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.     

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.     

Replica exchange and expanded ensemble simulations as Gibbs sampling: simple improvements for enhanced mixing

The widespread popularity of replica exchange and expanded ensemble algorithms for simulating complex molecular systems in chemistry and biophysics has generated much interest in discovering new ways to enhance the phase space mixing of these protocols in order to improve sampling of uncorrelated configurations. Here, we demonstrate how both of these classes of algorithms can be considered as special cases of Gibbs sampling within a Markov chain Monte Carlo framework. Gibbs sampling is a well-studied scheme in the field of statistical inference in which different random variables are alternately updated from conditional distributions. While the update of the conformational degrees of freedom by Metropolis Monte Carlo or molecular dynamics unavoidably generates correlated samples, we show how judicious updating of the thermodynamic state indices--corresponding to thermodynamic parameters such as temperature or alchemical coupling variables--can substantially increase mixing while still sampling from the desired distributions. We show how state update methods in common use can lead to suboptimal mixing, and present some simple, inexpensive alternatives that can increase mixing of the overall Markov chain, reducing simulation times necessary to obtain estimates of the desired precision. These improved schemes are demonstrated for several common applications, including an alchemical expanded ensemble simulation, parallel tempering, and multidimensional replica exchange umbrella sampling.     

The native ensemble and folding of a protein molten-globule: functional consequence of downhill folding

The continually emerging functional significance of intrinsic disorder and conformational flexibility in proteins has challenged the long-standing dogma of a well-defined structure contributing to a specific function. Molten-globular states, a class of proteins with significant secondary-structure but a fluid hydrophobic core, is one such example. They have however been difficult to characterize due to the complexity of experimental data and lack of computational avenues. Here, we dissect the folding mechanism of the α-helical molten-globular protein NCBD from three fundamentally different approaches: statistical-mechanical variable barrier model, C(α)-based Gō-model and explicit water all-atom molecular dynamics (MD) simulations. We find that NCBD displays the characteristics of a one-state globally downhill folder but is significantly destabilized. Using simulation techniques, we generate a highly constrained but a heterogeneous native ensemble of the molten-globule for the first time that is consistent with experimental data including small angle X-ray scattering (SAXS), circular dichroism (CD), and nuclear magnetic resonance (NMR). The resulting native ensemble populates conformations reported in other bound-forms providing direct evidence to the mechanism of conformational selection for binding multiple partners in this domain. Importantly, our simulations reveal a connection between downhill folding and large conformational flexibility in this domain that has been evolutionarily selected and functionally exploited resulting in large binding promiscuity. Finally, the multimodel approach we employ here serves as a powerful methodology to study mechanisms and suggests that the thermodynamic features of molten-globules fall within the array of folding mechanisms available to small single-domain proteins.     

Helical content of a β(3)-octapeptide in methanol: molecular dynamics simulations explain a seeming discrepancy between conclusions derived from CD and NMR data

Connecting experimental observables with the underlying conformational ensemble is a long-standing problem in the structure determination of biomolecules. The simulations described in this article attempt to resolve a seeming discrepancy between the conformational features derived from measured NOE intensities, (3)J-coupling constants, and circular dichroism (CD) spectra for two β-peptides differing in a linker between two side-chains. Although both peptides are very similar in terms of the r(-6) averaged distances between atom pairs involved in the observed NOEs, the molecular dynamics trajectories suggest why the CD spectra show a greater 3(14)-helical propensity for the linked, cyclic peptide than for the linear one, whereas slightly more NMR NOE peaks are observed and assigned for the latter. The nine 100 ns unrestrained simulations show better agreement with the observed experimental data than the single conformations derived from the published NMR structures by additional energy minimization with the GROMOS force field. They show why the seemingly contradictory quantities obtained by NMR and CD spectroscopy can arise from a single conformational ensemble.     

Comparison of aqueous molecular dynamics with NMR relaxation and residual dipolar couplings favors internal motion in a mannose oligosaccharide.

An investigation has been performed to assess how aqueous dynamical simulations of flexible molecules can be compared against NMR data. The methodology compares state-of-the-art NMR data (residual dipolar coupling, NOESY, and (13)C relaxation) to molecular dynamics simulations in water over several nanoseconds. In contrast to many previous applications of residual dipolar coupling in structure investigations of biomolecules, the approach described here uses molecular dynamics simulations to provide a dynamic representation of the molecule. A mannose pentasaccharide, alpha-D-Manp-(1-->3)-alpha-D-Manp-(1-->3)-alpha-D-Manp-(1-->3)-alpha-D-Manp-(1-->2)-D-Manp, was chosen as the model compound for this study. The presence of alpha-linked mannan is common to many glycopeptides, and therefore an understanding of the structure and the dynamics of this molecule is of both chemical and biological importance. This paper sets out to address the following questions. (1) Are the single structures which have been used to interpret residual dipolar couplings a useful representation of this molecule? (2) If dynamic flexibility is included in a representation of the molecule, can relaxation and residual dipolar coupling data then be simultaneously satisfied? (3) Do aqueous molecular dynamics simulations provide a reasonable representation of the dynamics present in the molecule and its interaction with water? In summary, two aqueous molecular dynamics simulations, each of 20 ns, were computed. They were started from two distant conformations and both converged to one flexible ensemble. The measured residual dipolar couplings were in agreement with predictions made by averaging the whole ensemble and from a specific single structure selected from the ensemble. However, the inclusion of internal motion was necessary to rationalize the relaxation data. Therefore, it is proposed that although residual dipolar couplings can be interpreted as a single-structure, this may not be a correct interpretation of molecular conformation in light of other experimental data. Second, the methodology described here shows that the ensembles from aqueous molecular dynamics can be effectively tested against experimental data sets. In the simulation, significant conformational motion was observed at each of the linkages, and no evidence for intramolecular hydrogen bonds at either alpha(1-->2) or alpha(1-->3) linkages was found. This is in contrast to simulations of other linkages, such as beta(1-->4), which are often predicted to maintain intramolecular hydrogen bonds and are coincidentally predicted to have less conformational freedom in solution.     

Application of paramagnetic NMR-validated molecular dynamics simulation to the analysis of a conformational ensemble of a branched oligosaccharide

Oligosaccharides of biological importance often exhibit branched covalent structures and dynamic conformational multiplicities. Here we report the application of a method that we developed, which combined molecular dynamics (MD) simulations and lanthanide-assisted paramagnetic NMR spectroscopy, to evaluate the dynamic conformational ensemble of a branched oligosaccharide. A lanthanide-chelating tag was attached to the reducing end of the branched tetrasaccharide of GM2 ganglioside to observe pseudocontact shifts as the source of long distance information for validating the conformational ensemble derived from MD simulations. By inspecting the results, the conformational space of the GM2 tetrasaccharide was compared with that of its nonbranched derivative, the GM3 trisaccharide.     

Molecular dynamics simulation reveals structural and thermodynamic features of kinase activation by cancer mutations within the epidermal growth factor receptor

The epidermal growth factor receptor (EGFR) is a major target for drugs in treating lung carcinoma as it promotes cell growth and tumor progression. Structural studies have demonstrated that EGFR exists in an equilibrium between catalytically active and inactive forms, and dramatic conformational transitions occur during its activation. It is known that EGFR mutations promote such conformational changes that affect its activation and drug efficacy. The most common point mutation in lung cancer patients is a leucine to arginine substitution at amino acid 834 (L834R). In a recent article, we have studied changes in drug binding affinities due to cancer mutations of EGFR using ensemble molecular dynamics (MD) simulations. Here, we address an enhanced activation mechanism thought to be associated with this mutation. Using extended timescale MD simulations, the structural and energetic properties are studied for both active and inactive conformations of EGFR. The thermodynamic stabilities of these two conformations are characterized by free energy landscapes estimated from molecular mechanics/Poisson-Boltzmann solvent area calculations. Our study reveals that the L834R mutation introduces conformational changes in both states, adjusting the relative stabilities of active and inactive conformations and hence the activation of the EGFR kinase.     

Conformational properties of penicillins: quantum chemical calculations and molecular dynamics simulations of benzylpenicillin

Herein, we present theoretical results on the conformational properties of benzylpenicillin, which are characterized by means of quantum chemical calculations (MP2/6-31G* and B3LYP/6-31G*) and classical molecular dynamics simulations (5 ns) both in the gas phase and in aqueous solution. In the gas phase, the benzylpenicillin conformer in which the thiazolidine ring has the carboxylate group oriented axially is the most favored one. Both intramolecular CH. O and dispersion interactions contribute to stabilize the axial conformer with respect to the equatorial one. In aqueous solution, a molecular dynamics simulation predicts a relative population of the axial:equatorial conformers of 0.70:0.30 in consonance with NMR experimental data. Overall, the quantum chemical calculations as well as the simulations give insight into substituent effects, the conformational dynamics of benzylpenicillin, the frequency of ring-puckering motions, and the correlation of side chain and ring-puckering motions.     

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

Replica exchange methods (REMs) are increasingly used to improve sampling in molecular dynamics (MD) simulations of biomolecular systems. However, despite having been shown to be very effective on model systems, the application of REM in complex systems such as for the simulation of protein and peptide folding in explicit solvent has not been objectively tested in detail. Here we present a comparison of conventional MD and temperature replica exchange MD (T-REMD) simulations of a beta-heptapeptide in explicit solvent. This system has previously been shown to undergo reversible folding on the time scales accessible to MD simulation and thus allows a direct one-to-one comparison of efficiency. The primary properties compared are the free energy of folding and the relative populations of different conformers as a function of temperature. It is found that to achieve a similar degree of precision T-REMD simulations starting from a random set of initial configurations were approximately an order of magnitude more computationally efficient than a single 800 ns conventional MD simulation for this system at the lowest temperature investigated (275 K). However, whereas it was found that T-REMD simulations are more than four times more efficient than multiple independent MD simulations at one temperature (300 K) the actual increase in conformation sampling was only twofold. The overall gain in efficiency using REMD resulted primarily from the ordering of different conformational states over temperature, as opposed to a large increase of conformational sampling. It is also shown that in this system exchanges are accepted primarily based on (random) fluctuations within the solvent and are not strongly correlated with the instantaneous peptide conformation raising questions in regard to the efficiency of T-REMD in larger systems.     

De novo structural prediction of transition metal complexes: application to technetium

De novo structural prediction of transition metal complexes is investigated. Technetium complexes are chosen given their importance in medical imaging and nuclear waste remediation and for the chemical diversity they display. A new conformational searching algorithm (LIGB) for transition metals is described that allows one to search for different conformational and geometric isomers within a single simulation. In the preponderance of cases, both conformational searching techniques (LIGB and high-temperature molecular dynamics/simulated annealing) provide comparable results, while LIGB is superior for macrocyclic complexes. A genetic algorithm-optimized PM3(tm) parametrization for Tc is compared with the standard implementation and found to yield a significant improvement in predictive ability for the most prevalent Tc structural motifs. The utility of a coupled molecular mechanics-semiempirical quantum mechanics protocol is demonstrated for very rapid, efficient, and effective de novo prediction of transition metal complex geometries.     

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.     

应用ABEEMσπ／MM模型探讨小α-螺旋在显性水中折叠／展开的可逆过程

应用ABEEMσπ／MM模型进行分子动力学模拟,研究了显性水溶液中小α-螺旋（短肽Ala5）折叠／展开的可逆过程．动力学分析显示,300K下α-螺旋可以保存2ns的时间,该结果支持Margulis等人的结论．每个结构与α-螺旋结构骨架重原子的均方根偏差的时间轨迹指出,“300K下螺旋成核现象在0．1ns内快速发生”的结论是不恰当的．通过对300、400和500K温度下的研究,首次定量地给出各温度下螺旋保存的时间分别为2ns、1～1．5ns和0．8ns,并且增加温度并不改变折叠／展开的方式,只是改变折叠／展开的速率．本文对“转化态集合”结构的分析表明,从螺旋到卷曲的转换,主要通过螺旋端的氢键断裂发生（92％）、尤其是C端的氢键断裂发生（50％）．氢键的破坏和形成在0．1ns的时间内完成．