A conformational dynamics study of alpha-l-Rhap-(1-->2)[alpha-l-Rhap-(1-->3)]-alpha-l-Rhap-OMe in solution by NMR experiments and molecular simulations

The conformational preference of alpha-l-Rhap-(1-->2)[alpha-l-Rhap-(1-->3)]-alpha-l-Rhap-OMe in solution has been studied by NMR spectroscopy using one-dimensional (1)H,(1)H T-ROESY experiments and measurement of trans-glycosidic (3)J(C,H) coupling constants. Molecular dynamics (MD) simulations with a CHARMM22 type of force field modified for carbohydrates were performed with water as the explicit solvent. The homonuclear cross-relaxation rates, interpreted as effective proton-proton distances, were compared to those obtained from simulation. Via a Karplus torsional relationship, (3)J(C,H) values were calculated from simulation and compared to experimental data. Good agreement was observed between experimental data and the MD simulation, except for one inter-residue T-ROE between protons in the terminal sugar residues. The results show that the trisaccharide exhibits substantial conformational flexibility, in particular along the psi glycosidic torsion angles. Notably, for these torsions, a high degree of correlation (77%) was observed in the MD simulation revealing either psi(2)(+) psi(3)(+) or psi(2)(-)psi(3)(-) states. The simulations also showed that non-exoanomeric conformations were present at the phi torsion angles, but to a limited extent, with the phi(3) state populated to a larger extent than the phi(2) state. Further NMR analysis of the trisaccharide by translational diffusion measurements and (13)C T(1) relaxation experiments quantified global reorientation using an anisotropic model together with interpretation of the internal dynamics via the "model-free" approach. Fitting of the dynamically averaged states to experimental data showed that the psi(2)(+)psi(3)(+) state is present to approximately 49%, psi(2)(-) psi(3)(-) to approximately 39%, and phi(3) (non-exo) to approximately 12%. Finally, using a dynamic and population-averaged model, (1)H,(1)H T-ROE buildup curves were calculated using a full relaxation matrix approach and were found to be in excellent agreement with experimental data, in particular for the above inter-residue proton-proton interaction between the terminal residues.     

Molecular dynamics of apo-adenylate kinase: a distance replica exchange method for the free energy of conformational fluctuations

A large domain motion in adenylate kinase from E. coli (AKE) is studied with molecular dynamics. AKE undergoes a large-scale rearrangement of its lid and AMP-binding domains when the open form closes over its substrates, AMP, and Mg2+-ATP, whereby the AMP-binding and lid domains come closer to the core. The third domain, the core, is relatively stable during this motion. A reaction coordinate that monitors the distance between the AMP-binding and core domains is selected to be able to compare with the results of energy transfer experiments. Sampling along this reaction coordinate is carried out by using a distance replica exchange method (DREM), where systems that differ by a restraint potential enforcing different reaction coordinate values are independently simulated with periodic attempts at exchange of these systems. Several methods are used to study the efficiency and convergence properties of the DREM simulation and compared with an analogous non-DREM simulation. The DREM greatly accelerates the rate and extent of configurational sampling and leads to equilibrium sampling as measured by monitoring collective modes obtained from a principal coordinate analysis. The potential of mean force along the reaction coordinate reveals a rather flat region for distances from the open to a relatively closed AKE conformation. The potential of mean force for smaller distances has a distinct minimum that is quite close to that found in the closed form X-ray structure. In concert with a decrease in the reaction coordinate distance (AMP-binding-to-core distance) the lid-to-core distance of AKE also decreases. Therefore, apo AKE can fluctuate from its open form to conformations that are quite similar to its closed form X-ray structure, even in the absence of its substrates.     

Conformational Dynamics of apo‐GlnBP Revealed by Experimental and Computational Analysis

The glutamine binding protein (GlnBP) binds l ‐glutamine and cooperates with its cognate transporters during glutamine uptake. Crystal structure analysis has revealed an open and a closed conformation for apo‐ and holo‐GlnBP, respectively. However, the detailed conformational dynamics have remained unclear. Herein, we combined NMR spectroscopy, MD simulations, and single‐molecule FRET techniques to decipher the conformational dynamics of apo‐GlnBP. The NMR residual dipolar couplings of apo‐GlnBP were in good agreement with a MD‐derived structure ensemble consisting of four metastable states. The open and closed conformations are the two major states. This four‐state model was further validated by smFRET experiments and suggests the conformational selection mechanism in ligand recognition of GlnBP.     

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

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

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.     

The relationship between peptide plane rotation (PPR) and similar conformations

Currently, several energy functions and conformational search methods have been developed that are based on the observed distribution of phi and psi angles in protein structures. The definition of phi and psi angles is directly related to the orientation of the peptide plane (CA CO NH CA). Starting from one conformation and rotating a single peptide plane, the angles psi for one residue and phi for the consecutive residue that are linked by the peptide plane, display a continuous range of values within one global conformation. When peptide plane rotation is analyzed in several different conformations generated from a restricted conformation database, a large number of these conformations are related. Based on these observations, a new simplified all-atom representation for protein folding simulations is presented where only one torsion angle variable is required for each residue. The underlying theme of this article is that conformational search methods using phi and psi torsion space, search through many redundant conformations. These conformations are related by anticorrelated torsion changes of peptide plane rotations. ©1999 John Wiley & Sons, Inc. J Comput Chem 20: 947–955, 1999     

Structure and dynamics of the homologous series of alanine peptides: a joint molecular dynamics/NMR study

The phi,psi backbone angle distribution of small homopolymeric model peptides is investigated by a joint molecular dynamics (MD) simulation and heteronuclear NMR study. Combining the accuracy of the measured scalar coupling constants and the atomistic detail of the all-atom MD simulations with explicit solvent, the thermal populations of the peptide conformational states are determined with an uncertainty of <5 %. Trialanine samples mainly ( approximately 90%) a poly-l-proline II helix-like structure, some ( approximately 10%) beta extended structure, but no alphaR helical conformations. No significant change in the distribution of conformers is observed with increasing chain length (Ala(3) to Ala(7)). Trivaline samples all three major conformations significantly. Triglycine samples the four corner regions of the Ramachandran space and exists in a slow conformational equilibrium between the cis and trans conformation of peptide bonds. The backbone angle distribution was also studied for the segment Ala3 surrounded by either three or eight amino acids on both N- and C-termini from a sequence derived from the protein hen egg white lysozyme. While the conformational distribution of the central three alanine residues in the 9mer is similar to that for the small peptides Ala(3)-Ala(7), major differences are found for the 19mer, which significantly (30-40%) samples alphaR helical stuctures.     

Insights into the dynamics of HIV-1 protease: a kinetic network model constructed from atomistic simulations

The conformational dynamics in the flaps of HIV-1 protease plays a crucial role in the mechanism of substrate binding. We develop a kinetic network model, constructed from detailed atomistic simulations, to determine the kinetic mechanisms of the conformational transitions in HIV-1 PR. To overcome the time scale limitation of conventional molecular dynamics (MD) simulations, our method combines replica exchange MD with transition path theory (TPT) to study the diversity and temperature dependence of the pathways connecting functionally important states of the protease. At low temperatures the large-scale flap opening is dominated by a small number of paths; at elevated temperatures the transition occurs through many structurally heterogeneous routes. The expanded conformation in the crystal structure 1TW7 is found to closely mimic a key intermediate in the flap-opening pathways at low temperature. We investigated the different transition mechanisms between the semi-open and closed forms. The calculated relaxation times reveal fast semi-open ? closed transitions, and infrequently the flaps fully open. The ligand binding rate predicted from this kinetic model increases by 38-fold from 285 to 309 K, which is in general agreement with experiments. To our knowledge, this is the first application of a network model constructed from atomistic simulations together with TPT to analyze conformational changes between different functional states of a natively folded protein.     

Ramachandran-type plots for glycosidic linkages: Examples from molecular dynamic simulations using the Glycam06 force field

The goals of this article are to (1) provide further validation of the Glycam06 force field, specifically for its use in implicit solvent molecular dynamic (MD) simulations, and (2) to present the extension of G.N. Ramachandran's idea of plotting amino acid phi and psi angles to the glycosidic phi, psi, and omega angles formed between carbohydrates. As in traditional Ramachandran plots, these carbohydrate Ramachandran-type (carb-Rama) plots reveal the coupling between the glycosidic angles by displaying the allowed and disallowed conformational space. Considering two-bond glycosidic linkages, there are 18 possible conformational regions that can be defined by (alpha, phi, psi) and (beta, phi, psi), whereas for three-bond linkages, there are 54 possible regions that can be defined by (alpha, phi, psi, omega) and (beta, phi, psi, omega). Illustrating these ideas are molecular dynamic simulations on an implicitly hydrated oligosaccharide (700 ns) and its eight constituent disaccharides (50 ns/disaccharide). For each linkage, we compare and contrast the oligosaccharide and respective disaccharide carb-Rama plots, validate the simulations and the Glycam06 force field through comparison to experimental data, and discuss the general trends observed in the plots.     

Free energy surfaces for the alpha(1 --> 4)-glycosidic linkage: implications for polysaccharide solution structure and dynamics

We present a potential of mean force surface for rotation about phi and psi dihedral angles of the alpha(1 --> 4)-glycosidic linkage in the maltose disaccharide (4-O-alpha-d-glucopyranosyl-d-glucopyranose) in aqueous solution. Comparison of the vacuum and solution free energy surfaces for maltose shows the principal effects of water to be an increase in the rotational freedom of the alpha(1 --> 4) linkage brought about by lowering the energy barrier for syn to anti conformational changes as well as expansion of the range of low-energy phi,psi conformations. This free energy analysis thus provides a thermodynamic and conformational rationale for the effects of water on alpha(1 --> 4)-linked polysaccharides and carbohydrate glasses.     

Single molecule conformational dynamics of adenylate kinase: energy landscape, structural correlations, and transition state ensembles

We developed a coarse grained two-well model to study the single molecule protein conformational dynamics in microscopic detail at the residue level, overcoming the often encountered computational bottleneck. In particular, we explored the underlying conformational energy landscape of adenylate kinase, a crucial protein for signal transduction in the cell, and identified two major kinetic pathways for the conformational switch between open and closed states through either the intermediate state or the transient state. Based on the parameters fitted to the room-temperature experimental data, we predicted open and closed kinetic rates at the whole temperature ranges from 10 to 50 degrees C, which agree well with the experimental turnover numbers. After uncovering the underlying mechanism for conformational dynamics and exploring the structural correlations, we found the crucial dynamical interplay between the nucleoside monophosphate binding domain (NMP) and the ATP-binding domain (LID) in controlling the conformational switch. The key residues and contacts responsible for the conformational transitions are identified by following the time evolution of the two-dimensional spatial contact maps and characterizing the transition state as well as intermediate structure ensembles through phi value analysis. Our model provides a general framework to study the conformational dynamics of biomolecules and can be applied to many other systems.     

Conformational elasticity theory of chain molecules

This paper develops a conformational elasticity theory of chain molecules, which is based on three key points: (i) the molecular model is the rotational isomeric state (RIS) model; (ii) the conformational distribution function of a chain molecule is described by a function of two variables, the end-to-end distance of a chain conformation and the energy of the conformation; (iii) the rule of changes in the chain conformational states during deformation is that a number of chain conformations would vanish. The ideal deformation behavior calculated by the theory shows that the change in chain conformations is physically able to make the upward curvature of the stress-strain curve at the large-scale deformation of natural rubber. With the theory, different deformation behaviors between polymers with different chemical structures can be described, the energy term of the stress in the deformations can be predicted, and for natural rubber the fraction of the energy term is around 13%, coinciding with the experi     

Glucose orientation and dynamics in alpha-, beta-, and gamma-cyclodextrins

We investigate, using molecular dynamics (MD) computer simulations, the conformational behavior of alpha-, beta-, and gamma-cyclodextrins (CDs). Our analysis of a 30 ns trajectory of CD solution dynamics reveals the underlying conformational behaviours of the CDs that explain their relative flexibility. The distributions of the torsion angles related to the glycosidic linkages, P(phi,psi) were calculated for the three CDs. Most noticeable is the limited range in phi torsion rotations compared with psi rotations for all the CDs. This difference between the three CDs is amplified in the motion and dynamics of their glucose monomers when we monitor their orientational and librational positions relative to the macrocyclic mean plane. The relaxation times of the monomers to their equilibrium orientations follow the pattern gamma-CD > alpha-CD > beta-CD. The root-mean-square deviations of the motion of the monomer centers of mass from the mean macrocyclic planes exhibit the same trend.     

Quantifying polypeptide conformational space: sensitivity to conformation and ensemble definition

Quantifying the density of conformations over phase space (the conformational distribution) is needed to model important macromolecular processes such as protein folding. In this work, we quantify the conformational distribution for a simple polypeptide (N-mer polyalanine) using the cumulative distribution function (CDF), which gives the probability that two randomly selected conformations are separated by less than a "conformational" distance and whose inverse gives conformation counts as a function of conformational radius. An important finding is that the conformation counts obtained by the CDF inverse depend critically on the assignment of a conformation's distance span and the ensemble (e.g., unfolded state model): varying ensemble and conformation definition (1 --> 2 A) varies the CDF-based conformation counts for Ala(50) from 10(11) to 10(69). In particular, relatively short molecular dynamics (MD) relaxation of Ala(50)'s random-walk ensemble reduces the number of conformers from 10(55) to 10(14) (using a 1 A root-mean-square-deviation radius conformation definition) pointing to potential disconnections in comparing the results from simplified models of unfolded proteins with those from all-atom MD simulations. Explicit waters are found to roughen the landscape considerably. Under some common conformation definitions, the results herein provide (i) an upper limit to the number of accessible conformations that compose unfolded states of proteins, (ii) the optimal clustering radius/conformation radius for counting conformations for a given energy and solvent model, (iii) a means of comparing various studies, and (iv) an assessment of the applicability of random search in protein folding.     

Comparison between self-guided Langevin dynamics and molecular dynamics simulations for structure refinement of protein loop conformations

This article presents a comparative analysis of two replica‐exchange simulation methods for the structure refinement of protein loop conformations, starting from low‐resolution predictions. The methods are self‐guided Langevin dynamics (SGLD) and molecular dynamics (MD) with a Nosé–Hoover thermostat. We investigated a small dataset of 8‐ and 12‐residue loops, with the shorter loops placed initially from a coarse‐grained lattice model and the longer loops from an enumeration assembly method (the Loopy program). The CHARMM22 + CMAP force field with a generalized Born implicit solvent model (molecular‐surface parameterized GBSW2) was used to explore conformational space. We also assessed two empirical scoring methods to detect nativelike conformations from decoys: the all‐atom distance‐scaled ideal‐gas reference state (DFIRE‐AA) statistical potential and the Rosetta energy function. Among the eight‐residue loop targets, SGLD out performed MD in all cases, with a median of 0.48 Å reduction in global root‐mean‐square deviation (RMSD) of the loop backbone coordinates from the native structure. Among the more challenging 12‐residue loop targets, SGLD improved the prediction accuracy over MD by a median of 1.31 Å, representing a substantial improvement. The overall median RMSD for SGLD simulations of 12‐residue loops was 0.91 Å, yielding refinement of a median 2.70 Å from initial loop placement. Results from DFIRE‐AA and the Rosetta model applied to rescoring conformations failed to improve the overall detection calculated from the CHARMM force field. We illustrate the advantage of SGLD over the MD simulation model by presenting potential‐energy landscapes for several loop predictions. Our results demonstrate that SGLD significantly outperforms traditional MD in the generation and populating of nativelike loop conformations and that the CHARMM force field performs comparably to other empirical force fields in identifying these conformations from the resulting ensembles. Published 2011 Wiley Periodicals, Inc. J Comput Chem, 2011     

Conformational equilibrium of cytochrome P450 BM-3 complexed with N-palmitoylglycine: a replica exchange molecular dynamics study

UV-vis absorbance measurements and associated studies of cytochrome P450 BM-3 in complex with N-palmitoylglycine (NPG) indicate that a conformational change occurs in the active site of the complex where the terminal atoms of the ligand move from a site distant from the heme iron, as seen in the low temperature crystal structure to a site proximal to the heme iron at biological temperatures. We employ replica exchange molecular dynamics simulations to study this conformational change. The population of the proximal state is found to increase with temperature in agreement with UV-vis absorbance and NMR measurements. In addition to the conformations characterized by X-ray crystallography and computer modeling, this study shows that a new conformational state is significantly populated at room temperature. The observed increase in the population of conformations where the terminal atoms of NPG are proximal to the heme iron with increasing temperature indicates that the proximal state is stabilized by conformational entropy. A proposal for the origin of this entropic stabilization is provided on the basis of the structure of the newly identified state. We use the temperature weighted histogram (T-WHAM) method to characterize the transition state regions of the conformational ensemble and propose a mechanism of interconversion between these low free energy conformational states.     

Investigations into conformational transitions and solvation structure of a 7-piperidino-5,9-methanobenzo[8] annulene in water

Solvation shell structure of a 7-piperidino-5,9-methanobenzo[8] annulene (PMA) in water has been investigated in ambient conditions using both molecular dynamics (MD) and Car-Parrinello molecular dynamics (CPMD) calculations. From the MD calculations, we find that this molecule exists in three major conformational states out of which two are in twist-boat forms and one in chair form. Due to the limited time scale accessible in CPMD simulations, we have studied all the three conformational states separately using CPMD. The molecular geometry, electronic charge distribution and solvation structure for all three forms are investigated. The stability order of the chair and twist-boat conformations in water solvent has been reversed when compared to the gaseous phase results and in the case of polar aprotic solvents (J. Org. Chem., 1999, 61, 5979). From the radial distribution function, we find that the solvent density around the chair form is significantly lower, which has to be directly related to the smaller solvent accessible area for this conformation and this is in complete agreement with earlier reports. Among the findings are that the solvation shell structure around the nitrogen atom in the chair form of PMA is considerably different from the open conformational forms or the twist-boat forms. The dipole moment for the closed form is found to be significantly larger when compared to the twist-boat forms.     

Simulation studies of the fidelity of biomolecular structure ensemble recreation

We examine the ability of Bayesian methods to recreate structural ensembles for partially folded molecules from averaged data. Specifically we test the ability of various algorithms to recreate different transition state ensembles for folding proteins using a multiple replica simulation algorithm using input from "gold standard" reference ensembles that were first generated with a Go-like Hamiltonian having nonpairwise additive terms. A set of low resolution data, which function as the "experimental" phi values, were first constructed from this reference ensemble. The resulting phi values were then treated as one would treat laboratory experimental data and were used as input in the replica reconstruction algorithm. The resulting ensembles of structures obtained by the replica algorithm were compared to the gold standard reference ensemble, from which those "data" were, in fact, obtained. It is found that for a unimodal transition state ensemble with a low barrier, the multiple replica algorithm does recreate the reference ensemble fairly successfully when no experimental error is assumed. The Kolmogorov-Smirnov test as well as principal component analysis show that the overlap of the recovered and reference ensembles is significantly enhanced when multiple replicas are used. Reduction of the multiple replica ensembles by clustering successfully yields subensembles with close similarity to the reference ensembles. On the other hand, for a high barrier transition state with two distinct transition state ensembles, the single replica algorithm only samples a few structures of one of the reference ensemble basins. This is due to the fact that the phi values are intrinsically ensemble averaged quantities. The replica algorithm with multiple copies does sample both reference ensemble basins. In contrast to the single replica case, the multiple replicas are constrained to reproduce the average phi values, but allow fluctuations in phi for each individual copy. These fluctuations facilitate a more faithful sampling of the reference ensemble basins. Finally, we test how robustly the reconstruction algorithm can function by introducing errors in phi comparable in magnitude to those suggested by some authors. In this circumstance we observe that the chances of ensemble recovery with the replica algorithm are poor using a single replica, but are improved when multiple copies are used. A multimodal transition state ensemble, however, turns out to be more sensitive to large errors in phi (if appropriately gauged) and attempts at successful recreation of the reference ensemble with simple replica algorithms can fall short.     

Non-natural amino acids as modulating agents of the conformational space of model glycopeptides

The synthesis and conformational analysis in aqueous solution of different alpha-methyl-alpha-amino acid diamides, derived from serine, threonine, beta-hydroxycyclobutane-alpha-amino acids, and their corresponding model beta-O-glucopeptides, are reported. The study reveals that the presence of an alpha-methyl group forces the model peptides to adopt helix-like conformations. These folded conformations are especially significant for cyclobutane derivatives. Interestingly, this feature was also observed in the corresponding model glucopeptides, thus indicating that the alpha-methyl group and not the beta-O-glucosylation process largely determines the conformational preference of the backbone in these structures. On the other hand, atypical conformations of the glycosidic linkage were experimentally determined. Therefore, when a methyl group was located at the Cbeta atom with an R configuration, the glycosidic linkage was rather rigid. Nevertheless, when the S configuration was displayed, a significant degree of flexibility was observed for the glycosidic linkage, thus showing both alternate and eclipsed conformations of the psi(s) dihedral angle. In addition, some derivatives exhibited an unusual value for the phi(s) angle, which was far from a value of -60 degrees expected for a conventional beta-O-glycosidic linkage. In this sense, the different conformations exhibited by these molecules could be a useful tool in obtaining systems with conformational preferences "à la carte".