Interpreting protein structural dynamics from NMR chemical shifts

In this investigation, semiempirical NMR chemical shift prediction methods are used to evaluate the dynamically averaged values of backbone chemical shifts obtained from unbiased molecular dynamics (MD) simulations of proteins. MD-averaged chemical shift predictions generally improve agreement with experimental values when compared to predictions made from static X-ray structures. Improved chemical shift predictions result from population-weighted sampling of multiple conformational states and from sampling smaller fluctuations within conformational basins. Improved chemical shift predictions also result from discrete changes to conformations observed in X-ray structures, which may result from crystal contacts, and are not always reflective of conformational dynamics in solution. Chemical shifts are sensitive reporters of fluctuations in backbone and side chain torsional angles, and averaged (1)H chemical shifts are particularly sensitive reporters of fluctuations in aromatic ring positions and geometries of hydrogen bonds. In addition, poor predictions of MD-averaged chemical shifts can identify spurious conformations and motions observed in MD simulations that may result from force field deficiencies or insufficient sampling and can also suggest subsets of conformational space that are more consistent with experimental data. These results suggest that the analysis of dynamically averaged NMR chemical shifts from MD simulations can serve as a powerful approach for characterizing protein motions in atomistic detail.     

Geometric algorithms for the conformational analysis of long protein loops

The efficient filtering of unfeasible conformations would considerably benefit the exploration of the conformational space when searching for minimum energy structures or during molecular simulation. The most important conditions for filtering are the maintenance of molecular chain integrity and the avoidance of steric clashes. These conditions can be seen as geometric constraints on a molecular model. In this article, we discuss how techniques issued from recent research in robotics can be applied to this filtering. Two complementary techniques are presented: one for conformational sampling and another for computing conformational changes satisfying such geometric constraints. The main interest of the proposed techniques is their application to the structural analysis of long protein loops. First experimental results demonstrate the efficacy of the approach for studying the mobility of loop 7 in amylosucrase from Neisseria polysaccharea. The supposed motions of this 17-residue loop would play an important role in the activity of this enzyme.     

A method for predicting protein conformational pathways by using molecular dynamics simulations guided by difference distance matrices

Here, an efficient method that predicts natural transition pathways between two endpoint states of an allosteric protein has been proposed. This method helps create structures that bridge these endpoints through multiple iterative and unbiased molecular dynamics simulations with explicit water. Difference distance matrices provide an approach for identifying states involving concerted slow motion. A series of structures are readily generated along the transition pathways of adenylate kinase. Predicted structures may be useful for an initial pathway to evaluate free energy landscapes via umbrella sampling and chain‐of‐states methods. © 2016 Wiley Periodicals, Inc.     

Metadynamics in the conformational space nonlinearly dimensionally reduced by Isomap

Atomic motions in molecules are not linear. This infers that nonlinear dimensionality reduction methods can outperform linear ones in analysis of collective atomic motions. In addition, nonlinear collective motions can be used as potentially efficient guides for biased simulation techniques. Here we present a simulation with a bias potential acting in the directions of collective motions determined by a nonlinear dimensionality reduction method. Ad hoc generated conformations of trans,trans-1,2,4-trifluorocyclooctane were analyzed by Isomap method to map these 72-dimensional coordinates to three dimensions, as described by Brown and co-workers [J. Chem. Phys. 129, 064118 (2008)]. Metadynamics employing the three-dimensional embeddings as collective variables was applied to explore all relevant conformations of the studied system and to calculate its conformational free energy surface. The method sampled all relevant conformations (boat, boat-chair, and crown) and corresponding transition structures inaccessible by an unbiased simulation. This scheme allows to use essentially any parameter of the system as a collective variable in biased simulations. Moreover, the scheme we used for mapping out-of-sample conformations from the 72D to 3D space can be used as a general purpose mapping for dimensionality reduction, beyond the context of molecular modeling.     

A distance geometry heuristic for expanding the range of geometries sampled during conformational search

A recent study of crystal structures of protein-ligand complexes has shown that bioactive conformations tend to be more extended than random ones (Diller and Merz, J. Comput. Aid. Mol. Des. 2002, 16, 105-112). Existing conformational sampling techniques produce molecular conformations with a distribution of geometric sizes that may not cover that of the bioactive conformations. Here, we describe a simple heuristic for biasing the conformational search toward more extended or compact conformations, while maintaining excellent sampling. The method uses a boosting strategy to generate a series of conformations, each of which is at least as extended (or compact) as the previous one. We demonstrate that this method significantly expands the range of geometric sizes generated during the search and thus increases the efficiency of sampling bioactive conformations.     

Understanding the role of the topology in protein folding by computational inverse folding experiments

Recent studies suggest that protein folding should be revisited as the emergent property of a complex system and that the nature allows only a very limited number of folds that seem to be strongly influenced by geometrical properties. In this work we explore the principles underlying this new view and show how helical protein conformations can be obtained starting from simple geometric considerations. We generated a large data set of C-alpha traces made of 65 points, by computationally solving a backbone model that takes into account only topological features of the all-alpha proteins; then, we built corresponding tertiary structures, by using the sequences associated to the crystallographic structures of four small globular all-alpha proteins from PDB, and analysed them in terms of structural and energetic properties. In this way we obtained four poorly populated sets of structures that are reasonably similar to the conformational states typical of the experimental PDB structures. These results show that our computational approach can capture the native topology of all-alpha proteins; furthermore, it generates backbone folds without the influence of the side chains and uses the protein sequence to select a specific fold among the generated folds. This agrees with the recent view that the backbone plays an important role in the protein folding process and that the amino acid sequence chooses its own fold within a limited total number of folds.     

Approximating protein flexibility through dynamic pharmacophore models: application to fatty acid amide hydrolase (FAAH)

A structure-based drug discovery method is described that incorporates target flexibility through the use of an ensemble of protein conformations. The approach was applied to fatty acid amide hydrolase (FAAH), a key deactivating enzyme in the endocannabinoid system. The resultant dynamic pharmacophore models are rapidly able to identify known FAAH inhibitors over drug-like decoys. Different sources of FAAH conformational ensembles were explored, with both snapshots from molecular dynamics simulations and a group of X-ray structures performing well. Results were compared to those from docking and pharmacophore models generated from a single X-ray structure. Increasing conformational sampling consistently improved the pharmacophore models, emphasizing the importance of incorporating target flexibility in structure-based drug design.     

A comparison of distance geometry and molecular dynamics simulation techniques for conformational analysis of β-cyclodextrin

Distance geometry and molecular dynamics simulation techniques were compared in their ability to search the conformational potential energy surface of β-cyclodextrin. Structures generated by the DISGEO program were minimized using three different atomic point charge sets. Some of these structures were used as starting points for molecular dynamics simulation in vacuo at 298K. The distance geometry results showed that the global features of the conformational potential energy surface were generally independent of the point charge set. The distance geometry technique was able to find structures of lower energy than those obtained by direct minimization of the X-ray or neutron diffraction structures. However, the molecular dynamics simulation technique was consistently able to find structures of lower energy than those generated by distance geometry. Root mean square fit of the trajectory structures to the starting structure showed that the simulation allowed the molecule to explore regions of the potential energy surface in the neighborhood of the starting structure. Both the distance geometry and molecular dynamics simulation techniques showed that β-cyclodextrin can adopt a wide range of conformations in the gas phase and that these conformations are much less symmetrical than the crystalline structure.     

The subspace iteration method in protein normal mode analysis

Normal mode analysis plays an important role in relating the conformational dynamics of proteins to their biological function. The subspace iteration method is a numerical procedure for normal mode analysis that has enjoyed widespread success in the structural mechanics community due to its numerical stability and computational efficiency in calculating the lowest normal modes of large systems. Here, we apply the subspace iteration method to proteins to demonstrate its advantageous properties in this area of computational protein science. An effective algorithm for choosing the number of iteration vectors in the method is established, offering a considerable improvement over the original implementation. In the present application, computational time scales linearly with the number of normal modes computed. Additionally, the method lends itself naturally to normal mode analyses of multiple neighboring macromolecular conformations, as demonstrated in a conformational change pathway analysis of adenylate kinase. These properties, together with its computational robustness and intrinsic scalability to multiple processors, render the subspace iteration method an effective and reliable computational approach to protein normal mode analysis. © 2009 Wiley Periodicals, Inc. J Comput Chem 2010     

Conformational heterogeneity observed in simulations of a pyrene-substituted DNA

NMR studies previously carried out for a DNA system with a pyrene-substituted base did not observe NOEs involving the adenine located 5' to the pyrene, and thus the conformation of the adenine was poorly defined in the resulting family of refined structures. However, chemical shift data suggested that an AT base pair may be present. We have carried out fully unrestrained molecular dynamics simulations starting from several members of the family of structures, and these simulations support the existence of an AT base pair for this region. Simulations in both explicit and implicit solvent were carried out, with each converging to either anti or syn conformation for adenine and base pairing in all cases. During these simulations, large and dramatic conformational changes are observed that suggest pathways for complex conformational changes in the highly packed DNA interior. Our analysis reveals little difference in the energies of these syn and anti conformations, in contrast to control calculations carried out for standard DNA (in the absence of a neighboring pyrene). While no interconversion between the conformations was observed in standard simulations, reversible anti/syn exchange was directly simulated using the locally enhanced sampling approach. No exchange was seen in the non-pyrene control sequence. Together, these results suggest that an increased flexibility is introduced as a consequence of the pyrene substitution, offering an explanation that is consistent with the available experimental data. These results increase our optimism that simulations in atomic detail may provide accurate models for experimental observations in complex systems.     

Insights into the conformational switching mechanism of the human vascular endothelial growth factor receptor type 2 kinase domain

Human vascular endothelial growth factor receptor type 2 (h-VEFGR2) is a receptor tyrosine kinase involved in the angiogenesis process and regarded as an interesting target for the design of anticancer drugs. Its activation/inactivation mechanism is related to conformational changes in its cytoplasmatic kinase domain, involving first among all the αC-helix in N-lobe and the A-loop in C-lobe. Affinity of inhibitors for the active or inactive kinase form could dictate the open or closed conformation of the A-loop, thus making the different conformations of the kinase domain receptor (KDR) domain different drug targets in drug discovery. In this view, a detailed knowledge of the conformational landscape of KDR domain is of central relevance to rationalize the efficiency and selectivity of kinase inhibitors. Here, molecular dynamics simulations were used to gain insight into the conformational switching activity of the KDR domain and to identify intermediate conformations between the two limiting active and inactive conformations. Specific energy barriers have been selectively removed to induce, and hence highlight at the atomistic level, the regulation mechanism of the A-loop opening. The proposed strategy allowed to repeatedly observe the escape of the KDR domain from the DFG-out free energy basin and to identify rare intermediate conformations between the DFG-out and the DFG-in structures to be employed in a structure-based drug discovery process.     

Enhanced sampling method in molecular simulations using genetic algorithm for biomolecular systems

We propose a molecular simulation method using genetic algorithm (GA) for biomolecular systems to obtain ensemble averages efficiently. In this method, we incorporate the genetic crossover, which is one of the operations of GA, to any simulation method such as conventional molecular dynamics (MD), Monte Carlo, and other simulation methods. The genetic crossover proposes candidate conformations by exchanging parts of conformations of a target molecule between a pair of conformations during the simulation. If the candidate conformations are accepted, the simulation resumes from the accepted ones. While conventional simulations are based on local update of conformations, the genetic crossover introduces global update of conformations. As an example of the present approach, we incorporated genetic crossover to MD simulations. We tested the validity of the method by calculating ensemble averages and the sampling efficiency by using two kinds of peptides, ALA3 and (AAQAA)₃. The results show that for ALA3 system, the distribution probabilities of backbone dihedral angles are in good agreement with those of the conventional MD and replica-exchange MD simulations. In the case of (AAQAA)₃ system, our method showed lower structural correlation of α-helix structures than the other two methods and more flexibility in the backbone ψ angles than the conventional MD simulation. These results suggest that our method gives more efficient conformational sampling than conventional simulation methods based on local update of conformations. © 2018 Wiley Periodicals, Inc.     

Monte Carlo simulations on short single-stranded oligonucleotides. I. Application to RNA trimers

Monte Carlo (MC) structural simulation of short RNA sequences has been carried out by random variations of the nucleotide conformational angles (i.e., phosphodiester chain torsional angles and sugar pucker pseudorotational angles). All of the chemical bond lengths and valence angles remained fixed during the structural simulation, except those of the sugar pucker ring. In this article we present the simulated structures of RNA trimers—r(AAA) and r(AAG)—obtained at 11°C and 70°C. The influence of various initial conformations (selected as starting points in the MC simulations) on the equilibrium conformations has been discussed. The simulated conformational angles have been compared with those estimated by nuclear magnetic resonance (NMR) spectroscopy. For both of the oligonucleotides studied here, the most stable structures are helical conformations with stacked bases, at 11°C and 70°C. However, when the starting point is a stretched chain, it is found that r(AAA) adopts a reverse-stacked structure at low temperature (11°C), in which the A3 base is located between the A1 and A2 bases. Although the energies of these conformations (helical and reverse stacked) are very close to each other, the potential barrier between them is extremely high (close to 30 kcal/mol). This hinders the conformational transition from one structure to the other at a given temperature (and in the course of a same MC simulation). However, it is possible to simulate this structural transition by heating the reverse-stacked structure up to 500°C and cooling down progressively to 70°C and 11°C: Canonical helical structures have been obtained by this procedure. © 1994 by john Wiley & Sons, Inc.     

Accelerated molecular dynamics simulations of protein folding

Folding of four fast‐folding proteins, including chignolin, Trp‐cage, villin headpiece and WW domain, was simulated via accelerated molecular dynamics (aMD). In comparison with hundred‐of‐microsecond timescale conventional molecular dynamics (cMD) simulations performed on the Anton supercomputer, aMD captured complete folding of the four proteins in significantly shorter simulation time. The folded protein conformations were found within 0.2–2.1 Å of the native NMR or X‐ray crystal structures. Free energy profiles calculated through improved reweighting of the aMD simulations using cumulant expansion to the second‐order are in good agreement with those obtained from cMD simulations. This allows us to identify distinct conformational states (e.g., unfolded and intermediate) other than the native structure and the protein folding energy barriers. Detailed analysis of protein secondary structures and local key residue interactions provided important insights into the protein folding pathways. Furthermore, the selections of force fields and aMD simulation parameters are discussed in detail. Our work shows usefulness and accuracy of aMD in studying protein folding, providing basic references in using aMD in future protein‐folding studies. © 2015 Wiley Periodicals, Inc.     

Impact of Stable Protein-protein Interaction on Protein Conformational Space

Backbone dihedral angle based clustering approach was applied to investigate the effect of protein complexation on backbone conformational space and the effect on protein dynamics. Three representative enzyme-inhibitor complexes and their comprised proteins were used as models for small-and moderate-sized globular proteins to compare available backbone conformational space before and after complexation. Microsecond time scale molecular dynamic simulations were generated to ensure sufficient statistics. The result suggests that stable protein-protein interactions lead to redistribution of protein backbone mobility and restriction of the protein backbone conformational space, especially for short time scale motions. Surprisingly, these effects are found to be uncorrelated with protein-protein interaction surface. Consistent with many experimental and computational observations, our results indicate that both induced-fit and conformational selection models play roles in stable protein complexation process, with the dominant role being different for different protein complexes.     

An approximate method in using molecular mechanics simulations to study slow protein conformational changes

The broad range of characteristic motions in proteins has limited the applicability of molecular dynamics simulations in studying large-scale conformational transitions. We present an approximate method, making use of standard MD simulations and using a much larger integration time step, to obtain the structural changes for slow systematic motions of large complex systems. We show the applicability of this method by simulating the open to closed Calmodulin calcium binding domain conformational changes. Starting with the Ca2+-bound X-ray structure, and after the removal of the Ca2+ ions, our calculation yielded intermediate conformations during the rearrangement of helices in each Ca2+ binding pocket, leading to a structure with a lowest rmsd of 1.56 A compared to the NMR apo-calmodulin structure.     

Replica exchange with guided annealing for accelerated sampling of disordered protein conformations

We critically examine a recently proposed convective replica exchange (cRE) method for enhanced sampling of protein conformation based on theoretical and numerical analysis. The results demonstrate that cRE and related replica exchange with guided annealing (RE‐GA) schemes lead to unbalanced exchange attempt probabilities and break detailed balance whenever the system undergoes slow conformational transitions (relative to the temperature diffusion timescale). Nonetheless, numerical simulations suggest that approximate canonical ensembles can be generated for systems with small conformational transition barriers. This suggests that RE‐GA maybe suitable for simulating intrinsically disordered proteins, an important class of newly recognized functional proteins. The efficacy of RE‐GA is demonstrated by calculating the conformational ensembles of intrinsically disordered kinase inducible domain protein. The results show that RE‐GA helps the protein to escape nonspecific compact states more efficiently and provides several fold speedups in generating converged and largely correct ensembles compared to the standard temperature RE. © 2014 Wiley Periodicals, Inc.     

Molecular dynamics of apo-adenylate kinase: a principal component analysis

Adenylate kinase from E. coli (AKE) is studied with molecular dynamics. AKE undergoes large-scale motions of its Lid and AMP-binding domains when its open form closes over its substrates, AMP and Mg2+-ATP. The third domain, the Core, is relatively stable during closing. The resulting trajectory is analyzed with a principal component analysis method that decomposes the atom motions into modes ordered by their decreasing contributions to the total protein fluctuation. Simulations at 303 K (normal T) and 500 K (high T) reveal that at both temperatures the first three modes account for 70% of the total fluctuation. The residues that contribute the most to these three modes are concentrated in the Lid and AMP-binding domains. Analysis of the normal T modes indicates that the Lid and AMP-binding domains sample a broad distribution of conformations indicating that AKE is designed to provide its substrates with a large set of conformations. The high T results show that the Lid initially closes toward the Core. Subsequently, the Lid rotates to a new stable conformation that is different from what is observed in the substrate-bound AKE. These results are discussed in the context of experimental data that indicate that adenylate kinases do sample more than one conformational state in solution and that each of these conformational states undergoes substantial fluctuations. A pair of residues is suggested for labeling that would be useful for monitoring distance fluctuations by energy transfer experiments.