectories is faster for TCW compared to TREx. Finally we apply the temperature methods to the 42 residue amyloid-β peptide in which we find non-negligible differences in the disordered ensemble using TCW compared to the standard TREx. All four methods have been made available as software through the OpenMM Omnia software consortium (http://www.omnia.md/).

Peptide Bond Isomerization in High-Temperature Simulations

Force fields for molecular simulation are generally optimized to model macromolecules such as proteins at ambient temperature and pressure. Nevertheless, elevated temperatures are frequently used to enhance conformational sampling, either during system setup or as a component of an advanced sampling technique such as temperature replica exchange. Because macromolecular force fields are now put upon to simulate temperatures and time scales that greatly exceed their original design specifications, it is appropriate to re-evaluate whether these force fields are up to the task. Here, we quantify the rates of peptide bond isomerization in high-temperature simulations of three octameric peptides and a small fast-folding protein. We show that peptide octamers with and without proline residues undergo cis/trans isomerization every 1-5 ns at 800 K with three classical atomistic force fields (AMBER99SB-ILDN, CHARMM22/CMAP, and OPLS-AA/L). On the low microsecond time scale, these force fields permit isomerization of nonprolyl peptide bonds at temperatures ≥500 K, and the CHARMM22/CMAP force field permits isomerization of prolyl peptide bonds ≥400 K. Moreover, the OPLS-AA/L force field allows chiral inversion about the Cα atom at 800 K. Finally, we show that temperature replica exchange permits cis peptide bonds developed at 540 K to subsequently migrate back to the 300 K ensemble, where cis peptide bonds are present in 2 ± 1% of the population of Trp-cage TC5b, including up to 4% of its folded state. Further work is required to assess the accuracy of cis/trans isomerization in the current generation of protein force fields.

Demonstrating an Order-of-Magnitude Sampling Enhancement in Molecular Dynamics Simulations of Complex Protein Systems

Molecular dynamics (MD) simulations can describe protein motions in atomic detail, but transitions between protein conformational states sometimes take place on time scales that are infeasible or very expensive to reach by direct simulation. Enhanced sampling methods, the aim of which is to increase the sampling efficiency of MD simulations, have thus been extensively employed. The effectiveness of such methods when applied to complex biological systems like proteins, however, has been difficult to establish because even enhanced sampling simulations of such systems do not typically reach time scales at which convergence is extensive enough to reliably quantify sampling efficiency. Here, we obtain sufficiently converged simulations of three proteins to evaluate the performance of simulated tempering, a member of a widely used class of enhanced sampling methods that use elevated temperature to accelerate sampling. Simulated tempering simulations with individual lengths of up to 100 μs were compared to (previously published) conventional MD simulations with individual lengths of up to 1 ms. With two proteins, BPTI and ubiquitin, we evaluated the efficiency of sampling of conformational states near the native state, and for the third, the villin headpiece, we examined the rate of folding and unfolding. Our comparisons demonstrate that simulated tempering can consistently achieve a substantial sampling speedup of an order of magnitude or more relative to conventional MD.

Simulated Solute Tempering

For the enhanced conformational sampling in molecular dynamics (MD) simulations, we present "simulated solute tempering" (SST) which is an easy to implement variant of simulated tempering. SST extends conventional simulated tempering (CST) by key concepts of "replica exchange with solute tempering" (REST, Liu et al. Proc. Natl. Acad. Sci. U.S.A. 2005, 102, 13749). We have applied SST, CST, and REST to molecular dynamics (MD) simulations of an alanine octapeptide in explicit water. The weight parameters required for CST and SST are determined by two different formulas whose performance is compared. For SST only one of them yields a uniform sampling of the temperature space. Compared to CST and REST, SST provides the highest exchange probabilities between neighboring rungs in the temperature ladder. Concomitantly, SST leads to the fastest diffusion of the simulation system through the temperature space, in particular, if the "even-odd" exchange scheme is employed in SST. As a result, SST exhibits the highest sampling speed of the investigated tempering methods.

How Efficient Is Replica Exchange Molecular Dynamics? An Analytic Approach

Replica exchange molecular dynamics (REMD) has become a standard technique for accelerating relaxation in biosimulations. Despite its widespread use, questions remain about its efficiency compared with conventional, constant temperature molecular dynamics (MD). An analytic approach is taken to describe the relative efficiency of REMD with respect to MD. This is applied to several simple two-state models and to several real proteins-protein L and the B domain of protein A-to predict the relative efficiency of REMD with respect to MD in actual applications. In agreement with others, we find the following: as long as there is a positive activation energy for folding, REMD is more efficient than MD; the effectiveness of REMD is strongly dependent on the activation enthalpy; and the efficiency of REMD for actual proteins is a strong function of the maximum temperature. Choosing the maximum temperature too high can result in REMD becoming significantly less efficient than conventional MD. A good rule of thumb appears to be to choose the maximum temperature of the REMD simulation slightly above the temperature at which the enthalpy for folding vanishes. Additionally, we find that the number of replicas in REMD, while important for simulations shorter than one or two relaxation times, has a minimal effect on the asymptotic efficiency of the method.

Effective Approximation of Molecular Volume Using Atom-Centered Dielectric Functions in Generalized Born Models

The generalized Born (GB) theory is a prime choice for implicit treatment of solvent that provides a favorable balance between efficiency and accuracy for reliable simulation of protein conformational equilibria. In GB, the dielectric boundary is a key physical property that needs to be properly described. While it is widely accepted that the molecular surface (MS) should provide the most physical description, most existing GB models are based on van der Waals (vdW)-like surfaces for computational simplicity and efficiency. A simple and effective approximation to molecular volume is explored here using atom-centered dielectric functions within the context of a generalized Born model with simple switching (GBSW). The new model, termed GBSW/MS2, is as efficient as the original vdW-like-surface-based GBSW model, but is able to reproduce the Born radii calculated from the "exact" Poisson-Boltzmann theory with a correlation of 0.95. More importantly, examination of the potentials of mean force of hydrogen-bonding and charge-charge interactions demonstrates that GBSW/MS2 correctly captures the first desolvation peaks, a key signature of true MS. Physical parameters including atomic input radii and peptide backbone torsion were subsequently optimized on the basis of solvation free energies of model compounds, potentials of mean force of their interactions, and conformational equilibria of a set of helical and β-hairpin model peptides. The resulting GBSW/MS2 protein force field reasonably recapitulates the structures and stabilities of these model peptides. Several remaining limitations and possible future developments are also discussed.

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.

Multiscale enhanced sampling of intrinsically disordered protein conformations

In a recently developed multiscale enhanced sampling (MSES) technique, topology-based coarse-grained (CG) models are coupled to atomistic force fields to enhance the sampling of atomistic protein conformations. Here, the MSES protocol is refined by designing more sophisticated Hamiltonian/temperature replica exchange schemes that involve additional parameters in the MSES coupling restraint potential, to more carefully control how conformations are coupled between the atomistic and CG models. A specific focus is to derive an optimal MSES protocol for simulating conformational ensembles of intrinsically disordered proteins (IDPs). The efficacy of the refined protocols, referred to as MSES-soft asymptote (SA), was evaluated using two model peptides with various levels of residual helicities. The results show that MSES-SA generates more reversible helix-coil transitions and leads to improved convergence on various ensemble conformational properties. This study further suggests that more detailed CG models are likely necessary for more effective sampling of local conformational transition of IDPs. © 2015 Wiley Periodicals, Inc.

Improving the replica-exchange molecular-dynamics method for efficient sampling in the temperature space

Replica-exchange molecular dynamics (REMD) is a popular sampling method in the molecular simulation. By frequently exchanging the replicas at different temperatures, the molecule can jump out of the minima and sample efficiently in the conformational space. Although REMD has been shown to be practical in a lot of applications, it does have a critical limitation. All the replicas at all the temperatures must be simulated for a period between the replica-exchange steps. This may be problematic for the reaction with high free energy barriers. In that case, too many replicas are required in the simulation. To reduce the calculation quantity and improve its performance, in this paper we propose a modified REMD method. During the simulation, each replica at each temperature can stay in either the active or inactive state and only switch between the states at the exchange step. In the active state, the replica moves freely in the canonical ensemble by the normal molecular dynamics, and in the inactive state, the replica is frozen temporarily until the next exchange step. The number of the replicas in the active states (active replicas) depends on the number of CPUs in the computer. Using the additional inactive replicas, one can perform an REMD simulation in a wider temperature space. The practical applications show that the modified REMD method is reliable. With the same number of active replicas, this REMD method can produce a more reasonable free energy surface around the free energy minima than the standard REMD method.