Mass-weighted molecular dynamics simulation of cyclic polypeptides.

A modified molecular dynamics (MD) method in which atomic masses are weighted was developed previously for studying the conformational flexibility of neuroregulating tetrapeptide Phe-Met-Arg-Phe-amide (FMRF-amide). The method has now been applied to longer and constrained molecules, namely a disulfide-linked cyclic hexapeptide, c[CYFQNC], and its linear and "pseudo-cyclic" analogues. The sampling of dehedral conformational space of teh linear hexapeptide in mass-weighted MD simulations was found to be improved significantly over conventional MD simulations, as in the case of the shorter FMRF-amide molecule studied previously. In the cyclic hexapeptide, the internal constraint of the molecule due to the intramolecular disulfide bond (hence the absence of free terminals in the molecule) does not adversely affect the significant improvement of conformational sampling in mass-weighted MD simulations over normal MD simulations. The pseudo-cyclic polypeptide is identical to the linear CYFQNC molecule in amino acid sequence (i.e., side chains of the cysteine residues are reduced), but the positions of its two terminal heavy atoms were held fixed in space such that the molecule has a nearly cyclic conformation. For this molecule, the mass-weighted MD simulation generated a wide range of polypeptide backbone conformations covering the internal dihedral degrees of freedom; moreover, the physical space of the pseudo-cyclic structure was also sampled in a complete revolution of the entire molecular fragment about the two fixed termini during the simulation. These characteristics suggest that mass-weighted MD can also be an extremely useful method for conformational analyses of constrained molecules and, in particular, for modeling loops on protein surfaces.     

Mass-weighted molecular dynamics simulation and conformational analysis of polypeptide.

Atomic motions in protein molecules have been studied by molecular dynamics (MD) simulations; dynamics simulation methods have also been employed in conformational studies of polypeptide molecules. It was found that when atomic masses are weighted, the molecular dynamics method can significantly increase the sampling of dihedral conformation space in such studies, compared to a conventional MD simulation of the same total simulation time length. Herein the theoretical study of molecular conformation sampling by the molecular dynamics-based simulation method in which atomic masses are weighted is reported in detail; moreover, a numerical scheme for analyzing the extensive conformational sampling in the simulation of a tetrapeptide amide molecule is presented. From numerical analyses of the mass-weighted molecular dynamics trajectories of backbone dihedral angles, low-resolution structures covering the entire backbone dihedral conformation space of the molecule were determined, and the distribution of rotationally stable conformations in this space were analyzed quantitatively. The theoretical analyses based on the computer simulation and numerical analytical methods suggest that distinctive regimes in the conformational space of the peptide molecule can be identified.     

Solvation Effects on the Conformational Behaviour of Gellan and Calcium Ion Binding to Gellan Double Helices

The contribution of the presence of solvent to the conformations adopted by disaccharide fragments within the repeat unit of gellan have been studied by molecular modelling techniques. Initial conformational energy searches, using a dielectric continuum to represent the solvent, provided starting geometries for a series of molecular dynamics simulations. The solution behaviour from these simulations was subsequently compared to fibre diffraction data of the potassium gellan salt. The present calculations indicate considerable flexibility of the glycosidic linkages, and this is discussed in relation to its effect on gel formation. One of the fragments was solvated with explicit water molecules. These calculations showed the same conformational behaviour as those simulations conducted in implicit solvent.Finally, a series of molecular dynamics (MD) simulations were performed to study the calcium binding to gellan. The results from this clearly showed a well defined binding site for this ion.Abbreviations MM molecular mechanics - MD molecular dynamics     

Ribosomal RNA kink-turn motif--a flexible molecular hinge

Ribosomal RNA K-turn motifs are asymmetric internal loops characterized by a sharp bend in the phosphodiester backbone resulting in "V" shaped structures, recurrently observed in ribosomes and showing a high degree of sequence conservation. We have carried out extended explicit solvent molecular dynamics simulations of selected K-turns, in order to investigate their intrinsic structural and dynamical properties. The simulations reveal an unprecedented dynamical flexibility of the K-turns around their X-ray geometries. The K-turns sample, on the nanosecond timescale, different conformational substates. The overall behavior of the simulations suggests that the sampled geometries are essentially isoenergetic and separated by minimal energy barriers. The nanosecond dynamics of isolated K-turns can be qualitatively considered as motion of two rigid helix stems controlled by a very flexible internal loop which then leads to substantial hinge-like motions between the two stems. This internal dynamics of K-turns is strikingly different for example from the bacterial 5S rRNA Loop E motif or BWYV frameshifting pseudoknot which appear to be rigid in the same type of simulations. Bistability and flexibility of K-turns was also suggested by several recent biochemical studies. Although the results of MD simulations should be considered as a qualitative picture of the K-turn dynamics due to force field and sampling limitations, the main advantage of the MD technique is its ability to investigate the region close to K-turn ribosomal-like geometries. This part of the conformational space is not well characterized by the solution experiments due to large-scale conformational changes seen in the experiments. We suggest that K-turns are well suited to act as flexible structural elements of ribosomal RNA. They can for example be involved in mediation of large-scale motions or they can allow a smooth assembling of the other parts of the ribosome.     

A coupling of homology modeling with multiple molecular dynamics simulation for identifying representative conformation of GPCR structures: a case study on human bombesin receptor subtype-3

In this study, a computational pipeline was therefore devised to overcome homology modeling (HM) bottlenecks. The coupling of HM with molecular dynamics (MD) simulation is useful in that it tackles the sampling deficiency of dynamics simulations by providing good-quality initial guesses for the native structure. Indeed, HM also relaxes the severe requirement of force fields to explore the huge conformational space of protein structures. In this study, the interaction between the human bombesin receptor subtype-3 and MK-5046 was investigated integrating HM, molecular docking, and MD simulations. To improve conformational sampling in typical MD simulations of GPCRs, as in other biomolecules, multiple trajectories with different initial conditions can be employed rather than a single long trajectory. Multiple MD simulations of human bombesin receptor subtype-3 with different initial atomic velocities are applied to sample conformations in the vicinity of the structure generated by HM. The backbone atom conformational space distribution of replicates is analyzed employing principal components analysis. As a result, the averages of structural and dynamic properties over the twenty-one trajectories differ significantly from those obtained from individual trajectories.     

Interpretation of Solution X-Ray Scattering by Explicit-Solvent Molecular Dynamics

Small- and wide-angle x-ray scattering (SWAXS) and molecular dynamics (MD) simulations are complementary approaches that probe conformational transitions of biomolecules in solution, even in a time-resolved manner. However, the structural interpretation of the scattering signals is challenging, while MD simulations frequently suffer from incomplete sampling or from a force-field bias. To combine the advantages of both techniques, we present a method that incorporates solution scattering data as a differentiable energetic restraint into explicit-solvent MD simulations, termed SWAXS-driven MD, with the aim to direct the simulation into conformations satisfying the experimental data. Because the calculations fully rely on explicit solvent, no fitting parameters associated with the solvation layer or excluded solvent are required, and the calculations remain valid at wide angles. The complementarity of SWAXS and MD is illustrated using three biological examples, namely a periplasmic binding protein, aspartate carbamoyltransferase, and a nuclear exportin. The examples suggest that SWAXS-driven MD is capable of refining structures against SWAXS data without foreknowledge of possible reaction paths. In turn, the SWAXS data accelerates conformational transitions in MD simulations and reduces the force-field bias.     

Advanced replica-exchange sampling to study the flexibility and plasticity of peptides and proteins

Molecular dynamics (MD) simulations are ideally suited to investigate protein and peptide plasticity and flexibility simultaneously at high spatial (atomic) and high time resolution. However, the applicability is still limited by the force field accuracy and by the maximum simulation time that can be routinely achieved in current MD simulations. In order to improve the sampling the replica-exchange (REMD) methodology has become popular and is now the most widely applied advanced sampling approach. Many variants of the REMD method have been designed to reduce the computational demand or to enhance sampling along specific sets of conformational variables. An overview on recent methodological advances and discussion of specific aims and advantages of the approaches will be given. Applications in the area of free energy simulations and advanced sampling of intrinsically disordered peptides and proteins will also be discussed. This article is part of a Special Issue entitled: The emerging dynamic view of proteins: Protein plasticity in allostery, evolution and self-assembly.     

Molecular dynamics simulations of Guanine quadruplex loops: advances and force field limitations

A computational analysis of d(GGGGTTTTGGGG)(2) guanine quadruplexes containing either lateral or diagonal four-thymidine loops was carried out using molecular dynamics (MD) simulations in explicit solvent, locally enhanced sampling (LES) simulations, systematic conformational search, and free energy molecular-mechanics, Poisson Boltzmann, surface area (MM-PBSA) calculations with explicit inclusion of structural monovalent cations. The study provides, within the approximations of the applied all-atom additive force field, a qualitatively complete analysis of the available loop conformational space. The results are independent of the starting structures. Major conformational transitions not seen in conventional MD simulations are observed when LES is applied. The favored LES structures consistently provide lower free energies (as estimated by molecular-mechanics, Poisson Boltzmann, surface area) than other structures. Unfortunately, the predicted optimal structure for the diagonal loop arrangement differs substantially from the atomic resolution experiments. This result is attributed to force field deficiencies, such as the potential misbalance between solute-cation and solvent-cation terms. The MD simulations are unable to maintain the stable coordination of the monovalent cations inside the diagonal loops as reported in a recent x-ray study. The optimal diagonal and lateral loop arrangements appear to be close in energy although a proper inclusion of the loop monovalent cations could stabilize the diagonal architecture.     

Ribosomal RNA Kink-turn Motif—A Flexible Molecular Hinge

Abstract

Ribosomal RNA K-turn motifs are asymmetric internal loops characterized by a sharp bend in the phosphodiester backbone resulting in “V” shaped structures, recurrently observed in ribosomes and showing a high degree of sequence conservation. We have carried out extended explicit solvent molecular dynamics simulations of selected K-turns, in order to investigate their intrinsic structural and dynamical properties. The simulations reveal an unprecedented dynamical flexibility of the K-turns around their X-ray geometries. The K-turns sample, on the nanosecond timescale, different conformational substates. The overall behavior of the simulations suggests that the sampled geometries are essentially isoenergetic and separated by minimal energy barriers. The nanosecond dynamics of isolated K-turns can be qualitatively considered as motion of two rigid helix stems controlled by a very flexible internal loop which then leads to substantial hinge-like motions between the two stems. This internal dynamics of K-turns is strikingly different for example from the bacterial 5S rRNA Loop E motif or BWYV frameshifting pseudoknot which appear to be rigid in the same type of simulations. Bistability and flexibility of K-turns was also suggested by several recent biochemical studies. Although the results of MD simulations should be considered as a qualitative picture of the K-turn dynamics due to force field and sampling limitations, the main advantage of the MD technique is its ability to investigate the region close to K-turn riboso- mal-like geometries. This part of the conformational space is not well characterized by the solution experiments due to large-scale conformational changes seen in the experiments. We suggest that K-turns are well suited to act as flexible structural elements of ribosomal RNA. They can for example be involved in mediation of large-scale motions or they can allow a smooth assembling of the other parts of the ribosome.     

Simulation of peptide folding with explicit water--a mean solvation method

A new approach to efficiently calculate solvent effect in computer simulation of macromolecular systems has been developed. Explicit solvent molecules are included in the simulation to provide a mean solvation force for the solute conformational search. Simulations of an alanine dipeptide in aqueous solution showed that the new approach is significantly more efficient than conventional molecular dynamics method in conformational search, mainly because the mean solvation force reduced the solvent damping effect. This approach allows the solute and solvent to be simulated separately with different methods. For the macromolecule, the rigid fragment constraint dynamics method we developed previously allows large time-steps. For the solvent, a combination of a modified force-bias Monte Carlo method and a preferential sampling can efficiently sample the conformational space. A folding simulation of a 16-residue peptide in water showed high efficiency of the new approach.     

Determination of conformational equilibrium of peptides in solution by NMR spectroscopy and theoretical conformational analysis: application to the calibration of mean-field solvation models.

Peptides occur in solution as ensembles of conformations rather than in a fixed conformation. The existing energy functions are usually inadequate to predict the conformational equilibrium in solution, because of failure to account properly for solvation, if the solvent is not considered explicitly (which is usually prohibitively expensive). NMR data are therefore widely incorporated into theoretical conformational analysis. Because of conformational flexibility, restrained molecular dynamics (with restraints derived from NMR data), which is usually applied to determine protein conformation is of limited use in the case of peptides. Instead, (a) the restraints are averaged within predefined time windows during molecular dynamics (MD) simulations (time averaging), (b) multiple-copy MD simulations are carried out and the restraints are averaged over the copies (ensemble averaging), or (c) a representative ensemble of sterically feasible conformations is generated and the weights of the conformations are then fitted so that the computed average observables match the experimental data (weight fitting). All these approaches are briefly discussed in this article. If an adequate force field is used, conformations with large statistical weights obtained from the weight-fitting procedure should also have low energies, which can be implemented in force field calibration. Such a procedure is particularly attractive regarding the parameterization of the solvation energy in nonaqueous solvents, e.g., dimethyl sulfoxide, for which thermodynamic solvation data are scarce. A method for calibration of solvation parameters in dimethyl sulfoxide, which is based on this principle was recently proposed by C. Baysal and H. Meirovitch (Journal of the American Chemical Society, 1998, Vol. 120, pp. 800--812), in which the energy gap between the conformations compatible with NMR data and the alternative conformations is maximized. In this work we propose an alternative method based on the principle that the best-fitting statistical weights of conformations should match the Boltzmann weights computed with the force field applied. Preliminary results obtained using three test peptides of varying conformational mobility: H-Ser(1)-Pro(2)-Lys(3)-Leu(4)-OH, Ac-Tyr(1)-D-Phe(2)-Ser(3)-Pro(4)-Lys(5)-Leu(6)-NH(2), and cyclo(Tyr(1)-D-Phe(2)-Ser(3)-Pro(4)-Lys(5)-Leu(6)) are presented.     

Assessment of flexible backbone protein design methods for sequence library prediction in the therapeutic antibody Herceptin-HER2 interface

Computational protein design methods can complement experimental screening and selection techniques by predicting libraries of low-energy sequences compatible with a desired structure and function. Incorporating backbone flexibility in computational design allows conformational adjustments that should broaden the range of predicted low-energy sequences. Here, we evaluate computational predictions of sequence libraries from different protocols for modeling backbone flexibility using the complex between the therapeutic antibody Herceptin and its target human epidermal growth factor receptor 2 (HER2) as a model system. Within the program RosettaDesign, three methods are compared: The first two use ensembles of structures generated by Monte Carlo protocols for near-native conformational sampling: kinematic closure (KIC) and backrub, and the third method uses snapshots from molecular dynamics (MD) simulations. KIC or backrub methods were better able to identify the amino acid residues experimentally observed by phage display in the Herceptin-HER2 interface than MD snapshots, which generated much larger conformational and sequence diversity. KIC and backrub, as well as fixed backbone simulations, captured the key mutation Asp98Trp in Herceptin, which leads to a further threefold affinity improvement of the already subnanomolar parental Herceptin-HER2 interface. Modeling subtle backbone conformational changes may assist in the design of sequence libraries for improving the affinity of antibody-antigen interfaces and could be suitable for other protein complexes for which structural information is available.     

Study and design of stability in GH5 cellulases

Thermostable enzymes that hydrolyze lignocellulosic materials provide potential advantages in process configuration and enhancement of production efficiency over their mesophilic counterparts in the bioethanol industry. In this study, the dynamics of β-1,4-endoglucanases (EC: 3.2.1.4) from family 5 of glycoside hydrolases (GH5) were investigated computationally. The conformational flexibility of 12 GH5 cellulases, ranging from psychrophilic to hyperthermophilic, was investigated by molecular dynamics (MD) simulations at elevated temperatures. The results indicated that the protein flexibility and optimum activity temperatures are appreciably correlated. Intra-protein interactions, packing density and solvent accessible area were further examined in crystal structures to investigate factors that are possibly involved in higher rigidity of thermostable cellulases. The MD simulations and the rules learned from analyses of stabilizing factors were used in design of mutations toward the thermostabilization of cellulase C, one of the GH5 endoglucanases. This enzyme was successfully stabilized both chemically and thermally by introduction of a new disulfide cross-link to its highly mobile 56-amino acid subdomain.     

Hybrid Monte Carlo with multidimensional replica exchanges: conformational equilibria of the hypervariable regions of a llama VHH antibody domain

Since the structural repertoire of the hypervariable regions of human antibodies is known to be more restricted than what is implied by sequence variability, a common approach to structural prediction is to use a knowledge-based (KB) method, such as the canonical structure model (C. Chothia and A. M. Lesk, Journal of Molecular Biology, 1987, Vol. 196, pp. 901-917). However, this model is less successful when applied to camelid heavy chain antibodies. In this study, molecular simulations were used to examine the conformational equilibria of the hypervariable regions (H1, H2, and H3) of a llama heavy chain variable domain, for which KB predictions are poor. Simulations were carried out using both conventional molecular dynamics (MD) and hybrid Monte Carlo with multidimensional replica exchanges (HYMREX). The advantage of the latter method is its ability to selectively target parts of the Hamiltonian that can most readily improve sampling. A novel variant of HYMREX was implemented in which, besides the temperature, torsional interactions and the range of nonbonded interactions were varied. To compare the sampling abilities of MD and this HYMREX scheme, simulations were started from a misfolded conformational state. Overall, MD yielded final conformations more similar to the initial state, implying quasi-ergodic sampling. In contrast, HYMREX achieved more ergodic sampling, and the majority of conformations that it sampled agreed well with the known crystal structure. The HYMREX simulation results were used to help identify the chief interactions governing the conformational equilibria and to reexamine the key assumptions underlying the KB predictions. The data show that the H1 region exhibited significant conformational freedom, in support of the hypothesis that main-chain structural variability in this region could play a greater role in antigen binding in camelid antibodies than it does in normal antibodies. Key H1 residues and associated inter-loop interactions are conjectured to account for the poor KB predictions.     

Crystallographic refinement by knowledge-based exploration of complex energy landscapes

Although X-ray crystallography remains the most versatile method to determine the three-dimensional atomic structure of proteins and much progress has been made in model building and refinement techniques, it remains a challenge to elucidate accurately the structure of proteins in medium-resolution crystals. This is largely due to the difficulty of exploring an immense conformational space to identify the set of conformers that collectively best fits the experimental diffraction pattern. We show here that combining knowledge-based conformational sampling in RAPPER with molecular dynamics/simulated annealing (MD/SA) vastly improves the quality and power of refinement compared to MD/SA alone. The utility of this approach is highlighted by the automated determination of a lysozyme mutant from a molecular replacement solution that is in congruence with a model prepared independently by crystallographers. Finally, we discuss the implications of this work on structure determination in particular and conformational sampling and energy minimization in general.     

Simulation vs. reality: a comparison of in silico distance predictions with DEER and FRET measurements

Site specific incorporation of molecular probes such as fluorescent- and nitroxide spin-labels into biomolecules, and subsequent analysis by F?rster resonance energy transfer (FRET) and double electron-electron resonance (DEER) can elucidate the distance and distance-changes between the probes. However, the probes have an intrinsic conformational flexibility due to the linker by which they are conjugated to the biomolecule. This property minimizes the influence of the label side chain on the structure of the target molecule, but complicates the direct correlation of the experimental inter-label distances with the macromolecular structure or changes thereof. Simulation methods that account for the conformational flexibility and orientation of the probe(s) can be helpful in overcoming this problem. We performed distance measurements using FRET and DEER and explored different simulation techniques to predict inter-label distances using the Rpo4/7 stalk module of the M. jannaschii RNA polymerase. This is a suitable model system because it is rigid and a high-resolution X-ray structure is available. The conformations of the fluorescent labels and nitroxide spin labels on Rpo4/7 were modeled using in vacuo molecular dynamics simulations (MD) and a stochastic Monte Carlo sampling approach. For the nitroxide probes we also performed MD simulations with explicit water and carried out a rotamer library analysis. Our results show that the Monte Carlo simulations are in better agreement with experiments than the MD simulations and the rotamer library approach results in plausible distance predictions. Because the latter is the least computationally demanding of the methods we have explored, and is readily available to many researchers, it prevails as the method of choice for the interpretation of DEER distance distributions.     

Assessing the effect of D59P mutation in the DE loop region in amyloid aggregation propensity of β2‐microglobulin: A molecular dynamics simulation study

Dialysis‐related amyloidosis (DRA) is a severe condition characterized by the accumulation of amyloidogenic β2‐microglobulin (β2m) protein around skeletal joints and bones. The recent studies highlighted a critical role of the DE loop region for β2m stability and amyloid aggregation propensity. Despite significant efforts, the molecular mechanism of enhanced aggregation due to D59P mutation in the DE loop region remain elusive. In the present study, explicit‐solvent molecular dynamics (MD) simulations were performed to examine the key changes in the structural and dynamic properties of wild type (wt) β2m upon D59P mutation. MD simulations reveal a decrease in the average number of hydrogen bonds in the loop regions on D59P mutation that enhances conformational flexibility, which lead to higher aggregation propensity of D59P as compare to wt β2m. The principal component analysis (PCA) highlight that D59P covers a larger region of phase space and display a higher trace value than wt β2m, which suggest an overall enhancement in the conformational flexibility. D59P display two minimum energy basins in the free energy landscape (FEL) that are associated with thermodynamically less stable conformational states as compare to single minimum energy basin in wt β2m. The present study provides theoretical insights into the molecular mechanism behind the higher aggregation propensity of D59P as compare to wt β2m.     

Flexibility of the Bacterial Chaperone Trigger Factor in Microsecond-Timescale Molecular Dynamics Simulations

The bacterial chaperone trigger factor (TF) is the first chaperone to be encountered by a nascent protein chain as it emerges from the ribosome exit tunnel. Experimental results suggest that TF possesses considerable conformational flexibility, and in an attempt to provide an atomic-level view of this flexibility, we have performed independent 1.5-μs molecular dynamics simulations of TF in explicit solvent using two different simulation force fields (OPLS-AA/L and AMBER ff99SB-ILDN). Both simulations indicate that TF possesses tremendous flexibility, with huge excursions from the crystallographic conformation caused by reorientations of the protein’s constituent domains; both simulations also predict the formation of extensive contacts between TF’s PPIase domain and the Arm 1 domain that is involved in nascent-chain binding. In the OPLS simulation, however, TF rapidly settles into a very compact conformation that persists for at least 1 μs, whereas in the AMBER simulation, it remains highly dynamic; additional simulations in which the two force fields were swapped suggest that these differences are at least partly attributable to sampling issues. The simulation results provide potential rationalizations of a number of experimental observations regarding TF’s conformational behavior and have implications for using simulations to model TF’s function on translating ribosomes.     

Characterization of Protein Flexibility Using Small-Angle X-Ray Scattering and Amplified Collective Motion Simulations

Large-scale flexibility within a multidomain protein often plays an important role in its biological function. Despite its inherent low resolution, small-angle x-ray scattering (SAXS) is well suited to investigate protein flexibility and determine, with the help of computational modeling, what kinds of protein conformations would coexist in solution. In this article, we develop a tool that combines SAXS data with a previously developed sampling technique called amplified collective motions (ACM) to elucidate structures of highly dynamic multidomain proteins in solution. We demonstrate the use of this tool in two proteins, bacteriophage T4 lysozyme and tandem WW domains of the formin-binding protein 21. The ACM simulations can sample the conformational space of proteins much more extensively than standard molecular dynamics (MD) simulations. Therefore, conformations generated by ACM are significantly better at reproducing the SAXS data than are those from MD simulations.