Protein Folding Simulations Combining Self-Guided Langevin Dynamics and Temperature-Based Replica Exchange

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.

Enhanced sampling and free energy calculations for protein simulations

Molecular dynamics simulation is a powerful computational technique to study biomolecular systems, which complements experiments by providing insights into the structural dynamics relevant to biological functions at atomic scale. It can also be used to calculate the free energy landscapes of the conformational transitions to better understand the functions of the biomolecules. However, the sampling of biomolecular configurations is limited by the free energy barriers that need to be overcome, leading to considerable gaps between the timescales reached by MD simulation and those governing biological processes. To address this issue, many enhanced sampling methodologies have been developed to increase the sampling efficiency of molecular dynamics simulations and free energy calculations. Usually, enhanced sampling algorithms can be classified into methods based on collective variables (CV-based) and approaches which do not require predefined CVs (CV-free). In this chapter, the theoretical basis of free energy estimation is briefly reviewed first, followed by the reviews of the most common CV-based and CV-free methods including the presentation of some examples and recent developments. Finally, the combination of different enhanced sampling methods is discussed.

Unperturbed Detection of the Dynamic Structure in the Hydrophobic Core of Trp-Cage via Two-Dimensional Infrared Spectroscopy

The tyrosine ring mode is an intrinsic non-perturbing site-specific infrared reporter for conformational dynamics within protein systems. This transition is influenced by direct and indirect interactions associated with the electron-donating ability and the hydrophobicity of the surrounding molecules. Utilizing an intrinsic tyrosine moiety, two-dimensional infrared spectra of Trp-cage, often called the "hydrogen atom" of protein folding, were measured in the folded and denatured states to uncover the dynamics of the hydrophobic core. The vibrational lifetimes and the correlation decays of the tyrosine ring mode showed significant changes upon both temperature and chemical denaturation of the Trp-cage miniprotein, indicating important structural features of the hydrophobic core and its dynamics. The observed Trp6-Tyr3 interactions are in good agreement with the prior studies of the folded state, but they reach beyond the static structure. These stacking interactions and orientations fluctuate on the picosecond time scale as measured through the spectral dephasing within a dehydrated environment.

Sequence Tolerance of a Single-Domain Antibody with a High Thermal Stability: Comparison of Computational and Experimental Fitness Profiles

The sequence fitness of a llama single-domain antibody with an unusually high thermal stability is explored by a combined computational and experimental study. Starting with the X-ray crystallographic structure, RosettaBackrub simulations were applied to model sequence-structure tolerance profiles and identify key substitution sites. From the model calculations, an experimental site-directed mutagenesis was used to produce a panel of mutants, and their melting temperatures were determined by thermal denaturation. The results reveal a sequence fitness of an excess stability of approximately 12 °C, a value taken from a decrease in the melting temperature of an electrostatic charge-reversal substitution in the CRD3 without a deleterious effect on the binding affinity to the antigen. The tolerance for the disruption of antigen recognition without loss in the thermal stability was demonstrated by the introduction of a proline in place of a tyrosine in the CDR2, producing a mutant that eliminated binding. To further assist the sequence design and the selection of engineered single-domain antibodies, an assessment of different computational strategies is provided of their accuracy in the detection of substitution "hot spots" in the sequence tolerance landscape.

Molecular basis for the increased affinity of an RNA recognition motif with re-engineered specificity: A molecular dynamics and enhanced sampling simulations study

The RNA recognition motif (RRM) is the most common RNA binding domain across eukaryotic proteins. It is therefore of great value to engineer its specificity to target RNAs of arbitrary sequence. This was recently achieved for the RRM in Rbfox protein, where four mutations R118D, E147R, N151S, and E152T were designed to target the precursor to the oncogenic miRNA 21. Here, we used a variety of molecular dynamics-based approaches to predict specific interactions at the binding interface. Overall, we have run approximately 50 microseconds of enhanced sampling and plain molecular dynamics simulations on the engineered complex as well as on the wild-type Rbfox·pre-miRNA 20b from which the mutated systems were designed. Comparison with the available NMR data on the wild type molecules (protein, RNA, and their complex) served to establish the accuracy of the calculations.

Free energy calculations suggest that further improvements in affinity and selectivity are achieved by the S151T replacement.

RNA is an outstanding target for oncological intervention. Engineering the most common RNA binding motif in human proteins (called RRM) so as to bind to a specific RNA has an enormous pharmacological potential. Yet, it is highly non trivial to design RRM-bearing protein variants with RNA selectivity and affinity sufficiently high for clinical applications. Here we present an extensive molecular simulation study which shed light on the exquisite molecular recognition of the empirically-engineered complex between the RRM-bearing protein Rbfox and its RNA target pre-miR21. The simulations allow predicting a variant, the S151T, which may lead to further enhancement of selectivity and affinity for pre-miR21.

Conformational Selection of a Polyproline Peptide by Ebola Virus VP30

An adaptive temperature-based replica-exchange simulation of a peptide extracted from the Ebola virus nucleoprotein containing a polyproline sequence motif is reported. The simulation results of applying the CHARMM36m force field with a generalized Born solvent model is presented. Conformational heterogeneity is described by potentials of mean force (PMFs) for a set of reaction coordinates that define the topological fold space. Starting from an extended backbone conformation of the peptide observed in an X-ray crystallographic assembly with the Ebola virus protein VP30, the PMFs report a conformational landscape populated by chain excursions to collapsed states with limited transitions to either an extended fold or a canonical polyproline type II helix. Clustering of the conformations and applying an elastic network interpolation model yield a multistep pathway of conformational selection that minimizes the net transition-state cost from the population hub to the bound state. Related difference between the pathway endpoints taken from the PMFs reveal a significant free-energy penalty in reaching a population shift. To evaluate sequence fitness of the Ebola virus peptide in generating probability distributions, two human sequence variants are modeled and are found to produce profiles that show extensive deviations, thus suggesting either dissimilar binding mechanisms or the lack of recognition by VP30.

Parallel Tempering of Dark Matter from the Ebola Virus Proteome: Comparison of CHARMM36m and CHARMM22 Force Fields with Implicit Solvent

Intrinsically disordered proteins are characterized by their large manifold of thermally accessible conformations and their related statistical weights, making them an interesting target of simulation studies. To assess the development of a computational framework for modeling this distinct class of proteins, this work examines temperature-based replica-exchange simulations to generate a conformational ensemble of a 28-residue peptide from the Ebola virus protein VP35. Starting from a prefolded helix-β-turn-helix topology observed in a crystallographic assembly, the simulation strategy tested is the recently refined CHARMM36m force field combined with a generalized Born solvent model. A comparison of two replica-exchange methods is provided, where one is a traditional approach with a fixed set of temperatures and the other is an adaptive scheme in which the thermal windows are allowed to move in temperature space. The assessment is further extended to include a comparison with equivalent CHARMM22 simulation data sets. The analysis finds CHARMM36m to shift the minimum in the potential of mean force (PMF) to a lower fractional helicity compared with CHARMM22, while the latter showed greater conformational plasticity along the helix-forming reaction coordinate. Among the simulation models, only the adaptive tempering method with CHARMM36m found an ensemble of conformational heterogeneity consisting of transitions between α-helix-β-hairpin folds and unstructured states that produced a PMF of fractional fold propensity in qualitative agreement with circular dichroism experiments reporting a disordered peptide.

Computational protein structure refinement: Almost there, yet still so far to go

Protein structures are essential in modern biology yet experimental methods are far from being able to catch up with the rapid increase in available genomic data. Computational protein structure prediction methods aim to fill the gap while the role of protein structure refinement is to take approximate initial template-based models and bring them closer to the true native structure. Current methods for computational structure refinement rely on molecular dynamics simulations, related sampling methods, or iterative structure optimization protocols. The best methods are able to achieve moderate degrees of refinement but consistent refinement that can reach near-experimental accuracy remains elusive. Key issues revolve around the accuracy of the energy function, the inability to reliably rank multiple models, and the use of restraints that keep sampling close to the native state but also limit the degree of possible refinement. A different aspect is the question of what exactly the target of high-resolution refinement should be as experimental structures are affected by experimental conditions and different biological questions require varying levels of accuracy. While improvement of the global protein structure is a difficult problem, high-resolution refinement methods that improves local structural quality such as favorable stereochemistry and the avoidance of atomic clashes are much more successful.

On the Helix Propensity in Generalized Born Solvent Descriptions of Modeling the Dark Proteome

Intrinsically disordered proteins that populate the so-called “Dark Proteome” offer challenging benchmarks of atomistic simulation methods to accurately model conformational transitions on a multidimensional energy landscape. This work explores the application of parallel tempering with implicit solvent models as a computational framework to capture the conformational ensemble of an intrinsically disordered peptide derived from the Ebola virus protein VP35. A recent X-ray crystallographic study reported a protein-peptide interface where the VP35 peptide underwent a folding transition from a disordered form to a helix-β-turn-helix topological fold upon molecular association with the Ebola protein NP. An assessment is provided of the accuracy of two generalized Born solvent models (GBMV2 and GBSW2) using the CHARMM force field and applied with temperature-based replica exchange dynamics to calculate the disorder propensity of the peptide and its probability density of states in a continuum solvent. A further comparison is presented of applying an explicit/implicit solvent hybrid replica exchange simulation of the peptide to determine the effect of modeling water interactions at the all-atom resolution.

Comparison of Replica Exchange Simulations of a Kinetically Trapped Protein Conformational State and its Native Form

Recently an X-ray crystallographic structure of a single-domain antibody was reported with the protein chain trapped in a rare homodimeric form. One of the conformers appears to exhibit a misfolded region, and thus presumably the configurational stability is less favorable. To investigate whether simulation methods can detect any difference between the conformers and buttress the notion that one conformation is trapped on a pathway that incurs lower activation energy to unfold, adaptive temperature-based replica exchange simulations were applied to each chain to model conformational transitions. Simulation results found that the observed crystallographic difference between the two chains in the complementarity determining region CDR2 induces a stark distinction in conformational populations on the energy landscape. An appraisal of the energetic difference between the CDR2 conformations at 300 K revealed a localized order-disorder free-energy transition of roughly equivalent to two peptide hydrogen bonds in solution. It was also found that interconversion between the conformers is slower than the rate to unfold and that near an unfolding transition temperature one conformer retained a greater fraction of native-like contacts and energy over a longer time span before fully populating the denatured state, thus verifying the coexistence of a metastable conformation in the crystallographic assembly.

Can template-based protein models guide the design of sequence fitness for enhanced thermal stability of single domain antibodies?

We investigate the practical use of comparative (template-based) protein models in replica-exchange simulations of single-domain antibody (sdAb) chains to evaluate if the models can correctly predict in rank order the thermal susceptibility to unfold relative to experimental melting temperatures. The baseline model system is the recently determined crystallographic structure of a llama sdAb (denoted as A3), which exhibits an unusually high thermal stability. An evaluation of the simulation results for the A3 comparative model and crystal structure shows that, despite the overall low Cα root-mean-square deviation between the two structures, the model contains misfolded regions that yields a thermal profile of unraveling at a lower temperature. Yet comparison of the simulations of four different comparative models for sdAb A3, C8, A3C8 and E9, where A3C8 is a design of swapping the sequence of the complementarity determining regions of C8 onto the A3 framework, discriminated among the sequences to detect the highest and lowest experimental melting transition temperatures. Further structural analysis of A3 for selected alanine substitutions by a combined computational and experimental study found unexpectedly that the comparative model performed admirably in recognizing substitution 'hot spots' when using a support-vector machine algorithm.

Evaluation of disulfide bond position to enhance the thermal stability of a highly stable single domain antibody

Single domain antibodies are the small recombinant variable domains derived from camelid heavy-chain-only antibodies. They are renowned for their stability, in large part due to their ability to refold following thermal or chemical denaturation. In addition to refolding after heat denaturation, A3, a high affinity anti-Staphylococcal Enterotoxin B single domain antibody, possesses a melting temperature of ∼84°C, among the highest reported for a single domain antibody. In this work we utilized the recently described crystal structure of A3 to select locations for the insertion of a second disulfide bond and evaluated the impact that the addition of this second bond had on the melting temperature. Four double-disulfide versions of A3 were constructed and each was found to improve the melting temperature relative to the native structure without reducing affinity. Placement of the disulfide bond at a previously published position between framework regions 2 and 3 yielded the largest improvement (>6°C), suggesting this location is optimal, and seemingly provides a universal route to raise the melting temperature of single domain antibodies. This study further demonstrates that even single domain antibodies with extremely high melting points can be further stabilized by addition of disulfide bonds.

Evaluation of unrestrained replica-exchange simulations using dynamic walkers in temperature space for protein structure refinement

A central problem of computational structural biology is the refinement of modeled protein structures taken from either comparative modeling or knowledge-based methods. Simulations are commonly used to achieve higher resolution of the structures at the all-atom level, yet methodologies that consistently yield accurate results remain elusive. In this work, we provide an assessment of an adaptive temperature-based replica exchange simulation method where the temperature clients dynamically walk in temperature space to enrich their population and exchanges near steep energetic barriers. This approach is compared to earlier work of applying the conventional method of static temperature clients to refine a dataset of conformational decoys. Our results show that, while an adaptive method has many theoretical advantages over a static distribution of client temperatures, only limited improvement was gained from this strategy in excursions of the downhill refinement regime leading to an increase in the fraction of native contacts. To illustrate the sampling differences between the two simulation methods, energy landscapes are presented along with their temperature client profiles.

Comparison of volume and surface area nonpolar solvation free energy terms for implicit solvent simulations

Implicit solvent models for molecular dynamics simulations are often composed of polar and nonpolar terms. Typically, the nonpolar solvation free energy is approximated by the solvent-accessible-surface area times a constant factor. More sophisticated approaches incorporate an estimate of the attractive dispersion forces of the solvent and∕or a solvent-accessible volume cavitation term. In this work, we confirm that a single volume-based nonpolar term most closely fits the dispersion and cavitation forces obtained from benchmark explicit solvent simulations of fixed protein conformations. Next, we incorporated the volume term into molecular dynamics simulations and find the term is not universally suitable for folding up small proteins. We surmise that while mean-field cavitation terms such as volume and SASA often tilt the energy landscape towards native-like folds, they also may sporadically introduce bottlenecks into the folding pathway that hinder the progression towards the native state.

Application of replica exchange umbrella sampling to protein structure refinement of nontemplate models

We provide an assessment of a computational strategy for protein structure refinement that combines self-guided Langevin dynamics with umbrella-potential biasing replica exchange using the radius of gyration as a coordinate (Rg -ReX). Eight structurally nonredundant proteins and their decoys were examined by sampling conformational space at room temperature using the CHARMM22/GBMV2 force field to generate the ensemble of structures. Two atomic statistical potentials (RWplus and DFIRE) were analyzed for structure identification and compared to the simulation force-field potential. The results show that, while the Rg -ReX simulations were able to sample conformational basins that were more structurally similar to the X-ray crystallographic structures than the starting first-order ranked decoys, the potentials failed to detect these basins from refinement. Of the three potential functions, RWplus yielded the highest accuracy for recognition of structures that refined to an average of nearly 20% increase in native contacts relative to the starting decoys. The overall performance of Rg -ReX is compared to an earlier study of applying temperature-based replica exchange to refine the same decoy sets and highlights the general challenge of achieving consistently the sampling and detection threshold of 70% fraction of native contacts.

Replica exchanging self-guided Langevin dynamics for efficient and accurate conformational sampling

This work presents a replica exchanging self-guided Langevin dynamics (RXSGLD) simulation method for efficient conformational searching and sampling. Unlike temperature-based replica exchanging simulations, which use high temperatures to accelerate conformational motion, this method uses self-guided Langevin dynamics (SGLD) to enhance conformational searching without the need to elevate temperatures. A RXSGLD simulation includes a series of SGLD simulations, with simulation conditions differing in the guiding effect and/or temperature. These simulation conditions are called stages and the base stage is one with no guiding effect. Replicas of a simulation system are simulated at the stages and are exchanged according to the replica exchanging probability derived from the SGLD partition function. Because SGLD causes less perturbation on conformational distribution than high temperatures, exchanges between SGLD stages have much higher probabilities than those between different temperatures. Therefore, RXSGLD simulations have higher conformational searching ability than temperature based replica exchange simulations. Through three example systems, we demonstrate that RXSGLD can generate target canonical ensemble distribution at the base stage and achieve accelerated conformational searching. Especially for large systems, RXSGLD has remarkable advantages in terms of replica exchange efficiency, conformational searching ability, and system size extensiveness.

Structure refinement of protein model decoys requires accurate side-chain placement

In this study, the application of temperature-based replica-exchange (T-ReX) simulations for structure refinement of decoys taken from the I-TASSER dataset was examined. A set of eight nonredundant proteins was investigated using self-guided Langevin dynamics (SGLD) with a generalized Born implicit solvent model to sample conformational space. For two of the protein test cases, a comparison of the SGLD/T-ReX method with that of a hybrid explicit/implicit solvent molecular dynamics T-ReX simulation model is provided. Additionally, the effect of side-chain placement among the starting decoy structures, using alternative rotamer conformations taken from the SCWRL4 modeling program, was investigated. The simulation results showed that, despite having near-native backbone conformations among the starting decoys, the determinant of their refinement is side-chain packing to a level that satisfies a minimum threshold of native contacts to allow efficient excursions toward the downhill refinement regime on the energy landscape. By repacking using SCWRL4 and by applying the RWplus statistical potential for structure identification, the SGLD/T-ReX simulations achieved refinement to an average of 38% increase in the number of native contacts relative to the original I-TASSER decoy sets and a 25% reduction in values of C(α) root-mean-square deviation. The hybrid model succeeded in obtaining a sharper funnel to low-energy states for a modeled target than the implicit solvent SGLD model; yet, structure identification remained roughly the same. Without meeting a threshold of near-native packing of side chains, the T-ReX simulations degrade the accuracy of the decoys, and subsequently, refinement becomes tantamount to the protein folding problem.

Solvent effect on the folding dynamics and structure of E6-associated protein characterized from ab initio protein folding simulations

Solvent effect on protein conformation and folding mechanism of E6-associated protein (E6ap) peptide are investigated using a recently developed charge update scheme termed as adaptive hydrogen bond-specific charge (AHBC). On the basis of the close agreement between the calculated helix contents from AHBC simulations and experimental results, we observed based on the presented simulations that the two ends of the peptide may simultaneously take part in the formation of the helical structure at the early stage of folding and finally merge to form a helix with lowest backbone RMSD of about 0.9 Å in 40% 2,2,2-trifluoroethanol solution. However, in pure water, the folding may start at the center of the peptide sequence instead of at the two opposite ends. The analysis of the free energy landscape indicates that the solvent may determine the folding clusters of E6ap, which subsequently leads to the different final folded structure. The current study demonstrates new insight to the role of solvent in the determination of protein structure and folding dynamics.

Enhanced Sampling in Free Energy Calculations: Combining SGLD with the Bennett's Acceptance Ratio and Enveloping Distribution Sampling Methods

One of the key requirements for the accurate calculation of free energy differences is proper sampling of conformational space. Especially in biological applications, molecular dynamics simulations are often confronted with rugged energy surfaces and high energy barriers, leading to insufficient sampling and, in turn, poor convergence of the free energy results. In this work, we address this problem by employing enhanced sampling methods. We explore the possibility of using self-guided Langevin dynamics (SGLD) to speed up the exploration process in free energy simulations. To obtain improved free energy differences from such simulations, it is necessary to account for the effects of the bias due to the guiding forces. We demonstrate how this can be accomplished for the Bennett's acceptance ratio (BAR) and the enveloping distribution sampling (EDS) methods. While BAR is considered among the most efficient methods available for free energy calculations, the EDS method developed by Christ and van Gunsteren is a promising development that reduces the computational costs of free energy calculations by simulating a single reference state. To evaluate the accuracy of both approaches in connection with enhanced sampling, EDS was implemented in CHARMM. For testing, we employ benchmark systems with analytical reference results and the mutation of alanine to serine. We find that SGLD with reweighting can provide accurate results for BAR and EDS where conventional molecular dynamics simulations fail. In addition, we compare the performance of EDS with other free energy methods. We briefly discuss the implications of our results and provide practical guidelines for conducting free energy simulations with SGLD.

Conformational sampling of peptides in the presence of protein crowders from AA/CG-multiscale simulations

Macromolecular crowding is recognized as an important factor influencing folding and conformational dynamics of proteins and nucleic acids. Previous views of crowding have focused on the mostly entropic volume exclusion effect of crowding, but recent studies are indicating the importance of enthalpic effects, in particular, changes in electrostatic interactions due to crowding. Here, temperature replica exchange molecular dynamics simulations of trp-cage and melittin in the presence of explicit protein crowders are presented to further examine the effect of protein crowders on peptide dynamics. The simulations involve a three-component multiscale modeling scheme where the peptides are represented at an atomistic level, the crowder proteins at a coarse-grained level, and the surrounding aqueous solvent as implicit solvent. This scheme optimally balances a physically realistic description for the peptide with computational efficiency. The multiscale simulations were compared with simulations of the same peptides in different dielectric environments with dielectric constants ranging from 5 to 80. It is found that the sampling in the presence of the crowders resembles sampling with reduced dielectric constants between 10 and 40. Furthermore, diverse conformational ensembles are generated in the presence of crowders including partially unfolded states for trp-cage. These findings emphasize the importance of enthalpic interactions over volume exclusion effects in describing the effects of cellular crowding.

Efficient and Unbiased Sampling of Biomolecular Systems in the Canonical Ensemble: A Review of Self-Guided Langevin Dynamics

This review provides a comprehensive description of the self-guided Langevin dynamics (SGLD) and the self-guided molecular dynamics (SGMD) methods and their applications. Example systems are included to provide guidance on optimal application of these methods in simulation studies. SGMD/SGLD has enhanced ability to overcome energy barriers and accelerate rare events to affordable time scales. It has been demonstrated that with moderate parameters, SGLD can routinely cross energy barriers of 20 kT at a rate that molecular dynamics (MD) or Langevin dynamics (LD) crosses 10 kT barriers. The core of these methods is the use of local averages of forces and momenta in a direct manner that can preserve the canonical ensemble. The use of such local averages results in methods where low frequency motion "borrows" energy from high frequency degrees of freedom when a barrier is approached and then returns that excess energy after a barrier is crossed. This self-guiding effect also results in an accelerated diffusion to enhance conformational sampling efficiency. The resulting ensemble with SGLD deviates in a small way from the canonical ensemble, and that deviation can be corrected with either an on-the-fly or a post processing reweighting procedure that provides an excellent canonical ensemble for systems with a limited number of accelerated degrees of freedom. Since reweighting procedures are generally not size extensive, a newer method, SGLDfp, uses local averages of both momenta and forces to preserve the ensemble without reweighting. The SGLDfp approach is size extensive and can be used to accelerate low frequency motion in large systems, or in systems with explicit solvent where solvent diffusion is also to be enhanced. Since these methods are direct and straightforward, they can be used in conjunction with many other sampling methods or free energy methods by simply replacing the integration of degrees of freedom that are normally sampled by MD or LD.

Force-momentum-based self-guided Langevin dynamics: a rapid sampling method that approaches the canonical ensemble

The self-guided Langevin dynamics (SGLD) is a method to accelerate conformational searching. This method is unique in the way that it selectively enhances and suppresses molecular motions based on their frequency to accelerate conformational searching without modifying energy surfaces or raising temperatures. It has been applied to studies of many long time scale events, such as protein folding. Recent progress in the understanding of the conformational distribution in SGLD simulations makes SGLD also an accurate method for quantitative studies. The SGLD partition function provides a way to convert the SGLD conformational distribution to the canonical ensemble distribution and to calculate ensemble average properties through reweighting. Based on the SGLD partition function, this work presents a force-momentum-based self-guided Langevin dynamics (SGLDfp) simulation method to directly sample the canonical ensemble. This method includes interaction forces in its guiding force to compensate the perturbation caused by the momentum-based guiding force so that it can approximately sample the canonical ensemble. Using several example systems, we demonstrate that SGLDfp simulations can approximately maintain the canonical ensemble distribution and significantly accelerate conformational searching. With optimal parameters, SGLDfp and SGLD simulations can cross energy barriers of more than 15 kT and 20 kT, respectively, at similar rates for LD simulations to cross energy barriers of 10 kT. The SGLDfp method is size extensive and works well for large systems. For studies where preserving accessible conformational space is critical, such as free energy calculations and protein folding studies, SGLDfp is an efficient approach to search and sample the conformational space.

Comparison of two adaptive temperature-based replica exchange methods applied to a sharp phase transition of protein unfolding-folding

Temperature-based replica exchange (T-ReX) enhances sampling of molecular dynamics simulations by autonomously heating and cooling simulation clients via a Metropolis exchange criterion. A pathological case for T-ReX can occur when a change in state (e.g., folding to unfolding of a protein) has a large energetic difference over a short temperature interval leading to insufficient exchanges amongst replica clients near the transition temperature. One solution is to allow the temperature set to dynamically adapt in the temperature space, thereby enriching the population of clients near the transition temperature. In this work, we evaluated two approaches for adapting the temperature set: a method that equalizes exchange rates over all neighbor temperature pairs and a method that attempts to induce clients to visit all temperatures (dubbed "current maximization") by positioning many clients at or near the transition temperature. As a test case, we simulated the 57-residue SH3 domain of alpha-spectrin. Exchange rate equalization yielded the same unfolding-folding transition temperature as fixed-temperature ReX with much smoother convergence of this value. Surprisingly, the current maximization method yielded a significantly lower transition temperature, in close agreement with experimental observation, likely due to more extensive sampling of the transition state.

Toward canonical ensemble distribution from self-guided Langevin dynamics simulation

This work derives a quantitative description of the conformational distribution in self-guided Langevin dynamics (SGLD) simulations. SGLD simulations employ guiding forces calculated from local average momentums to enhance low-frequency motion. This enhancement in low-frequency motion dramatically accelerates conformational search efficiency, but also induces certain perturbations in conformational distribution. Through the local averaging, we separate properties of molecular systems into low-frequency and high-frequency portions. The guiding force effect on the conformational distribution is quantitatively described using these low-frequency and high-frequency properties. This quantitative relation provides a way to convert between a canonical ensemble and a self-guided ensemble. Using example systems, we demonstrated how to utilize the relation to obtain canonical ensemble properties and conformational distributions from SGLD simulations. This development makes SGLD not only an efficient approach for conformational searching, but also an accurate means for conformational sampling.

Comparison between self-guided Langevin dynamics and molecular dynamics simulations for structure refinement of protein loop conformations

This article presents a comparative analysis of two replica-exchange simulation methods for the structure refinement of protein loop conformations, starting from low-resolution predictions. The methods are self-guided Langevin dynamics (SGLD) and molecular dynamics (MD) with a Nosé-Hoover thermostat. We investigated a small dataset of 8- and 12-residue loops, with the shorter loops placed initially from a coarse-grained lattice model and the longer loops from an enumeration assembly method (the Loopy program). The CHARMM22 + CMAP force field with a generalized Born implicit solvent model (molecular-surface parameterized GBSW2) was used to explore conformational space. We also assessed two empirical scoring methods to detect nativelike conformations from decoys: the all-atom distance-scaled ideal-gas reference state (DFIRE-AA) statistical potential and the Rosetta energy function. Among the eight-residue loop targets, SGLD out performed MD in all cases, with a median of 0.48 Å reduction in global root-mean-square deviation (RMSD) of the loop backbone coordinates from the native structure. Among the more challenging 12-residue loop targets, SGLD improved the prediction accuracy over MD by a median of 1.31 Å, representing a substantial improvement. The overall median RMSD for SGLD simulations of 12-residue loops was 0.91 Å, yielding refinement of a median 2.70 Å from initial loop placement. Results from DFIRE-AA and the Rosetta model applied to rescoring conformations failed to improve the overall detection calculated from the CHARMM force field. We illustrate the advantage of SGLD over the MD simulation model by presenting potential-energy landscapes for several loop predictions. Our results demonstrate that SGLD significantly outperforms traditional MD in the generation and populating of nativelike loop conformations and that the CHARMM force field performs comparably to other empirical force fields in identifying these conformations from the resulting ensembles.

Advances in implicit models of water solvent to compute conformational free energy and molecular dynamics of proteins at constant pH

Modern implicit solvent models for macromolecular simulations in water-proton bath are considered. The fundamental quantity that implicit models approximate is the solute potential of mean force, which is obtained by averaging over solvent degrees of freedom. The implicit solvent models suggest practical ways to calculate free energies of macromolecular conformations taking into account equilibrium interactions with water solvent and proton bath, while the explicit solvent approach is unable to do that due to the need to account for a large number of solvent degrees of freedom. The most advanced realizations of the implicit continuum models by different research groups are discussed, their accuracy are examined, and some applications of the implicit solvent models to macromolecular modeling, such as free energy calculations, protein folding, and constant pH molecular dynamics are highlighted.