Well-tempered Ensemble Research Articles

Solvent Dependent Folding of an Amphiphilic Polyaramid.

A series of synthetic alternating and amphiphilic aromatic amide polymers were synthesized by a step growth polymerization. Alternating meta- and para-linkages were introduced to force the polymer chain into a helical shape in the highly polar solvent water. The polymers were analyzed by 1H NMR spectroscopy and SEC in polar aprotic solvents such as DMSO and DMF. However, the polymers also showed good solubility in water. 1H NMR spectroscopy, small-angle X-ray scattering, and dynamic light scattering provided clear evidence of polymer folding in water but not DMF. We employed parallel tempering metadynamics in the well-tempered ensemble (PTMetaD-WTE) to simulate the free energy surfaces of an analogous model polymer in DMF and water. The simulations gave a molecular model of an unfolded structure in DMF and a helically folded tubular structure in water.

Molecular View on the iRGD Peptide Binding Mechanism: Implications for Integrin Activity and Selectivity Profiles.

Receptor-selective peptides are widely used as smart carriers for specific tumor-targeted delivery. A remarkable example is the cyclic nonapeptide iRGD (CRGDKPGDC, 1) that couples intrinsic cytotoxic effects with striking tumor-homing properties. These peculiar features are based on a rather complex multistep mechanism of action, where the primary event is the recognition of RGD integrins. Despite the high number of preclinical studies and the recent success of a phase I trial for the treatment of pancreatic ductal adenocarcinoma (PDAC), there is little information available about the iRGD three-dimensional (3D) structure and integrin binding properties. Here, we re-evaluate the peptide's affinity for cancer-related integrins including not only the previously known targets αvβ3 and αvβ5 but also the αvβ6 isoform, which is known to drive cell growth, migration, and invasion in many malignancies including PDAC. Furthermore, we use parallel tempering in the well-tempered ensemble (PT-WTE) metadynamics simulations to characterize the in-solution conformation of iRGD and extensive molecular dynamics calculations to fully investigate its binding mechanism to integrin partners. Finally, we provide clues for fine-tuning the peptide's potency and selectivity profile, which, in turn, may further improve its tumor-homing properties.

Predicting protein-membrane interfaces using molecular simulations and ensemble machine learning.

Abnormal protein-membrane attachment is involved in deregulated cellular pathways and in disease. The possibility to modulate protein-membrane interactions represents a new promising therapeutic strategy for membrane proteins. In this talk, we explore the free energy landscape of membrane protein dimerization using parallel tempering metadynamics simulations in the well-tempered ensemble and coarse-grained force fields and reproduce the structure and energetics of the dimerization process of membrane proteins and proteins in an aqueous solution in reasonable accuracy and throughput. We propose that the use of enhanced sampling simulations with a refined coarse-grained force field and appropriately defined collective variables is a robust approach for studying the protein dimerization process, although one should be cautious of the energy minima ranking. Moreover, we study oncogenes, including the H1047R and E545K hotspot mutants of PI3Kα, and KRAS-4B to understand the basis of protein overactivation. We calculate their allosteric pathways and show residues important in delivering communication signals between functional domains of each protein. Finally, we describe an ensemble machine learning methodology to predict protein-membrane interfaces of peripheral membrane proteins and present a drug design pipeline for drugging protein-membrane interfaces using the DREAMM web-server https://dreamm.ni4os.eu. Taking into account these results, we investigate opportunities for allosteric drug design.

Binding modes of prothrombin cleavage site sequences to the factor Xa catalytic triad: Insights from atomistic simulations

Prothrombin is a key zymogen of the coagulation process and can be converted to thrombin by the prothrombinase complex, which consists of factor Xa (FXa), cofactor Va (FVa), and phospholipids. Prothrombin can be activated at two cleavage sites, R271 and R320, which generates two intermediates: prethrombin-2 via the initial cleavage at R271, and meizothrombin via the first cleavage at R320. Several mechanisms have been proposed to explain this activation preference, but the role of cleavage site sequences in prothrombin activation has not been thoroughly investigated. Here, we used an advanced sampling technique, parallel tempering metadynamics with a well-tempered ensemble (PTMetaD-WTE), to study the binding modes of prothrombin cleavage site sequences R266AIEGRTATSEY277 (denoted as Pep271) and S315YIDGRIVEGSD326 (denoted as Pep320) to the FXa catalytic triad. Our study indicates that there exist three binding modes for Pep271 to the FXa catalytic triad but only one binding mode for Pep320 to the FXa catalytic triad. Further molecular dynamics simulations revealed that due to the strong electrostatic interactions, especially the H-bond interactions and salt bridges formed between Pep320 and FXa, the binding mode in the Pep320-FXa system is more stable than the binding modes in the Pep271-FXa system. In view of experimental observations and our results that there exists only one binding mode for Pep320 to the FXa catalytic triad and especially R320 in Pep320 can stably bind to the FXa catalytic triad, we believe that the first cleavage at R320 is favored.

Metadynamics Simulations to Study the Structural Ensembles and Binding Processes of Intrinsically Disordered Proteins.

The structures of intrinsically disordered proteins (IDPs) are highly dynamic. It is hard to characterize the structures of these proteins experimentally. Molecular dynamics (MD) simulation is a powerful tool in the understanding of protein dynamic structures and function. This chapter describes the application of metadynamics-based enhanced sampling methods in the study of phosphorylation regulation on the structure of kinase-inducible domains (KID). The structural properties of free pKID and KID were obtained by parallel tempering metadynamics combined with well-tempered ensemble (PTMetaD WTE) method, and the binding free energy surfaces of pKID/KID and KIX were characterized by bias-exchanged metadynamics (BE-MetaD) simulations.

Evaluating the Efficiency of the Martini Force Field to Study Protein Dimerization in Aqueous and Membrane Environments.

Protein-protein complex assembly is one of the major drivers of biological response. Understanding the mechanisms of protein oligomerization/dimerization would allow one to elucidate how these complexes participate in biological activities and could ultimately lead to new approaches in designing novel therapeutic agents. However, determining the exact association pathways and structures of such complexes remains a challenge. Here, we use parallel tempering metadynamics simulations in the well-tempered ensemble to evaluate the performance of Martini 2.2P and Martini open-beta 3 (Martini 3) force fields in reproducing the structure and energetics of the dimerization process of membrane proteins and proteins in an aqueous solution in reasonable accuracy and throughput. We find that Martini 2.2P systematically overestimates the free energy of association by estimating large barriers in distinct areas, which likely leads to overaggregation when multiple monomers are present. In comparison, the less viscous Martini 3 results in a systematic underestimation of the free energy of association for proteins in solution, while it performs well in describing the association of membrane proteins. In all cases, the near-native dimer complexes are identified as minima in the free energy surface albeit not always as the lowest minima. In the case of Martini 3, we find that the spurious supramolecular protein aggregation present in Martini 2.2P multimer simulations is alleviated and thus this force field may be more suitable for the study of protein oligomerization. We propose that the use of enhanced sampling simulations with a refined coarse-grained force field and appropriately defined collective variables is a robust approach for studying the protein dimerization process, although one should be cautious of the ranking of energy minima.

Fundamental Challenges and Outlook in Simulating Liquid–Liquid Phase Separation of Intrinsically Disordered Proteins

Intrinsically disordered proteins (IDPs) populate an ensemble of dynamic conformations, making their structural characterization by experiments challenging. Many IDPs undergo liquid-liquid phase separation into dense membraneless organelles with myriad cellular functions. Multivalent interactions in low-complexity IDPs promote the formation of these subcellular coacervates. While solution NMR, Förster resonance energy transfer (FRET), and small-angle X-ray scattering (SAXS) studies on IDPs have their own challenges, recent computational methods draw a rational trade-off to characterize the driving forces underlying phase separation. In this Perspective, we critically evaluate the scope of approximation-free field theoretic simulations, well-tempered ensemble methods, enhanced sampling techniques, coarse-grained force fields, and slab simulation approaches to offer an improved understanding of phase separation. A synergy between simulation length scale and model resolution would reduce the existing caveats and enable theories of polymer physics to elucidate finer details of liquid-liquid phase separation (LLPS). These computational advances offer promise for rigorous characterization of the IDP proteome and designing peptides with tunable material and self-assembly properties.

Impact of Glutamate Carboxylation in the Adsorption of the α-1 Domain of Osteocalcin to Hydroxyapatite and Titania.

One proposed mechanism of implant fouling is attributed to the nonspecific adsorption of non-collagenous bone matrix proteins (NCPs) onto a newly implanted interface. With the goal of capturing the fundamental mechanistic and thermodynamic forces that govern changes in these NCP recognition domains as a function of γ-carboxyglutamic acid (Gla) post-translational modification and surface chemistry, we probe the adsorption process of the most commonly occurring NCP, osteocalcin, onto a mineral and metal oxide surface. Here, we apply two enhanced sampling methods to independently probe the effects of post-translational modification and peptide structure on adsorption. First, well-tempered metadynamics was used to capture the binding of acetyl and N-methylamide capped glutamic acid and Gla single amino acids onto crystalline hydroxyapatite and titania model surfaces at physiological pH. Following this, parallel tempering metadynamics in the well-tempered ensemble (PTMetaD-WTE) was used to study adsorption of the α-1 domain of osteocalcin onto hydroxyapatite and titania. Simulations were performed for the α-1 domain of osteocalcin in both its fully decarboxylated (dOC) and fully carboxylated (OC) form. Our simulations find that increased charge density due to carboxylation results in increased interactions at the interface, and stronger adsorption of the single amino acids to both surfaces. Interestingly, the role of Gla in promoting compact and helical structure in the α-1 domain resulted in disparate binding modes at the two surfaces, which is attributed to differences in interfacial water behavior. Overall, this work provides a benchmark for understanding the mechanisms that drive adsorption of Gla-containing mineralizing proteins onto different surface chemistries.

Enhanced Molecular Dynamics Simulations of Intrinsically Disordered Proteins.

Molecular dynamics simulations represent a powerful tool to gain insights into structural and dynamical features of biomolecular systems. Nevertheless, their recognized limitation in terms of achievable timescales becomes particularly severe when dealing with slow processes. In such cases, the employment of enhanced sampling methods, which allow accelerating the characterization of rare events in a timeframe consistent with conventional computational resources, results as crucial. In particular, such advanced techniques have proven highly valuable in the context of protein folding and, specifically, to explore the conformational ensemble spanned by intrinsically disordered proteins (IDPs). Here, we describe how to set up molecular dynamics simulations with one of these enhanced sampling approaches (namely, Parallel Tempering Metadynamics in the Well-Tempered Ensemble) using the NTAIL peptide as a test case.

Insulin dimer dissociation in aqueous solution: A computational study of free energy landscape and evolving microscopic structure along the reaction pathway

The dissociation of an insulin dimer to two monomers is an important life process. Although the monomer is the biologically active form of the hormone, it is stored in the β-cells of the pancreas in the hexameric form. The latter, when the need comes, dissociates to dimers and the dimers in turn to monomers to maintain the endogenous delivery of the hormone. In order to understand insulin dimer dissociation at a molecular level, we perform biased molecular dynamics simulations (parallel tempering metadynamics in the well-tempered ensemble) of the dissociation of the insulin dimer in water using two order parameters and an all-atom model of the protein in explicit water. The two order parameters selected (after appropriate studies) are the distance (RMM) between the center of mass of two monomers and the number of contacts (NMM) among the backbone-Cα atoms of the two monomers. We calculated the free energy landscape as a function of these two order parameters and determined the minimum free energy pathway of dissociation. We find that the pathway involves multiple minima and multiple barriers. In the initial stage of dissociation, the distance between the monomers does not change significantly but the NMM decreases rapidly. In the latter stage of separation, the opposite occurs, that is, the distance RMM increases at nearly a constant low value of NMM. The configurations of the two monomeric proteins so formed are found to be a bit different due to the entropic reasons. Water is seen to play a key role in the dissociation process stabilizing the intermediates along the reaction path. Our study reveals interesting molecular details during the dissociation, such as the variation in the structural and relative orientational arrangement of the amino acid residues along the minimum energy path. The conformational changes of monomeric insulin in the stable dimer and in the intermediate states during dimer dissociation have been studied in detail.

Optimization of replica exchange temperature ladder under the well-tempered ensemble

Selection of temperature sequence and bias factor is a critical step for the preparation of Parallel Tempering simulations in a Well-Tempered Ensemble (PT-WTE). We provide a scheme in this study to generate the temperature sequence and the corresponding bias factor optimally. The number of replicas for a complete coverage of a specific temperature range is adjustable in this scheme, while keeping the average acceptance probability (AAP) between neighboring replica-pairs unchanged. Two series of PT-WTE simulations were tested with the number of replicas as 16 and 8 respectively. This work leads to a better understanding and application of PT-WTE simulations.

Combining enhanced sampling with experiment-directed simulation of the GYG peptide

Experiment-directed simulation (EDS) is a technique to minimally bias molecular dynamics simulations to match experimentally observed results. The method improves accuracy but does not address the sampling problem of molecular dynamics simulations of large systems. This work combines EDS with both the parallel-tempering or parallel-tempering well-tempered ensemble replica-exchange methods to enhance sampling. These methods are demonstrated on the GYG tripeptide in explicit water. The collective variables biased by EDS are chemical shifts, where the set-points are determined by NMR experiments. The results show that it is possible to enhance sampling with either parallel-tempering and parallel-tempering well-tempered ensemble in the EDS method. This combination of methods provides a novel approach for both accurately and exhaustively simulating biological systems.

Binding Modes of Teixobactin to Lipid II: Molecular Dynamics Study

Teixobactin (TXB) is a newly discovered antibiotic targeting the bacterial cell wall precursor Lipid II (LII). In the present work, four binding modes of TXB on LII were identified by a contact-map based clustering method. The highly flexible binary complex ensemble was generated by parallel tempering metadynamics simulation in a well-tempered ensemble (PTMetaD-WTE). In agreement with experimental findings, the pyrophosphate group and the attached first sugar subunit of LII are found to be the minimal motif for stable TXB binding. Three of the four binding modes involve the ring structure of TXB and have relatively higher binding affinities, indicating the importance of the ring motif of TXB in LII recognition. TXB-LII complexes with a ratio of 2:1 are also predicted with configurations such that the ring motif of two TXB molecules bound to the pyrophosphate-MurNAc moiety and the glutamic acid residue of one LII, respectively. Our findings disclose that the ring motif of TXB is critical to LII binding and novel antibiotics can be designed based on its mimetics.

Prion protein β2–α2 loop conformational landscape

In transmissible spongiform encephalopathies (TSEs), which are lethal neurodegenerative diseases that affect humans and a wide range of other mammalian species, the normal "cellular" prion protein ([Formula: see text]) is transformed into amyloid aggregates representing the "scrapie form" of the protein ([Formula: see text]). Continued research on this system is of keen interest, since new information on the physiological function of [Formula: see text] in healthy organisms is emerging, as well as new data on the mechanism of the transformation of [Formula: see text] to [Formula: see text] In this paper we used two different approaches: a combination of the well-tempered ensemble (WTE) and parallel tempering (PT) schemes and metadynamics (MetaD) to characterize the conformational free-energy surface of [Formula: see text] The focus of the data analysis was on an 11-residue polypeptide segment in mouse [Formula: see text](121-231) that includes the [Formula: see text]2-[Formula: see text]2 loop of residues 167-170, for which a correlation between structure and susceptibility to prion disease has previously been described. This study includes wild-type mouse [Formula: see text] and a variant with the single-residue replacement Y169A. The resulting detailed conformational landscapes complement in an integrative manner the available experimental data on [Formula: see text], providing quantitative insights into the nature of the structural transition-related function of the [Formula: see text]2-[Formula: see text]2 loop.

Essential slow degrees of freedom in protein-surface simulations: A metadynamics investigation

Many proteins exhibit strong binding affinities to surfaces, with binding energies much greater than thermal fluctuations. When modelling these protein-surface systems with classical molecular dynamics (MD) simulations, the large forces that exist at the protein/surface interface generally confine the system to a single free energy minimum. Exploring the full conformational space of the protein, especially finding other stable structures, becomes prohibitively expensive. Coupling MD simulations with metadynamics (enhanced sampling) has fast become a common method for sampling the adsorption of such proteins. In this paper, we compare three different flavors of metadynamics, specifically well-tempered, parallel-bias, and parallel-tempering in the well-tempered ensemble, to exhaustively sample the conformational surface-binding landscape of model peptide GGKGG. We investigate the effect of mobile ions and ion charge, as well as the choice of collective variable (CV), on the binding free energy of the peptide. We make the case for explicitly biasing ions to sample the true binding free energy of biomolecules when the ion concentration is high and the binding free energies of the solute and ions are similar. We also make the case for choosing CVs that apply bias to all atoms of the solute to speed up calculations and obtain the maximum possible amount of information about the system.

Sampling conformational space of intrinsically disordered proteins in explicit solvent: Comparison between well-tempered ensemble approach and solute tempering method

Intrinsically disordered proteins (IDPs) are a class of proteins that expected to be largely unstructured under physiological conditions. Due to their heterogeneous nature, experimental characterization of IDP is challenging. Temperature replica exchange molecular dynamics (T-REMD) is a widely used enhanced sampling method to probe structural characteristics of these proteins. However, its application has been hindered due to its tremendous computational cost, especially when simulating large systems in explicit solvent. Two methods, parallel tempering well-tempered ensemble (PT-WTE) and replica exchange with solute tempering (REST), have been proposed to alleviate the computational expense of T-REMD. In this work, we select three different IDP systems to compare the sampling characteristics and efficiencies of the two methods Both the two methods could efficiently sample the conformational space of IDP and yield highly consistent results for all the three IDPs. The efficiencies of the two methods: are compatible, with about 5–6 times better than the plain T-REMD. Besides, the advantages and disadvantages of each method are also discussed. Specially, the PT-WTE method could provide temperature dependent data of the system which could not be achieved by REST, while the REST method could readily be used to a part of the system, which is quite efficient to simulate some biological processes.

Effects of Polymer Conjugation on Hybridization Thermodynamics of Oligonucleic Acids.

In this work, we perform coarse-grained (CG) and atomistic simulations to study the effects of polymer conjugation on hybridization/melting thermodynamics of oligonucleic acids (ONAs). We present coarse-grained Langevin molecular dynamics simulations (CG-NVT) to assess the effects of the polymer flexibility, length, and architecture on hybridization/melting of ONAs with different ONA duplex sequences, backbone chemistry, and duplex concentration. In these CG-NVT simulations, we use our recently developed CG model of ONAs in implicit solvent, and treat the conjugated polymer as a CG chain with purely repulsive Weeks-Chandler-Andersen interactions with all other species in the system. We find that 8-100-mer linear polymer conjugation destabilizes 8-mer ONA duplexes with weaker Watson-Crick hydrogen bonding (WC H-bonding) interactions at low duplex concentrations, while the same polymer conjugation has an insignificant impact on 8-mer ONA duplexes with stronger WC H-bonding. To ensure the configurational space is sampled properly in the CG-NVT simulations, we also perform CG well-tempered metadynamics simulations (CG-NVT-MetaD) and analyze the free energy landscape of ONA hybridization for a select few systems. We demonstrate that CG-NVT-MetaD simulation results are consistent with the CG-NVT simulations for the studied systems. To examine the limitations of coarse-graining in capturing ONA-polymer interactions, we perform atomistic parallel tempering metadynamics simulations at well-tempered ensemble (AA-MetaD) for a 4-mer DNA in explicit water with and without conjugation to 8-mer poly(ethylene glycol) (PEG). AA-MetaD simulations also show that, for a short DNA duplex at T = 300 K, a condition where the DNA duplex is unstable, conjugation with PEG further destabilizes DNA duplex. We conclude with a comparison of results from these three different types of simulations and discuss their limitations and strengths.

Computational Insights into the Stability and Folding Pathways of Human Telomeric DNA G-Quadruplexes.

G-quadruplex is a noncanonical yet crucial secondary structure of nucleic acids, which has proven its importance in cell aging, anticancer therapies, gene expression, and genome stability. In this study, the stability and folding dynamics of human telomeric DNA G-quadruplexes were investigated via enhanced sampling techniques. First, temperature-replica exchange MD (REMD) simulations were employed to compare the thermal stabilities among the five established folding topologies. The hybrid-2 type adopted by extended human telomeric sequence is revealed to be the most stable conformation in our simulations. Next, the free energy landscapes and folding intermediates of the hybrid-1 and -2 types were investigated with parallel tempering metadynamics simulations in the well-tempered ensemble. It was observed that the N-glycosidic conformations of guanines can flip over to accommodate into the cyclic Hoogsteen H-bonding on G-tetrads in which they were not originally involved. Furthermore, a hairpin and a triplex intermediate were identified for the folding of the hybrid-1 type conformation, whereas for the hybrid-2 type, there were no folding intermediates observed from its free energy surface. However, the energy barrier from its native topology to the transition structure is found to be extremely high compared to that of the hybrid-1 type, which is consistent with our stability predictions from the REMD simulations. We hope the insights presented in this work can help to complement current understanding on the stability and dynamics of G-quadruplexes, which is necessary not only to stabilize the structures but also to intervene their formation in genome.

Strong Electrostatic Interactions Lead to Entropically Favorable Binding of Peptides to Charged Surfaces.

Thermodynamic analyses can provide key insights into the origins of protein self-assembly on surfaces, protein function, and protein stability. However, obtaining quantitative measurements of thermodynamic observables from unbiased classical simulations of peptide or protein adsorption is challenging because of sampling limitations brought on by strong biomolecule/surface binding forces as well as time scale limitations. We used the parallel tempering metadynamics in the well-tempered ensemble (PTMetaD-WTE) enhanced sampling method to study the adsorption behavior and thermodynamics of several explicitly solvated model peptide adsorption systems, providing new molecular-level insight into the biomolecule adsorption process. Specifically studied were peptides LKα14 and LKβ15 and trpcage miniprotein adsorbing onto a charged, hydrophilic self-assembled monolayer surface functionalized with a carboxylic acid/carboxylate headgroup and a neutral, hydrophobic methyl-terminated self-assembled monolayer surface. Binding free energies were calculated as a function of temperature for each system and decomposed into their respective energetic and entropic contributions. We investigated how specific interfacial features such as peptide/surface electrostatic interactions and surface-bound ion content affect the thermodynamic landscape of adsorption and lead to differences in surface-bound conformations of the peptides. Results show that upon adsorption to the charged surface, configurational entropy gains of the released solvent molecules dominate the configurational entropy losses of the bound peptide. This behavior leads to an apparent increase in overall system entropy upon binding and therefore to the surprising and seemingly nonphysical result of an apparent increased binding free energy at elevated temperatures. Opposite effects and conclusions are found for the neutral surface. Additional simulations demonstrate that by adjusting the ionic strength of the solution, results that show the expected physical behavior, i.e., peptide binding strength that decreases with increasing temperature or is independent of temperature altogether, can be recovered on the charged surface. On the basis of this analysis, an overall free energy for the entire thermodynamic cycle for peptide adsorption on charged surfaces is constructed and validated with independent simulations.

Thermodynamical Description of a Quasi-First-Order Phase Transition from the Well-Tempered Ensemble.

We explore the performance of the well-tempered ensemble combined with parallel tempering (PT-WTE) in obtaining a thermodynamical description of a given molecular system. We carefully explain the theoretical procedure employed to extract all the relevant thermodynamical quantities from a PT-WTE simulation. As a specific molecular system, we consider a Lennard-Jones cluster of 147 particles, which is a prototypical case of a finite-size system exhibiting a quasi-first-order phase transition, characterized by a range of temperatures where two distinct phases are thermodynamically stable and coexist. Two separate PT-WTE simulations, which investigate the thermodynamical behavior on different levels of detail, give equally accurate descriptions of the critical phase-coexistence region, indicating the good quality of the PT-WTE results. The positive performance observed here clearly demonstrates that the PT-WTE approach is an effective option when thermodynamical properties are needed.