Temperature‐shuffled parallel cascade selection molecular dynamics accelerates the structural transitions of proteins

Parallel cascade selection molecular dynamics (PaCS‐MD) is an enhanced conformational sampling method for searching structural transition pathways from a given reactant to a product. Recently, a temperature‐aided PaCS‐MD (Vinod et al., Eur. Biophys. J. 2016, 45, 463) has been proposed as its extension, in which the temperatures were introduced as additional parameters in conformational resampling, whereas the temperature is fixed in the original PaCS‐MD. In the present study, temperature‐shuffled PaCS‐MD is proposed as a further extension of temperature‐aided PaCS‐MD in which the temperatures are shuffled among different replicas at the beginning of each cycle of conformational resampling. To evaluate their conformational sampling efficiencies, the original, temperature‐aided, and temperature‐shuffled PaCS‐MD were applied to a protein‐folding process of Trp‐cage, and their minimum computational costs to identify the native state were addressed. Through the evaluation, it was confirmed that temperature‐shuffled PaCS‐MD remarkably accelerated the protein‐folding process of Trp‐cage compared with the other methods. © 2017 Wiley Periodicals, Inc.     

Protein folding pathways extracted by OFLOOD: Outlier FLOODing method

The Outlier FLOODing method (OFLOOD) is proposed as an efficient conformational sampling method to extract biologically rare events such as protein folding. In OFLOOD, sparse distributions (outliers in the conformational space) were regarded as relevant states for the transitions. Then, the transitions were enhanced through conformational resampling from the outliers. This evidence indicates that the conformational resampling of the sparse distributions might increase chances for promoting the transitions from the outliers to other meta‐stable states, which resembles a conformational flooding from the outliers to the neighboring clusters. OFLOOD consists of (i) detections of outliers from conformational distributions and (ii) conformational resampling from the outliers by molecular dynamics (MD) simulations. Cycles of (i) and (ii) are simply repeated. As demonstrations, OFLOOD was applied to folding of Chignolin and HP35. In both cases, OFLOOD automatically extracted folding pathways from unfolded structures with ns‐order computational costs, although µs‐order canonical MD failed to extract them. © 2014 Wiley Periodicals, Inc.     

A Method to Explore Protein Side Chain Conformational Variability Using Experimental Data

Experimentally measured values of molecular properties or observables of biomolecules such as proteins are generally averages over time and space, which do not contain su?cient information to determine the underlying conformational distribution of the molecules in solution. The relationship between experimentally measured NMR ³J‐coupling values and the corresponding dihedral angle values is a particularly complicated case due to its nonlinear, multiple‐valued nature. Molecular dynamics (MD) simulations at constant temperature can generate Boltzmann ensembles of molecular structures that are free from a priori assumptions about the nature of the underlying conformational distribution. They suffer, however, from limited sampling with respect to time and conformational space. Moreover, the quality of the obtained structures is dependent on the choice of force ?eld and solvation model. A recently proposed method that uses time‐averaging with local‐elevation (LE) biasing of the conformational search provides an elegant means of overcoming these three problems. Using a set of side chain ³J‐coupling values for the FK506 binding protein (FKBP), we ?rst investigate the uncertainty in the angle values predicted theoretically. We then propose a simple MD‐based technique to detect inconsistencies within an experimental data set and identify degrees of freedom for which conformational averaging takes place or for which force ?eld parameters may be de?cient. Finally, we show that LE MD is the best method for producing ensembles of structures that, on average, ?t the experimental data.     

Interpreting protein structural dynamics from NMR chemical shifts

In this investigation, semiempirical NMR chemical shift prediction methods are used to evaluate the dynamically averaged values of backbone chemical shifts obtained from unbiased molecular dynamics (MD) simulations of proteins. MD-averaged chemical shift predictions generally improve agreement with experimental values when compared to predictions made from static X-ray structures. Improved chemical shift predictions result from population-weighted sampling of multiple conformational states and from sampling smaller fluctuations within conformational basins. Improved chemical shift predictions also result from discrete changes to conformations observed in X-ray structures, which may result from crystal contacts, and are not always reflective of conformational dynamics in solution. Chemical shifts are sensitive reporters of fluctuations in backbone and side chain torsional angles, and averaged (1)H chemical shifts are particularly sensitive reporters of fluctuations in aromatic ring positions and geometries of hydrogen bonds. In addition, poor predictions of MD-averaged chemical shifts can identify spurious conformations and motions observed in MD simulations that may result from force field deficiencies or insufficient sampling and can also suggest subsets of conformational space that are more consistent with experimental data. These results suggest that the analysis of dynamically averaged NMR chemical shifts from MD simulations can serve as a powerful approach for characterizing protein motions in atomistic detail.     

Coulomb replica‐exchange method: Handling electrostatic attractive and repulsive forces for biomolecules

We propose a new type of the Hamiltonian replica‐exchange method (REM) for molecular dynamics (MD) and Monte Carlo simulations, which we refer to as the Coulomb REM (CREM). In this method, electrostatic charge parameters in the Coulomb interactions are exchanged among replicas while temperatures are exchanged in the usual REM. By varying the atom charges, the CREM overcomes free‐energy barriers and realizes more efficient sampling in the conformational space than the REM. Furthermore, this method requires only a smaller number of replicas because only the atom charges of solute molecules are used as exchanged parameters. We performed Coulomb replica‐exchange MD simulations of an alanine dipeptide in explicit water solvent and compared the results with those of the conventional canonical, replica exchange, and van der Waals REMs. Two force fields of AMBER parm99 and AMBER parm99SB were used. As a result, the CREM sampled all local‐minimum free‐energy states more frequently than the other methods for both force fields. Moreover, the Coulomb, van der Waals, and usual REMs were applied to a fragment of an amyloid‐β peptide (Aβ) in explicit water solvent to compare the sampling efficiency of these methods for a larger system. The CREM sampled structures of the Aβ fragment more efficiently than the other methods. We obtained β‐helix, α‐helix, 3₁₀‐helix, β‐hairpin, and β‐sheet structures as stable structures and deduced pathways of conformational transitions among these structures from a free‐energy landscape. © 2012 Wiley Periodicals, Inc.     

Using the local elevation method to construct optimized umbrella sampling potentials: Calculation of the relative free energies and interconversion barriers of glucopyranose ring conformers in water

A method is proposed to combine the local elevation (LE) conformational searching and the umbrella sampling (US) conformational sampling approaches into a single local elevation umbrella sampling (LEUS) scheme for (explicit‐solvent) molecular dynamics (MD) simulations. In this approach, an initial (relatively short) LE build‐up (searching) phase is used to construct an optimized biasing potential within a subspace of conformationally relevant degrees of freedom, that is then used in a (comparatively longer) US sampling phase. This scheme dramatically enhances (in comparison with plain MD) the sampling power of MD simulations, taking advantage of the fact that the preoptimized biasing potential represents a reasonable approximation to the negative of the free energy surface in the considered conformational subspace. The method is applied to the calculation of the relative free energies of β‐D ‐glucopyranose ring conformers in water (within the GROMOS 45A4 force field). Different schemes to assign sampled conformational regions to distinct states are also compared. This approach, which bears some analogies with adaptive umbrella sampling and metadynamics (but within a very distinct implementation), is shown to be: (i) efficient (nearly all the computational effort is invested in the actual sampling phase rather than in searching and equilibration); (ii) robust (the method is only weakly sensitive to the details of the build‐up protocol, even for relatively short build‐up times); (iii) versatile (a LEUS biasing potential database could easily be preoptimized for small molecules and assembled on a fragment basis for larger ones). © 2009 Wiley Periodicals, Inc. J Comput Chem 2010     

PyRETIS: A well‐done,medium‐sized python library for rare events

Transition path sampling techniques are becoming common approaches in the study of rare events at the molecular scale. More efficient methods, such as transition interface sampling (TIS) and replica exchange transition interface sampling (RETIS), allow the investigation of rare events, for example, chemical reactions and structural/morphological transitions, in a reasonable computational time. Here, we present PyRETIS, a Python library for performing TIS and RETIS simulations. PyRETIS directs molecular dynamics (MD) simulations in order to sample rare events with unbiased dynamics. PyRETIS is designed to be easily interfaced with any molecular simulation package and in the present release, it has been interfaced with GROMACS and CP2K, for classical and ab initio MD simulations, respectively. © 2017 Wiley Periodicals, Inc.     

DIRECT‐ID: An automated method to identify and quantify conformational variations—application to β2‐adrenergic GPCR

The conformational dynamics of a macromolecule can be modulated by a number of factors, including changes in environment, ligand binding, and interactions with other macromolecules, among others. We present a method that quantifies the differences in macromolecular conformational dynamics and automatically extracts the structural features responsible for these changes. Given a set of molecular dynamics (MD) simulations of a macromolecule, the norms of the differences in covariance matrices are calculated for each pair of trajectories. A matrix of these norms thus quantifies the differences in conformational dynamics across the set of simulations. For each pair of trajectories, covariance difference matrices are parsed to extract structural elements that undergo changes in conformational properties. As a demonstration of its applicability to biomacromolecular systems, the method, referred to as DIRECT‐ID, was used to identify relevant ligand‐modulated structural variations in the β₂‐adrenergic (β₂AR) G‐protein coupled receptor. Micro‐second MD simulations of the β₂AR in an explicit lipid bilayer were run in the apo state and complexed with the ligands: BI‐167107 (agonist), epinephrine (agonist), salbutamol (long‐acting partial agonist), or carazolol (inverse agonist). Each ligand modulated the conformational dynamics of β₂AR differently and DIRECT‐ID analysis of the inverse‐agonist vs. agonist‐modulated β₂AR identified residues known through previous studies to selectively propagate deactivation/activation information, along with some previously unidentified ligand‐specific microswitches across the GPCR. This study demonstrates the utility of DIRECT‐ID to rapidly extract functionally relevant conformational dynamics information from extended MD simulations of large and complex macromolecular systems. © 2015 Wiley Periodicals, Inc.     

Local relaxation of polymers in dense media: Cooperative kinematics theory and applications

Cooperative kinematics (CK) theory and its recent applications are presented. CK theory has been developed as an efficient approach for predicting the mechanism of segmental relaxation processes in bulk polymers. The theory aims at determining the most probable changes in atomic coordinates, occurring collectively in response to a given, external or localized, structural perturbation. The basic postulate is the minimization of the energy change involved in the overall conformational motion, which naturally yields the optimal pathway of cooperative relaxation. Attention has been confined here to the collective motions accompanying the rotational transitions of backbone bonds in polyethylene (PE) and polybutadiene (PB). The strong dependence of the mechanism of motions on the geometry of the repeat unit and on chain connectivity is emphasized. The differences in the types of correlated transitions operating in different structures, the effective conformational energy changes triggered by bond rotational jumps, and the correlation lengths for particular bond isomerizations are analyzed. The reorientations of C H bond vectors in cis- and trans-PB are also examined to explain the shorter correlation time of cis units, compared to trans, detected by NMR. A good agreement between various CK predictions and results from molecular dynamics (MD) simulations is obtained. The fact that CK calculations are at least two orders of magnitude faster than MD simulations invites attention to the utility of the CK method as an efficient tool for elucidating the pathway of motion in complex systems.     

Enhanced conformational sampling method for proteins based on the TaBoo SeArch algorithm: Application to the folding of a mini‐protein,chignolin

The conformational samplings are indispensible for obtaining reliable canonical ensembles, which provide statistical averages of physical quantities such as free energies. However, the samplings of vast conformational space of biomacromolecules by conventional molecular dynamics (MD) simulations might be insufficient, due to their inadequate accessible time‐scales for investigating biological functions. Therefore, the development of methodologies for enhancing the conformational sampling of biomacromolecules still remains as a challenging issue in computational biology. To tackle this problem, we newly propose an efficient conformational search method, which is referred as TaBoo SeArch (TBSA) algorithm. In TBSA, an inverse energy histogram is used to select seeds for the conformational resampling so that states with high frequencies are inhibited, while states with low frequencies are efficiently sampled to explore the unvisited conformational space. As a demonstration, TBSA was applied to the folding of a mini‐protein, chignolin, and automatically sampled the native structure (C_α root mean square deviation < 1.0 Å) with nanosecond order computational costs started from a completely extended structure, although a long‐time 1‐µs normal MD simulation failed to sample the native structure. Furthermore, a multiscale free energy landscape method based on the conformational sampling of TBSA were quantitatively evaluated through free energy calculations with both implicit and explicit solvent models, which enable us to find several metastable states on the folding landscape. © 2015 Wiley Periodicals, Inc.     

Predictive power of molecular dynamics receptor structures in virtual screening

Molecular dynamics (MD) simulation is a well-established method for understanding protein dynamics. Conformations from unrestrained MD simulations have yet to be assessed for blind virtual screening (VS) by docking. This study presents a critical analysis of the predictive power of MD snapshots to this regard, evaluating two well-characterized systems of varying flexibility in ligand-bound and unbound configurations. Results from such VS predictions are discussed with respect to experimentally determined structures. In all cases, MD simulations provide snapshots that improve VS predictive power over known crystal structures, possibly due to sampling more relevant receptor conformations. Additionally, MD can move conformations previously not amenable to docking into the predictive range.     

Enhanced sampling method in molecular simulations using genetic algorithm for biomolecular systems

We propose a molecular simulation method using genetic algorithm (GA) for biomolecular systems to obtain ensemble averages efficiently. In this method, we incorporate the genetic crossover, which is one of the operations of GA, to any simulation method such as conventional molecular dynamics (MD), Monte Carlo, and other simulation methods. The genetic crossover proposes candidate conformations by exchanging parts of conformations of a target molecule between a pair of conformations during the simulation. If the candidate conformations are accepted, the simulation resumes from the accepted ones. While conventional simulations are based on local update of conformations, the genetic crossover introduces global update of conformations. As an example of the present approach, we incorporated genetic crossover to MD simulations. We tested the validity of the method by calculating ensemble averages and the sampling efficiency by using two kinds of peptides, ALA3 and (AAQAA)₃. The results show that for ALA3 system, the distribution probabilities of backbone dihedral angles are in good agreement with those of the conventional MD and replica-exchange MD simulations. In the case of (AAQAA)₃ system, our method showed lower structural correlation of α-helix structures than the other two methods and more flexibility in the backbone ψ angles than the conventional MD simulation. These results suggest that our method gives more efficient conformational sampling than conventional simulation methods based on local update of conformations. © 2018 Wiley Periodicals, Inc.     

On the Use of a Supramolecular Coarse‐Grained Model for the Solvent in Simulations of the Folding Equilibrium of an Octa‐β‐peptide in MeOH and H2O

Molecular dynamics (MD) simulation can give a detailed picture of conformational equilibria of biomolecules, but it is only reliable if the force field used in the simulation is accurate, and the sampling of the conformational space accessible to the biomolecule shows many (un)folding transitions to allow for precise averages of observable quantities. Here, the use of coarse‐grained (CG) solvent MeOH and H₂O models to speed up the sampling of the conformational equilibria of an octa‐β‐peptide is investigated. This peptide is thought to predominantly adopt a 3₁₄‐helical fold when solvated in MeOH, and a hairpin fold when solvated in H₂O on the basis of the NMR data. Various factors such as the chirality of a residue, a force‐field modification for the solute, coarse‐graining of the solvent model, and an extension of the nonbonded interaction cut‐off radius are shown to influence the simulated conformational equilibria and the agreement with the experimental NMR data for the octa‐β‐peptide.     

Estimating kinetic rates from accelerated molecular dynamics simulations: alanine dipeptide in explicit solvent as a case study

Molecular dynamics (MD) simulation is the standard computational technique used to obtain information on the time evolution of the conformations of proteins and many other molecular systems. However, for most biological systems of interest, the time scale for slow conformational transitions is still inaccessible to standard MD simulations. Several sampling methods have been proposed to address this issue, including the accelerated molecular dynamics method. In this work, we study the extent of sampling of the phi/psi space of alanine dipeptide in explicit water using accelerated molecular dynamics and present a framework to recover the correct kinetic rate constant for the helix to beta-strand transition. We show that the accelerated MD can drastically enhance the sampling of the phi/psi conformational phase space when compared to normal MD. In addition, the free energy density plots of the phi/psi space show that all minima regions are accurately sampled and the canonical distribution is recovered. Moreover, the kinetic rate constant for the helix to beta-strand transition is accurately estimated from these simulations by relating the diffusion coefficient to the local energetic roughness of the energy landscape. Surprisingly, even for such a low barrier transition, it is difficult to obtain enough transitions to accurately estimate the rate constant when one uses normal MD.     

Validation of the GROMOS 54A7 Force Field Regarding Mixed α/β‐Peptide Molecules

A molecular‐dynamics (MD) simulation study of two heptapeptides containing α‐ and β‐amino acid residues is presented. According to NMR experiments, the two peptides differ in dominant fold when solvated in MeOH: peptide 3 adopts predominantly β‐hairpin‐like conformations, while peptide 8 adopts a 14/15‐helical fold. The MD simulations largely reproduce the experimental data. Application of NOE atom? atom distance restraining improves the agreement with experimental data, but reduces the conformational sampling. Peptide 3 shows a variety of conformations, while still agreeing with the NOE and ³J‐coupling data, whereas the conformational ensemble of peptide 8 is dominated by one helical conformation. The results confirm the suitability of the GROMOS 54A7 force field for simulation or structure refinement of mixed α/β‐peptides in MeOH.     

Hamiltonian replica‐exchange simulations with adaptive biasing of peptide backbone and side chain dihedral angles

A Hamiltonian Replica‐Exchange Molecular Dynamics (REMD) simulation method has been developed that employs a two‐dimensional backbone and one‐dimensional side chain biasing potential specifically to promote conformational transitions in peptides. To exploit the replica framework optimally, the level of the biasing potential in each replica was appropriately adapted during the simulations. This resulted in both high exchange rates between neighboring replicas and improved occupancy/flow of all conformers in each replica. The performance of the approach was tested on several peptide and protein systems and compared with regular MD simulations and previous REMD studies. Improved sampling of relevant conformational states was observed for unrestrained protein and peptide folding simulations as well as for refinement of a loop structure with restricted mobility of loop flanking protein regions. © 2013 Wiley Periodicals, Inc.     

Convergence of replica exchange molecular dynamics

Replica exchange molecular dynamics (REMD) method is one of the generalized-ensemble algorithms which performs random walk in energy space and helps a system to escape from local energy traps. In this work, we studied the accuracy and efficiency of REMD by examining its ability to reproduce the results of multiple extended conventional molecular dynamics (MD) simulations and to enhance conformational sampling. Two sets of REMD simulations with different initial configurations, one from the fully extended and the other from fully helical conformations, were conducted on a fast-folding 21-amino-acid peptide with a continuum solvent model. Remarkably, the two REMD simulation sets started to converge even within 1.0 ns, despite their dramatically different starting conformations. In contrast, the conventional MD within the same time and with identical starting conformations did not show obvious signs of convergence. Excellent convergence between the REMD sets for T>300 K was observed after 14.0 ns REMD simulations as measured by the average helicity and free-energy profiles. We also conducted a set of 45 MD simulations at nine different temperatures with each trajectory simulated to 100.0 and 200.0 ns. An excellent agreement between the REMD and the extended MD simulation results was observed for T>300 K, showing that REMD can accurately reproduce long-time MD results with high efficiency. The autocorrelation times of the calculated helicity demonstrate that REMD can significantly enhance the sampling efficiency by 14.3+/-6.4, 35.1+/-0.2, and 71.5+/-20.4 times at, respectively, approximately 360, approximately 300, and approximately 275 K in comparison to the regular MD. Convergence was less satisfactory at low temperatures (T<300 K) and a slow oscillatory behavior suggests that longer simulation time was needed to reach equilibrium. Other technical issues, including choice of exchange frequency, were also examined.     

Vase‐Kite Equilibrium of Resorcin[4]arene Cavitands Investigated Using Molecular Dynamics Simulations with Ball‐and‐Stick Local Elevation Umbrella Sampling

A key feature of resorcin[4]arene cavitands is their ability to switch between a closed/contracted (Vase ) and an open/expanded (Kite ) conformation. The mechanism and dynamics of this interconversion remains, however, elusive. In the present study, the Vase ‐Kite transitions of a quinoxaline‐based and of a dinitrobenzene‐based resorcin[4]arene are investigated using molecular dynamics (MD) simulations in three environments (vacuum, chloroform, and toluene) and at three temperatures (198.15, 248.15, and 298.15 K). The challenge of sampling the Vase ‐Kite transition, which occurs experimentally on the millisecond time scale, is overcome by calculating relative free energies using ball‐and stick local elevation umbrella sampling (B&S‐LEUS) to enhance the statistics on the relevant states and to promote interconversion transitions. Associated unbiased MD simulations also evidence for the first time a complete Vase ‐to‐Kite transition, as well as transitions between degenerate Kite 1 and Kite 2 forms and solvent‐exchange events. The calculated Vase ‐to‐Kite free‐energy changes ΔG are in qualitative agreement with the experimental magnitudes and trends. The level of quantitative agreement is, however, limited by the force‐field accuracy and, in particular, by the approximate treatment of intramolecular interactions at the classical level. The results are in line with a less stable Vase state for the dinitrobenzene compared to the quinoxaline compound, and a negative entropy change ΔS for the Vase ‐to‐Kite transition of the latter compound. Relative free energies calculated for intermediates also suggest that the Vase ‐Kite transition does not follow a concerted mechanism, but an asynchronous one with sequential opening of the flaps. In particular, the conformation involving two adjacent flaps open in a parallel direction (cis‐p) represents a likely intermediate, which has not been observed experimentally to date.     

Sparsity‐weighted outlier FLOODing (OFLOOD) method: Efficient rare event sampling method using sparsity of distribution

As an extension of the Outlier FLOODing (OFLOOD) method [Harada et al., J. Comput. Chem. 2015, 36, 763], the sparsity of the outliers defined by a hierarchical clustering algorithm, FlexDice, was considered to achieve an efficient conformational search as sparsity‐weighted “OFLOOD.” In OFLOOD, FlexDice detects areas of sparse distribution as outliers. The outliers are regarded as candidates that have high potential to promote conformational transitions and are employed as initial structures for conformational resampling by restarting molecular dynamics simulations. When detecting outliers, FlexDice defines a rank in the hierarchy for each outlier, which relates to sparsity in the distribution. In this study, we define a lower rank (first ranked), a medium rank (second ranked), and the highest rank (third ranked) outliers, respectively. For instance, the first‐ranked outliers are located in a given conformational space away from the clusters (highly sparse distribution), whereas those with the third‐ranked outliers are nearby the clusters (a moderately sparse distribution). To achieve the conformational search efficiently, resampling from the outliers with a given rank is performed. As demonstrations, this method was applied to several model systems: Alanine dipeptide, Met‐enkephalin, Trp‐cage, T4 lysozyme, and glutamine binding protein. In each demonstration, the present method successfully reproduced transitions among metastable states. In particular, the first‐ranked OFLOOD highly accelerated the exploration of conformational space by expanding the edges. In contrast, the third‐ranked OFLOOD reproduced local transitions among neighboring metastable states intensively. For quantitatively evaluations of sampled snapshots, free energy calculations were performed with a combination of umbrella samplings, providing rigorous landscapes of the biomolecules. © 2015 Wiley Periodicals, Inc.     

Increasing the time step with mass scaling in Born‐Oppenheimer ab initio QM/MM molecular dynamics simulations

Born‐Oppenheimer ab initio QM/MM molecular dynamics simulation with umbrella sampling is a state‐of‐the‐art approach to calculate free energy profiles of chemical reactions in complex systems. To further improve its computational efficiency, a mass‐scaling method with the increased time step in MD simulations has been explored and tested. It is found that by increasing the hydrogen mass to 10 amu, a time step of 3 fs can be employed in ab initio QM/MM MD simulations. In all our three test cases, including two solution reactions and one enzyme reaction, the resulted reaction free energy profiles with 3 fs time step and mass scaling are found to be in excellent agreement with the corresponding simulation results using 1 fs time step and the normal mass. These results indicate that for Born‐Oppenheimer ab initio QM/MM molecular dynamics simulations with umbrella sampling, the mass‐scaling method can significantly reduce its computational cost while has little effect on the calculated free energy profiles. © 2009 Wiley Periodicals, Inc. J Comput Chem, 2009