A method for the characterization of foldings in protein ribbon models

The ribbon model of chain macromolecules is a useful tool for analyzing some of the targe-scale shape features of these complex systems. Up to now, the ribbon model has been used mostly to produce graphical displays, which are usually analyzed by visual inspection. In this work we suggest a computational method for characterizing automatically, in a concise and algebraic fashion, some of the important shape features of these ribbon models. The procedure is based on a graph-theoretical and knot-theoretical characterization of three well-defined projections of a space curve associated with the ribbon. The labeled graphs can be characterized by the handedness of the crossovers in the ribbon that are the vertices of the graph. The method can be used to provide a fully algebraic representation of the changes occurring when a molecule, such as a protein, undergoes conformational rearrangements (folding), as well as to provide a shape comparison for a pair of related molecular ribbons. This algebraic representation is well suited for easy storage, retrieval, and computer manipulation of the information on the ribbon's shape. Illustrative examples of the method are provided.     

Algorithm for ribbon models of proteins

A method is presented to draw smooth, 3D ribbon models of proteins. The procedure calculates closely-spaced guide coordinates based on the peptide plane and passes regular, nearly parallel B-spline curves through them. This becomes a simple process with a graphics device having built-in B-spline generating capabilities such as the Evans and Sutherland PS300. Examination of ribbons such as these provides a useful tool for the crystallographer. Any irregularity in the ribbon is a strong visual cue, suggestive of potential problem areas during the refinement process.     

Partner-aware prediction of interacting residues in protein-protein complexes from sequence data

Computational prediction of residues that participate in protein-protein interactions is a difficult task, and state of the art methods have shown only limited success in this arena. One possible problem with these methods is that they try to predict interacting residues without incorporating information about the partner protein, although it is unclear how much partner information could enhance prediction performance. To address this issue, the two following comparisons are of crucial significance: (a) comparison between the predictability of inter-protein residue pairs, i.e., predicting exactly which residue pairs interact with each other given two protein sequences; this can be achieved by either combining conventional single-protein predictions or making predictions using a new model trained directly on the residue pairs, and the performance of these two approaches may be compared: (b) comparison between the predictability of the interacting residues in a single protein (irrespective of the partner residue or protein) from conventional methods and predictions converted from the pair-wise trained model. Using these two streams of training and validation procedures and employing similar two-stage neural networks, we showed that the models trained on pair-wise contacts outperformed the partner-unaware models in predicting both interacting pairs and interacting single-protein residues. Prediction performance decreased with the size of the conformational change upon complex formation; this trend is similar to docking, even though no structural information was used in our prediction. An example application that predicts two partner-specific interfaces of a protein was shown to be effective, highlighting the potential of the proposed approach. Finally, a preliminary attempt was made to score docking decoy poses using prediction of interacting residue pairs; this analysis produced an encouraging result.     

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.     

Optimized Null Model for Protein Structure Networks

Much attention has recently been given to the statistical significance of topological features observed in biological networks. Here, we consider residue interaction graphs (RIGs) as network representations of protein structures with residues as nodes and inter-residue interactions as edges. Degree-preserving randomized models have been widely used for this purpose in biomolecular networks. However, such a single summary statistic of a network may not be detailed enough to capture the complex topological characteristics of protein structures and their network counterparts. Here, we investigate a variety of topological properties of RIGs to find a well fitting network null model for them. The RIGs are derived from a structurally diverse protein data set at various distance cut-offs and for different groups of interacting atoms. We compare the network structure of RIGs to several random graph models. We show that 3-dimensional geometric random graphs, that model spatial relationships between objects, provide the best fit to RIGs. We investigate the relationship between the strength of the fit and various protein structural features. We show that the fit depends on protein size, structural class, and thermostability, but not on quaternary structure. We apply our model to the identification of significantly over-represented structural building blocks, i.e., network motifs, in protein structure networks. As expected, choosing geometric graphs as a null model results in the most specific identification of motifs. Our geometric random graph model may facilitate further graph-based studies of protein conformation space and have important implications for protein structure comparison and prediction. The choice of a well-fitting null model is crucial for finding structural motifs that play an important role in protein folding, stability and function. To our knowledge, this is the first study that addresses the challenge of finding an optimized null model for RIGs, by comparing various RIG definitions against a series of network models.     

Small libraries of protein fragments model native protein structures accurately

Prediction of protein structure depends on the accuracy and complexity of the models used. Here, we represent the polypeptide chain by a sequence of rigid fragments that are concatenated without any degrees of freedom. Fragments chosen from a library of representative fragments are fit to the native structure using a greedy build-up method. This gives a one-dimensional representation of native protein three-dimensional structure whose quality depends on the nature of the library. We use a novel clustering method to construct libraries that differ in the fragment length (four to seven residues) and number of representative fragments they contain (25-300). Each library is characterized by the quality of fit (accuracy) and the number of allowed states per residue (complexity). We find that the accuracy depends on the complexity and varies from 2.9A for a 2.7-state model on the basis of fragments of length 7-0.76A for a 15-state model on the basis of fragments of length 5. Our goal is to find representations that are both accurate and economical (low complexity). The models defined here are substantially better in this regard: with ten states per residue we approximate native protein structure to 1A compared to over 20 states per residue needed previously.For the same complexity, we find that longer fragments provide better fits. Unfortunately, libraries of longer fragments must be much larger (for ten states per residue, a seven-residue library is 100 times larger than a five-residue library). As the number of known protein native structures increases, it will be possible to construct larger libraries to better exploit this correlation between neighboring residues. Our fragment libraries, which offer a wide range of optimal fragments suited to different accuracies of fit, may prove to be useful for generating better decoy sets for ab initio protein folding and for generating accurate loop conformations in homology modeling.     

A novel method for predicting and using distance constraints of high accuracy for refining protein structure prediction

The principal bottleneck in protein structure prediction is the refinement of models from lower accuracies to the resolution observed by experiment. We developed a novel constraints‐based refinement method that identifies a high number of accurate input constraints from initial models and rebuilds them using restrained torsion angle dynamics (rTAD). We previously created a Bayesian statistics‐based residue‐specific all‐atom probability discriminatory function (RAPDF) to discriminate native‐like models by measuring the probability of accuracy for atom type distances within a given model. Here, we exploit RAPDF to score (i.e., filter) constraints from initial predictions that may or may not be close to a native‐like state, obtain consensus of top scoring constraints amongst five initial models, and compile sets with no redundant residue pair constraints. We find that this method consistently produces a large and highly accurate set of distance constraints from which to build refinement models. We further optimize the balance between accuracy and coverage of constraints by producing multiple structure sets using different constraint distance cutoffs, and note that the cutoff governs spatially near versus distant effects in model generation. This complete procedure of deriving distance constraints for rTAD simulations improves the quality of initial predictions significantly in all cases evaluated by us. Our procedure represents a significant step in solving the protein structure prediction and refinement problem, by enabling the use of consensus constraints, RAPDF, and rTAD for protein structure modeling and refinement. Proteins 2009. © 2009 Wiley‐Liss, Inc.     

Depositional processes of ribbon carbonates in Middle Cambrian of Iran (Deh-Sufiyan Formation,Central Alborz)

A variety of ribbon carbonates of the Deh-Sufiyan Formation (Middle Cambrian) in Central Alborz Range of northern Iran are studied to provide facies characterization and paleoenvironmental interpretation of ribbon carbonates on shallow-marine carbonate platforms. Seven types of ribbon carbonates are divided based mainly on sedimentary structures, ichnofossils, and bed geometry, which represent deposition during different phases of storm-induced processes. The different features of the storm deposits in ribbon carbonates such as hummocky and swaley cross-stratification, planar lamination, and combined-flow-ripple cross-stratification were formed by combined flows. Identification and interpretation of ichnological signatures and the spatial arrangement of succession of sedimentary structures are used to further refine sedimentary interpretations of parameters such as wave energy, substrate properties, variability in sedimentation rates, and proximality-distality trends of a wave-dominated marine ramp sequence. Successions from individual storm events reflect deposition during increasing combined oscillatory and unidirectional flow succeeded by the waning stages. The study provides depositional processes and models of various ribbon carbonates that may be useful for facies interpretation of ribbon rocks elsewhere.     

Protein-protein docking on molecular models of Aspergillus niger RNase and human actin: novel target for anticancer therapeutics

The 3D models of human actin protein and A.niger RNase were designed using the templates ACTBIND (PDB ID: 3D3Z) and crystalline profilin-beta-actin (PDB ID: 2BTF), respectively in Modeller9v5. These models are testified using several validation methods including PROCHECK, ERRAT, WHAT-IF, PROSA2003 and VERIFY-3D. The stereo-chemical quality of the models was judged by Ramachandran plot with PROCHECK. The total quality G-factor −0.2, shows a good quality model. The ERRAT score for the human actin and A.niger RNase models are 86.104 and 84.615, respectively, fit well within the range of a high quality model. The ERRAT score for the templates 2BTF and 3D3Z are 91.111 and 97.391, respectively. The WHAT-IF evaluation justifies a reasonable homology model structure as none of the scores for each residue in the homology model is lower than −5.0. The energy-minimized model of human actin with PROSA reveals the Z-score value −10.52 between native conformations of the crystal structures. The VERIFY 3D average score is 0.36. All evidence suggests that the geometric quality of the backbone conformation, the residue interaction, the residue contact and the energy profile of the structures were well within the limits of reliable structures. The interaction energy of docking was calculated using the HEX server. The Etotal, lowest docked energy, and calculated RMSD values were −1.608 kcal mol⁻¹, -8.369 kcal mol⁻¹ and 0.617 Å, respectively. The study presented in the current project may be useful to design molecules that may have anticancer activity.

     

Shapes and functions of species–area curves (II): a review of new models and parameterizations

This paper has extended and updated my earlier list and analysis of candidate models used in theoretical modelling and empirical examination of species–area relationships (SARs). I have also reviewed trivariate models that can be applied to include a second independent variable (in addition to area) and discussed extensively the justifications for fitting curves to SARs and the choice of model. There is also a summary of the characteristics of several new candidate models, especially extended power models, logarithmic models and parameterizations of the negative-exponential family and the logistic family. I have, moreover, examined the characteristics and shapes of trivariate linear, logarithmic and power models, including combination variables and interaction terms. The choice of models according to best fit may conflict with problems of non-normality or heteroscedasticity. The need to compare parameter estimates between data sets should also affect model choice. With few data points and large scatter, models with few parameters are often preferable. With narrow-scale windows, even inflexible models such as the power model and the logarithmic model may produce good fits, whereas with wider-scale windows where inflexible models do not fit well, more flexible models such as the second persistence (P2) model and the cumulative Weibull distribution may be preferable. When extrapolations and expected shapes are important, one should consider models with expected shapes, e.g. the power model for sample area curves and the P2 model for isolate curves. The choice of trivariate models poses special challenges, which one can more effectively evaluate by inspecting graphical plots.     

The Ribbon of Hydrogen Bonds in the Three-Dimensional Structure of Globular Proteins

We report quantum mechanical computations and experimental evidence which suggest that the backbone conformation of globular proteins depends generally on the conservation of that part of the hydrogen bond network or ribbon which is joined, in general, directly to the backbone and is largely independent of the remainder of this whole network of hydrogen bonds. The familiar hydrogen bonds of the helix and the sheet form about one-half of this ribbon of hydrogen bonds. Both water molecules and hydrogen bonding side chain groups are involved in the formation of the ribbon.This view of the three-dimensional structure of globular proteins in terms of the `molecule' allows us to deal with the non-secondary structure as well as with the familiar secondary structure. It also suggests that the ribbon contains approximately the same number of hydrogen bonds within all three structures – the helix, the sheet and the coil – and that this is the reason for the ease of interconversion of these three structures.The quantum mechanical computations on hydrogen bonding suggest that delocalised water molecules which have substantial mobility are an essential part of the ribbon. This situation arises because the hydrogen bonding groups of the protein molecule are not free to move to optimise the hydrogen bonding geometries as are the oxygen atoms in the waters and ices. Such delocalised water molecules either have high B values or are invisible in the X-ray data and yet are able to form a structure which is as strong as a normal hydrogen bond.The experimental data on the point mutations of the THRI57 residue of the T4 phage lysome provides an initial test of this model. Both the local backbone conformation and the ribbon of hydrogen bonds are conserved throughout all the mutations of residue 157,providing that the delocalised water molecules are accepted as a genuine part of the structure. These mutations include the introduction of hydrocarbon side chains at position 157 when water molecules or other side chain groups take over the formation of the hydrogen bonds.We suggest that, provided steric effects are not important, many point mutations succeed because they leave the ribbon of hydrogen bonds (and so the backbone conformation) largely unchanged.     

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.     

Thermodynamic study of the native and phosphorylated regulatory domain of the CFTR

The regulatory domain (RD) of the cystic fibrosis transmembrane conductance regulator (CFTR), the defective protein in cystic fibrosis, is the region of the channel that regulates the CFTR activity with multiple phosphorylation sites. This domain is an intrinsically disordered protein, characterized by lack of stable or unique tertiary structure. The disordered character of a protein is directly correlated with its function. The flexibility of RD may be important for its regulatory role: the continuous conformational change may be necessary for the progressive phosphorylation, and thus activation, of the channel. However, the lack of a defined and stable structure results in a considerable limitation when trying to in build a unique molecular model for the RD. Moreover, several evidences indicate significant structural differences between the native, non-phosphorylated state, and the multiple phosphorylated state of the protein. The aim of our work is to provide data to describe the conformations and the thermodynamic properties in these two functional states of RD. We have done the circular dichroism (CD) spectra in samples with a different degree of phosphorylation, from the non-phosphorylated state to a bona fide completely phosphorylated state. Analysis of CD spectra showed that the random coil and β-sheets secondary structure decreased with the polypeptide phosphorylation, at expenses of an increase of α-helix. This observation lead to interpret phosphorylation as a mechanism favoring a more structured state. We also studied the thermal denaturation curves of the protein in the two conditions, monitoring the changes of the mean residue ellipticity measured at 222 nm as a function of temperature, between 20 and 95 °C. The thermodynamic analysis of the denaturation curves shows that phosphorylation of the protein induces a state of lower stability of R domain, characterized by a lower transition temperature, and by a smaller Gibbs free energy difference between the native and the unfolded states.     

Mena–GRASP65 interaction couples actin polymerization to Golgi ribbon linking

In mammalian cells, the Golgi reassembly stacking protein 65 (GRASP65) has been implicated in both Golgi stacking and ribbon linking by forming trans-oligomers through the N-terminal GRASP domain. Because the GRASP domain is globular and relatively small, but the gaps between stacks are large and heterogeneous, it remains puzzling how GRASP65 physically links Golgi stacks into a ribbon. To explore the possibility that other proteins may help GRASP65 in ribbon linking, we used biochemical methods and identified the actin elongation factor Mena as a novel GRASP65-binding protein. Mena is recruited onto the Golgi membranes through interaction with GRASP65. Depleting Mena or disrupting actin polymerization resulted in Golgi fragmentation. In cells, Mena and actin were required for Golgi ribbon formation after nocodazole washout; in vitro, Mena and microfilaments enhanced GRASP65 oligomerization and Golgi membrane fusion. Thus Mena interacts with GRASP65 to promote local actin polymerization, which facilitates Golgi ribbon linking.     

A Bayesian network model for protein fold and remote homologue recognition

MOTIVATION: The Bayesian network approach is a framework which combines graphical representation and probability theory, which includes, as a special case, hidden Markov models. Hidden Markov models trained on amino acid sequence or secondary structure data alone have been shown to have potential for addressing the problem of protein fold and superfamily classification. RESULTS: This paper describes a novel implementation of a Bayesian network which simultaneously learns amino acid sequence, secondary structure and residue accessibility for proteins of known three-dimensional structure. An awareness of the errors inherent in predicted secondary structure may be incorporated into the model by means of a confusion matrix. Training and validation data have been derived for a number of protein superfamilies from the Structural Classification of Proteins (SCOP) database. Cross validation results using posterior probability classification demonstrate that the Bayesian network performs better in classifying proteins of known structural superfamily than a hidden Markov model trained on amino acid sequences alone.     

Use of molecular mechanics for secondary structure prediction. Is it possible to reveal alpha-helix?

A new approach to predicting protein standard conformations is suggested. The idea consists in modeling by molecular mechanics tools a continuous alpha-helical conformation for the whole protein. The profile of energy along the model alpha-helix reveals minima corresponding to real alpha-helical segments in the native protein. The 3/10-helices and beta-turns including a local alpha-helical conformation may be detected as well. All alpha-helical segments in the test sample are delineated; mean residue by residue accuracy Q(3alpha) is 79%. This non-statistical approach can shed light on the physical grounds of alpha-helix formation.