Protein flexibility and dynamics using constraint theory

A new approach is presented for determining the rigid regions in proteins and the flexible joints between them. The short-range forces in proteins are modeled as constraints and we use a recently developed formalism from graph theory to analyze flexibility in the bond network. Forces included in the analysis are the covalent bond-stretching and bond-bending forces, salt bridges, and hydrogen bonds. We use a local function to associate an energy with individual hydrogen bonds, which then can be included or excluded depending on the bond strength. Colored maps of the rigid and flexible regions provide a direct visualization of where the motion of the protein can take place, consistent with these distance constraints. We also define a flexibility index that quantifies the local density of flexible or floppy modes, in terms of the dihedral angles that remain free to rotate in each flexible region. A negative flexibility index provides a measure of the density of redundant bonds in rigid regions. A new application of this approach is to simulate the maximal range of possible motions of the flexible regions by introducing Monte Carlo changes in the free dihedral angles, subject to the distance constraints. This is done using a method that maintains closure of the rings formed by covalent and hydrogen bonds in the flexible parts of the protein, and van der Waals overlaps between atoms are avoided. We use the locus of the possible motions of HIV protease as an example: movies of its motion can be seen at http://www.pa.msu.edu/~lei.     

Steered unfolding of ricin A and B chains

Highly toxic, heterodimeric protein ricin binds itself to the cell surface glycolipids or glycoproteins via its B-chain. The toxic A-chain halts protein synthesis by inactivating the ribosomes, leading to cell death. The translocation step requires partial unfolding of the protein. In this work mechanical unfolding of intact ricin as well as the individual A- and B-chains has been studied. A total of 110 ns simulation run has been performed to observe the unfolding of ricin dimer using steered molecular dynamics simulation. A gradual unfolding against a constant pulling velocity is observed for the ricin A-chain leaving the B-chain in its native-like structure. The breakage of the disulfide linkage connecting the two chains and reversal of the pulling ends of B-chain surprisingly reversed the picture as the B-chain starts to unfold from its N-terminal end. Due to the unfolding of B-chain from N-terminal end, the A-chain appears structurally rigid, which comes from the strong interfacial interactions (hydrophobic, hydrogen bonding, salt bridge). Mechanical unfolding of the individual monomers has also been performed to compare their stabilities in the monomeric and dimeric forms.     

Shielding effect in protein folding

One of the most important interactions responsible for protein folding and stability are hydrogen bonds between peptide groups. There is a constant competition between the water molecules and peptide groups in a hydrogen bond formation. Also side-chains take part in this process by reducing hydration of peptide group (shielding effect) that promotes the protein folding. In this paper, a new approach to take into account a shielding effect is presented. A modification of the energy function is derived and incorporated into the UNited RESidue (UNRES) force field. Canonical Molecular Dynamics and Replica Exchange Molecular Dynamics with UNRES force field is applied to study the influence of this effect on protein structure, folding kinetics and free energy landscapes. The results of test calculations suggest that even small contribution of this effect into energy function changes force field behavior as well as speeds up the folding process significantly.     

Detection of unusual RNA folding regions in HIV and SIV sequences

We have developed a method for detecting more stable and significant folding regions relative to others in the sequence. The algorithm is based on the calculation of the lowest free energy of RNA secondary structures and Monte Carlo simulation. For any given RNA segment, the stability and statistical significance of RNA folding are assessed by two measures: the stability score and the significance score. The stability score measures the degree of thermodynamic stability of the segment between all possible biological segments in the RNA sequence. The significance score characterizes the specific arrangement of the nucleotides in the segment that could imply a structural role for the sequence information. Using these two measures, we are able to detect a series of distinct folding regions where highly stable and statistically significant secondary structures occur in human immunodeficiency virus (HIV) and simian immunodeficiency virus (SIV) sequences.     

FUS: a system to simulate conformational changes in biological macromolecules

In order to study the dynamics of protein and nucleic acid conformations, a molecular folding-unfolding system (FUS written in Lisp) has been developed. Secondary structure features of protein and nucleic acids are graphically represented by cubes in a modified 'Blocks World' paradigm. Modeling of protein and nucleic acid unfolding (denaturation) and folding of their three-dimensional structure is possible by the use of high level 'block' operators which allow displacement of these structural features in space. Due to the flexible nature of this program, FUS is a useful tool for the rapid evaluation of user-defined rules governing conformational changes. The use of FUS to unfold three common proteins (prealbumin, flavodoxin and triose phosphate isomerase) and a tRNA is presented.     

Experimental approaches to protein folding based on the concept of a slow hydrogen exchange core

In a review of protein hydrogen exchange, we concluded that the slow exchange core is the folding core. By this we mean that the elements of secondary structure carrying the slowest exchanging backbone amides will tend to be the elements of secondary structure to fold first, that partially folded proteins will tend to be most organized in the core, and that peptides made to mimic the slow exchange core will tend to show nativelike structure. These generalizations have led us to ask several experimental questions that will be examined here: (1) In partially folded and unfolded proteins, how do the dynamics and structure of core regions differ from noncore regions? (2) Can we make protein 'core modules' as peptides corresponding to the slow exchange core? Can core modules be covalently linked to make a native state in which one conformation is significantly more stable than all other accessible conformations? (3) In a mutant perturbed outside the core, what are the effects on hydrogen exchange and folding?     

Thermotoga martima嗜热木聚糖酶化学修饰结果与其结构特性关系研究

应用化学修饰的实验方法,结合蛋白质结构信息的计算来研究酶蛋白中氨基酸残基化学修饰与结构信息之间的关系。以Thermotoga maritima嗜热木聚糖酶为对象,采用PDB数据库中的1VBR为模板计算其序列中色氨酸、谷氨酸、天冬氨酸的溶剂可及性、氢键、盐桥数等结构特性,并与该酶化学修饰的实验结果相对比。结果表明酶活性中心3个色氨酸中,可及性大的Trp802与Trp602两个残基对酶的活性影响较大;序列中谷氨酸与天冬氨酸的氢键、盐桥数较多,修饰其对酶的热稳定性有很大影响。此结果有助于深入了解蛋白质中与化学修饰有关的结构特性,并为基于蛋白质结构的酶蛋白改性奠定了基础。     

Consistent Sets of Secondary Structures in Proteins

Ab initio predictions of secondary structures in proteins have to combine local predictions, based on short fragments of the protein sequence, with consistency restrictions, as not all locally plausible predictions may be simultaneously true. We use the fact that secondary structures are patterns of hydrogen bonds and that a single residue can participate in hydrogen bonds of at most one secondary structure. Consistency of fixed-sized pieces of secondary structures is the easiest to approximate and we formalize it as 1-2 matching problem. Consistency of entire secondary structures is a version of set packing. We also investigate how to form a simple problem if we add the requirement that the secondary structure and the loops that connect them fit together in a metric space. Every problem that we investigated is MAX-SNP hard and it has a constant factor approximation. Computational experience suggests that in biological instances, we can find nearly optimal solutions using heuristics.     

Barnase thermal titration via molecular dynamics simulations: detection of early denaturation sites

The thermal stability of barnase has been studied using constant pressure and temperature (CPT) molecular dynamics at different temperatures. Barnase X-ray coordinates were obtained from the Research Collaboratory for Structural Bioinformatics (RCSB) Protein Data Bank (PDB code:1rnb). Simulations were performed at 285, 295, 300, 335, 345, and 395 K in explicit water under periodic boundary conditions for 280 ps. For each simulation, conformations were saved every 0.2 ps. Root mean square deviation (RMSD) values were calculated relative to the starting structure at 300 K and at time t = 0. Root mean square fluctuation (RMSF) values were calculated relative to the average structure obtained from the 300K simulation. Both root mean square deviation and fluctuation analysis indicated the presence of discrete regions of hyper-sensitivity along the barnase polypeptide chain. These regions exhibited spikes in flexibility prior to any global structural changes. The specific changes in barnase backbone flexibility are accompanied by increased phi/psi angle fluctuations. These results suggest the presence of early denaturation sites or denaturation nuclei whose local structure is disrupted prior to global structure disruption. Identification of denaturation nuclei suggests that appropriate amino acid replacements at these sites may lead to the design and development of more stable barnase mutants. This strategy of identifying denaturation nuclei in protein structures may represent a first step in the design of more stable protein structures.     

The designability of protein structures

It has been noted that natural proteins adapt only a limited number of folds. Several researchers have investigated why and how nature has selected this small number of folds. Using simple models of protein folding, we demonstrate systematically that there is a "designability principle" behind nature's selection of protein folds. The designability of a structure (fold) is measured by the number of sequences that can design the structure--that is, sequences that possess the structure as their unique ground state. Structures differ drastically in terms of their designability. A small number of highly designable structures emerge with a number of associated sequences much larger than the average. These highly designable structures possess proteinlike secondary structures, motifs, and even tertiary symmetries. In addition, they are thermodynamically more stable and fold faster than other structures. These results suggest that protein structures are selected in nature because they are readily designed and stable against mutations, and that such a selection simultaneously leads to thermodynamic stability.     

Regression model for predicting pathogenic properties of SOD1 mutants based on the analysis of conformational stability and conservation of hydrogen bonds

Intracellular aggregation of proteins is thought to be involved in the aetiology of various neurodegenerative diseases. In particular, mutations in the SOD1 gene are linked to the familial form of amyotrophic lateral sclerosis (ALS). Recently, we developed a regression model for estimating the survival time of ALS patients carrying mutations in SOD1. This model was built based on an analysis of the stability of hydrogen bonds formed in SOD1 mutant proteins during a molecular dynamics (MD) simulation. In the present paper, the regression model was improved by taking into account a new hydrogen-bond property that reflects the conservation measure of a hydrogen bond in the space of protein conformational states. Conformational conservation of hydrogen bonds, being obtained with elastic network (EN) models, allowed us to find eight hydrogen bonds that might affect the pathogenic SOD1 mutants’ properties in addition to the bonds that were found via MD in our previous work. The correlation coefficient between survival time of patients with ALS-linked mutations in SOD1 predicted within the improved model and that observed in the literature was 0.91. SOD1 amino acid residues forming these pathogenic hydrogen bonds are found in zinc-binding and electrostatic loops as well as at zinc-binding sites and are in contact with SOD1 aggregates, which implies that these regions are sensitive to perturbations from pathogenic mutations.     

Contribution of main chain and side chain atoms and their locations to the stability of thermophilic proteins

Proteins belonging to the same class, having similar structures thus performing the same function are known to have different thermal stabilities depending on the source— thermophile or mesophile. The variation in thermo-stability has not been attributed to any unified factor yet and understanding this phenomenon is critically needed in several areas, particularly in protein engineering to design stable variants of the proteins. Toward this motive, the present study focuses on the sequence and structural investigation of a dataset of 373 pairs of proteins; a thermophilic protein and its mesophilic structural analog in each pair, from the perspectives of hydrophobic free energy, hydrogen bonds, physico-chemical properties of amino acids and residue–residue contacts. Our results showed that the hydrophobic free energy due to carbon, charged nitrogen and charged oxygen atoms was stronger in 65% of thermophilic proteins. The number of hydrogen bonds which bridges the buried and exposed regions of proteins was also greater in case of thermophiles. Amino acids of extended shape, volume and molecular weight along with more medium and long range contacts were observed in many of the thermophilic proteins. These results highlight the preference of thermophiles toward the amino acids with larger side chain and charged to make up greater free energy, better packing of residues and increase the overall compactness.     

Prediction of the 3-D structure of rat MrgA G protein-coupled receptor and identification of its binding site

Mrg receptors are orphan G protein-coupled receptors (GPCRs) located mainly at the specific set of sensory neurons in the dorsal root ganglia, suggesting a role in nociception. We report here the 3-D structure of rat MrgA (rMrgA) receptor [obtained from homology modeling to the recently validated predicted structures of mouse MrgA1 and MrgC11] and the structure of adenine (a known agonist, K(i)=18nM) bound to rMrgA. This predicted binding site is located within transmembrane helical domains (TMs) 3, 4, 5 and 6, with Asn residues in TM3 and TM4 identified as the key residues for adenine binding. Here the side chain of Asn88 (TM3) forms two pairs of hydrogen bonds with N3 and N9 of adenine while Asn146 (TM4) makes two pairs of hydrogen bonds with N1 and N6 of adenine. These interactions lock adenine tightly in the binding pocket. We also predict the binding site of guanine (not an agonist) and seven other derivatives. Guanine cannot make the hydrogen bond to Asn146 (TM4), leading to binding too weak to be observed experimentally. The predicted binding affinity for other adenine derivatives correlates with the availability of the hydrogen bonds to these two Asn residues. These results validate the predicted structure for rat MrgA and suggest mutation experiments that could further validate the structure. Moreover, the predicted structure and binding site should be useful for seeking other small molecule agonists and antagonists.     

A connection rule for alpha-carbon coarse-grained elastic network models using chemical bond information

A sparser but more efficient connection rule (called a bond-cutoff method) for a simplified alpha-carbon coarse-grained elastic network model is presented. One of conventional connection rules for elastic network models is the distance-cutoff method, where virtual springs connect an alpha-carbon with all neighbor alpha-carbons within predefined distance-cutoff value. However, though the maximum interaction distance between alpha-carbons is reported as 7 angstroms, this cutoff value can make the elastic network unstable in many cases of protein structures. Thus, a larger cutoff value (>11 angstroms) is often used to establish a stable elastic network model in previous researches. To overcome this problem, a connection rule for backbone model is proposed, which satisfies the minimum condition to stabilize an elastic network. Based on the backbone connections, each type of chemical interactions is considered and added to the elastic network model: disulfide bonds, hydrogen bonds, and salt-bridges. In addition, the van der Waals forces between alpha-carbons are modeled by using the distance-cutoff method. With the proposed connection rule, one can make an elastic network model with less than 7 angstroms distance cutoff, which can reveal protein flexibility more sharply. Moreover, the normal modes from the new elastic network model can reflect conformational changes of a given protein better than ones by the distance-cutoff method. This method can save the computational cost when calculating normal modes of a given protein structure, because it can reduce the total number of connections. As a validation, six example proteins are tested. Computational times and the overlap values between the conformational change and infinitesimal motion calculated by normal mode analysis are presented. Those animations are also available at UMass Morph Server (http://biomechanics.ecs.umass.edu/umms.html).     

Studies of frequently recurring substructures in human alpha-like globin mRNA precursors

In general, the results obtained from secondary structure prediction algorithms are often inconsistent with those obtained experimentally. The reason for this disagreement is that the experimentally determined structures have higher free energies (as judged by the currently used "energy rules") than the predicted ones. To overcome this limitation we have developed a new approach which incorporates the frequencies of occurrence of substructures in the growing mRNA chain. This has been accomplished by simulating the folding process of pre-mRNAs. Using this approach we have significantly improved current helical structural prediction for 142 analyzed tRNAs and 16 S rRNA. We have next applied this method to the human alpha-like globins. Comparison of the structures obtained by running the currently used algorithms with those computed by the new method indicates that the final most stable secondary structure contains some infrequently occurring substructures. In addition, some of the frequently recurring substructures are not included in the final structure. Comparison of the simulated folding processes of the human alpha-like globin pre-mRNAs reveals some conserved helices and hairpin loop structures in those frequently recurring substructures. Among these several compensating base changes (transitions and transversions) have been identified.     

基于卷积长短时记忆神经网络的蛋白质二级结构预测

鉴于不同类型氨基酸的相互作用对蛋白质结构预测的影响不同,文中融合卷积神经网络和长短时记忆神经网络模型,提出卷积长短时记忆神经网络,并应用到蛋白质8类二级结构的预测中.首先基于氨基酸序列的类别信息和氨基酸结构的进化信息表示蛋白质序列,并采用卷积提取氨基酸残基之间的局部相关特征,然后利用双向长短时记忆神经网络提取蛋白质序列内部残基之间的远程相互作用,最后将提取的蛋白质的局部相关特征和远程相互作用用于蛋白质8类二级结构的预测.实验表明,相比基准方法,文中模型提高8类二级结构预测的精度,并具有良好的可扩展性.     

Self-contacts in Asx and Glx residues of high-resolution protein structures: role of local environment and tertiary interactions

In protein structures, side-chains of asparagine and aspartic acid (Asx) and glutamine and glutamic acid (Glx) can approach their own backbone nitrogen or carbonyl group. We have systematically analyzed intra-residue contacts in Asx and Glx residues and their secondary structure preferences in two different datasets consisting of 500 and 1506 high-resolution structures. Intra-residue contact in an Asx/Glx residue between the heavy atoms of side-chain and main-chain functional groups of the same residue was investigated irrespective of whether such contacts are due to hydrogen bonding or not. Our search yielded 563 and 1462 cases of self-contacting Asx and Glx residues from the two datasets. Two important observations have been made in this analysis. First, self-contacts involving side-chain oxygen and backbone nitrogen atoms in majority of Asx residues are not due to hydrogen bonds. In the second instance, surprisingly, side-chain and backbone carbonyl oxygens of a significant number of Asx and Glx residues approach each other. For a wide-range of accessible surface areas, self-contacting residues are surrounded by less number of polar groups compared to all other Asx/Glx residues. In buried and partially buried regions, side-chain and main-chain functional groups of these residues together participate in simultaneous interactions with the available polar groups or water molecules. Asx/Glx residues with self-contacts are rarely observed in the middle of an α-helix or a β-strand. Asx/Glx side-chain having contact with its own backbone nitrogen shows different capping preferences compared to those having contact with its backbone oxygen. Examples of proteins with multiple self-contacting Asx/Glx residues are found. We speculate that mutation of a self-contacting residue in the buried or partially buried region of a protein will destabilize the structure. The results of this analysis will help in engineering protein structures and site-directed mutagenesis experiments.     

用同源建模法探索提高脂肪酶的耐热性

分析常温脂肪酶和耐热蛋白质结构的差异,确定影响脂肪酶耐热性的关键氨基酸为Glu,Lys,Ala,Asp,Thr和Gln;继而重构常温脂肪酶的分子,并利用支持向量机分类器预测其耐热性;再用同源建模法模型化。比较重构前后的分子发现:它们的二级结构和三维结构十分相似,但重构后分子中的盐桥和盐桥网络数却明显增加。     

Computational prediction of the three-dimensional structures for the Caenorhabditis elegans tubulin family

In this article we characterize, from a structural point of view, all 16 members of the tubulin gene family of Caenorhabditis elegans (9 alpha-tubulins, 6 beta-tubulins, and 1 gamma-tubulin). We obtained their tertiary structures by computationally modifying the X-ray crystal structure of the pig brain alpha/beta-tubulin dimer published by Nogales et al. [Nature (London) 1998;391:199-203]. Our computational protocol involves changing the amino acids (with MIDAS; Jarvis et al., UCSF MIDAS. University of California, San Francisco, 1986) in the 3D structure of pig brain alpha/beta-tubulin dimer followed by geometry optimization with the AMBER force field (Perlman et al., AMBER 4. University of California, San Francisco, 1990). We subsequently analyze and compare the resulting structures in terms of the differences in their secondary and tertiary structures. In addition, we compare the pattern of hydrogen bonds and hydrophobic contacts in the guanosine triphosphate (GTP)-binding site for all members of the tubulin family. Our computational results show that, except for gamma-tubulin, all members of the C. elegans tubulin family have similar secondary and 3D structures and that the change in the pattern of hydrogen bonds in the GTP-binding site may be used to assess the relative stability of different alpha/beta-tubulin dimers formed by monomers of the tubulin family.     

蛋白质折叠过程中的长短程作用研究

基于蛋白质二维HP非格模型和改进的模拟退火算法研究了长短程作用在蛋白质折叠过程中的作用。通过试验得出1ECD、2RNS、1PHT、1WBC等序列的折叠构型,并根据PDB中所提供的上述序列的结构信息,具体讨论了长程作用对蛋白质构型的影响,说明了：长程作用在三级结构的形成和稳定中,位于诸多影响因素的首位。