An Automatic Search for Similar Spatial Arrangements of α-Helices and β-Strands in Globular Proteins

Abstract

A fast search algorithm to reveal similar polypeptide backbone structural motifs in proteins is proposed. It is based on the vector representation of a polypeptide chain fold in which the elements of regular secondary structures are approximated by linear segments (Abagyan and Maiorov, J. Biomol. Struct. Dyn. 5, 1267–1279 (1988)). The algorithm permits insertions and deletions in the polypeptide chain fragments to be compared. The fast search algorithm implemented in FASEAR program is used for collecting βαβ supersecondary structure units in a number of α/β proteins of Brookhaven Data Bank. Variation of geometrical parameters specifying backbone chain fold is estimated. It appears that the conformation of the majority of the fragments, although almost all of them are right-handed, is quite different from that of standard βαβ units. Apart from searching for specific type of secondary structure motif, the algorithm allows automatically to identify new recurrent folding patterns in proteins. It may be of particular interest for the development of tertiary template approach for prediction of protein three-dimensional structure as well for constructing artificial polypeptides with goal-oriented conformation.     

Theory of protein molecule self-organization. III. A calculating method for the probabilities of the secondary structure formation in an unfolded polypeptide chain

A mathematical model is developed adequately describing an unfolded polypeptide chain without long-range interactions in which fluctuating hydrogen-bonded α-helices, β-bends, fragments of helices 3₁₀, and other local structures are formed. The obtained model is a modification of a one-dimensional Ising model for a heteropolymer and allows one to determine the probability of formation of different secondary structures in various parts of a polypeptide chain, provided the whole set of structural thermodynamic parameters exists.     

Protein Structure Evaluation using an All-Atom Energy Based Empirical Scoring Function

Abstract

Arriving at the native conformation of a polypeptide chain characterized by minimum most free energy is a problem of long standing interest in protein structure prediction endeavors. Owing to the computational requirements in developing free energy estimates, scoring functions—energy based or statistical—have received considerable renewed attention in recent years for distinguishing native structures of proteins from non-native like structures. Several cleverly designed decoy sets, CASP (Critical Assessment of Techniques for Protein Structure Prediction) structures and homology based internet accessible three dimensional model builders are now available for validating the scoring functions. We describe here an all-atom energy based empirical scoring function and examine its performance on a wide series of publicly available decoys. Barring two protein sequences where native structure is ranked second and seventh, native is identified as the lowest energy structure in 67 protein sequences from among 61,659 decoys belonging to 12 different decoy sets. We further illustrate a potential application of the scoring function in bracketing native-like structures of two small mixed alpha/beta globular proteins starting from sequence and secondary structural information. The scoring function has been web enabled at www.scfbio-iitd.res.in/utility/proteomics/energy.jsp     

A Kinetic Approach to the Prediction of RNA Secondary Structures

Abstract

A new approach to the prediction of secondary RNA structures based on the analysis of the kinetics of molecular self-organisation is proposed herein. The Markov process is used to describe structural reconstructions during secondary structure formation. This process is modelled by a Monte-Carlo method. Examples of the calculation by this method of the secondary structures kinetic ensemble are given. Distribution of time-dependent probabilities within the ensembles is obtained.

An effective method for search for the equilibrium ensemble is also suggested. This method is based on the construction of a tree of all possible secondary structures of RNA. By ascribing a probability for each structure (according to its free energy) the Boltzmann equilibrium ensemble can be obtained.     

RNA multi-structure landscapes

Statistical properties of RNA folding landscapes obtained by the partition function algorithm (McCaskill 1990) are investigated in detail. The pair correlation of free energies as a function of the Hamming distance is used as a measure for the ruggedness of the landscape. The calculation of the partition function contains information about the entire ensemble of secondary structures as a function of temperature and opens the door to all quantities of thermodynamic interest, in contrast with the conventional minimal free energy approach. A metric distance of structure ensembles is introduced and pair correlations at the level of the structures themselves are computed. Just as with landscapes based on most stable secondary structure prediction, the landscapes defined on the full biophysical GCAU alphabet are much smoother than the landscapes restricted to pure GC sequences and the correlation lengths are almost constant fractions of the chain lengths. Correlation functions for multi-structure landscapes exhibit an increased correlation length, especially near the melting temperature. However, the main effect on evolution is rather an effective increase in sampling for finite populations where each sequence explores multiple structures. Correspondence to: P. Schuster     

The Genetic Algorithm and the Conformational Search of Polypeptides and Proteins

Abstract

The genetic algorithm is a technique of function optimization derived from the principles of evolutionary theory. We have adapted it to perform conformational search on polypeptides and proteins. The algorithm was first tested on several small polypeptides and the 46 amino acid protein crambin under the AMBER potential energy function. The probable global minimum conformations of the polypeptides were located 90% of the time and a non-native conformation of crambin was located that was 150kcal/mol lower in potential energy than the minimized crystal structure conformation. Next, we used a knowledge-based potential function to predict the structures of melittin, pancreatic polypeptide, and crambin. A 2.31 Å ΔRMS conformation of melittin and a 5.33 Å ΔRMS conformation of pancreatic polypeptide were located by genetic algorithm-based conformational search under the knowledge-based potential function. Although the ΔRMS of pancreatic polypeptide was somewhat high, most of the secondary structure was correct. The secondary structure of crambin was predicted correctly, but the potential failed to promote packing interactions. Finally, we tested the packing aspects of our potential function by attempting to predict the tertiary structure of cytochrome b ₅₆₂ given correct secondary structure as a constraint. The final predicted conformation of cytochrome b ₅₆₂ was an almost completely extended continuous helix which indicated that the knowledge-based potential was useless for tertiary structure prediction. This work serves as a warning against testing potential functions designed for tertiary structure prediction on small proteins.     

A three dimensional visualisation approach to protein heavy-atom structure reconstruction

Background

A commonly recurring problem in structural protein studies, is the determination of all heavy atom positions from the knowledge of the central α-carbon coordinates.

Results

We employ advances in virtual reality to address the problem. The outcome is a 3D visualisation based technique where all the heavy backbone and side chain atoms are treated on equal footing, in terms of the C_α coordinates. Each heavy atom is visualised on the surfaces of a different two-sphere, that is centered at another heavy backbone and side chain atoms. In particular, the rotamers are visible as clusters, that display a clear and strong dependence on the underlying backbone secondary structure.

Conclusions

We demonstrate that there is a clear interdependence between rotameric states and secondary structure. Our method easily detects those atoms in a crystallographic protein structure which are either outliers or have been likely misplaced, possibly due to radiation damage. Our approach forms a basis for the development of a new generation, visualization based side chain construction, validation and refinement tools. The heavy atom positions are identified in a manner which accounts for the secondary structure environment, leading to improved accuracy.

     

On A Six-Dimensional Representation of RNA Secondary Structures

Abstract

In this paper, we proposed a 6-D representation of RNA secondary structures. The use of the 6-D representation is illustrated by constructing structure invariants. Comparisons with the similarity/dissimilarity results based on 6-D representation for a set of RNA secondary structures, are considered to illustrate the use of our structure invariants based on the entries in derived sequence matrices restricted to a selected width of a band along the main diagonal.     

Accuracy of Secondary Structure and Solvent Accessibility Predictions for a Clostridial Neurotoxin C-Fragment

Earlier studies used Rost and Sander's artificial neural network [(1993a), J. Mol. Biol. 232, 584–599] to predict the secondary structures [Lebeda and Olson (1994), Proteins 20, 293–300] and residue solvent accessibilities [Lebeda and Olson (1997), J. Protein Chem. 16, 607–618] of the clostridial neurotoxins. Because the X-ray crystal structure of the 50-kDa C-terminal half of the heavy chain of tetanus toxin was recently determined, this report evaluates the accuracy of these network-derived predictions. For this predominantly -strand-containing fragment, predictions, on a per-residue basis, for both secondary structure and solvent accessibility were about 70% accurate. A more flexible and realistic analysis based on overlapping segments yielded accuracies of over 80% for the three-state secondary structure and for the two-state accessibility predictions. Because the accuracies of these predictions are comparable to those made by Rost and Sander using a dataset of 126 nonhomologous globular proteins, our predictions provide a quantitative foundation for gauging the results when building by homology the structures of related proteins.     

A Simple Qualitative Representation of Polypeptide Chain Folds: Comparison of Protein Tertiary Structures

Abstract

A new simple quantitative representation of three-dimensional structure of globular proteins is proposed which is useful for comparison of distantly related problems, computer sorting of large sets of conformations, and search of structurally similar domains in protein data base. The folding course of the polypeptide backbone is approximated by a set of successive vectors corresponding to the elements of regular secondary structure (e.g. α-helices, strands of β- sheets) and non-regular segments. The parameters specifying the spatial organization of segments in this vector model are internal coordinates, namely, lengths of the vectors, planar and dihedral angles. Quantitative representation proposed allows to circumvent the problem of insertions/deletions and to avoid the stage of best superposition during protein comparison An application was made to the comparison of three-dimensional structures of scorpion toxins Centruroides sculpturatus Ewing v-3, Buthus eupeus M₉ and I_5A, which have different chain lengths and low sequence similarity.     

Lysozyme Folded In Silico According to the Limited Conformational Sub-space

Abstract

The conformational sub-space oriented on early-stage protein folding is applied to lysozyme folding. The part of the Ramachandran map distinguished on the basis of a geometrical model of the polypeptide chain limited to the mutual orientation of the peptide bond planes is shown to deliver the initial structure of the polypeptide for the energy minimization procedure in the ab initio model of protein folding prediction. Two forms of energy minimization and molecular dynamics simulation procedures were applied to the assumed early-stage protein folding of lysozyme. One of them included the disulphide bond system and the other excluded it. The post-energy-minimization and post-dynamics structures were compared using RMS-D and non-bonding contact maps to estimate the degree of approach to the native, target structure of the protein molecule obtained using the limited conformational sub-space for the early stage of folding.     

Main-chain Dynamics of a Partially Folded Protein:15N NMR Relaxation Measurements of Hen Egg White Lysozyme Denatured in Trifluoroethanol

¹⁵N NMR relaxation measurements have been used to study the dynamic behaviour of the main-chain of hen lysozyme in a partially folded state, formed in a 70% (v/v) trifluoroethanol (TFE)/30% water mixture at 37°C and pH 2. This state is characterised by helical secondary structure in the absence of extensive tertiary interactions. The NMR relaxation data were interpreted by mapping of spectral density functions and by derivation of segmental as well as global order parameters. The results imply that the dynamics of lysozyme in TFE can, at least for the great majority of residues, be adequately described by internal motions which are superimposed on an overall isotropic tumbling of the molecule. Although the dynamic behaviour shows substantial variations along the polypeptide chain, it correlates well with the conformational preferences identified in the TFE state by other NMR parameters. Segments of the polypeptide chain which are part of persistent helical structures are highly restricted in their motion (S²> 0.8, with effective internal correlation times τ_e< 200 ps) but are also found to experience conformational exchange on a millisecond timescale. Regions which are stabilised in less persistent helical structure possess greater flexibility (0.6 <S²< 0.8, 200 ps < τ_e< 1 ns) and those which lack defined conformational preferences are highly flexible (S²< 0.6, τ_e∼1 ns). The dynamic behaviour of the main-chain was found to be correlated with other local features of the polypeptide chain, including hydrophobicity and the position of the disulphide bridges. Despite the absence of extensive tertiary interactions, preferential stabilisation of native-like secondary structure by TFE results in a pattern of main-chain dynamics which is similar to that of the native state.     

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.     

A Full-automatic Sequence Design Algorithm for Branched DNA Structures

Abstract

Production of various structures by self-assembling single stranded DNA molecules is a widely used technology in the filed of DNA nanotechnology. Base sequences of single strands do predict the shape of the resulting nanostructure. Therefore, sequence design is crucial for the successful structure fabrication. This paper presents a sequence design algorithm based on mismatch minimization that can be applied to every desired DNA structure. With this algorithm, junctions, loops, single as well as double stranded regions, and very large structures up to several thousand base pairs can be handled. Thereby, the algorithm is fast for the most structures. Algorithm is Java-implemented. Its implementation is called Seed and is available publicly. As an example for a successful sequence generation, this paper presents the fabrication of DNA chain molecules consisting of double-crossover (DX) tiles as well.     

Molecular Mechanics Calculations of Proteins. Comparison of Different Energy Minimization Strategies

Abstract

A general strategy for performing energy minimization of proteins using the SYBYL molecular modelling program has been developed. The influence of several variables including energy minimization procedure, solvation, dielectric function and dielectric constant have been investigated in order to develop a general method, which is capable of producing high quality protein structures. Avian pancreatic polypeptide (APP) and bovine pancreatic phospholipase A2 (BP PLA2) were selected for the calculations, because high quality X-ray structures exist and because all classes of secondary structure are represented in the structures. The energy minimized structures were evaluated relative to the corresponding X-ray structures. The overall similarity was checked by calculating RMS distances for all atom positions. Backbone conformation was checked by Ramachandran plots and secondary structure elements evaluated by the length on hydrogen bonds. The dimensions of active site in BP PLA2 is very dependent on electrostatic interactions, due to the presence of the positively charged calcium ion. Thus, the distances between calcium and the calcium-coordinating groups were used as a quality index for this protein. Energy minimized structures of the trimeric PLA2 from Indian cobra (N.n.n. PLA2) were used for assessing the impact of protein-protein interactions. Based on the above mentioned criteria, it could be concluded that using the following conditions: Dielectric constant ? = 4 or 20; a distance dependent dielectric function and stepwise energy minimization, it is possible to reproduce X-ray structures very accurately without including explicit solvent molecules.     

Studies on the Structure of Feather Keratin: II. A β-Helix Model for the Structure of Feather Keratin

The assumption that the proline residues in feather keratin, which comprise 12 per cent of the total, are periodically located along the polypeptide chain is shown to lead to an essentially unique structure for this fibrous protein. The structure is based on a β-helix; i.e., an extended chain which coils slowly to form a helix of relatively large pitch. Such helices tend to aggregate by hydrogen bonding to form cylindrical units, which in turn can aggregate further into cable-like structures. This model has been tested with respect to its predictions concerning the x-ray diffraction pattern, infrared spectrum, mechanical properties, and chemical behavior of feather keratin. Preliminary results indicate that it is better capable of accounting for the data than previously proposed structures.     

Backbones of Folded Proteins Reveal Novel Invariant Amino Acid Neighborhoods

Abstract

Folding of naturally occurring proteins has eluded a universal molecular level explanation till date. Rather, there is an abundance of diverse views on dominant factors governing protein folding. Through rigorous analyses of several thousand crystal structures, we observe that backbones of folded proteins display some remarkable invariant features. Folded proteins are characterized by spatially well-defined, distance dependent, and universal, neighborhoods of amino acids which defy any of the conventionally prevalent views. These findings present a compelling case for a newer view of protein folding which takes into account solvent mediated and amino acid shape and size assisted optimization of the tertiary structure of the polypeptide chain to make a functional protein.     

Simulated annealing approach to the study of protein structures

One of the most difficult problems in predicting the three dimensional structure of proteins is how to deal with the local minimum problem. In many cases of practical interest this problem has been reduced to how to select an appropriate set of starting conformations for carrying out energy minimizations. How these starting conformations are selected, however, is often based on the physical intuition of the person doing the calculations, and hence it is hard to avoid bearing some sort of arbitrariness. To improve such a situation, we introduced the simulated annealing Monte Carlo algorithm to locate the optimal starting conformations for energy minimizations. The method developed here is valid for both single and multiple polypeptide chain systems. The annealing process can be conducted with respect to either the internal dihedral angles of a polypeptide chain or the external rotations and translations of various constituent polypeptide chains, and hence is particularly useful for studying the packing arrangements of secondary structures in proteins, such as helix/helix packing, helix/sheet packing and sheet/sheet packing. It was shown via a number of comparative calculations that the final structures obtained through the annealing process not only had lower energies than the corresponding energy-minimized structures reported previously, but also assumed the forms closer to the observations in proteins. All these results indicate that a better result can be obtained in search of low-energy structures of proteins by incorporating the simulated annealing approach.(ABSTRACT TRUNCATED AT 250 WORDS)     

Selective Binding of Synthetic Polypeptides to DNA of Varying Composition and Sequence: Effect of Minor Groove Binding Drugs

Abstract

Repetitive basic polypeptides containing lysine or arginine as every third amino acid were shown to cause DNA condensation at physiological salt concentration connected with selective DNA binding with respect to DNA composition and sequence. This selectivity is very similar to that existing in the case of histone H1 and other basic proteins and does not depend on polypeptide chain conformation. The effect of the minor groove binding drugs netropsin and distamycin was tested to elucidate the origin of the binding selectivity. The results suggest that the binding preferences are due to the variations in the conformation in various types of B-DNA that depend on DNA composition and sequence. The most important factor affecting the selectivity is probably the value of the negative electrostatic potential in the minor groove.     

Folding of Oligoglutamines: A Theoretical Approach Based Upon Thermodynamics and Molecular Mechanics

Abstract

Folding of oligoglutamine chains of different lengths is of crucial interest for exploring the molecular mechanisms of Huntington's disease. A simple oligoglutamine model based upon the Flory-Huggins theory of polymer solutions demonstrates a random coil instability in chains containing more than 40 glutamine residues with respect to β-sheet formation. This is in striking quantitative agreement with biochemical results on the chain length dependence of polyglutamine aggregation in vivo and in vitro, as well as with clinical data on the polyglutamine chain length dependence of the onset of Huntington's disease. Furthermore, a detailed molecular-mechanical investigation of a polypeptide chain carrying 40 glutamine residues was performed. Two possible folding modes of such an oligoglutamine chain were revealed: a) a β-hairpin and b) a highly compact random coil entity stabilized by a wealth of H-bonds among the glutamine side chains. A possible role of these folding modes in polyglutamine aggregation, as well as in the onset of Huntington's disease, is discussed.