Alpha Atoms Research Articles

Dimeric capsule vs columnar polymer: Structural factors determining the aggregation behavior of amino acid functionalized benzene-1,3,5-tricarboxamides in solution and in the solid-state

The non-covalent aggregation of four benzene-1,3,5-tricarboxamide (BTA) derivatives formed from glycine or l-valine esters (-Me, -iPr), has been investigated in the solid-state and in chloroform solution by means of several analytical methods (NMR, FT-IR, and single crystal XRD). Two types of self-assembled structures were characterized: a dimeric capsule formed by –NH···OC- (ester) bonding and a columnar assembly with characteristic –NH···OC- (amide) bonds (alongside with monomers). In-depth solid-state studies revealed the significant role of the steric bulk of the C-terminus protecting group in supramolecular aggregation in the solid-state. Increasing the bulk of the ester group prevents the molecule from assembling into a columnar structure and instead a dimeric assembly is observed. On the other hand, it has no effect in chloroform solution, where the amino acid sidechain determines the self-assembly outcome. Our study points out the essential influence of substituent steric bulk in both positions: the alpha atom of the amino acid ester and in the ester group itself. Systematic study of these structurally similar molecules also allows identification of the moiety having the greater influence on the nature and stability of BTA aggregates in distinct phases (bulk, solution).

Deeper inside the specificity of lysozyme when degrading chitosan. A structural bioinformatics study

Lysozymes that were used in numerous in vitro experiments of chitosan degradation were regularly from hen egg-white. Human lysozyme has been proved to be more active than hen egg-white lysozyme when exerting its bacteriostatic effect and there is possible that the two enzymes have some different structural properties. Consequently, within this study, we compared the structural and physicochemical properties of the human and egg-white lysozymes and used the molecular docking approach to obtain information concerning the specificity of the interactions between chitooligosaccharides with these enzymes. There is 60.47% of identity between the sequences of the human and the hen egg-white lysozymes, but the amino acids that are involved in the interactions of considered lysozymes with N-acetylchitohexaose are well conserved. Superimposition of the structures of investigated lysozymes reveals their structural similarity, the RMSD value being 1.198 Å for 118 equivalent carbon alpha atom pairs from a total of 129. There are some local physicochemical properties like the distribution of the electrostatic potential and the hydrophobicity of the catalytic cavities of the enzyme that are quite different. Substrate specificities of human and hen egg-white lysozyme with respect to chito-oligosaccharides are not clearly distinguishable but they are dependent on the molecular weight, deacetylation degree and pattern of deacetylation.

Weighted protein residue networks based on joint recurrences between residues.

BackgroundWeighted and un-weighted protein residue networks can predict key functional residues in proteins based on the closeness centrality C and betweenness centrality B values for each residue. A static snapshot of the protein structure, and a cutoff distance, are used to define edges between the network nodes. In this work we apply the weighted network approach to study the β-Lactamase Inhibitory Protein (BLIP). Joint recurrences extracted from molecular dynamics MD trajectory positions of the protein residue carbon alpha atoms are used to define edge weights between nodes, and no cutoff distance is used. The results for B and C from our approach are compared with those extracted from an un-weighted network, and a weighted network that uses interatomic contacts to define edge weights between nodes, respectively.ResultsThe joint recurrence weighted network approach performs well in pointing out key protein residues. Furthermore, it seems to emphasize residues with medium to high relative solvent accessibility that lie in loop regions between secondary structure elements of the protein.ConclusionsProtein residue networks that use joint recurrences extracted from molecular dynamics simulations of a solvated protein perform well in pointing to hotspot residues and hotspot clusters. This approach uses no distance cutoff threshold, and does not exclude any interactions between the residues, including water-mediated interactions.

The ALPHA – detector: Module Production and Assembly

ALPHA is one of the experiments situated at CERN's Antiproton Decelerator (AD). A Silicon Vertex Detector (SVD) is placed to surround the ALPHA atom trap. The main purpose of the SVD is to detect and locate antiproton annihilation events by means of the emitted charged pions. The SVD system is presented with special focus given to the design, fabrication and performance of the modules.

Small-World and Random Networks in Contact Maps of Protein Channels

Although it is estimated that protein channels constitute large portion of all proteins, the number of their experimental structures is extremely small compared to other proteins. Lipid environment and great size of the channels impede the development. Improvement could contribute to drug design and resolving mechanisms of channelopathies. Modeling 3D structure of transmembrane channels can be enhanced by constraints defined by their contact sites distribution, supporting proper selection of protein decoys in the modeling process. We represent a protein as a network of contact sites and characterize topology of the graph. As a contact site we consider residues within a defined distance between protein backbone C alpha (or beta) atoms that are separated by a certain number of amino acids. Characteristics of the graph model is tested, with regard to protein secondary structure and location of the residues in the membrane or outside. We investigate how the topological characteristics of protein channels compare to other proteins and how definition of the contact site, in terms of the distance and separation threshold values, affects the network topology. The results indicate that the graph model of ionic channel has distinct features. The network topology of proteins proved sensitive to the contact site definition, showing that the graph obeys typical real world network characteristics (“small-world” graph) only if the distance and the separation in the contact site definition are within certain limits, which are not always in accordance with typically assumed. Otherwise a random (Erdos-Renyi) network is observed. Transmembrane helices are much less sensitive to the contact site definition and fall into the “small world” more easily than other structures.

Olefin Epoxidation by H2O2/MeCN Catalysed by Cyclopentadienyloxidotungsten(VI) and Molybdenum(VI) Complexes: Experiments and Computations

Compounds [Cp*(2)M(2)O(5)] (M = Mo, 1; W, 2) are efficient pre-catalysts for cyclooctene (COE) epoxidation by aqueous H(2)O(2) in acetonitrile/toluene. The reaction is quantitative, selective and takes place approximately 50 times faster for the W system (k(obs) = 4.32(9)x10(-4) s(-1) at 55 degrees C and 3x10(-3) M concentration for the dinuclear complex, vs. 1.06(7)x10(-5) s(-1) for the Mo system). The rate law is first order in catalyst and COE substrate (k = 0.138(7) M(-1) s(-1) for the W system at 55 degrees C), whereas increasing the concentration of H(2)O(2) slows down the reaction because of an inhibiting effect of the greater amount of water. The activation parameters for the more active W systems (DeltaH(double dagger) = 10.2(6) kcal mol(-1); DeltaS(double dagger) = -32(2) cal mol(-1) K(-1)) were obtained from an Eyring study in the 25-55 degrees C temperature range. The H(2)O(2)urea adduct was less efficient as an oxidant than the aqueous H(2)O(2) solution. Replacement of toluene with diethyl ether did not significantly affect the catalyst efficiency, whereas replacement with THF slowed down the process. The epoxidation of ethylene as a model olefin, catalysed by the [Cp*MO(2)Cl] systems (M = W, Mo) in the presence of H(2)O(2) as oxidant and acetonitrile as solvent, has been investigated by DFT calculations with the use of the conductor-like polarisable continuum model (CPCM). For both metal systems, the rate-limiting step is the transfer of the hydroperoxido O(alpha) atom to the olefin, in accordance with the first-order dependence on the substrate and the zero-order dependence on H(2)O(2) found experimentally in the catalytic data. The activation barrier corresponding to the rate-limiting step is 4 kcal lower for the W complex than for the corresponding Mo analogue (32.3 vs. 28.3 kcal mol(-1)). This result reproduces well the higher catalytic activity of the W species. The different catalytic behaviour between the two systems is rationalised by a natural bond orbital (NBO) study and natural population analyses (NPA). Compared to Mo, the W(VI) centre withdraws more electron density from the sigma bonding [O-O] orbital and favours, as a consequence, the nucleophilic attack of the external olefin on the sigma*[O-O] orbital.

M═Nα Cycloaddition and Nα−Nβ Insertion in the Reactions of Titanium Hydrazido Compounds with Alkynes: A Combined Experimental and Computational Study

A combined experimental and DFT study of the reactions of diamide-amine supported titanium hydrazides with alkynes is presented. Reaction of Ti(N2N(py))(NNPh2)(py) (1, N2N(py) = (2-NC5H4)CMe(CH2NSiMe3)2) with terminal and internal aryl alkynes ArCCR (Ar = Ph or substituted phenyl, R = Me or H) at room temperature gave the fully authenticated azatitanacyclobutenes Ti(N2N(py)){N(NPh2)C(R)CAr} via ArCCR [2 + 2] cycloaddition to the Ti=N(alpha) bond of the hydrazide ligand. In contrast, reaction of 1 with PhCCMe at 60 degrees C, or of Ti(N2NMe)(NNPh2)(py) (11, N2NMe = MeN(CH2CH2NSiMe3)2) with RCCMe (R = Me, Ph or substituted phenyl) at room temperature or below, gave vinyl imido compounds of the type Ti(N2N(R')){NC(R)C(Me)NPh2}(py), in which RCCMe had undergone net insertion into the N(alpha)-N(beta) bond. These are the first examples of this type of reaction for any metal hydrazide. The reaction of 11 with PhCCMe had the activation parameters DeltaH(double dagger) = 18.8(4) kcal mol(-1), DeltaS(double dagger) = 1(1) cal mol(-1) K(-1) and DeltaG(298)(double dagger) = 18.5(7) kcal mol(-1). Mechanistic and DFT studies for 1 and 11 found that the N(alpha)-N(beta) insertion event is preceded by alkyne cycloaddition to Ti=N(alpha), and that N(alpha)-N(beta) bond "insertion" is really an intramolecular N(alpha) atom migration process within the azatitanacyclobutenes following intramolecular chelation of NPh2 of the hydrazide ligand. Electron-withdrawing aryl groups on ArCCMe stabilize the azatitanacyclobutenes and also promote a specific regiochemistry (ArC carbon bound to Ti). This in turn defines the regiochemistry of the overall N(alpha)-N(beta) insertion reaction (ArC carbon bound to N(alpha)). In contrast, electron-releasing aryl groups promote the final N(alpha) migration stage of the mechanism, and a Hammett analysis of the rates of insertion of (4-C6H4X)CCMe into the N(alpha)-N(beta) bond of 11 found a reaction constant, rho, of -0.74(5), consistent with NPA charge changes of ArC along the DFT reaction coordinate.

A Computational Study of the Olefin Epoxidation Mechanism Catalyzed by Cyclopentadienyloxidomolybdenum(VI) Complexes

A DFT analysis of the epoxidation of C(2)H(4) by H(2)O(2) and MeOOH (as models of tert-butylhydroperoxide, TBHP) catalyzed by [Cp*MoO(2)Cl] (1) in CHCl(3) and by [Cp*MoO(2)(H(2)O)](+) in water is presented (Cp*=pentamethylcyclopentadienyl). The calculations were performed both in the gas phase and in solution with the use of the conductor-like polarizable continuum model (CPCM). A low-energy pathway has been identified, which starts with the activation of ROOH (R=H or Me) to form a hydro/alkylperoxido derivative, [Cp*MoO(OH)(OOR)Cl] or [Cp*MoO(OH)(OOR)](+) with barriers of 24.9 (26.5) and 28.7 (29.2) kcal mol(-1) for H(2)O(2) (MeOOH), respectively, in solution. The latter barrier, however, is reduced to only 1.0 (1.6) kcal mol(-1) when one additional water molecule is explicitly included in the calculations. The hydro/alkylperoxido ligand in these intermediates is eta(2)-coordinated, with a significant interaction between the Mo center and the O(beta) atom. The subsequent step is a nucleophilic attack of the ethylene molecule on the activated O(alpha) atom, requiring 13.9 (17.8) and 16.1 (17.7) kcal mol(-1) in solution, respectively. The corresponding transformation, catalyzed by the peroxido complex [Cp*MoO(O(2))Cl] in CHCl(3), requires higher barriers for both steps (ROOH activation: 34.3 (35.2) kcal mol(-1); O atom transfer: 28.5 (30.3) kcal mol(-1)), which is attributed to both greater steric crowding and to the greater electron density on the metal atom.

Structure/function studies on two type 1 ribosome inactivating proteins: Bouganin and lychnin

The three-dimensional structures of two type 1 RIPs, bouganin and lychnin, has been solved. Their adenine polynucleotide glycosylase activity was also determined together with other known RIPs: dianthin 30, PAP-R, momordin I, ricin A chain and saporin-S6. Saporin-S6 releases the highest number of adenine molecules from rat ribosomes, and poly(A), while its efficiency is similar to dianthin 30, bouganin and PAP-R on herring sperm DNA. Measures of the protein synthesis inhibitory activity confirmed that saporin-S6 is the most active. The overall structure of bouganin and lychnin is similar to the other considered RIPs and the typical RIP fold is conserved. The superimpositioning of their C(alpha) atoms highlights some differences in the N-terminal and C-terminal domains. A detailed structural analysis indicates that the efficiency of saporin-S6 on various polynucleotides can be ascribed to a negative electrostatic surface potential at the active site and several exposed positively charged residues in the region around that site. These two conditions, not present at the same time in other examined RIPs, could guarantee an efficient interaction with the substrate and an efficient catalysis.

Influence of Backbone Fluorine Substitution upon the Folding Equilibrium of a β-Heptapeptide

Explicit solvent molecular dynamics (MD) simulations of three beta-heptapeptides with a central beta- HAla(alpha-F) amino acid (Figure 1) in methanol are reported. They aim at an analysis of the conformational consequences of C(alpha) carbon atom bound fluoro atoms, and the particular configuration of the central fluoro-beta-amino acid: peptide 3 with an S configuration of the C(alpha) bound fluor atom, peptide 4 with an R configuration of the C(alpha) bound fluor atom, and peptide 5 with a difluoro substitution at the C(alpha) atom of residue 4. The NMR and CD spectra of these three beta-peptides were earlier (Mathad et al. Helv. Chim. Acta 2005, 88, 266-280) interpreted to indicate a decrease in propensity of 3(14)-helical structure from peptide 4 to peptide 5 to peptide 3. This result was at odds with previous experimental data for beta-heptapeptides with a central beta-HAla(alpha-Me) amino acid which showed that the beta-heptapeptide with the S,S configuration of the central beta-HAla(alpha-Me) was the most 3(14)-helical, whereas the S,R configuration did not lead to any detected helicity. The reported MD simulations resolve this paradox. The MD trajectories of all three peptides do agree with the primary, measured data: NMR nuclear Overhauser effect (NOE) atom-atom distance bounds and (3)J-coupling constants. A conformational analysis of the MD trajectory conformations shows, however, a decrease in 3(14)-helical character from peptide 3 to peptide 5 to peptide 4, which is in line with the results for the nonfluorinated peptides. It is shown that interpretation of NMR NOE data using single-structure refinement in vacuo based on local (along the sequence) and limited atom-atom distance data as in ref 1 (Mathad et al. Helv. Chim. Acta 2005, 88, 266-280) may lead to molecular structures that are not representative for the ensemble of molecular conformations.

Molecular dynamics studies on the interactions of PTP1B with inhibitors: from the first phosphate-binding site to the second one

Protein tyrosine phosphatases 1B (PTP1B) is a major negative regulator of both insulin and leptin signaling pathways. In view of this, it becomes an important target for drug development against cancers, diabetes and obesity. The aim of the current study is to use the long time-scale molecular dynamics (MD) simulations to investigate the structural and dynamic factors that cause its inhibition by INTA and INTB, the two most potent and highly selective PTP1B inhibitors known so far. In order to investigate the mode of collective motions that is vitally important to the biological function, the covariance matrix of C(alpha) atoms was introduced for performing the dynamic analysis of the inhibition systems. It has been observed that the conformational and dynamic features of WPD-Loop, R-Loop and S-Loop play a key role in providing a smooth entrance for the inhibitors moving into the binding pocket as well as a favorable microenvironment to stabilize them. Furthermore, the hydrogen bonding networks formed around the active site with INTA and INTB may be the main reason of why the inhibition of PTP1B by the two ligands is so potent and selective. All these findings might provide useful insights for developing novel and effective drugs to treat cancer, diabetes and obesity.

Recognition of Interaction Interface Residues in Low-Resolution Structures of Protein Assemblies Solely from the Positions of Cα Atoms

BackgroundThe number of available structures of large multi-protein assemblies is quite small. Such structures provide phenomenal insights on the organization, mechanism of formation and functional properties of the assembly. Hence detailed analysis of such structures is highly rewarding. However, the common problem in such analyses is the low resolution of these structures. In the recent times a number of attempts that combine low resolution cryo-EM data with higher resolution structures determined using X-ray analysis or NMR or generated using comparative modeling have been reported. Even in such attempts the best result one arrives at is the very course idea about the assembly structure in terms of trace of the Cα atoms which are modeled with modest accuracy.Methodology/Principal FindingsIn this paper first we present an objective approach to identify potentially solvent exposed and buried residues solely from the position of Cα atoms and amino acid sequence using residue type-dependent thresholds for accessible surface areas of Cα. We extend the method further to recognize potential protein-protein interface residues.Conclusion/ SignificanceOur approach to identify buried and exposed residues solely from the positions of Cα atoms resulted in an accuracy of 84%, sensitivity of 83–89% and specificity of 67–94% while recognition of interfacial residues corresponded to an accuracy of 94%, sensitivity of 70–96% and specificity of 58–94%. Interestingly, detailed analysis of cases of mismatch between recognition of interface residues from Cα positions and all-atom models suggested that, recognition of interfacial residues using Cα atoms only correspond better with intuitive notion of what is an interfacial residue. Our method should be useful in the objective analysis of structures of protein assemblies when positions of only Cα positions are available as, for example, in the cases of integration of cryo-EM data and high resolution structures of the components of the assembly.

A Fully Atomistic Model of the Cx32 Connexon

Connexins are plasma membrane proteins that associate in hexameric complexes to form channels named connexons. Two connexons in neighboring cells may dock to form a “gap junction” channel, i.e. an intercellular conduit that permits the direct exchange of solutes between the cytoplasm of adjacent cells and thus mediate cell–cell ion and metabolic signaling. The lack of high resolution data for connexon structures has hampered so far the study of the structure–function relationships that link molecular effects of disease–causing mutations with their observed phenotypes. Here we present a combination of modeling techniques and molecular dynamics (MD) to infer side chain positions starting from low resolution structures containing only Cα atoms. We validated this procedure on the structure of the KcsA potassium channel, which is solved at atomic resolution. We then produced a fully atomistic model of a homotypic Cx32 connexon starting from a published model of the Cα carbons arrangement for the connexin transmembrane helices, to which we added extracellular and cytoplasmic loops. To achieve structural relaxation within a realistic environment, we used MD simulations inserted in an explicit solvent–membrane context and we subsequently checked predictions of putative side chain positions and interactions in the Cx32 connexon against a vast body of experimental reports. Our results provide new mechanistic insights into the effects of numerous spontaneous mutations and their implication in connexin-related pathologies. This model constitutes a step forward towards a structurally detailed description of the gap junction architecture and provides a structural platform to plan new biochemical and biophysical experiments aimed at elucidating the structure of connexin channels and hemichannels.

Comparative architecture of octahedral protein cages. II. Interplay between structural elements

In paper I [Janner (2008). Acta Cryst. A64, 494-502], the enclosing forms of the monomers of four octahedral holoenzymes (bacterio and mitochondrial ferritins, small heat-shock protein and sulfur oxygenase reductase) were derived, with vertices at points of a cubic lattice and indexed accordingly. The correspondence between vertices and neighboring residues allows a sequential ordering of the vertices within the polyline defined by the C(alpha) atoms of the primary structure. The alignment of these sequences shows that the form vertices denoted as turning points delimit the elements of the secondary structure (alpha-helices, beta-strands and loops). This relation is analyzed further in a plot of angular changes in orientations of the polyline segments and planes as a function of the residue numbers and of the form vertices, respectively, leading to an alternative characterization of the ternary structure. Finally, two simple connectivity models of monomers, oriented according to the symmetry axes of the octahedral point group 432, suggest possible patterns in the self-assembly process from clusters of monomers to the quaternary structure of the cubic cage.

A knowledge-driven approach for crystallographic protein model completion

One of the most cumbersome and time-demanding tasks in completing a protein model is building short missing regions or ;loops'. A method is presented that uses structural and electron-density information to build the most likely conformations of such loops. Using the distribution of angles and dihedral angles in pentapeptides as the driving parameters, a set of possible conformations for the C(alpha) backbone of loops was generated. The most likely candidate is then selected in a hierarchical manner: new and stronger restraints are added while the loop is built. The weight of the electron-density correlation relative to geometrical considerations is gradually increased until the most likely loop is selected on map correlation alone. To conclude, the loop is refined against the electron density in real space. This is started by using structural information to trace a set of models for the C(alpha) backbone of the loop. Only in later steps of the algorithm is the electron-density correlation used as a criterion to select the loop(s). Thus, this method is more robust in low-density regions than an approach using density as a primary criterion. The algorithm is implemented in a loop-building program, Loopy, which can be used either alone or as part of an automatic building cycle. Loopy can build loops of up to 14 residues in length within a couple of minutes. The average root-mean-square deviation of the C(alpha) atoms in the loops built during validation was less than 0.4 A. When implemented in the context of automated model building in ARP/wARP, Loopy can increase the completeness of the built models.

Molecular Dynamics Simulations for Water and Ions in Protein Crystals

The spatial and temporal properties of water and ions in bionanoporous materials-protein crystals-have been investigated using molecular dynamics simulations. Three protein crystals are considered systematically with different morphologies and chemical topologies: tetragonal lysozyme, orthorhombic lysozyme, and tetragonal thermolysin. It is found that the thermal fluctuations of C(alpha) atoms in the secondary structures of protein molecules are relatively weak due to hydrogen bonding. The solvent-accessible surface area per residue is nearly identical in the three protein crystals; the hydrophobic and hydrophilic residues in each crystal possess approximately the same solvent-accessible surface area. Water distributes heterogeneously and has different local structures within the biological nanopores of the three protein crystals. The mobility of water and ions in the crystals is enhanced as the porosity increases and also by the fluctuations of protein atoms particularly in the two lysozyme crystals. Anisotropic diffusion is found preferentially along the pore axis, as experimentally observed. The anisotropy of the three crystals increases in the order: tetragonal thermolysin < tetragonal lysozyme < orthorhombic lysozyme.

Collective motions of rigid fragments in protein structures from smoothed electron density distributions

In this work, the Gaussian Network Model (GNM) and Anisotropic Network Model (ANM) approaches are applied to describe the dynamics of protein structure graphs built from calculated promolecular electron density (ED) distribution functions. A first set of analyses is carried out on results obtained from ED maxima calculated at various smoothing levels. A second set is achieved for ED networks whose edges are weighted by ED overlap integral values. Results are compared with those obtained through the classical GNM and ANM approaches applied to networks of C(alpha) atoms. It is shown how the network model and the consideration of crystal packing as well as of the side chains may lead to various improvements dependent upon the structure under study. The selected protein structures are Crambin and Pancreatic Trypsin Inhibitor because of their small size and numerous dynamical data obtained by other authors.

Pi-Turns: types, systematics and the context of their occurrence in protein structures

BackgroundFor a proper understanding of protein structure and folding it is important to know if a polypeptide segment adopts a conformation inherent in the sequence or it depends on the context of its flanking secondary structures. Turns of various lengths have been studied and characterized starting from three-residue γ-turn to six-residue π-turn. The Schellman motif occurring at the C-terminal end of α-helices is a classical example of hydrogen bonded π-turn involving residues at (i) and (i+5) positions. Hydrogen bonded and non-hydrogen bonded β- and α-turns have been identified previously; likewise, a systematic characterization of π-turns would provide valuable insight into turn structures.ResultsAn analysis of protein structures indicates that at least 20% of π-turns occur independent of the Schellman motif. The two categories of π-turns, designated as π-HB and SCH, have been further classified on the basis of backbone conformation and both have AAAa as the major class. They differ in the residue usage at position (i+1), the former having a large preference for Pro that is absent in the latter. As in the case of shorter length β- and α-turns, π-turns have also been identified not only on the basis of the existence of hydrogen bond, but also using the distance between terminal Cα-atoms, and this resulted in a comparable number of non-hydrogen-bonded π-turns (π-NHB). The presence of shorter β- and α-turns within all categories of π-turns, the subtle variations in backbone torsion angles along the turn residues, the location of the turns in the context of tertiary structures have been studied.Conclusionπ-turns have been characterized, first using hydrogen bond and the distance between Cα atoms of the terminal residues, and then using backbone torsion angles. While the Schellman motif has a structural role in helix termination, many of the π-HB turns, being located on surface cavities, have functional role and there is also sequence conservation.

The geometry of α‐sheet: Implications for its possible function as amyloid precursor in proteins

alpha-sheet has been proposed as the main constituent of the prefibrillar intermediate during amyloid formation. Here the helical parameters of the alpha-sheet strand are calculated from average main-chain dihedral angles reported from molecular dynamics simulations. It is an almost linear polypeptide that forms a right-handed helix of about 100 A diameter, with 100 residues and a rise of 30 A per turn. The strands are curved but untwisted, which implies that neighboring strands need not coil to make interstrand hydrogen bonds. This suggests that compared to beta-sheets in native folded proteins, alpha-sheets can be larger and stack more easily to create extensive 3D blocks. It is shown that alpha-sheet is related to a category of structures termed "mirror" structures. Mirror structures have repetitive pairs of main-chain dihedral angles at residues i and i+1 that satisfy the condition phi(i) (+1) = -psi(i), psi(i) (+1) = -phi(i). They are uniquely identified by the two orientations of their peptide planes, specified by phi(i) and psi(i). Their side chains point alternately in opposite directions. Interestingly, their conformations are insensitive to phi(i) and psi(i) in that the pseudo dihedral angle formed by four consecutive C(alpha) atoms is always close to 180 degrees . There are two types: "beta-mirror" and "alpha-mirror" structure; beta-mirror structures relate to beta-sheet by small peptide plane rotations, of less than 90 degrees , while alpha-mirror structures are close to alpha-sheet and relate to beta-sheet by approximately 180 degrees peptide plane flips. Most mirror structures, and in particular the alpha-mirror, form wide helices with diameters 50-70 A. Their gentle curvature, and therefore that of the alpha-sheet, arises from the orientation of successive peptide units causing the difference in the bond angles at the C and N atoms of the peptide unit to gradually change the direction of the chain.

Convergent algorithms for protein structural alignment.

BackgroundMany algorithms exist for protein structural alignment, based on internal protein coordinates or on explicit superposition of the structures. These methods are usually successful for detecting structural similarities. However, current practical methods are seldom supported by convergence theories. In particular, although the goal of each algorithm is to maximize some scoring function, there is no practical method that theoretically guarantees score maximization. A practical algorithm with solid convergence properties would be useful for the refinement of protein folding maps, and for the development of new scores designed to be correlated with functional similarity.ResultsIn this work, the maximization of scoring functions in protein alignment is interpreted as a Low Order Value Optimization (LOVO) problem. The new interpretation provides a framework for the development of algorithms based on well established methods of continuous optimization. The resulting algorithms are convergent and increase the scoring functions at every iteration. The solutions obtained are critical points of the scoring functions. Two algorithms are introduced: One is based on the maximization of the scoring function with Dynamic Programming followed by the continuous maximization of the same score, with respect to the protein position, using a smooth Newtonian method. The second algorithm replaces the Dynamic Programming step by a fast procedure for computing the correspondence between Cα atoms. The algorithms are shown to be very effective for the maximization of the STRUCTAL score.ConclusionThe interpretation of protein alignment as a LOVO problem provides a new theoretical framework for the development of convergent protein alignment algorithms. These algorithms are shown to be very reliable for the maximization of the STRUCTAL score, and other distance-dependent scores may be optimized with same strategy. The improved score optimization provided by these algorithms provide means for the refinement of protein fold maps and also for the development of scores designed to match biological function. The LOVO strategy may be also used for more general structural superposition problems such as flexible or non-sequential alignments. The package is available on-line at http://www.ime.unicamp.br/~martinez/lovoalign.