Structure and energy landscape of a photoswitchable peptide: a replica exchange molecular dynamics study

A replica exchange molecular dynamics (REMD) simulation of a bicyclic azobenzene peptide in explicit dimethyl sulfoxide solution is presented in order to characterize the conformational structures and energy landscape of a photoswitchable peptide. It is shown that an enhanced-sampling technique such as the REMD method is essential to obtain a converged conformational sampling of the peptide at room temperature. This is because conventional MD simulations of less than approximately 100-ns length are either trapped in local minima (at 295 K) or-if run at high temperature-do not resemble the room-temperature REMD results. Calculating various nuclear Overhauser effects (NOEs) and (3)J-couplings, a good overall agreement between the REMD simulations and the NMR experiments of Renner et al. (Biopolymers 2000;54:501-514) is found. In particular, the REMD study confirms the general picture drawn by Renner et al. that the trans-isomer of the azobenzene peptide exhibits a well-defined structure, while the cis-isomer is a conformational heterogeneous system; that is, the trans-isomer occurs in 2 well-defined conformers, while the cis-isomer represents an energetically frustrated system that leads to an ensemble of conformational structures. Employing a principal component analysis of the REMD data, the free energy landscape of the systems is studied at various temperatures. The implications for the folding and unfolding pathways of the system are discussed.     

Binding mechanism of spinosine and venenatine molecules with p300 HAT enzyme: Molecular screening,molecular dynamics and free-energy analysis

The chromatin modification is regulated by the histone acetyltransferase (HAT) and histone deacetyltransferase (HDAC) enzymes; abnormal function of these enzymes leads to several malignant diseases. The inhibition of these enzymes using natural ligand molecules is an emerging technique to cure these diseases. The in vitro analysis of natural molecules, venenatine, spinosine, palmatine and taxodione are giving the best inhibition rate against p300 HAT enzyme. However, the detailed understanding of binding and the stability of these molecules with p300 HAT is not yet known. The aim of the present study is focused to determine the binding strength of the molecules from molecular dynamics simulation analysis. The docking analysis confirms that, the venenatine (−6.97 kcal/mol - conformer 8), spinosine (−6.52 kcal/mol conformer −10), palmatine (−5.72 kcal/mol conformer-3) and taxodione (−4.99 kcal/mol conformer-4) molecules form strong hydrogen bonding interactions with the key amino acid residues (Arg1410, Thr1411 and Trp1466) present in the active site of p300. In the molecular dynamics (MD) simulation, the spinosine retain these key interactions with the active site amino acid residues (Arg1410, Thr1411, and Trp1466) than venenatine and are stable throughout the simulation. The RMSD value of spinosine (0.5 to 1.3 Å) and venenatine (0.3 to 1.3 Å) are almost equal during the MD simulation. However, during the MD simulation, the intermolecular interaction between venenatine and the active site amino acid residues (Arg1410, Thr1411, and Trp1466) decreased on comparing with the spinosine-p300 interaction. The binding free energy of the spinosine (−15.30 kcal/mol) is relatively higher than the venenatine (−11.8 kcal/mol); this increment is attributed to the strong hydrogen bonding interactions of spinosine molecule with the active site amino acid residues of p300.     

A simple way to compute protein dynamics without a mechanical model

We found that in proteins the average atomic fluctuation is linearly related to the square of the atomic distance from the center of mass of the protein. Using this simple relation, we can accurately compute the temperature factors of proteins of a wide range of sizes and folds, and the correlation of the fluctuations in proteins. This simple relation provides a direct link between protein dynamics and the static protein's geometrical shape and offers a simple way to compute protein dynamics without either long time trajectory integration or any matrix operations.     

Shortening a loop can increase protein native state entropy

Protein loops are essential structural elements that influence not only function but also protein stability and folding rates. It was recently reported that shortening a loop in the AcP protein may increase its native state conformational entropy. This effect on the entropy of the folded state can be much larger than the lower entropic penalty of ordering a shorter loop upon folding, and can therefore result in a more pronounced stabilization than predicted by polymer model for loop closure entropy. In this study, which aims at generalizing the effect of loop length shortening on native state dynamics, we use all‐atom molecular dynamics simulations to study how gradual shortening a very long or solvent‐exposed loop region in four different proteins can affect their stability. For two proteins, AcP and Ubc7, we show an increase in native state entropy in addition to the known effect of the loop length on the unfolded state entropy. However, for two permutants of SH3 domain, shortening a loop results only with the expected change in the entropy of the unfolded state, which nicely reproduces the observed experimental stabilization. Here, we show that an increase in the native state entropy following loop shortening is not unique to the AcP protein, yet nor is it a general rule that applies to all proteins following the truncation of any loop. This modification of the loop length on the folded state and on the unfolded state may result with a greater effect on protein stability. Proteins 2015; 83:2137–2146. © 2015 Wiley Periodicals, Inc.     

Structural basis of hierarchical multiple substates of a protein. II: Monte Carlo simulation of native thermal fluctuations and energy minimization

Conformational fluctuations in a globular protein, bovine pancreatic trypsin inhibitor, in the time range between picoseconds and nanoseconds are studied by a Monte Carlo simulation method. Multiple energy minima are derived from sampled conformations by minimizing their energy. They are distributed in clusters in the conformational space. A hierarchical structure is observed in the simulated dynamics. In the time range between 10(-14) and 10(-10) seconds dynamics is well represented by a superposition of vibrational motions within an energy well with transitions among minima within each cluster. Transitions among clusters take place in the time range of nanoseconds or longer.     

基于CLUE-S模型验证的海岸围垦区景观驱动因子贡献率

基于1990、2000、2009年TM影像、社会统计数据、野外调查数据,采用冗余分析和主成分分析方法对长江口奉贤段围垦区海岸带景观动态变化驱动力因子的贡献度进行分析,并利用Kappa指数对CLUE-S模型所选驱动力模拟效力进行验证.结果表明:海岸带围垦区景观动态变化的人为驱动因子贡献度(57.1％)大于自然驱动因子贡献度(42.9％).CLUE-S模型模拟的正确率达82％,研究区主要景观类型(耕地、未利用地和养殖塘)的Kappa指数均大于0.75,CLUE-S模型的模拟效果较理想,所选驱动力因子很好地模拟了规则景观突变的空间分布特征.     

Structural basis of hierarchical multiple substates of a protein. I: Introduction

A computer experiment of protein dynamics is carried out, which consists of two steps: (1) A Monte Carlo simulation of thermal fluctuations in the native state of a globular protein, bovine pancreatic trypsin inhibitor; and (2) a simulation of the quick freezing of fluctuating conformations into energy minima by minimization of the energy of a number of conformations sampled in the Monte Carlo simulation. From the analysis of results of the computer experiment is obtained the following picture of protein dynamics: multiple energy minima exist in the native state, and they are distributed in clusters in the conformational space. The dynamics has a hierarchical structure which has at least two levels. In the first level, dynamics is restricted within one of the clusters of minima. In the second, transitions occur among the clusters. Local parts of a protein molecule, side chains and local main chain segments, can take multiple locally stable conformations in the native state. Many minima result from combinations of these multiple local conformations. The hierarchical structure in the dynamics comes from interactions among the local parts. Protein molecules have two types of flexibility, each associated with elastic and plastic deformations, respectively.     

Local feature analysis: a statistical theory for reproducible essential dynamics of large macromolecules

Multivariate statistical methods are widely used to extract functional collective motions from macromolecular molecular dynamics (MD) simulations. In principal component analysis (PCA), a covariance matrix of positional fluctuations is diagonalized to obtain orthogonal eigenvectors and corresponding eigenvalues. The first few eigenvectors usually correspond to collective modes that approximate the functional motions in the protein. However, PCA representations are globally coherent by definition and, for a large biomolecular system, do not converge on the time scales accessible to MD. Also, the forced orthogonalization of modes leads to complex dependencies that are not necessarily consistent with the symmetry of biological macromolecules and assemblies. Here, we describe for the first time the application of local feature analysis (LFA) to construct a topographic representation of functional dynamics in terms of local features. The LFA representations are low dimensional, and like PCA provide a reduced basis set for collective motions, but they are sparsely distributed and spatially localized. This yields a more reliable assignment of essential dynamics modes across different MD time windows. Also, the intrinsic dynamics of local domains is more extensively sampled than that of globally coherent PCA modes.     

Comment on: "Energy landscape of a small peptide revealed by dihedral angle principal component analysis"

The dihedral angle principal component analysis method published recently by Mu, Nguyen, and Stock, is shown to produce distortions of the free energy landscape due to the neglect of constraints in the coordinates. It is further shown that these distortions can create artificial minima and energy barriers. The rugged energy landscape that the authors find for a small peptide chain might thus be an artifact of their method.     

Mechanisms involved in proteolytic degradation of globular proteins: The role of local and global fluctuations in the native structure

The mechanisms involved in degradation of the native protein structure was analyzed by comparing the temperature dependences of the hydrogen exchange (HE) and proteolytic cleavage rates of hen egg lysozyme (HEL), human hemoglobin (Hb), and its apoform (apoHb). Acceleration of the burstlike (all or none) proteolytic degradation of HEL in a high temperature range results from the intensification of global fluctuations with overal structure unfolding, indicated by HE. The rates of Hb and apoHb burstlike degradation and HE weakly depend on the temperature in the range where only local fluctuations of the native structure are detectable by HE. These two proteins are cleaved according to a self-accelerated burstlike mechanism with the initial rate-limiting single cleavage due to local fluctuations in the native structure. Such fluctuations play an important role in intracellular burstlike proteolytic degradation of native proteins.     

Protein-inhibitor flexible docking by a multicanonical sampling: native complex structure with the lowest free energy and a free-energy barrier distinguishing the native complex from the others

Flexible docking between a protein (lysozyme) and an inhibitor (tri-N-acetyl-D-glucosamine, tri-NAG) was carried out by an enhanced conformational sampling method, multicanonical molecular dynamics simulation. We used a flexible all-atom model to express lysozyme, tri-NAG, and water molecules surrounding the two bio-molecules. The advantages of this sampling method are as follows: the conformation of system is widely sampled without trapping at energy minima, a thermally equilibrated conformational ensemble at an arbitrary temperature can be reconstructed from the simulation trajectory, and the thermodynamic weight can be assigned to each sampled conformation. During the simulation, exchanges between the binding and free (i.e., unbinding) states of the protein and the inhibitor were repeatedly observed. The conformational ensemble reconstructed at 300 K involved various conformational clusters. The main outcome of the current study is that the most populated conformational cluster (i.e., the cluster of the lowest free energy) was assigned to the native complex structure (i.e., the X-ray complex structure). The simulation also produced non-native complex structures, where the protein and the inhibitor bound with different modes from that of the native complex structure, as well as the unbinding structures. A free-energy barrier (i.e., activation free energy) was clearly detected between the native complex structures and the other structures. The thermal fluctuations of tri-NAG in the lowest free-energy complex correlated well with the X-ray B-factors of tri-NAG in the X-ray complex structure. The existence of the free-energy barrier ensures that the lowest free-energy structure can be discriminated naturally from the other structures. In other words, the multicanonical molecular dynamics simulation can predict the native complex structure without any empirical objective function. The current study also manifested that the flexible all-atom model and the physico-chemically defined atomic-level force field can reproduce the native complex structure. A drawback of the current method is that it requires a time consuming computation due to the exhaustive conformational sampling. We discussed a possibility for combining the current method with conventional docking methods.     

Ab initio simulation of a 57-residue protein in explicit solvent reproduces the native conformation in the lowest free-energy cluster

An enhanced conformational sampling method, multicanonical molecular dynamics (McMD), was applied to the ab intio folding of the 57-residue first repeat of human glutamyl- prolyl-tRNA synthetase (EPRS-R1) in explicit solvent. The simulation started from a fully extended structure of EPRS-R1 and did not utilize prior structural knowledge. A canonical ensemble, which is a conformational ensemble thermodynamically probable at an arbitrary temperature, was constructed by reweighting the sampled structures. Conformational clusters were obtained from the canonical ensemble at 300 K, and the largest cluster (i.e., the lowest free-energy cluster), which contained 34% of the structures in the ensemble, was characterized by the highest similarity to the NMR structure relative to all alternative clusters. This lowest free-energy cluster included native-like structures composed of two anti-parallel α-helices. The canonical ensemble at 300 K also showed that a short Gly-containing segment, which adopts an α-helix in the native structure, has a tendency to be structurally disordered. Atomic-level analyses demonstrated clearly that inter-residue hydrophobic interactions drive the helix formation of the Gly-containing segment, and that increasing the hydrophobic contacts accompanies exclusion of water molecules from the vicinity of this segment. This study has shown, for the first time, that the free-energy landscape of a structurally well-ordered protein of about 60 residues is obtainable with an all atom model in explicit water without prior structural knowledge.     

Relation between sequence and structure of HIV-1 protease inhibitor complexes: a model system for the analysis of protein flexibility.

The flexibility of different regions of HIV-1 protease was examined by using a database consisting of 73 X-ray structures that differ in terms of sequence, ligands or both. The root-mean-square differences of the backbone for the set of structures were shown to have the same variation with residue number as those obtained from molecular dynamics simulations, normal mode analyses and X-ray B-factors. This supports the idea that observed structural changes provide a measure of the inherent flexibility of the protein, although specific interactions between the protease and the ligand play a secondary role. The results suggest that the potential energy surface of the HIV-1 protease is characterized by many local minima with small energetic differences, some of which are sampled by the different X-ray structures of the HIV-1 protease complexes. Interdomain correlated motions were calculated from the structural fluctuations and the results were also in agreement with molecular dynamics simulations and normal mode analyses. Implications of the results for the drug-resistance engendered by mutations are discussed briefly.     

Testing a flexible-receptor docking algorithm in a model binding site

Sampling receptor flexibility is challenging for database docking. We consider a method that treats multiple flexible regions of the binding site independently, recombining them to generate different discrete conformations. This algorithm scales linearly rather than exponentially with the receptor's degrees of freedom. The method was first evaluated for its ability to identify known ligands of a hydrophobic cavity mutant of T4 lysozyme (L99A). Some 200000 molecules of the Available Chemical Directory (ACD) were docked against an ensemble of cavity conformations. Surprisingly, the enrichment of known ligands from among a much larger number of decoys in the ACD was worse than simply docking to the apo conformation alone. Large decoys, accommodated in the larger cavity conformations sampled in the ensemble, were ranked better than known small ligands. The calculation was redone with an energy correction term that considered the cost of forming the larger cavity conformations. Enrichment improved, as did the balance between high-ranking large and small ligands. In a second retrospective test, the ACD was docked against a conformational ensemble of thymidylate synthase. Compared to docking against individual enzyme conformations, the flexible receptor docking approach improved enrichment of known ligands. Including a receptor conformational energy weighting term improved enrichment further. To test the method prospectively, the ACD database was docked against another cavity mutant of lysozyme (L99A/M102Q). A total of 18 new compounds predicted to bind this polar cavity and to change its conformation were tested experimentally; 14 were found to bind. The bound structures for seven ligands were determined by X-ray crystallography. The predicted geometries of these ligands all corresponded to the observed geometries to within 0.7A RMSD or better. Significant conformational changes of the cavity were observed in all seven complexes. In five structures, part of the observed accommodations were correctly predicted; in two structures, the receptor conformational changes were unanticipated and thus never sampled. These results suggest that although sampling receptor flexibility can lead to novel ligands that would have been missed when docking a rigid structure, it is also important to consider receptor conformational energy.     

Sequence-dependent dynamical instability of the human prion protein: a comparative simulation study

The present study aimed to explore the most probable regions of the human prion protein backbone for which the initial steps of conformational transitions as a result of intrinsic and extrinsic perturbing factors on the protein structure can be assigned. A total of 0.3-μs molecular dynamics simulations on several analog structures of the protein have been performed. To mimic the impact of the extrinsic and intrinsic destructive parameters on the dynamical characteristics of the protein, mild acidic conditions and R208H mutation have been simulated. The findings indicated that distribution of conformational flexibilities along the protein chain was almost independent of the induced perturbing factors, and was mostly centralized on certain distinct parts of the structure comprising residues 132–145 and 187–203. Analyses also revealed that the segment comprising residues 187–203 may be considered as a peptide sequence, possessing high potential to start the initial steps of conformational rearrangements due to the induced physicochemical alterations. Sequence alignment and molecular dynamics data also revealed that segment 178–203 prefers to accommodate in extended structures rather than α-helices. Region 178–203 may be considered as a peptide switch capable of initiating the conformational transitions due to the introduced modifications and perturbing parameters.     

A dynamic model of long-range conformational adaptations triggered by nucleotide binding in GroEL-GroES

The molecular chaperone, GroEL, essential for correct protein folding in E. coli, is composed of 14 identical subunits organized in two interacting rings, each providing a folding chamber for non‐native substrate proteins. The oligomeric assembly shows positive cooperativity within each ring and negative cooperativity between the rings. Although it is well known that ATP and long‐range allosteric interactions drive the functional cycle of GroEL, an atomic resolution view of how ligand binding modulates conformational adaptations over long distances remains a major challenge. Moreover, little is known on the relation between equilibrium dynamics at physiological temperatures and the allosteric transitions in GroEL. Here we present multiple all‐atom molecular dynamics simulations of the GroEL‐GroES assemblies at different stages of the functional cycle. Combined with an extensive analysis of the complete set of experimentally available structures, principal component analysis and conformer plots, we provide an explicit evaluation of the accessible conformational space of unliganded GroEL. Our results suggest the presence of pre‐existing conformers at the equatorial domain level, and a shift of the conformational ensemble upon ATP‐binding. At the inter‐ring interface the simulations capture a remarkable offset motion of helix D triggered by ATP‐binding to the folding active ring. The reorientation of helix D, previously only observed upon GroES association, correlates with a change of the internal dynamics in the opposite ring. This work contributes to the understanding of the molecular mechanisms in GroEL and highlights the ability of all‐atom MD simulations to model long‐range structural changes and allosteric events in large systems. Proteins 2012;. © 2012 Wiley Periodicals, Inc.     

Effects of substrate binding on the dynamics of RNase A: Molecular dynamics simulations of UpA bound and native RNase A

RNase A has been extensively used as a model protein in several biophysical and biochemical studies. Using the available structural and biochemical results, RNase A-UpA interaction has been computationally modeled at an atomic level. In this study, the molecular dynamics (MD) simulations of native and UpA bound RNase A have been carried out. The gross dynamical behavior and atomic fluctuations of the free and UpA bound RNase A have been characterized. Principal component analysis is carried out to identify the important modes of collective motion and to analyze the changes brought out in these modes of RNase A upon UpA binding. The hydrogen bonds are monitored to study the atomic details of RNase A-UpA interactions and RNase A-water interactions. Based on these analysis, the stability of the free and UpA bound RNase A are discussed. © 1997 John Wiley & Sons, Inc. Biopoly 42: 505–520, 1997     

Bias-free separation of internal and overall motion of biomolecules

Collective internal motions are known to be important for the function of biological macromolecules. It has been discussed in the past whether the application of superimposing algorithms to remove the overall motion from a structural ensemble introduces artificial correlations between distant atoms. Here we present a new method to eliminate residual rotation and translation from cartesian modes derived from a normal mode analysis or from a principal component analysis. Bias-free separation is based on the idea that the addition of modes of pure rotation/translation can compensate the residual overall motion. Removal of overall motion must reduce the "total amount of motion" (TAM) in the mode. Our algorithm allows to back-calculate revised covariance matrices. The approach was applied to two model systems that show residual overall motion, when analyzed using all atoms as reference for the superimposing algorithm. In both cases, our algorithm was capable of eliminating residual covariances caused by the overall motion, while retaining internal covariances even for very distant atoms. A structural ensemble obtained for a 13-ns molecular dynamics simulation of the protein Ribonuclease T1 showed a covariance matrix of the corrected modes with significantly sharper contours after applying the bias-free separation.