Monte Carlo vs molecular dynamics for all-atom polypeptide folding simulations

An efficient Monte Carlo (MC) algorithm including concerted rotations is directly compared to molecular dynamics (MD) in all-atom statistical mechanics folding simulations of small polypeptides. The previously reported algorithm "concerted rotations with flexible bond angles" (CRA) has been shown to successfully locate the native state of small polypeptides. In this study, the folding of three small polypeptides (trpzip2/H1/Trp-cage) is investigated using MC and MD, for a combined sampling time of approximately 10(11) MC configurations and 8 micros, respectively. Both methods successfully locate the experimentally determined native states of the three systems, but they do so at different speed, with 2-2.5 times faster folding of the MC runs. The comparison reveals that thermodynamic and dynamic properties can reliably be obtained by both and that results from folding simulations do not depend on the algorithm used. Similar to previous comparisons of MC and MD, it is found that one MD integration step of 2 fs corresponds to one MC scan, revealing the good sampling of MC. The simplicity and efficiency of the MC method will enable its future use in folding studies involving larger systems and the combination with replica exchange algorithms.     

Molecular dynamics study of peptides in implicit water: ab initio folding of beta-hairpin, beta-sheet, and beta beta alpha-motif

In this communication, we have demonstrated that molecular dynamics simulations using a GB implicit solvation model with the all-atom based force field (CHARMM19) can describe the spontaneous folding of small peptides in aqueous solution. The native structures of peptides with various structural motifs (beta-hairpin, beta-sheet, and betabetaalpha-moiety) were successfully predicted within reasonable time scales by MD simulations at moderately elevated temperatures. It is expected that the present simulations provide further insight into mechanism/pathways of the peptide folding.     

Mechanism of ligand exchange studied using transition path sampling

The mechanism of intermolecular ligand exchange has been studied using transition path sampling (TPS) based molecular dynamics (MD) simulations. Specifically, the exchange of solvent molecules bound to unsaturated Cr(CO)5 in methanol solution has been investigated. The results of the TPS simulations have shown that there are multiple steps in the reaction mechanism. The first involves partial dissociation of the coordinated solvent from the Cr metal center followed by association with a new methanol molecule between the normally void first and second solvent layers. After diffusive motion of the exchanging ligands, the last step involves the originally bound methanol molecule moving into the bath continuum followed by solvation of the Cr metal fragment by the exchanging ligand. It has been found that the reaction center (defined as the organometallic fragment and two exchanging ligands only) and the solvent bath have favorable interactions. This is likely due to the adiabatic nature of the ligand exchange transition. The ability to understand the microscopic molecular dynamics of a chemical process based on a free energy analysis is also discussed.     

The balance between side-chain and backbone-driven association in folding of the α-helical influenza A transmembrane peptide

The correct balance between attractive, repulsive and peptide hydrogen bonding interactions must be attained for proteins to fold correctly. To investigate these important contributors, we sought a comparison of the folding between two 25-residues peptides, the influenza A M2 protein transmembrane domain (M2TM) and the 25-Ala (Ala₂₅). M2TM forms a stable α-helix as is shown by circular dichroism (CD) experiments. Molecular dynamics (MD) simulations with adaptive tempering show that M2TM monomer is more dynamic in nature and quickly interconverts between an ensemble of various α-helical structures, and less frequently turns and coils, compared to one α-helix for Ala₂₅. DFT calculations suggest that folding from the extended structure to the α-helical structure is favored for M2TM compared with Ala₂₅. This is due to CH⋯O attractive interactions which favor folding to the M2TM α-helix, and cannot be described accurately with a force field. Using natural bond orbital (NBO) analysis and quantum theory atoms in molecules (QTAIM) calculations, 26 CH⋯O interactions and 22 NH⋯O hydrogen bonds are calculated for M2TM. The calculations show that CH⋯O hydrogen bonds, although individually weaker, have a cumulative effect that cannot be ignored and may contribute as much as half of the total hydrogen bonding energy, when compared to NH⋯O, to the stabilization of the α-helix in M2TM. Further, a strengthening of NH⋯O hydrogen bonding interactions is calculated for M2TM compared to Ala₂₅. Additionally, these weak CH⋯O interactions can dissociate and associate easily leading to the ensemble of folded structures for M2TM observed in folding MD simulations.     

MM-PBSA free energy analysis of endo-1,4-xylanase II (XynII)-substrate complexes: binding of the reactive sugar in a skew boat and chair conformation

The binding of xylotetraose in different conformations to the active site of endo-1,4-beta-xylanase II (XynII) from Trichoderma reesei was studied using molecular dynamics (MD) simulations and free energy analyses employing the MM-PBSA (Molecular Mechanics-Poisson-Boltzmann Surface Area) method. MD simulations of 1 ns were done for the substrate xylotetraose having the reactive sugar, which is bound in the -1 subsite of XynII in the 4C1 (chair) and 2So (skew boat) ground state conformations, and for the transition state of the XynII catalysed hydrolysis of the beta-glycosidic linkage. According to the simulations and free energy analysis, XynII binds the substrate with the -1 sugar in the 2So conformation 59.8 kJ mol(-1) tighter than the substrate with the sugar in the 4C1 conformation. The reactive 2So conformation resembles closely the reaction transition state and has the breaking glycosidic bond in a pseudo-axial orientation ready for facile bond cleavage. The transition state was calculated to be bound 77.1 kJ mol(-1) tighter than the 4C1 ground state conformation. The molecular mechanical interaction energy between the enzyme and the reactive pyranoside unit at the -1 subsite was 75.7 kJ mol(-1) more favorable for the binding of the 2So conformation than the 2C1 conformation, explaining the clearly tighter binding of the reactive structure The results of this study indicate that in the Michaelis complex XynII, a member of the family 11 xylanase, the substrate is bound in a skew boat conformation and in the catalytic reaction, the -1 sugar proceeds from the 4C1 conformation through 2So to the transition state with the -1 sugar in the 2,5B conformation.     

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.     

Molecular dynamics with the united-residue model of polypeptide chains. II. Langevin and Berendsen-bath dynamics and tests on model alpha-helical systems

The implementation of molecular dynamics (MD) with our physics-based protein united-residue (UNRES) force field, described in the accompanying paper, was extended to Langevin dynamics. The equations of motion are integrated by using a simplified stochastic velocity Verlet algorithm. To compare the results to those with all-atom simulations with implicit solvent in which no explicit stochastic and friction forces are present, we alternatively introduced the Berendsen thermostat. Test simulations on the Ala(10) polypeptide demonstrated that the average kinetic energy is stable with about a 5 fs time step. To determine the correspondence between the UNRES time step and the time step of all-atom molecular dynamics, all-atom simulations with the AMBER 99 force field and explicit solvent and also with implicit solvent taken into account within the framework of the generalized Born/surface area (GBSA) model were carried out on the unblocked Ala(10) polypeptide. We found that the UNRES time scale is 4 times longer than that of all-atom MD simulations because the degrees of freedom corresponding to the fastest motions in UNRES are averaged out. When the reduction of the computational cost for evaluation of the UNRES energy function is also taken into account, UNRES (with hydration included implicitly in the side chain-side chain interaction potential) offers about at least a 4000-fold speed up of computations relative to all-atom simulations with explicit solvent and at least a 65-fold speed up relative to all-atom simulations with implicit solvent. To carry out an initial full-blown test of the UNRES/MD approach, we ran Berendsen-bath and Langevin dynamics simulations of the 46-residue B-domain of staphylococcal protein A. We were able to determine the folding temperature at which all trajectories converged to nativelike structures with both approaches. For comparison, we carried out ab initio folding simulations of this protein at the AMBER 99/GBSA level. The average CPU time for folding protein A by UNRES molecular dynamics was 30 min with a single Alpha processor, compared to about 152 h for all-atom simulations with implicit solvent. It can be concluded that the UNRES/MD approach will enable us to carry out microsecond and, possibly, millisecond simulations of protein folding and, consequently, of the folding process of proteins in real time.     

Comparison of the glass transition temperature and fragility parameter of isomalto-olygomer predicted by molecular dynamics simulations with those measured by differential scanning calorimetry

The purpose of this study is to examine whether molecular dynamics (MD) simulations using a commercially available software for personal computers can estimate the glass transition temperature (Tg) of amorphous systems containing pharmaceutically-relevant excipients. MD simulations were carried out with an amorphous matrix model constructed from isomaltoheptaose, and the Tg estimated from the calculated density versus temperature profile was compared with the Tg measured by differential scanning calorimetry (DSC) for freeze-dried isomalto-oligomer having an average molecular weight close to that of isomaltoheptaose. The Tg values determined by DSC were lower by 10 to 20 K than those extrapolated from the Tg values estimated by MD simulation. Fragility parameter was estimated to be 56 and 51 from MD simulation and from DSC measurement, respectively. Thus, the results suggest that MD simulation can provide approximate estimates for the Tg and fragility parameter of amorphous formulations. However, a reduction of the cooling rate, achievable by sufficiently elongating the simulation duration, is necessary for more accurate estimation.     

Efficient evaluation of sampling quality of molecular dynamics simulations by clustering of dihedral torsion angles and Sammon mapping

A direct conformational clustering and mapping approach for peptide conformations based on backbone dihedral angles has been developed and applied to compare conformational sampling of Met-enkephalin using two molecular dynamics (MD) methods. Efficient clustering in dihedrals has been achieved by evaluating all combinations resulting from independent clustering of each dihedral angle distribution, thus resolving all conformational substates. In contrast, Cartesian clustering was unable to accurately distinguish between all substates. Projection of clusters on dihedral principal component (PCA) subspaces did not result in efficient separation of highly populated clusters. However, representation in a nonlinear metric by Sammon mapping was able to separate well the 48 highest populated clusters in just two dimensions. In addition, this approach also allowed us to visualize the transition frequencies between clusters efficiently. Significantly, higher transition frequencies between more distinct conformational substates were found for a recently developed biasing-potential replica exchange MD simulation method allowing faster sampling of possible substates compared to conventional MD simulations. Although the number of theoretically possible clusters grows exponentially with peptide length, in practice, the number of clusters is only limited by the sampling size (typically much smaller), and therefore the method is well suited also for large systems. The approach could be useful to rapidly and accurately evaluate conformational sampling during MD simulations, to compare different sampling strategies and eventually to detect kinetic bottlenecks in folding pathways.     

Simulation of chaperonin effect on protein folding: a shift from nucleation-condensation to framework mechanism

The iterative annealing mechanism (IAM) of chaperonin-assisted protein folding is explored in a framework of a well-established coarse-grained protein modeling tool, which enables the study of protein dynamics in a time-scale well beyond classical all-atom molecular mechanics. The chaperonin mechanism of action is simulated for two paradigm systems of protein folding, B domain of protein A (BdpA) and B1 domain of protein G (GB1), and compared to chaperonin-free simulations presented here for BdpA and recently published for GB1. The prediction of the BdpA transition state ensemble (TSE) is in perfect agreement with experimental findings. It is shown that periodic distortion of the polypeptide chains by hydrophobic chaperonin interactions can promote rapid folding and leads to a decrease in folding temperature. It is also demonstrated how chaperonin action prevents kinetically trapped conformations and modulates the observed folding mechanisms from nucleation-condensation to a more framework-like.     

p53突变体Y220C小分子稳定剂的虚拟筛选

为了获得p53突变体的稳定剂,依次利用利宾斯基五原则,通过2次分子对接和全原子分子动力学(MD)模拟从Drug Bank 4.0数据库中筛选获得了潜在的稳定剂他克林.利用MD模拟进一步验证他克林和目标蛋白质之间的亲和作用.结果表明,他克林能够紧密结合到Y220C突变所形成的疏水空腔之中;他克林和目标蛋白质之间的主要作用力为疏水和静电相互作用,其中疏水相互作用占主导地位.此外,他克林分别与目标蛋白质的残基Leu145,Val147和Asp228形成3个氢键.基于MD模拟轨迹分析了他克林与p53CY220C的结合过程.由硫黄素T荧光光谱进一步证明他克林能够提高p53C-Y220C突变体的稳定性.     

Probability distributions of molecular observables computed from Markov models

Molecular dynamics (MD) simulations can be used to estimate transition rates between conformational substates of the simulated molecule. Such an estimation is associated with statistical uncertainty, which depends on the number of observed transitions. In turn, it induces uncertainties in any property computed from the simulation, such as free energy differences or the time scales involved in the system's kinetics. Assessing these uncertainties is essential for testing the reliability of a given observation and also to plan further simulations in such a way that the most serious uncertainties will be reduced with minimal effort. Here, a rigorous statistical method is proposed to approximate the complete statistical distribution of any observable of an MD simulation provided that one can identify conformational substates such that the transition process between them may be modeled with a memoryless jump process, i.e., Markov or Master equation dynamics. The method is based on sampling the statistical distribution of Markov transition matrices that is induced by the observed transition events. It allows physically meaningful constraints to be included, such as sampling only matrices that fulfill detailed balance, or matrices that produce a predefined equilibrium distribution of states. The method is illustrated on mus MD simulations of a hexapeptide for which the distributions and uncertainties of the free energy differences between conformations, the transition matrix elements, and the transition matrix eigenvalues are estimated. It is found that both constraints, detailed balance and predefined equilibrium distribution, can significantly reduce the uncertainty of some observables.     

Nanoscale dewetting transition in protein complex folding

In a previous study, a surprising drying transition was observed to take place inside the nanoscale hydrophobic channel in the tetramer of the protein melittin. The goal of this paper is to determine if there are other protein complexes capable of displaying a dewetting transition during their final stage of folding. We searched the entire protein data bank (PDB) for all possible candidates, including protein tetramers, dimers, and two-domain proteins, and then performed the molecular dynamics (MD) simulations on the top candidates identified by a simple hydrophobic scoring function based on aligned hydrophobic surface areas. Our large scale MD simulations found several more proteins, including three tetramers, six dimers, and two two-domain proteins, which display a nanoscale dewetting transition in their final stage of folding. Even though the scoring function alone is not sufficient (i.e., a high score is necessary but not sufficient) in identifying the dewetting candidates, it does provide useful insights into the features of complex interfaces needed for dewetting. All top candidates have two features in common: (1) large aligned (matched) hydrophobic areas between two corresponding surfaces, and (2) large connected hydrophobic areas on the same surface. We have also studied the effect on dewetting of different water models and different treatments of the long-range electrostatic interactions (cutoff vs PME), and found the dewetting phenomena is fairly robust. This work presents a few proteins other than melittin tetramer for further experimental studies of the role of dewetting in the end stages of protein folding.     

Solvent effects on isomerization and spectral properties of photochromic-switching diarythene derivatives in polar and apolar solutions

The photocyclization behavior and dynamic conformational transition of photochromic switches of diarythene derivatives in solutions are investigated by using the density functional theory (DFT) and molecular dynamics (MD) simulations. Three possible conformations, antiparallel (anti), parallel (para), and twist, for the open-ring isomers of 1,2-bis(2-methylbenzothiophene-3-yl)maleic anhydride are located. Both PCM-B3LYP/6-31G* calculations and MD simulations demonstrate that anti and twist open-ring isomers can interconvert freely in n-hexane and acetonitrile solutions at room temperature. The statistical ratio of twist to anti isomers from MD simulations is 2.09 in n-hexane and 1.07 in CH(3)CN, in qualitative agreement with those (1.18 in n-hexane and 1.05 in CH(3)CN) estimated from Arrhenius analysis of DFT activation energies. The solvent polarity has little influence on the isomerization of open-ring isomers in the ground state. Due to the evident charge transfer upon excitations, the solvent effects on the electronic structures and absorption spectra of low-lying excited states (S(1) and S(2)) are more significant. For such charge-transfer excited states, the long-range corrected functional CAM-B3LYP gives better agreement with the experimental spectra than B3LYP. The solvent polarity and polarization of the charge-transfer excited states are crucial for fabricating the novel functionalized photochromic molecular switches.     

Single‐Molecule Detection Reveals Knot Sliding in TrmD Denaturation

An increasing number of proteins are found to contain a knot in their polypeptide chain. Although some studies have looked into the folding mechanism of knotted proteins, why and how these complex topologies form are still far from being fully answered. Moreover, no experimental information about how the knot moves during the protein‐folding process is available. Herein, by combining single‐molecule fluorescence resonance energy transfer (smFRET) experiments with molecular dynamics (MD) simulations, we performed a detailed study to characterize the knot in the denatured state of TrmD, a knotted tRNA (guanosine‐1) methyltransferase from Escherichia coli, as a model system. We found that the knot still existed in the unfolded state of TrmD, consistent with the results for two other knotted proteins, YibK and YbeA. More interestingly, both smFRET experiments and MD simulations revealed that the knot slid towards the C‐terminal during the unfolding process, which could be explained by the relatively strong interactions between the β‐sheet core at the N terminal of the native knot region. The size of the knot in the unfolded state is not larger than that in the native state. In addition, the knot slid in a “downhill” mode with simultaneous chain collapse in the denatured state.