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.     

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.     

Reversible scaling of dihedral angle barriers during molecular dynamics to improve structure prediction of cyclic peptides.

Peptide cyclization or chemical cross-linking has frequently been used to restrict the conformational freedom of a peptide, for example, to enhance its capacity for selective binding to a target receptor molecule. Structure prediction of cyclic peptides is important to evaluate possible conformations prior to synthesis. Because of the conformational constraints imposed by cyclization low energy conformations of cyclic peptides can be separated by large energy barriers. In order to improve the conformational search properties of molecular dynamics (MD) simulations a potential scaling method has been designed. The approach consists of several consecutive MD simulations with a specific lowering of dihedral energy barriers and reduced nonbonded interactions between atoms separated by three atoms followed by gradually scaling the potential until the original barriers are reached. Application to four cyclic penta- and hexa-peptide test cases and a protein loop of known structure indicates that the potential scaling method is more efficient and faster in locating low energy conformations than standard MD simulations. Combined with a generalized Born implicit solvation model the low energy cyclic peptide conformations and the loop structure are in good agreement with experiment. Applications in the presence of explicit water molecules during the simulations showed also improved convergence to structures close to experiment compared with regular MD.     

Conformational properties of a cyclic peptide bradykinin B2 receptor antagonist using experimental and theoretical methods.

The solution conformation of the cyclic peptide J324 (cyclo0,6-[Lys0,Glu6,D-Phe7]BK), an antagonist targeted at the bradykinin (BK) B2 receptor, has been investigated using experimental and theoretical methods. In order to gain insight into the structural requirements essential for BK antagonism, we carried out molecular dynamics (MD) simulations using simulated annealing as the sampling protocol. Following a free MD simulation we performed simulations using nuclear Overhauser enhancement (NOE) distance constraints determined by NMR experiments. The low-energy structures obtained were compared with each other, grouped into families and analyzed with respect to the presence of secondary structural elements in their backbone. We also introduced new ways of plotting structural data for a more comprehensive analysis of large conformational sets. Finally, the relationship between characteristic backbone conformations and the spatial arrangement of specific pharmacophore centers was investigated.     

Enhanced conformational diversity search of CDR-H3 in antibodies: role of the first CDR-H3 residue

Through a conformation search by a simulation calculation, the relationships between the amino acid sequences and the conformations of the third complementarity-determining region of the antibody heavy chain (CDR-H3) were investigated to characterize the large conformational varieties of antibodies. Here, we focused on the structural role of the first CDR-H3 residue, and we selected two antibodies, 28B4 and PLG, whose CDR-H3 conformations are significantly different, having Trp and Gly at the first position, respectively. Multicanonical molecular dynamics simulations, with the advantage of enhanced sampling efficiency, were performed for the CDR-H3 fragments of 28B4 and PLG, and a modified CDR-H3 model of 28B4, where the first Trp residue was substituted with Gly. When the first CDR-H3 residue is Trp, almost all of the observed CDR-H3 loops were bent at the first residue. In contrast, when the first residue is Gly, large varieties of loop conformations were observed. The structural role of this Gly residue is discussed from the perspective of the other antibody structures in the database. When the surrounding residues were included in the calculations, CDR-H3 loop structures similar to those in the crystal structures were reproduced as the major conformations for both the 28B4 and PLG antibodies.     

Locally accessible conformations of proteins: multiple molecular dynamics simulations of crambin.

Multiple molecular dynamics (MD) simulations of crambin with different initial atomic velocities are used to sample conformations in the vicinity of the native structure. Individual trajectories of length up to 5 ns sample only a fraction of the conformational distribution generated by ten independent 120 ps trajectories at 300 K. The backbone atom conformational space distribution is analyzed using principal components analysis (PCA). Four different major conformational regions are found. In general, a trajectory samples only one region and few transitions between the regions are observed. Consequently, the averages of structural and dynamic properties over the ten trajectories differ significantly from those obtained from individual trajectories. The nature of the conformational sampling has important consequences for the utilization of MD simulations for a wide range of problems, such as comparisons with X-ray or NMR data. The overall average structure is significantly closer to the X-ray structure than any of the individual trajectory average structures. The high frequency (less than 10 ps) atomic fluctuations from the ten trajectories tend to be similar, but the lower frequency (100 ps) motions are different. To improve conformational sampling in molecular dynamics simulations of proteins, as in nucleic acids, multiple trajectories with different initial conditions should be used rather than a single long trajectory.     

Comprehensive analysis of the factors contributing to the stability and solubility of autonomous human VH domains

We report a comprehensive analysis of sequence features that allow for the production of autonomous human heavy chain variable (V(H)) domains that are stable and soluble in the absence of a light chain partner. Using combinatorial phage-displayed libraries and conventional biophysical methods, we analyzed the entire former light chain interface and the third complementarity determining region (CDR3). Unlike the monomeric variable domains of camelid heavy chain antibodies (V(H)H domains), in which autonomous behavior depends on interactions between the hydrophobic former light chain interface and CDR3, we find that the stability of many in vitro evolved V(H) domains is essentially independent of the CDR3 sequence and instead derives from mutations that increase the hydrophilicity of the former light chain interface by replacing exposed hydrophobic residues with structurally compatible hydrophilic substitutions. The engineered domains can be expressed recombinantly at high yield, are predominantly monomeric at high concentrations, unfold reversibly, and are even more thermostable than typical camelid V(H)H domains. Many of the stabilizing mutations are rare in natural V(H) and V(H)H domains and thus could not be predicted by studying natural sequences and structures. The results demonstrate that autonomous V(H) domains with structural properties beyond the scope of natural frameworks can be derived by using non-natural mutations, which differ from those found in camelid V(H)H domains. These findings should enable the development of libraries of synthetic V(H) domains with CDR3 diversities unconstrained by structural demands.     

Calculation of protein ionization equilibria with conformational sampling: pK(a) of a model leucine zipper, GCN4 and barnase.

The use of conformational ensembles provided by nuclear magnetic resonance (NMR) experiments or generated by molecular dynamics (MD) simulations has been regarded as a useful approach to account for protein motions in the context of pK(a) calculations, yet the idea has been tested occasionally. This is the first report of systematic comparison of pK(a) estimates computed from long multiple MD simulations and NMR ensembles. As model systems, a synthetic leucine zipper, the naturally occurring coiled coil GCN4, and barnase were used. A variety of conformational averaging and titration curve-averaging techniques, or combination thereof, was adopted and/or modified to investigate the effect of extensive global conformational sampling on the accuracy of pK(a) calculations. Clustering of coordinates is proposed as an approach to reduce the vast diversity of MD ensembles to a few structures representative of the average electrostatic properties of the system in solution. Remarkable improvement of the accuracy of pK(a) predictions was achieved by the use of multiple MD simulations. By using multiple trajectories the absolute error in pK(a) predictions for the model leucine zipper was reduced to as low as approximately 0.25 pK(a) units. The validity, advantages, and limitations of explicit conformational sampling by MD, compared with the use of an average structure and a high internal protein dielectric value as means to improve the accuracy of pK(a) calculations, are discussed.     

Partition decoupling for multi-gene analysis of gene expression profiling data

Background

Molecular dynamics (MD) simulations are powerful tools to investigate the conformational dynamics of proteins that is often a critical element of their function. Identification of functionally relevant conformations is generally done clustering the large ensemble of structures that are generated. Recently, Self-Organising Maps (SOMs) were reported performing more accurately and providing more consistent results than traditional clustering algorithms in various data mining problems. We present a novel strategy to analyse and compare conformational ensembles of protein domains using a two-level approach that combines SOMs and hierarchical clustering.

Results

The conformational dynamics of the α-spectrin SH3 protein domain and six single mutants were analysed by MD simulations. The Cα's Cartesian coordinates of conformations sampled in the essential space were used as input data vectors for SOM training, then complete linkage clustering was performed on the SOM prototype vectors. A specific protocol to optimize a SOM for structural ensembles was proposed: the optimal SOM was selected by means of a Taguchi experimental design plan applied to different data sets, and the optimal sampling rate of the MD trajectory was selected. The proposed two-level approach was applied to single trajectories of the SH3 domain independently as well as to groups of them at the same time. The results demonstrated the potential of this approach in the analysis of large ensembles of molecular structures: the possibility of producing a topological mapping of the conformational space in a simple 2D visualisation, as well as of effectively highlighting differences in the conformational dynamics directly related to biological functions.

Conclusions

The use of a two-level approach combining SOMs and hierarchical clustering for conformational analysis of structural ensembles of proteins was proposed. It can easily be extended to other study cases and to conformational ensembles from other sources.     

Molecular dynamics simulations of Ac-3Aib-Cage-3Aib-NHMe

Solvents play a stabilising role with the more stable conformations obtained in polar solvents than in vacuo. We investigate to what extent the structural propensities of the pentacyclo-undecane (PCU) cage polypeptide chain of the type Ac-3Aib-Cage-3Aib-NHMe are influenced in implicit water and in explicit solvents: methanol (MEOH), dimethyl sulphoxide (DMSO) and TIP3P water. The sampling of the α-helical conformations of the PCU cage polypeptide was investigated using the in-house modified PARM94 force-field parameters. Analysis of 50 ns molecular dynamics (MD) simulations revealed a tendency of the PCU cage polypeptide to assume bent structures, especially in polar solvents. The choice of solvents was designed to relate the simulations to physiological conditions. The individual amino-isobutyric acid residues predominantly sampled the right-handed and left-handed 3₁₀-helical conformations, indicating that the helical conformations are preferred in all four environments (in vacuo, MEOH, water and DMSO). Additionally, the 100 ns replica exchange MD (REMD) simulations of the PCU cage polypeptide in implicit water revealed more conformational variety present than in explicit solvents, and is more consistent with previous theoretical studies on the PCU cage residue. The present theoretical results may help in rationalising experimental results on these PCU cage polypeptides, and definitely show the importance of a dynamical approach for a correct interpretation and prediction of the conformational behaviour of the PCU cage molecules in different environments.     

Conformational transitions of flanking purines in HIV-1 RNA dimerization initiation site kissing complexes studied by CHARMM explicit solvent molecular dynamics

Dimerization of HIV-1 genomic RNA is initiated by kissing loop interactions at the Dimerization Initiation Site (DIS). Dynamics of purines that flank the 5' ends of the loop-loop helix in HIV-1 DIS kissing complex were explored using explicit solvent molecular dynamics (MD) simulations with the CHARMM force field. Multiple MD simulations (200 ns in total) of X-ray structures for HIV-1 DIS Subtypes A, B, and F revealed conformational variability of flanking purines. In particular, the flanking purines, which in the starting X-ray structures are bulged-out and stack in pairs, formed a consecutive stack of four bulged-out adenines at the beginning of several simulations. This conformation is seen in the crystal structure of DIS Subtype F with no interference from crystal packing, and was frequently reported in our preceding MD studies performed with the AMBER force field. However, as CHARMM simulations progressed, the four continuously stacked adenines showed conformational transitions from the bulged-out into the bulged-in geometries. Although such an arrangement has not been seen in any X-ray structure, it has been suggested by a recent NMR investigation. In CHARMM simulations, in the longer time scale, the flanking purines display the tendency to move to bulged-in conformations. This is in contrast with the AMBER simulations, which indicate a modest prevalence for bulged-out flanking base positions in line with the X-ray data. The simulations also suggest that the intermolecular stacking between purines from the opposite hairpins can additionally stabilize the kissing complex.     

Multi‐scale characterization of the energy landscape of proteins with application to the C3D/Efb‐C complex

We present a novel multi‐level methodology to explore and characterize the low energy landscape and the thermodynamics of proteins. Traditional conformational search methods typically explore only a small portion of the conformational space of proteins and are hard to apply to large proteins due to the large amount of calculations required. In our multi‐scale approach, we first provide an initial characterization of the equilibrium state ensemble of a protein using an efficient computational conformational sampling method. We then enrich the obtained ensemble by performing short Molecular Dynamics (MD) simulations on selected conformations from the ensembles as starting points. To facilitate the analysis of the results, we project the resulting conformations on a low‐dimensional landscape to efficiently focus on important interactions and examine low energy regions. This methodology provides a more extensive sampling of the low energy landscape than an MD simulation starting from a single crystal structure as it explores multiple trajectories of the protein. This enables us to obtain a broader view of the dynamics of proteins and it can help in understanding complex binding, improving docking results and more. In this work, we apply the methodology to provide an extensive characterization of the bound complexes of the C3d fragment of human Complement component C3 and one of its powerful bacterial inhibitors, the inhibitory domain of Staphylococcus aureus extra‐cellular fibrinogen‐binding domain (Efb‐C) and two of its mutants. We characterize several important interactions along the binding interface and define low free energy regions in the three complexes. Proteins 2010. © 2009 Wiley‐Liss, Inc.     

Temperature‐accelerated molecular dynamics gives insights into globular conformations sampled in the free state of the AC catalytic domain

The catalytic domain of the adenyl cyclase (AC) toxin from Bordetella pertussis is activated by interaction with calmodulin (CaM), resulting in cAMP overproduction in the infected cell. In the X‐ray crystallographic structure of the complex between AC and the C terminal lobe of CaM, the toxin displays a markedly elongated shape. As for the structure of the isolated protein, experimental results support the hypothesis that more globular conformations are sampled, but information at atomic resolution is still lacking. Here, we use temperature‐accelerated molecular dynamics (TAMD) simulations to generate putative all‐atom models of globular conformations sampled by CaM‐free AC. As collective variables, we use centers of mass coordinates of groups of residues selected from the analysis of standard molecular dynamics (MD) simulations. Results show that TAMD allows extended conformational sampling and generates AC conformations that are more globular than in the complexed state. These structures are then refined via energy minimization and further unrestrained MD simulations to optimize inter‐domain packing interactions, thus resulting in the identification of a set of hydrogen bonds present in the globular conformations. Proteins 2014; 82:2483–2496. © 2014 Wiley Periodicals, Inc.     

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.     

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.     

Exploration of the conformational space of myosin recovery stroke via molecular dynamics

Muscle contractions are driven by cyclic conformational changes of myosin, whose molecular mechanisms of operation are being elucidated by recent advances in crystallographic studies and single molecule experiments. To complement such structural studies and consider the energetics of the conformational changes of myosin head, umbrella sampling molecular dynamics (MD) simulations were performed with the all-atom model of the scallop myosin sub-fragment 1 (S1) with a bound ATP in solution in explicit water using the crystallographic near-rigor and transition state conformations as two references. The constraints on RMSD reaction coordinates used for the umbrella sampling were found to steer the conformational changes efficiently, and relatively close correlations have been observed between the set of characteristic structural changes including the lever arm rotation and the closing of the nucleotide binding pocket. The lever arm angle and key residue interaction distances in the nucleotide binding pocket and the relay helix show gradual changes along the recovery stroke reaction coordinate, consistent with previous crystallographic and computational minimum energy studies. Thermal fluctuations, however, appear to make the switch-2 coordination of ATP more flexible than suggested by crystal structures. The local solvation environment of the fluorescence probe, Trp 507 (scallop numbering), also appears highly mobile in the presence of thermal fluctuations.     

Conformational space exploration of Met- and Leu-enkephalin using the MOLS method, molecular dynamics, and Monte Carlo simulation--a comparative study

We report here a comparative study of the molecular conformational energy landscape generated using the mutually orthogonal Latin squares (MOLS) method, molecular dynamics (MD), and Monte Carlo (MC) simulation. The MOLS method, as described earlier from our laboratory, uses an experimental design technique to rapidly and exhaustively sample the low energy conformations of a molecule. MD and MC simulations have been used to perform similar tasks. In the comparison reported here, the three methods were applied to a pair of neuropeptides, namely Met- and Leu-enkephalin. A set of 1500 conformations of these enkephalins were generated using these methods with CHARMM22 force field, and the resulting samples were analyzed to determine the extent and nature of coverage of the conformational space. The results indicate that the MOLS method samples a larger number of possible conformations and identifies conformations closer to the experimental structures than the MD and MC simulations.     

Computation of nitroxide-nitroxide distances in spin-labeled DNA duplexes

Nanometer distances in nucleic acids can be measured by EPR using two 1-oxyl-2,2,5,5-tetramethylpyrroline radicals, with each label attached via a methylene group to a phosphorothioate-substituted backbone position as one of two phosphorothioate diastereomers (R(P) and S(P)). Correlating the internitroxide distance to the geometry of the parent molecule requires computational analysis of the label conformers. Here, we report sixteen 4-ns MD simulations on a DNA duplex d(CTACTGCTTTAG) .d(CTAAAGCAGTAG) with label pairs at C7/C19, T5/A17, and T2/T14, respectively. For each labeled duplex, four simulations were performed with S(P)/S(P), R(P)/R(P), S(P)/R(P), and R(P)/S(P) labels, with initial all trans label conformations. Another set of four simulations was performed for the 7/19-labeled duplex using a different label starting conformation. The average internitroxide distance r(MD) was within 0.2 A for the two sets of simulations for the 7/19-labeled duplex, indicating sufficient sampling of conformational space. For all three labeled duplexes studied, r(MD) agreed with experimental values, as well as with average distances obtained from an efficient conformer search algorithm (NASNOX). The simulations also showed that the labels have conformational preferences determined by the linker chemistry and label-DNA interactions. These results establish computational algorithms that allow use of the 1-oxyl-2,2,5,5-tetramethylpyrroline label for mapping global structures of nucleic acids.