A distance-dependent atomic knowledge-based potential for improved protein structure selection.

A heavy atom distance-dependent knowledge-based pairwise potential has been developed. This statistical potential is first evaluated and optimized with the native structure z-scores from gapless threading. The potential is then used to recognize the native and near-native structures from both published decoy test sets, as well as decoys obtained from our group's protein structure prediction program. In the gapless threading test, there is an average z-score improvement of 4 units in the optimized atomic potential over the residue-based quasichemical potential. Examination of the z-scores for individual pairwise distance shells indicates that the specificity for the native protein structure is greatest at pairwise distances of 3.5-6.5 A, i.e., in the first solvation shell. On applying the current atomic potential to test sets obtained from the web, composed of native protein and decoy structures, the current generation of the potential performs better than residue-based potentials as well as the other published atomic potentials in the task of selecting native and near-native structures. This newly developed potential is also applied to structures of varying quality generated by our group's protein structure prediction program. The current atomic potential tends to pick lower RMSD structures than do residue-based contact potentials. In particular, this atomic pairwise interaction potential has better selectivity especially for near-native structures. As such, it can be used to select near-native folds generated by structure prediction algorithms as well as for protein structure refinement.     

Evaluation of the suitability of free-energy minimization using nearest-neighbor energy parameters for RNA secondary structure prediction

Background

A detailed understanding of an RNA's correct secondary and tertiary structure is crucial to understanding its function and mechanism in the cell. Free energy minimization with energy parameters based on the nearest-neighbor model and comparative analysis are the primary methods for predicting an RNA's secondary structure from its sequence. Version 3.1 of Mfold has been available since 1999. This version contains an expanded sequence dependence of energy parameters and the ability to incorporate coaxial stacking into free energy calculations. We test Mfold 3.1 by performing the largest and most phylogenetically diverse comparison of rRNA and tRNA structures predicted by comparative analysis and Mfold, and we use the results of our tests on 16S and 23S rRNA sequences to assess the improvement between Mfold 2.3 and Mfold 3.1.

Results

The average prediction accuracy for a 16S or 23S rRNA sequence with Mfold 3.1 is 41%, while the prediction accuracies for the majority of 16S and 23S rRNA structures tested are between 20% and 60%, with some having less than 20% prediction accuracy. The average prediction accuracy was 71% for 5S rRNA and 69% for tRNA. The majority of the 5S rRNA and tRNA sequences have prediction accuracies greater than 60%. The prediction accuracy of 16S rRNA base-pairs decreases exponentially as the number of nucleotides intervening between the 5' and 3' halves of the base-pair increases.

Conclusion

Our analysis indicates that the current set of nearest-neighbor energy parameters in conjunction with the Mfold folding algorithm are unable to consistently and reliably predict an RNA's correct secondary structure. For 16S or 23S rRNA structure prediction, Mfold 3.1 offers little improvement over Mfold 2.3. However, the nearest-neighbor energy parameters do work well for shorter RNA sequences such as tRNA or 5S rRNA, or for larger rRNAs when the contact distance between the base-pairs is less than 100 nucleotides.     

Predicting helical coaxial stacking in RNA multibranch loops

The hypothesis that RNA coaxial stacking can be predicted by free energy minimization using nearest-neighbor parameters is tested. The results show 58.2% positive predictive value (PPV) and 65.7% sensitivity for accuracy of the lowest free energy configuration compared with crystal structures. The probability of each stacking configuration can be predicted using a partition function calculation. Based on the dependence of accuracy on the calculated probability of the stacks, a probability threshold of 0.7 was chosen for predicting coaxial stacks. When scoring these likely stacks, the PPV was 66.7% at a sensitivity of 51.9%. It is observed that the coaxial stacks of helices that are not separated by unpaired nucleotides can be predicted with a significantly higher accuracy (74.0% PPV, 66.1% sensitivity) than the coaxial stacks mediated by noncanonical base pairs (55.9% PPV, 36.5% sensitivity). It is also shown that the prediction accuracy does not show any obvious trend with multibranch loop complexity as measured by three different parameters.     

RNA pseudoknot prediction in energy-based models.

RNA molecules are sequences of nucleotides that serve as more than mere intermediaries between DNA and proteins, e.g., as catalytic molecules. Computational prediction of RNA secondary structure is among the few structure prediction problems that can be solved satisfactorily in polynomial time. Most work has been done to predict structures that do not contain pseudoknots. Allowing pseudoknots introduces modeling and computational problems. In this paper we consider the problem of predicting RNA secondary structures with pseudoknots based on free energy minimization. We first give a brief comparison of energy-based methods for predicting RNA secondary structures with pseudoknots. We then prove that the general problem of predicting RNA secondary structures containing pseudoknots is NP complete for a large class of reasonable models of pseudoknots.     

Local interactions in protein folding determined through an inverse folding model

We adopt a model of inverse folding in which folding stability results from the combination of the hydrophobic effect with local interactions responsible for secondary structure preferences. Site-specific amino acid distributions can be calculated analytically for this model. We determine optimal parameters for the local interactions by fitting the complete inverse folding model to the site-specific amino acid distributions found in the Protein Data Bank. This procedure reduces drastically the influence on the derived parameters of the preference of different secondary structures for buriedness, which affects local interaction parameters determined through the standard approach based on amino acid propensities. The quality of the fit is evaluated through the likelihood of the observed amino acid distributions given the model and the Bayesian Information Criterion, which indicate that the model with optimal local interaction parameters is strongly preferable to the model where local interaction parameters are determined through propensities. The optimal model yields a mean correlation coefficient r = 0.96 between observed and predicted amino acid distributions. The local interaction parameters are then tested in threading experiments, in combination with contact interactions, for their capacity to recognize the native structure and structures similar to the native against unrelated ones. In a challenging test, proteins structurally aligned with the Mammoth algorithm are scored with the effective free energy function. The native structure gets the highest stability score in 100% of the cases, a high recognition rate comparable to that achieved against easier decoys generated by gapless threading. We then examine proteins for which at least one highly similar template exists. In 61% of the cases, the structure with the highest stability score excluding the native belongs to the native fold, compared to 60% if we use local interaction parameters derived from the usual amino acid propensities and 52% if we use only contact interactions. A highly similar structure is present within the five best stability scores in 82%, 81%, and 76% of the cases, for local interactions determined through inverse folding, through propensity, and set to zero, respectively. These results indicate that local interactions improve substantially the performances of contact free energy functions in fold recognition, and that similar structures tend to get high stability scores, although they are often not high enough to discriminate them from unrelated structures. This work highlights the importance to apply more challenging tests, as the recognition of homologous structures, for testing stability scores for protein folding.     

Mutational and structural analysis of stem-loop IIIC of the hepatitis C virus and GB virus B internal ribosome entry sites

Translation of the open reading frames (ORF) of the hepatitis C virus (HCV) and closely related GB virus B (GBV-B) genomes is driven by internal ribosome entry site (IRES) elements located within the 5' non-translated RNA. The functioning of these IRES elements is highly dependent on primary and higher order RNA structures. We present here the solution structures of a common, critical domain within each of these IRESs, stem-loop IIIc. These ten-nucleotide hairpins have nearly identical sequences and similar overall tertiary folds. The final refined structure of each shows a stem with three G:C base-pairs and a novel tetraloop fold. Although the bases are buckled, the first and fourth nucleotides of both tetraloops form a Watson-Crick type base-pair, while the apical nucleotides are located in the major groove where they adopt C(2)-endo sugar puckering with B-form geometry. No hydrogen bonding interactions were observed involving the two apical residues of the tetraloop. Stability of the loops appears to be derived primarily from the stacking of bases, and the hydrogen bonding between the fourth and seventh residues. Mutational analysis shows that the primary sequence of stem-loop IIIc is important for IRES function and that the stem and first and fourth nucleotides of the tetraloop contribute to the efficiency of internal ribosome entry. Base-pair formation between these two positions is essential. In contrast, the apical loop nucleotides differ between HCV and GBV-B, and substitutions in this region of the hairpin are tolerated without major loss of function.     

基于PDB数据库的三个RNA二级结构预测软件评估

随着21世纪分子生物学研究的蓬勃发展,RNA二级结构预测成为其中一项重要内容。由于RNA二级结构预测的准确性最为关键,因此寻找高精度且易操作的二级结构预测工具显得非常重要。本文选取三种简单且易操作的二级结构预测软件,先基于PDB数据库收录的318个RNA发夹序列进行二级结构预测,进而通过比较预测结果与实验测定结果进行软件预测性能评估。比较结果显示,RNAstructure为三个软件中性能最优的RNA二级结构预测软件。     

A reduced protein model with accurate native-structure identification ability

A protein model that is simple enough to be used in protein-folding simulations but accurate enough to identify a protein native fold is described. Its geometry consists of describing the residues by one, two, or three pseudoatoms, depending on the residue size. Its energy is given by a pairwise, knowledge-based potential obtained for all the pseudoatoms as a function of their relative distance. The pseudoatomic potential is also a function of the primary chain separation and residue order. The model is tested by gapless threading on a large, representative set of known protein and decoy structures obtained from the "Decoys 'R' Us" database. It is also tested by threading on gapped decoys generated for proteins with many homologs. The gapless threading tests show near 98% native-structure recognition as the lowest energy structure and almost 100% as one of the three lowest energy structures for over 2200 test proteins. In decoy threading tests, the model recognized the majority of the native structures. It is also able to recognize native structures among gapped decoys, in spite of close structural similarities. The results indicate that the pseudoatomic model has native recognition ability similar to comparable atomic-based models but much better than equivalent residue-based models.     

A novel long distance base-pairing interaction in human immunodeficiency virus type 1 RNA occludes the Gag start codon

The 5'-untranslated region (5'-UTR) is the most conserved part of the HIV-1 RNA genome, and it contains regulatory motifs that mediate various steps in the viral life cycle. Previous work showed that the 5'-terminal 290 nucleotides of HIV-1 RNA adopt two mutually exclusive secondary structures, long distance interaction (LDI) and branched multiple hairpin (BMH). BMH has multiple hairpins, including the dimer initiation signal (DIS) hairpin that mediates RNA dimerization. LDI contains a long distance base-pairing interaction that occludes the DIS region. Consequently, the two conformations differ in their ability to form RNA dimers. In this study, we have presented evidence that the full-length 5'-UTR also adopts the LDI and BMH conformations. The downstream 290-352 region, including the Gag start codon, folds differently in the context of the LDI and BMH structures. These nucleotides form an extended hairpin structure in the LDI conformation, but the same sequences create a novel long distance interaction with upstream U5 sequences in the BMH conformation. The presence of this U5-AUG duplex was confirmed by computer-assisted RNA structure prediction, biochemical analyses, and a phylogenetic survey of different virus isolates. The U5-AUG duplex may influence translation of the Gag protein because it occludes the start codon of the Gag open reading frame.     

Averaging interaction energies over homologs improves protein fold recognition in gapless threading.

Protein structure prediction is limited by the inaccuracy of the simplified energy functions necessary for efficient sorting over many conformations. It was recently suggested (Finkelstein, Phys Rev Lett 1998;80:4823-4825) that these errors can be reduced by energy averaging over a set of homologous sequences. This conclusion is confirmed in this study by testing protein structure recognition in gapless threading. The accuracy of recognition was estimated by the Z-score values obtained in gapless threading tests. For threading, we used 20 target proteins, each having from 20 to 70 homologs taken from the HSSP sequence base. The energy of the native structures was compared with the energy from 34 to 75 thousand of alternative structures generated by threading. The energy calculations were done with our recently developed Calpha atom-based phenomenological potentials. We show that averaging of protein energies over homologs reduces the Z-score from approximately -6.1 (average Z-score for individual chains) to approximately -8.1. This means that a correct fold can be found among 3 x 10(9) random folds in the first case and among 3 x 10(15) in the second. Such increase in selectivity is important for recognition of protein folds.     

Correlation of RNA Secondary Structure Statistics with Thermodynamic Stability and Applications to Folding

The accurate prediction of the secondary and tertiary structure of an RNA with different folding algorithms is dependent on several factors, including the energy functions. However, an RNA higher-order structure cannot be predicted accurately from its sequence based on a limited set of energy parameters. The inter- and intramolecular forces between this RNA and other small molecules and macromolecules, in addition to other factors in the cell such as pH, ionic strength, and temperature, influence the complex dynamics associated with transition of a single stranded RNA to its secondary and tertiary structure. Since all of the factors that affect the formation of an RNAs 3D structure cannot be determined experimentally, statistically derived potential energy has been used in the prediction of protein structure. In the current work, we evaluate the statistical free energy of various secondary structure motifs, including base-pair stacks, hairpin loops, and internal loops, using their statistical frequency obtained from the comparative analysis of more than 50,000 RNA sequences stored in the RNA Comparative Analysis Database (rCAD) at the Comparative RNA Web (CRW) Site. Statistical energy was computed from the structural statistics for several datasets. While the statistical energy for a base-pair stack correlates with experimentally derived free energy values, suggesting a Boltzmann-like distribution, variation is observed between different molecules and their location on the phylogenetic tree of life. Our statistical energy values calculated for several structural elements were utilized in the Mfold RNA-folding algorithm. The combined statistical energy values for base-pair stacks, hairpins and internal loop flanks result in a significant improvement in the accuracy of secondary structure prediction; the hairpin flanks contribute the most.     

Derivation of protein-specific pair potentials based on weak sequence fragment similarity

A method is presented for the derivation of knowledge-based pair potentials that corrects for the various compositions of different proteins. The resulting statistical pair potential is more specific than that derived from previous approaches as assessed by gapless threading results. Additionally, a methodology is presented that interpolates between statistical potentials when no homologous examples to the protein of interest are in the structural database used to derive the potential, to a Go-like potential (in which native interactions are favorable and all nonnative interactions are not) when homologous proteins are present. For cases in which no protein exceeds 30% sequence identity, pairs of weakly homologous interacting fragments are employed to enhance the specificity of the potential. In gapless threading, the mean z score increases from -10.4 for the best statistical pair potential to -12.8 when the local sequence similarity, fragment-based pair potentials are used. Examination of the ab initio structure prediction of four representative globular proteins consistently reveals a qualitative improvement in the yield of structures in the 4 to 6 A rmsd from native range when the fragment-based pair potential is used relative to that when the quasichemical pair potential is employed. This suggests that such protein-specific potentials provide a significant advantage relative to generic quasichemical potentials.     

Revolutions in RNA secondary structure prediction

RNA structure formation is hierarchical and, therefore, secondary structure, the sum of canonical base-pairs, can generally be predicted without knowledge of the three-dimensional structure. Secondary structure prediction algorithms evolved from predicting a single, lowest free energy structure to their current state where statistics can be determined from the thermodynamic ensemble. This article reviews the free energy minimization technique and the salient revolutions in the dynamic programming algorithm methods for secondary structure prediction. Emphasis is placed on highlighting the recently developed method, which statistically samples structures from the complete Boltzmann ensemble.     

An iterated loop matching approach to the prediction of RNA secondary structures with pseudoknots

MOTIVATION: Pseudoknots have generally been excluded from the prediction of RNA secondary structures due to its difficulty in modeling. Although, several dynamic programming algorithms exist for the prediction of pseudoknots using thermodynamic approaches, they are neither reliable nor efficient. On the other hand, comparative methods are more reliable, but are often done in an ad hoc manner and require expert intervention. Maximum weighted matching, an algorithm for pseudoknot prediction with comparative analysis, suffers from low-prediction accuracy in many cases. RESULTS: Here we present an algorithm, iterated loop matching, for reliably and efficiently predicting RNA secondary structures including pseudoknots. The method can utilize either thermodynamic or comparative information or both, thus is able to predict pseudoknots for both aligned and individual sequences. We have tested the algorithm on a number of RNA families. Using 8-12 homologous sequences, the algorithm correctly identifies more than 90% of base-pairs for short sequences and 80% overall. It correctly predicts nearly all pseudoknots and produces very few spurious base-pairs for sequences without pseudoknots. Comparisons show that our algorithm is both more sensitive and more specific than the maximum weighted matching method. In addition, our algorithm has high-prediction accuracy on individual sequences, comparable with the PKNOTS algorithm, while using much less computational resources. AVAILABILITY: The program has been implemented in ANSI C and is freely available for academic use at http://www.cse.wustl.edu/~zhang/projects/rna/ilm/ Supplementary information: http://www.cse.wustl.edu/~zhang/projects/rna/ilm/     

Structure and structure formation of viroids

The structure of viroids and the mechanism of structure formation were investigated by different methods. Results from gel analysis, partial degradation pattern, electron microscopy, dye binding, hydrodynamic studies, and temperature-jump kinetics were interpreted in a common structural and mechanistic scheme. Gel analysis, electron microscopy and kinetic investigations show that viroids may assume the native as well as metastable conformations under the same conditions. The native conformation is obtained by complete renaturation, i.e. slow cooling throughout the transition range (e.g. 52 to 48 ° C for potato spindle tuber viroid (PST viroid) in 0.01 m-sodium cacodylate, pH 6.8). In contrast, metastable conformations were trapped if viroids were redissolved in the cold from their ethanol precipitate or if they were denatured and cooled quickly.The native secondary structure of the recently sequenced PST viroid (Gross et al., 1978) was optimized for the free energy of base-pairing. The scheme agrees with that proposed by Gross et al. (1978), which was derived from chemical arguments. The extended structure does not undergo tertiary structure folding under a wide range of conditions, as was concluded from electron microscopy, sedimentation measurements and binding studies of ethidium bromide and a new dye specific for A · U pairs (2-(4′-aminophenyl)-5-(4′-methylpiperazin-1″yl)-benzirnidazol).Intermediate structures during viroid denaturation were analysed on theoretical and experimental grounds. The experimental data, in combination with the model calculations, show that all of the native base-pairs of viroids are dissociated in one highly co-operative main transition, and that during the same process very stable hairpins are formed that are not present in the native structure. The formation of stable hairpins induces a new type of long range cooperativity, which is responsible in part for the high co-operativity observed experimentally. This interpretation is in good agreement with kinetic results presented elsewhere (Henco et al., 1979).In order to understand the uniqueness of viroids, the structure and the conformational transitions of circular RNA molecules of the same base composition as PST viroids but with 359 nucleotides arranged randomly, were studied theoretically. Common viroid features, such as the number of base-pairs, the high co-operativity and the formation of very stable hairpins, are found to be improbable in such random sequences. It is concluded that various viroid species, although differing in nucleotide sequence, follow common principles of structure and structure formation.     

Novel and efficient RNA secondary structure prediction using hierarchical folding.

Algorithms for prediction of RNA secondary structure-the set of base pairs that form when an RNA molecule folds-are valuable to biologists who aim to understand RNA structure and function. Improving the accuracy and efficiency of prediction methods is an ongoing challenge, particularly for pseudoknotted secondary structures, in which base pairs overlap. This challenge is biologically important, since pseudoknotted structures play essential roles in functions of many RNA molecules, such as splicing and ribosomal frameshifting. State-of-the-art methods, which are based on free energy minimization, have high run-time complexity (typically Theta(n(5)) or worse), and can handle (minimize over) only limited types of pseudoknotted structures. We propose a new approach for prediction of pseudoknotted structures, motivated by the hypothesis that RNA structures fold hierarchically, with pseudoknot-free (non-overlapping) base pairs forming first, and pseudoknots forming later so as to minimize energy relative to the folded pseudoknot-free structure. Our HFold algorithm uses two-phase energy minimization to predict hierarchically formed secondary structures in O(n(3)) time, matching the complexity of the best algorithms for pseudoknot-free secondary structure prediction via energy minimization. Our algorithm can handle a wide range of biological structures, including kissing hairpins and nested kissing hairpins, which have previously required Theta(n(6)) time.     

When and how can homologs overcome errors in the energy estimates and make the 3D structure prediction possible

One still cannot predict the 3D fold of a protein from its amino acid sequence, mainly because of errors in the energy estimates underlying the prediction. However, a recently developed theory [1] shows that having a set of homologs (i.e., the chains with equal, in despite of numerous mutations, 3D folds) one can average the potential of each interaction over the homologs and thus predict the common 3D fold of protein family even when a correct fold prediction for an individual sequence is impossible because the energies are known only approximately. This theoretical conclusion has been verified by simulation of the energy spectra of simplified models of protein chains [2], and the further investigation of these simplified models shows that their true "native" fold can be found by folding of the chain where each interaction potential is averaged over the homologs. In conclusion, the applicability of the "homolog-averaging" approach is tested by recognition of real protein 3D structures. Both the gapless threading of sequences onto the known protein folds [3] and the more practically important gapped threading (which allows to consider not only the known 3D structures, but the more or less similar to them folds as well) shows a significant increase in selectivity of the native chain fold recognition.     

Incorporating global features of RNA motifs in predictions for an ensemble of secondary structures for encapsidated MS2 bacteriophage RNA

The secondary structure of encapsidated MS2 genomic RNA poses an interesting RNA folding challenge. Cryoelectron microscopy has demonstrated that encapsidated MS2 RNA is well-ordered. Models of MS2 assembly suggest that the RNA hairpin-protein interactions and the appropriate placement of hairpins in the MS2 RNA secondary structure can guide the formation of the correct icosahedral particle. The RNA hairpin motif that is recognized by the MS2 capsid protein dimers, however, is energetically unfavorable, and thus free energy predictions are biased against this motif. Computer programs called Crumple, Sliding Windows, and Assembly provide useful tools for prediction of viral RNA secondary structures when the traditional assumptions of RNA structure prediction by free energy minimization may not apply. These methods allow incorporation of global features of the RNA fold and motifs that are difficult to include directly in minimum free energy predictions. For example, with MS2 RNA the experimental data from SELEX experiments, crystallography, and theoretical calculations of the path for the series of hairpins can be incorporated in the RNA structure prediction, and thus the influence of free energy considerations can be modulated. This approach thoroughly explores conformational space and generates an ensemble of secondary structures. The predictions from this new approach can test hypotheses and models of viral assembly and guide construction of complete three-dimensional models of virus particles.