Structural analysis based on state-space modeling.

A new method has been developed to compute the probability that each amino acid in a protein sequence is in a particular secondary structural element. Each of these probabilities is computed using the entire sequence and a set of predefined structural class models. This set of structural classes is patterned after Jane Richardson''s taxonomy for the domains of globular proteins. For each structural class considered, a mathematical model is constructed to represent constraints on the pattern of secondary structural elements characteristic of that class. These are stochastic models having discrete state spaces (referred to as hidden Markov models by researchers in signal processing and automatic speech recognition). Each model is a mathematical generator of amino acid sequences; the sequence under consideration is modeled as having been generated by one model in the set of candidates. The probability that each model generated the given sequence is computed using a filtering algorithm. The protein is then classified as belonging to the structural class having the most probable model. The secondary structure of the sequence is then analyzed using a "smoothing" algorithm that is optimal for that structural class model. For each residue position in the sequence, the smoother computes the probability that the residue is contained within each of the defined secondary structural elements of the model. This method has two important advantages: (1) the probability of each residue being in each of the modeled secondary structural elements is computed using the totality of the amino acid sequence, and (2) these probabilities are consistent with prior knowledge of realizable domain folds as encoded in each model. As an example of the method''s utility, we present its application to flavodoxin, a prototypical alpha/beta protein having a central beta-sheet, and to thioredoxin, which belongs to a similar structural class but shares no significant sequence similarity.     

Prediction of geometrically feasible three-dimensional structures of pseudoknotted RNA through free energy estimation

Accurate free energy estimation is essential for RNA structure prediction. The widely used Turner''s energy model works well for nested structures. For pseudoknotted RNAs, however, there is no effective rule for estimation of loop entropy and free energy. In this work we present a new free energy estimation method, termed the pseudoknot predictor in three-dimensional space (pk3D), which goes beyond Turner''s model. Our approach treats nested and pseudoknotted structures alike in one unifying physical framework, regardless of how complex the RNA structures are. We first test the ability of pk3D in selecting native structures from a large number of decoys for a set of 43 pseudoknotted RNA molecules, with lengths ranging from 23 to 113. We find that pk3D performs slightly better than the Dirks and Pierce extension of Turner''s rule. We then test pk3D for blind secondary structure prediction, and find that pk3D gives the best sensitivity and comparable positive predictive value (related to specificity) in predicting pseudoknotted RNA secondary structures, when compared with other methods. A unique strength of pk3D is that it also generates spatial arrangement of structural elements of the RNA molecule. Comparison of three-dimensional structures predicted by pk3D with the native structure measured by nuclear magnetic resonance or X-ray experiments shows that the predicted spatial arrangement of stems and loops is often similar to that found in the native structure. These close-to-native structures can be used as starting points for further refinement to derive accurate three-dimensional structures of RNA molecules, including those with pseudoknots.     

Bioinformatics approaches for structural and functional analysis of proteins in secondary metabolism in Withania somnifera

Withania somnifera (Ashwagandha) is an affluent storehouse of large number of pharmacologically active secondary metabolites known as withanolides. These secondary metabolites are produced by withanolide biosynthetic pathway. Very less information is available on structural and functional aspects of enzymes involved in withanolides biosynthetic pathways of Withiana somnifera. We therefore performed a bioinformatics analysis to look at functional and structural properties of these important enzymes. The pathway enzymes taken for this study were 3-Hydroxy-3-methylglutaryl coenzyme A reductase, 1-Deoxy-d-xylulose-5-phosphate synthase, 1-Deoxy-d-xylulose-5-phosphate reductase, farnesyl pyrophosphate synthase, squalene synthase, squalene epoxidase, and cycloartenol synthase. The prediction of secondary structure was performed for basic structural information. Three-dimensional structures for these enzymes were predicted. The physico-chemical properties such as pI, AI, GRAVY and instability index were also studied. The current information will provide a platform to know the structural attributes responsible for the function of these protein until experimental structures become available.     

RAG-3D: a search tool for RNA 3D substructures

To address many challenges in RNA structure/function prediction, the characterization of RNA''s modular architectural units is required. Using the RNA-As-Graphs (RAG) database, we have previously explored the existence of secondary structure (2D) submotifs within larger RNA structures. Here we present RAG-3D—a dataset of RNA tertiary (3D) structures and substructures plus a web-based search tool—designed to exploit graph representations of RNAs for the goal of searching for similar 3D structural fragments. The objects in RAG-3D consist of 3D structures translated into 3D graphs, cataloged based on the connectivity between their secondary structure elements. Each graph is additionally described in terms of its subgraph building blocks. The RAG-3D search tool then compares a query RNA 3D structure to those in the database to obtain structurally similar structures and substructures. This comparison reveals conserved 3D RNA features and thus may suggest functional connections. Though RNA search programs based on similarity in sequence, 2D, and/or 3D structural elements are available, our graph-based search tool may be advantageous for illuminating similarities that are not obvious; using motifs rather than sequence space also reduces search times considerably. Ultimately, such substructuring could be useful for RNA 3D structure prediction, structure/function inference and inverse folding.     

G.U base pairing motifs in ribosomal RNA.

An increasing number of recognition mechanisms in RNA are found to involve G.U base pairs. In order to detect new functional sites of this type, we exhaustively analyzed the sequence alignments and secondary structures of eubacterial and chloroplast 16S and 23S rRNA, seeking positions with high levels of G.U pairs. Approximately 120 such sites were identified and classified according to their secondary structure and sequence environment. Overall biases in the distribution of G.U pairs are consistent with previously proposed structural rules: the side of the wobble pair that is subject to a loss of stacking is preferentially exposed to a secondary structure loop, where stacking is not as essential as in helical regions. However, multiple sites violate these rules and display highly conserved G.U pairs in orientations that could cause severe stacking problems. In addition, three motifs displaying a conserved G.U pair in a specific sequence/structure environment occur at an unusually high frequency. These motifs, of which two had not been reported before, involve sequences 5''UG3'' 3''GA5'' and 5''UG3'' 3''GU5'', as well as G.U pairs flanked by a bulge loop 3'' of U. The possible structures and functions of these recurrent motifs are discussed.     

Mechanical property of a TIM-barrel protein

The mechanical response of a TIM-barrel protein to an applied pressure has been studied. We generated structures under an applied pressure by assuming the volume change to be a linear function of normal mode variables. By Delaunay tessellation, the space occupied by protein atoms is divided uniquely into tetrahedra, whose four vertices correspond to atomic positions. Based on the atoms that define them, the resulting Delaunay tetrahedra are classified as belonging to various secondary structures in the protein. The compressibility of various regions identified with respect to secondary structural elements in this protein is obtained from volume changes of respective regions in two structures with and without an applied pressure. We found that the β barrel region located at the core of the protein is quite soft. The interior of the β barrel, occupied by side chains of β strands, is the softest. The helix, strand, and loop segments themselves are extremely rigid, while the regions existing between these secondary structural elements are soft. These results suggest that the regions between secondary structural elements play an important role in protein dynamics. Another aspect of tetrahedra, referred to as bond distance, is introduced to account for rigidities of the tetrahedra. Bond distance is a measure of separation of the atoms of a tetrahedron in terms of number of bonds along the polypeptide chain or side chains. Tetrahedra with longer bond distances are found to be softer on average. From this behavior, we derive a simple empirical equation, which well describes the compressibilities of various regions. © 1997 Wiley-Liss Inc.     

Secondary Structural Studies of Bovine Caseins: Structure and Temperature Dependence of β-Casein Phosphopeptide (1-25) as Analyzed by Circular Dichroism, FTIR Spectroscopy, and Analytical Ultracentrifugation

The defining structural feature of all of the caseins is their common phosphorylation sequence. In milk, these phosphoserine residues combine with inorganic calcium and phosphate to form colloidal complexes. In addition, nutritional benefits have been ascribed to the phosphopeptides from casein. To obtain a molecular basis for the functional, chemical, and biochemical properties of these casein peptides, the secondary structure of the phosphopeptide of bovine β-casein (1–25) was reexamined using Fourier transform infrared (FTIR) and circular dichroism (CD) spectroscopies. Both methods predict secondary structures for the peptide which include polyproline II elements as well as β-extended sheet and turn-like elements. These structural elements were highly stable from 5° to 70°C. Reexamination of previously published ¹H NMR data using chemical shift indices suggests structures in accord with the CD and FTIR data. Dephosphorylation showed little or no secondary structural changes, as monitored by CD and FTIR, but the modified peptide demonstrated pronounced self-association. The polymers formed were not highly temperature sensitive, but were pressure sensitive as judged by analytical ultracentrifugation at selected rotor speeds. Molecular dynamics (MD) simulations demonstrated relatively large volume changes for the dephosphorylated peptide, in accord with the pressure dependent aggregation observed in the analytical ultracentrifuge data. In contrast the native peptide in MD remained relatively rigid. The physical properties of the peptide suggest how phosphorylation can alter its biochemical and physiological properties.     

A simple two-dimensional representation for the common secondary structural elements of polypeptides and proteins

A simple method is presented for projecting the conformation of extended secondary structure elements of peptides and proteins that extend over four C^αatoms onto a simple two-dimensional surface. A new set of two degrees of freedom is defined, a pseudo-dihedral involving four sequential C^αatoms, as well as the triple scalar product for the vectors describing the orientation of the three intervening peptide groups. The method provides a reduction in dimensionality, from the usual combination of multiple ϕ,ψ pairs to a single pair, yielding valuable information concerning the structure and dynamics of these important elements. The new two-dimensional surface is explored by reference to 63 selected protein crystal structures together with a comparison of model built peptides representing the common secondary structural elements. Dynamical aspects on this new surface are examined using a molecular dynamics trajectory of Basic Pancreatic Trypsin Inhibitor. © 1997 Wiley-Liss, Inc.     

Evidence of Pervasive Biologically Functional Secondary Structures within the Genomes of Eukaryotic Single-Stranded DNA Viruses

Single-stranded DNA (ssDNA) viruses have genomes that are potentially capable of forming complex secondary structures through Watson-Crick base pairing between their constituent nucleotides. A few of the structural elements formed by such base pairings are, in fact, known to have important functions during the replication of many ssDNA viruses. Unknown, however, are (i) whether numerous additional ssDNA virus genomic structural elements predicted to exist by computational DNA folding methods actually exist and (ii) whether those structures that do exist have any biological relevance. We therefore computationally inferred lists of the most evolutionarily conserved structures within a diverse selection of animal- and plant-infecting ssDNA viruses drawn from the families Circoviridae, Anelloviridae, Parvoviridae, Nanoviridae, and Geminiviridae and analyzed these for evidence of natural selection favoring the maintenance of these structures. While we find evidence that is consistent with purifying selection being stronger at nucleotide sites that are predicted to be base paired than at sites predicted to be unpaired, we also find strong associations between sites that are predicted to pair with one another and site pairs that are apparently coevolving in a complementary fashion. Collectively, these results indicate that natural selection actively preserves much of the pervasive secondary structure that is evident within eukaryote-infecting ssDNA virus genomes and, therefore, that much of this structure is biologically functional. Lastly, we provide examples of various highly conserved but completely uncharacterized structural elements that likely have important functions within some of the ssDNA virus genomes analyzed here.     

Quantitative assessment of automatic reconstructions of branching systems obtained from laser scanning

Background and Aims

Automatic acquisition of plant architecture is a major challenge for the construction of quantitative models of plant development. Recently, 3-D laser scanners have made it possible to acquire 3-D images representing a sampling of an object''s surface. A number of specific methods have been proposed to reconstruct plausible branching structures from this new type of data, but critical questions remain regarding their suitability and accuracy before they can be fully exploited for use in biological applications.

Methods

In this paper, an evaluation framework to assess the accuracy of tree reconstructions is presented. The use of this framework is illustrated on a selection of laser scans of trees. Scanned data were manipulated by experienced researchers to produce reference tree reconstructions against which comparisons could be made. The evaluation framework is given two tree structures and compares both their elements and their topological organization. Similar elements are identified based on geometric criteria using an optimization algorithm. The organization of these elements is then compared and their similarity quantified. From these analyses, two indices of geometrical and structural similarities are defined, and the automatic reconstructions can thus be compared with the reference structures in order to assess their accuracy.

Key Results

The evaluation framework that was developed was successful at capturing the variation in similarities between two structures as different levels of noise were introduced. The framework was used to compare three different reconstruction methods taken from the literature, and allowed sensitive parameters of each one to be determined. The framework was also generalized for the evaluation of root reconstruction from 2-D images and demonstrated its sensitivity to higher architectural complexity of structure which was not detected with a global evaluation criterion.

Conclusions

The evaluation framework presented quantifies geometric and structural similarities between two structures. It can be applied to the characterization and comparison of automatic reconstructions of plant structures from laser scanner data and 2-D images. As such, it can be used as a reference test for comparing and assessing reconstruction procedures.     

Statistics of RNA secondary structures

A statistical reference for RNA secondary structures with minimum free energies is computed by folding large ensembles of random RNA sequences. Four nucleotide alphabets are used: two binary alphabets, AU and GC, the biophysical AUGC and the synthetic GCXK alphabet. RNA secondary structures are made of structural elements, such as stacks, loops, joints, and free ends. Statistical properties of these elements are computed for small RNA molecules of chain lengths up to 100. The results of RNA structure statistics depend strongly on the particular alphabet chosen. The statistical reference is compared with the data derived from natural RNA molecules with similar base frequencies. Secondary structures are represented as trees. Tree editing provides a quantitative measure for the distance d_t, between two structures. We compute a structure density surface as the conditional probability of two structures having distance t given that their sequences have distance h. This surface indicates that the vast majority of possible minimum free energy secondary structures occur within a fairly small neighborhood of any typical (random) sequence. Correlation lengths for secondary structures in their tree representations are computed from probability densities. They are appropriate measures for the complexity of the sequence-structure relation. The correlation length also provides a quantitative estimate for the mean sensitivity of structures to point mutations. © 1993 John Wiley & Sons, Inc.     

Multiscale Characterization of Casein Micelles Under NaCl Range Conditions

Micellar casein (MC) dispersions were studied at a constant protein concentration of 5 wt % in high NaCl environment. The micellar edifices were characterized as to their morphology, size, and content of proteins in the supernatant after ultracentrifugation. Additionally, changes in secondary structures of the protein upon salt increase were followed by Fourier Transform Infrared Spectroscopy (FTIR). For the first time, the estimations of secondary structural elements (irregular, ß-sheet, ??-helix and turn) from Amide III assignments were correlated with results from Amide I. Casein micelles dispersions in water were characterized by Transmission Electron Microscopy (TEM) by a spherical shape and a size between 100 and 200 nm. A salt increase resulted to a destabilization of the micelle and the formation of mini-micelles more or less aggregated. The size of the new edifice was almost similar to the native micelle. These TEM observations were confirmed by a constant casein micelle hydrodynamic diameter determined by Dynamic Light Scattering (DLS) and ranging between 150 and 180 nm. Upon salt increase, FTIR revealed an increase in irregular structures and a concurrent decrease in ß-sheet structures. Secondary structural elements percentages were almost similar from Amide I and Amide III. The use of these multiscale techniques led to a better understanding of the micellar edifice under high salt environment. Around 3% NaCl addition, a good correlation was observed between destabilization of the micellar edifice, modifications of the caseins secondary structure and repartition of caseins between supernatant and pellet after ultracentrifugation.     

Circular dichroism and the secondary structure of the ROF2 protein from Arabidopsis thaliana

The protein ROF2 from the plant Arabidopsis thaliana acts as a heat stress modulator, being involved in the long-term acquired thermotolerance of the plant. Here we investigate the relationship between the biological function and the structure of ROF2, inferred by circular dichroism (CD) spectroscopy. The far-UV CD spectra, analyzed with the CDPro and DICHROWEB program packages, yield the percentages of α-helices, β-sheets, unordered regions, turns and poly(Pro)II-helices in the secondary structure of ROF2. According to the analysis, the percentages of the structural elements of ROF2 are about 40% for β-sheets, 30% for unordered regions, 17% for turns, 10% for poly(Pro)II-helices and 3% for α-helices. The near-UV CD spectra suggest that ROF2 proteins can associate, forming super-secondary structures. Our CD experiments performed at temperatures between 5 °C and 97 °C indicate that the thermal denaturation of ROF2 caused by a raise in temperature up to 55 °C is followed by a thermal refolding of the protein as the temperature is raised further. The new secondary structure, acquired around 65 °C, remains stable up to 97 °C. The structural stability of ROF2 at high temperatures might play an important role in the experimentally observed thermotolerance of Arabidopsis thaliana.     

Functional analysis of the tick-borne encephalitis virus cyclization elements indicates major differences between mosquito-borne and tick-borne flaviviruses

The linear, positive-stranded RNA genome of flaviviruses is thought to adopt a circularized conformation via interactions of short complementary sequence elements located within its terminal regions. This process of RNA cyclization is a crucial precondition for RNA replication. In the case of mosquito-borne flaviviruses, highly conserved cyclization sequences (CS) have been identified, and their functionality has been experimentally confirmed. Here, we provide an experimental identification of CS elements of tick-borne encephalitis virus (TBEV). These elements, termed 5'-CS-A and 3'-CS-A, are conserved among various tick-borne flaviviruses, but they are unrelated to the mosquito-borne CS elements and are located at different genomic positions. The 5'-CS-A element is situated upstream rather than downstream of the AUG start codon and, in contrast to mosquito-borne flaviviruses, it was found that the entire protein C coding region is not essential for TBEV replication. The complementary 3'-CS-A element is located within the bottom stem rather than upstream of the characteristic 3'-terminal stem-loop structure, implying that this part of the proposed structure cannot be formed when the genome is in its circularized conformation. Finally, we demonstrate that the CS-A elements can also mediate their function when the 5'-CS-A element is moved from its natural position to one corresponding to the mosquito-borne CS. The recognition of essential RNA elements and their differences between mosquito-borne and tick-borne flaviviruses has practical implications for the design of replicons in vaccine and vector development.