新型平均势函数在蛋白质反向折叠中的应用

利用蛋白质主链的极性分数及主链二面角为参量,构建了一种基于蛋白质结构数据库的势函数。将该势函数应用于蛋白质反向折叠研究中,发现该函数可成功地将蛋白质分子的天然构象从构建的构象库中识别出来;将一目标序列与构象库的每一可能的构象匹配,并用该势函数计算相应的能量,结果表明对绝大多数蛋白质分子来说,天然的构象的能量值总是最低。此外,该函数还将一些序列相似性较低,而结构相似性较高的蛋白质分子识别出来。我们认     

Identification of folding preferences of cleavage junctions of HIV-1 precursor proteins for regulation of cleavability

Human immunodeficiency virus type 1 protease (HIV-1 PR) cleaves two viral precursor proteins, Gag and Gag-Pol, at multiple sites. Although the processing proceeds in the rank order to assure effective viral replication, the molecular mechanisms by which the order is regulated are not fully understood. In this study, we used bioinformatics approaches to examine whether the folding preferences of the cleavage junctions influence their cleavabilities by HIV-1 PR. The folding of the eight-amino-acid peptides corresponding to the seven cleavage junctions of the HIV-1_HXB2 Gag and Gag-Pol precursors were simulated in the PR-free and PR-bound states with molecular dynamics and homology modeling methods, and the relationships between the folding parameters and the reported kinetic parameters of the HIV-1_HXB2 peptides were analyzed. We found that a folding preference for forming a dihedral angle of Cβ (P1)-Cα (P1)- Cα (P1’)-Cβ (P1’) in the range of 150 to 180 degrees in the PR-free state was positively correlated with the 1/K_m (R = 0.95, P = 0.0008) and that the dihedral angle of the O (P2)-C (P2)- C (P1)- O (P1) of the main chains in the PR-bound state was negatively correlated with k_cat (R = 0.94, P = 0.001). We further found that these two folding properties influenced the overall cleavability of the precursor protein when the sizes of the side chains at the P1 site were similar. These data suggest that the dihedral angles at the specific positions around the cleavage junctions before and after binding to PR are both critical for regulating the cleavability of precursor proteins by HIV-1 PR.     

Statistical and conformational analysis of the electron density of protein side chains

Protein side chains make most of the specific contacts between proteins and other molecules, and their conformational properties have been studied for many years. These properties have been analyzed primarily in the form of rotamer libraries, which cluster the observed conformations into groups and provide frequencies and average dihedral angles for these groups. In recent years, these libraries have improved with higher resolution structures and using various criteria such as high thermal factors to eliminate side chains that may be misplaced within the crystallographic model coordinates. Many of these side chains have highly non-rotameric dihedral angles. The origin of side chains with high B-factors and/or with non-rotameric dihedral angles is of interest in the determination of protein structures and in assessing the prediction of side chain conformations. In this paper, using a statistical analysis of the electron density of a large set of proteins, it is shown that: (1) most non-rotameric side chains have low electron density compared to rotameric side chains; (2) up to 15% of chi1 non-rotameric side chains in PDB models can clearly be fit to density at a single rotameric conformation and in some cases multiple rotameric conformations; (3) a further 47% of non-rotameric side chains have highly dispersed electron density, indicating potentially interconverting rotameric conformations; (4) the entropy of these side chains is close to that of side chains annotated as having more than one chi(1) rotamer in the crystallographic model; (5) many rotameric side chains with high entropy clearly show multiple conformations that are not annotated in the crystallographic model. These results indicate that modeling of side chains alternating between rotamers in the electron density is important and needs further improvement, both in structure determination and in structure prediction.     

Accelerating all-atom protein folding simulations through reduced dihedral barriers

Protein folding requires extensive changes of backbone and sidechain dihedral angles, whose energy barriers constitute obstacles for the folding kinetics. Folding of small proteins is furthermore thought to be path-independent. Here, we propose that time-consuming all-atom protein folding simulations may be accelerated through a reduction of the dihedral barriers of the force field. In order to investigate this hypothesis, we performed various folding simulations of two small proteins. We report an acceleration towards smaller root-mean-square deviations from the native protein structure using our proposed method.     

Conformational analysis of molecular chains using nano-kinematics

We present algorithms for 3–D manipulation and conforma–tionalanalysis of molecular chains, when bond lengths, bond anglesand related dihedral angles remain fixed. These algorithms areuseful for local deformations of linear molecules, exact ringclosure in cyclic molecules and molecular embedding for shortchains. Other possible applications include structure prediction,protein folding, conformation energy analysis and 3D molecularmatching and docking. The algorithms are applicable to all serialmolecular chains and make no asssumptions about their geometry.We make use of results on direct and inverse kinematics fromrobotics and mechanics literature and show the correspondencebetween kinematics and conformational analysis of molecules.In particular, we pose these problems algebraically and computeall the solutions making use of the structure of these equationsand matrix computations. The algorithms have been implementedand perform well in practice. In particular, they take tensof milliseconds on current workstations for local deformationsand chain closures on molecular chains consisting of six orfewer rotatable dihedral angles     

A knowledge-based move set for protein folding

The free energy landscape of protein folding is rugged, occasionally characterized by compact, intermediate states of low free energy. In computational folding, this landscape leads to trapped, compact states with incorrect secondary structure. We devised a residue-specific, protein backbone move set for efficient sampling of protein-like conformations in computational folding simulations. The move set is based on the selection of a small set of backbone dihedral angles, derived from clustering dihedral angles sampled from experimental structures. We show in both simulated annealing and replica exchange Monte Carlo (REMC) simulations that the knowledge-based move set, when compared with a conventional move set, shows statistically significant improved ability at overcoming kinetic barriers, reaching deeper energy minima, and achieving correspondingly lower RMSDs to native structures. The new move set is also more efficient, being able to reach low energy states considerably faster. Use of this move set in determining the energy minimum state and for calculating thermodynamic quantities is discussed.     

Identification of regions of potential flexibility in protein structures: folding units and correlations with intron positions

An algorithm has been developed to estimate flexibility for potential hinge motion at specified residues, that is, the mutual movement of two domains by rotation around a set of main-chain dihedral angles with torsion angles of neighboring side chains as variables. Such conformational changes must occur without severe atomic collisions. Flexible hinges have been found that satisfy such criteria. Sequence flexibility charts were obtained by plotting the flexibility of each residue against the residue number. Such charts were calculated for 10 proteins (ovomucoid third domain, cytochrome c, lysozyme, hemoglobin β-chain, α-chymotrypsin, elastase, carboxypeptidase A, dihydrofolate reductase, triosephosphate isomerase, and alcohol dehydrogenase) taken from the Protein Data Bank. The first step of unfolding is likely to occur at the hinge point with the largest flexibility. Following this idea, the polypeptide chain can be dissected into several folding units according to the sequence flexibility chart. When two domains are separated by conformational changes at such a hinge, the sequence flexibility chart for each domain changes, and it is recalculated and used to indicate subsequent unfolding steps. In this process of iterative estimation of flexibile hinges, some well-isolated hinges, or the border line between flexible and inflexible regions, were found to be directly at or close to the positions of splice junctions in the eukaryotic genes. Of a total of 45 splice junctions in the 10 proteins examined in this paper, 38 junctions can be identified as flexible hinges between folding units. We suggest that the iterative estimation of flexible hinges may define an array of possible folding/unfolding paths, and that the exon–intron arrangement in the gene may be closely correlated with the folding process of the protein.     

New Insights into the Interdependence between Amino Acid Stereochemistry and Protein Structure

To successfully design new proteins and understand the effects of mutations in natural proteins, we must understand the geometric and physicochemical principles underlying protein structure. The side chains of amino acids in peptides and proteins adopt specific dihedral angle combinations; however, we still do not have a fundamental quantitative understanding of why some side-chain dihedral angle combinations are highly populated and others are not. Here we employ a hard-sphere plus stereochemical constraint model of dipeptide mimetics to enumerate the side-chain dihedral angles of leucine (Leu) and isoleucine (Ile), and identify those conformations that are sterically allowed versus those that are not as a function of the backbone dihedral angles ? and ψ. We compare our results with the observed distributions of side-chain dihedral angles in proteins of known structure. With the hard-sphere plus stereochemical constraint model, we obtain agreement between the model predictions and the observed side-chain dihedral angle distributions for Leu and Ile. These results quantify the extent to which local, geometrical constraints determine protein side-chain conformations.     

Conformational folding of xyloglucan side chains in aqueous solution from molecular dynamics simulation

Molecular dynamics simulation was carried out on xyloglucan with explicit water molecules to investigate the folding mechanism of side chains onto a main chain in aqueous solution. The model xyloglucan was composed of 12 beta-D-glucopyranoses as a main chain substituted with six galactoses and three xyloses as side chains. Two conditions were set for the ribbon-like main chain; one is restricted to be 'flat' and the other is without restriction. The free main chain of xyloglucan has a 'twisted' conformation as the major one. Conformational folding of side chains onto the main chain was analyzed with dihedral angles at each glycosidic linkage. In a 5-ns calculation, the xyloglucan has a tendency to contract in both the restricted and the free systems, but the mode of contraction is different. Side chains tend to stick onto the flat surface of the main chain in the restricted system, while they do not tightly do so in the free one; instead the main chain takes a twisted and sometimes embowed conformation. This result indicates that the main chain has greater attractive forces to bind side chains when it is flat, while it loses the ability as it is twisted.     

Side-chain conformational changes upon Protein-Protein Association

Conformational changes upon protein-protein association are the key element of the binding mechanism. The study presents a systematic large-scale analysis of such conformational changes in the side chains. The results indicate that short and long side chains have different propensities for the conformational changes. Long side chains with three or more dihedral angles are often subject to large conformational transition. Shorter residues with one or two dihedral angles typically undergo local conformational changes not leading to a conformational transition. A relationship between the local readjustments and the equilibrium fluctuations of a side chain around its unbound conformation is suggested. Most of the side chains undergo larger changes in the dihedral angle most distant from the backbone. The frequencies of the core-to-surface interface transitions of six nonpolar residues and Tyr are larger than the frequencies of the opposite surface-to-core transitions. The binding increases both polar and nonpolar interface areas. However, the increase of the nonpolar area is larger for all considered classes of protein complexes, suggesting that the protein association perturbs the unbound interfaces to increase the hydrophobic contribution to the binding free energy. To test modeling approaches to side-chain flexibility in protein docking, conformational changes in the X-ray set were compared with those in the docking decoy sets. The results lead to a better understanding of the conformational changes in proteins and suggest directions for efficient conformational sampling in docking protocols.     

New Insights into the Interdependence between Amino Acid Stereochemistry and Protein Structure

To successfully design new proteins and understand the effects of mutations in natural proteins, we must understand the geometric and physicochemical principles underlying protein structure. The side chains of amino acids in peptides and proteins adopt specific dihedral angle combinations; however, we still do not have a fundamental quantitative understanding of why some side-chain dihedral angle combinations are highly populated and others are not. Here we employ a hard-sphere plus stereochemical constraint model of dipeptide mimetics to enumerate the side-chain dihedral angles of leucine (Leu) and isoleucine (Ile), and identify those conformations that are sterically allowed versus those that are not as a function of the backbone dihedral angles ϕ and ψ. We compare our results with the observed distributions of side-chain dihedral angles in proteins of known structure. With the hard-sphere plus stereochemical constraint model, we obtain agreement between the model predictions and the observed side-chain dihedral angle distributions for Leu and Ile. These results quantify the extent to which local, geometrical constraints determine protein side-chain conformations.     

Normal mode analysis as a method to derive protein dynamics information from the Protein Data Bank

Normal mode analysis (NMA) can facilitate quick and systematic investigation of protein dynamics using data from the Protein Data Bank (PDB). We developed an elastic network model-based NMA program using dihedral angles as independent variables. Compared to the NMA programs that use Cartesian coordinates as independent variables, key attributes of the proposed program are as follows: (1) chain connectivity related to the folding pattern of a polypeptide chain is naturally embedded in the model; (2) the full-atom system is acceptable, and owing to a considerably smaller number of independent variables, the PDB data can be used without further manipulation; (3) the number of variables can be easily reduced by some of the rotatable dihedral angles; (4) the PDB data for any molecule besides proteins can be considered without coarse-graining; and (5) individual motions of constituent subunits and ligand molecules can be easily decomposed into external and internal motions to examine their mutual and intrinsic motions. Its performance is illustrated with an example of a DNA-binding allosteric protein, a catabolite activator protein. In particular, the focus is on the conformational change upon cAMP and DNA binding, and on the communication between their binding sites remotely located from each other. In this illustration, NMA creates a vivid picture of the protein dynamics at various levels of the structures, i.e., atoms, residues, secondary structures, domains, subunits, and the complete system, including DNA and cAMP. Comparative studies of the specific protein in different states, e.g., apo- and holo-conformations, and free and complexed configurations, provide useful information for studying structurally and functionally important aspects of the protein.     

Equilibrium transitions between side‐chain conformations in leucine and isoleucine

Despite recent improvements in computational methods for protein design, we still lack a quantitative, predictive understanding of the intrinsic probabilities for amino acids to adopt particular side‐chain conformations. Surprisingly, this question has remained unsettled for many years, in part because of inconsistent results from different experimental approaches. To explicitly determine the relative populations of different side‐chain dihedral angles, we performed all‐atom hard‐sphere Langevin Dynamics simulations of leucine (Leu) and isoleucine (Ile) dipeptide mimetics with stereo‐chemical constraints and repulsive‐only steric interactions between non‐bonded atoms. We determine the relative populations of the different χ₁ and χ₂ dihedral angle combinations as a function of the backbone dihedral angles ? and ψ. We also propose, and test, a mechanism for inter‐conversion between the different side‐chain conformations. Specifically, we discover that some of the transitions between side‐chain dihedral angle combinations are very frequent, whereas others are orders of magnitude less frequent, because they require rare coordinated motions to avoid steric clashes. For example, to transition between different values of χ₂, the Leu side‐chain bond angles κ₁ and κ₂ must increase, whereas to transition in χ₁, the Ile bond angles λ₁ and λ₂ must increase. These results emphasize the importance of computational approaches in stimulating further experimental studies of the conformations of side‐chains in proteins. Moreover, our studies emphasize the power of simple steric models to inform our understanding of protein structure, dynamics, and design. Proteins 2015; 83:1488–1499. © 2015 Wiley Periodicals, Inc.     

Proteins wriggle

We propose an algorithmic strategy for improving the efficiency of Monte Carlo searches for the low-energy states of proteins. Our strategy is motivated by a model of how proteins alter their shapes. In our model, when proteins fold under physiological conditions, their backbone dihedral angles change synchronously in groups of four or more to avoid steric clashes and respect the kinematic conservation laws. They wriggle; they do not thrash. We describe a simple algorithm that can be used to incorporate wriggling in Monte Carlo simulations of protein folding. We have tested this wriggling algorithm against a code in which the dihedral angles are varied independently (thrashing). Our standard of success is the average root-mean-square distance (rmsd) between the alpha-carbons of the folding protein and those of its native structure. After 100,000 Monte Carlo sweeps, the relative decrease in the mean rmsd, as one switches from thrashing to wriggling, rises from 11% for the protein 3LZM with 164 amino acids (aa) to 40% for the protein 1A1S with 313 aa and 47% for the protein 16PK with 415 aa. These results suggest that wriggling is useful and that its utility increases with the size of the protein. One may implement wriggling on a parallel computer or a computer farm.     

Secondary structures without backbone: an analysis of backbone mimicry by polar side chains in protein structures.

Backbone mimicry by the formation of closed-loop C7, C10 and C13 (mimics of gamma-, beta- and alpha-turns) conformations through side chain-main chain hydrogen bonds by polar groups is a frequent observation in protein structures. A data set of 250 non-homologous and high-resolution protein crystal structures was used to analyze these conformations for their characteristic features. Seven out of the nine polar residues (Ser, Thr, Asn, Asp, Gln, Glu and His) have hydrogen bonding groups in their side chains which can participate in such mimicry and as many as 15% of all these polar residues engage in such conformations. The distributions of dihedral angles of these mimics indicate that only certain combinations of the dihedral angles involved aid the formation of these mimics. The observed examples were categorized into various classes based on these combinations, resulting in well defined motifs. Asn and Asp residues show a very high capability to perform such backbone secondary structural mimicry. The most highly mimicked backbone structure is of the C10 conformation by the Asx residues. The mimics formed by His, Ser, Thr and Glx residues are also discussed. The role of such conformations in initiating the formation of regular secondary structures during the course of protein folding seems significant.     

Unique Optimal Foldings of Proteins on a Triangular Lattice

Background: A problem for unique protein folding was raised in 1998: are there proteins having unique optimal foldings for all lengths in the hydrophobic-hydrophilic (hydrophobic-polar; HP) model? To such a question, it was proved that on a square lattice there are (i) closed chains of monomers having unique optimal foldings for all even lengths and (ii) open monomer chains having unique optimal foldings for all lengths divisible by four. In this article, we aim to extend the previous work on a square lattice to the optimal foldings of proteins on a triangular lattice by examining the uniqueness property or stability of HP chain folding. Method: We consider this protein folding problem on a triangular lattice using graph theory. For an HP chain with length n > 13, generally it is very time-consuming to enumerate all of its possible folding conformations. Hence, one can hardly know whether or not it has a unique optimal folding. A natural problem is to determine for what value of n there is an n-node HP chain that has a unique optimal folding on a triangular lattice. Results and conclusion: Using graph theory, this article proves that there are both closed and open chains having unique optimal foldings for all lengths >19 in a triangular lattice. This result is not only general from the theoretical viewpoint, but also can be expected to apply to areas of protein structure prediction and protein design because of their close relationship with the concept of energy state and designability.     

Studying backbone torsional dynamics of intrinsically disordered proteins using fluorescence depolarization kinetics

Intrinsically disordered proteins (IDPs) do not autonomously adopt a stable unique 3D structure and exist as an ensemble of rapidly interconverting structures. They are characterized by significant conformational plasticity and are associated with several biological functions and dysfunctions. The rapid conformational fluctuation is governed by the backbone segmental dynamics arising due to the dihedral angle fluctuation on the Ramachandran ?–ψ conformational space. We discovered that the intrinsic backbone torsional mobility can be monitored by a sensitive fluorescence readout, namely fluorescence depolarization kinetics, of tryptophan in an archetypal IDP such as α-synuclein. This methodology allows us to map the site-specific torsional mobility in the dihedral space within picosecond-nanosecond time range at a low protein concentration under the native condition. The characteristic timescale of ~?1.4 ns, independent of residue position, represents collective torsional dynamics of dihedral angles (? and ψ) of several residues from tryptophan and is independent of overall global tumbling of the protein. We believe that fluorescence depolarization kinetics methodology will find broad application to study both short-range and long-range correlated motions, internal friction, binding-induced folding, disorder-to-order transition, misfolding and aggregation of IDPs.     

N-linked oligosaccharide chains of Sendai virus fusion protein determine the interaction with endoplasmic reticulum molecular chaperones

The selectivity and individual roles of the N-linked oligosaccharide chains of Sendai virus fusion protein (F protein) in the interaction with endoplasmic reticulum molecular chaperones were investigated by analyses of transient expression of single N-glycosylation mutants and sequential immunoprecipitation. We demonstrated differential interactions depending on the location of the N-linked oligosaccharide chain, and showed that these interactions were correlated with the folding and transport of F proteins. Moreover, mutant F proteins that lacked the specific N-linked oligosaccharide chains required for disulfide bond formation showed increased association with ERp57.     

Local and non-local native topologies reveal the underlying folding landscape of proteins

Due to Plaxco, Simons, Baker and others, it is now well known that the two-state single domain protein folding rate is fairly well predicted from knowledge of the topology of the native structure. Plaxco et al found that the folding rates of two-state proteins correlate with the average degree to which native contacts are 'local' within the chain sequence: fast-folders usually have mostly local structures. Here, we dissected the native topology further by focusing on non-local and local contacts using lower and upper bounds of allowable sequence separation in computing the average contact order. We analyzed non-local and local contacts of 82 two-state proteins whose experimental folding rates span over six orders of magnitude. We observed that both the number of non-local contacts and the average sequence separation of non-local contacts (non-local CO) are both negatively correlated with the folding rate, showing that the non-local contacts dominate the barrier-crossing process. Surprisingly, the local contact orders of the proteins also correlate with the folding rates. However, this correlation shows a strong positive trend indicating the role of a diffusive search in the denatured basin.