Interactions between an alpha-helix and a beta-sheet. Energetics of alpha/beta packing in proteins

Conformational energy computations have been carried out to determine the favorable ways of packing a right-handed alpha-helix on a right-twisted antiparallel or parallel beta-sheet. Co-ordinate transformations have been developed to relate the position and orientation of the alpha-helix to the beta-sheet. The packing was investigated for a CH3CO-(L-Ala)16-NHCH3 alpha-helix interacting with five-stranded beta-sheets composed of CH3CO-(L-Val)6-NHCH3 chains. All internal and external variables for both the alpha-helix and the beta-sheet were allowed to change during energy minimization. Four distinct classes of low-energy packing arrangements were found for the alpha-helix interacting with both the parallel and the anti-parallel beta-sheet. The classes differ in the orientation of the axis of the alpha-helix relative to the direction of the strands of the right-twisted beta-sheet. In the class with the most favorable arrangement, the alpha-helix is oriented along the strands of the beta-sheet, as a result of attractive non-bonded side-chain-side-chain interactions along the entire length of the alpha-helix. A class with nearly perpendicular orientation of the helix axis to the strands is also of low energy, because it allows similarly extensive attractive interactions. In the other two classes, the helix is oriented diagonally relative to the strands of the beta-sheet. In one of them, it interacts with the convex surface near the middle of the saddle-shaped twisted beta-sheet. In the other, it is oriented along the concave diagonal of the beta-sheet and, therefore, it interacts only with the corner regions of the sheet, so that this packing is energetically less favorable. The packing arrangements involving an antiparallel and a parallel beta-sheet are generally similar, although the antiparallel beta-sheet has been found to be more flexible. The major features of 163 observed alpha/beta packing arrangements in 37 proteins are accounted for in terms of the computed structural preferences. The energetically most favored packing arrangement is similar to the right-handed beta alpha beta crossover structure that is observed in proteins; thus, the preference for this connectivity arises in large measure from this energetically favorable interaction.     

Energy of stabilization of the right-handed beta alpha beta crossover in proteins

An explanation in terms of conformational energies is provided for the observed nearly exclusive preference of the beta alpha beta structure for forming a right-handed, rather than a left-handed, crossover connection. Conformational energy computations have been carried out on a model beta alpha beta structure, consisting of two six-residue Val beta-strands and of a 12-residue Ala alpha-helix, connected by two flexible four-residue Ala links to the strands. The energy of the most favorable right-handed crossover is 15.51 kcal/mol lower than that of the corresponding left-handed cross-over. The right-handed crossover is a strain-free structure. Its energy of stabilization arises largely from the interactions of the two beta-strands with one another and with the alpha-helix. On the other hand, the left-handed crossover is either disrupted after energy minimization or it remains conformationally strained, as indicated by an energetically unfavorable left twisting of the beta-sheet and by the presence of high-energy local residue conformations. In the energetically most favorable right-handed crossover, the right twisting of the beta-sheet and its manner of interacting with the alpha-helix are identical with those computed earlier for isolated beta-sheets and for packed alpha/beta structures. This result supports a proposed principle that it is possible to account for the main features of frequently occurring structural arrangements in globular proteins in terms of the properties of their component structural elements.     

Structural principles of alpha/beta barrel proteins: the packing of the interior of the sheet

Alpha/beta barrel structures very similar to that first observed in triose phosphate isomerase are now known to occur in 14 enzymes. To understand the origin of this fold, we analyzed in three of these proteins the geometry of the eight-stranded beta-sheets and the packing of the residues at the center of the barrel. The packing in this region is seen in its simplest form in glycolate oxidase. It consists of 12 residues arranged in three layers. Each layer contains four side chains. The packing of RubisCO and TIM can be understood in terms of distortions of this simple pattern, caused by residues with small side chains at some of the positions inside the barrel. Two classes of packing are found. In one class, to which RubisCO and TIM belong, the central layer is formed by a residue from the first, third, fifth, and seventh strands; the upper and lower layers are formed by residues from the second, fourth, sixth, and eighth strands. In the second class, to which GAO belongs, this is reversed: it is side chains from the even-numbered strands that form the central layer, and side chains from the odd-numbered strands that form the outer layers. Our results suggest that not all proteins with this fold are related by evolution, but that they represent a common favorable solution to the structural problems involved in the creation of a closed beta barrel.     

Domain association in immunoglobulin molecules. The packing of variable domains

We have analyzed the structure of the interface between VL and VH domains in three immunoglobulin fragments: Fab KOL, Fab NEW and Fab MCPC 603. About 1800 A2 of protein surface is buried between the domains. Approximately three quarters of this interface is formed by the packing of the VL and VH beta-sheets in the conserved "framework" and one quarter from contacts between the hypervariable regions. The beta-sheets that form the interface have edge strands that are strongly twisted (coiled) by beta-bulges. As a result, the edge strands fold back over their own beta-sheet at two diagonally opposite corners. When the VL and VH domains pack together, residues from these edge strands form the central part of the interface and give what we call a three-layer packing; i.e. there is a third layer composed of side-chains inserted between the two backbone side-chain layers that are usually in contact. This three-layer packing is different from previously described beta-sheet packings. The 12 residues that form the central part of the three observed VL-VH packings are absolutely or very strongly conserved in all immunoglobulin sequences. This strongly suggests that the structure described here is a general model for the association of VL and VH domains and that the three-layer packing plays a central role in forming the antibody combining site.     

Sequence-specific 1H NMR assignments and secondary structure of the streptococcal protein G B2-domain.

Two-dimensional NMR spectroscopy has been used to obtain sequence-specific 1H NMR assignments for the IgG-binding B2-domain of streptococcal protein G. Secondary structure elements were identified from analysis of characteristic backbone-backbone NOE patterns and amide proton exchange data. The B2-domain contains a four-stranded beta-sheet region in which the two inner strands form a parallel beta-sheet with each other and antiparallel beta-sheets with the outer strands. The outer strands are connected via a 16-residue alpha-helix and short loops on both ends of the helix. The alpha-helix and beta-sheet structures contain well-defined polar and apolar sides, and numerous long-range NOEs from the apolar helix to apolar sheet regions were used to derive a model for the global fold of the B2-domain. While the overall fold is similar to that obtained for B1-type domains, differences in amide proton exchange rates and hydrophobic packing are observed.     

The orientation of beta-sheets in porin. A polarized Fourier transform infrared spectroscopic investigation.

The orientation of the protein secondary structures in porin is investigated by Fourier transform infrared (FTIR) linear dichroism of oriented multilayers of porin reconstituted in lipid vesicles. The FTIR absorbance spectrum shows the amide I band at 1,631 cm-1 and several shoulders around 1,675 cm-1 and at 1,696 cm-1 indicative of antiparallel beta-sheets. The amide II is centered around 1,530 cm-1. The main dichroic signals peak at 1,738, 1,698, 1,660, 1,634, and 1,531 cm-1. The small magnitude of the 1,634 cm-1 and 1,531 cm-1 positive dichroism bands demonstrates that the transition moments of the amide I and amide II vibrations are on the average tilted at 47 degrees +/- 3 degrees from the membrane normal. This indicates that the plane of the beta-sheets is approximately perpendicular to the bilayer. From these IR dichroism results and previously reported diffuse x-ray data which revealed that a substantial number of beta-strands are nearly perpendicular to the membrane, a model for the packing of beta-strands in porin is proposed which satisfies both IR and x-ray requirements. In this model, the porin monomer consists of at least two beta-sheet domains, both with their plane perpendicular to the membrane. One sheet has its strands direction lying nearly parallel to the membrane normal while the other sheet has its strands inclined at a small angle away from the membrane plane.     

Role of proline …︁ proline interactions in the packing of collagenlike poly(tripeptide) triple helices

Conformational energy computations were carried out on the packing of two identical collagenlike poly(tripeptide) triple helices in order to determine the energetics of favorable packing arrangements as a function of composition and chain length. The triple helices considered were [CH₃CO-(Gly-Pro-Pro)_nt-NHCH₃]₃ and [CH₃CO-(Gly-Pro-Ala)_nt-NHCH₃]₃, with n_t = 3, 4, and 5. The packing arrangements were characterized in terms of their intermolecular energies and orientation angles Ω₀ of the axes of the two triple helices. For short triple helices (n_t = 3 or 4), many low-energy orientations, with a wide range of values of Ω₀, can occur. When the triple helices are longer (n_t = 5), the only low-energy packing arrangements of two poly(Gly-Pro-Pro) triple helices are those with a nearly parallel orientation of the two helix axes, with Ω₀ ≈ ?10°. This result accounts for the observed parallel (rather than antiparallel) arrangement of collagen molecules in microfibril assembly and stands in contrast to the preferred antiparallel arrangement of a pair of α-helices. Since the preference for a parallel arrangement of these collagenlike triple helices is less pronounced in the case of poly(Gly-Pro-Ala), it appears that this preference is a consequence of the frequent presence of imino acids in position Y of the Gly-X-Y repeating triplet. In poly(Gly-Pro-Ala), most of the low-energy packing arrangements are parallel, but a few arrangements with low energies and high values of |Ω₀| occur. These packing arrangements have a high energy, however, when Pro is substituted for Ala, and thus they are not accessible for collagen with natural amino (imino) acid sequences. The computations reported here account for some of the characteristic features of collagen packing in terms of the local interaction energies of a pair of triple helices.     

beta-Trefoil fold. Patterns of structure and sequence in the Kunitz inhibitors interleukins-1 beta and 1 alpha and fibroblast growth factors.

Previous crystallographic analyses of the Kunitz inhibitors from soybean. Erythrina caffra and wheat, the interleukins-1 beta and 1 alpha and the acidic and basic fibroblast growth factors have shown that they contain a most unusual fold. It is formed by six two-stranded hairpins. Three of these form a barrel structure and the other three are in a triangular array that caps the barrel. The arrangement of the secondary structures gives the molecules a pseudo 3-fold axis. Although the different proteins have very similar structures, many of their sequences have no significant similarities overall. The structural determinants of this fold are described and discussed in this paper. The barrels in the different proteins have the same geometrical features: six strands tilted at 56 degrees to the barrel axis; a barrel diameter of 16 A, and the beta-sheet hydrogen bonded so that it is staggered with a shear number of 12. These features fit McLachlan's equations for ideal barrels formed by beta-sheets. The wide diameter of the barrels is filled by layers of residues that, while not identical in the different proteins, are, in almost all cases, large. The structure of the triangular array of hairpins is determined by the coiling of the strands and the packing of hairpin residues against each other and against residues from the interior of the barrel. The major sequence requirements of this fold are large or medium hydrophobic residues at 18 buried sites. In the different structures the total volume of these residues is 3000 (+/- 120) A. The polyhedron model of protein architecture is used to demonstrate that the main, and in particular the symmetrical, features of this fold arise from the ideal and equal packing of six hairpins, modified only slightly to form hydrogen bonds between the hairpins.     

Minimal surface as a model of beta-sheets

The purpose of this article is to present arguments based on experimental data that the beta-sheet structures in proteins are the result of the tendency to minimize surface areas. Thus, we propose the model that all beta-sheet structures are almost minimal surfaces, namely, their mean curvatures are nearly zero. To support this model, we chose 1740 disjoint beta-sheets with less than 10 strands from the all beta-protein class in a nonredundant 40% Structural Classification of Proteins (SCOP) database and applied the least-squares method to fit the minimal surface catenoid (and in some rare cases, the plane) to the beta-sheet structures. The fitting errors were extremely small: The error of 1729 beta-sheets with catenoid minimal surface is 0.90 +/- 0.55 A and the error of the remaining 11 flat sheets with the plane is 0.64 +/- 0.46 A. The fact that the commonly used models for some beta-sheet surfaces (i.e., the hyperboloid and strophoid) have very small mean curvatures (< 0.05) supports our model. Moreover, we showed that this model also includes the isotropically stressed configuration model proposed by Salemme, in which the intrastrand tendency of the individual chains to twist or coil is in equilibrium with the tendency of the interstrand hydrogen bonding to resist twisting of the sheet as a whole. As an application we used our model to quantify the two principal independent modes in the flexibility of beta-sheets, that is, the bending parameter of beta-sheets and the inclined angle of beta-strands in a sheet.     

Extended form of a retro-inverso peptide stabilized by beta-sheet unidirectional H-bonds: Crystallographic and NMR evidence.

The crystallographic investigation of the retro-inverso peptide Bz-S-gAla-R-mAla-NHPh reveals an extended backbone conformation where the NH groups of the gem-diamino alkyl moiety and the CO groups of the malonyl residue face side by side. This extended conformation, presenting all carbonyls on opposite sides of the NH groups, is stabilized by interstrand H-bonds running in a single direction of the parallel beta-sheets that characterize the crystal packing. These sheets differ from the beta-sheets formed by native amino acids only. (1)H-NMR nuclear Overhauser effect spectroscopy (NOESY) experiments suggest that a conformation similar to that found in the crystal also prevails in dimethylsulfoxide solution. Previous potential energy calculations of gem-diamino alkyl (g) and malonyl (m) Ala residues predicted that extended forms were less stable than the helical ones because of strong electrostatic repulsions between the parallel polar groups. Similar arguments were invoked to give more weight to helical forms of the retro-peptide units in the proposal of packing models of some nylons in their crystalline polar regions. The present findings show that both g and m Ala residues can experience the extended conformation in the beta-sheet aggregation. The energy increase occurring in one strand, due to the parallel orientation of consecutive peptide dipoles, is more than compensated by favorable cooperative interactions among head-to-tail aligned peptide dipoles of facing strands, resulting in the formation of two C==O...H==N H-bonds per residue.     

Folding pattern of the alpha-crystallin domain in alphaA-crystallin determined by site-directed spin labeling

The folding pattern of the alpha-crystallin domain, a conserved protein module encoding the molecular determinants of structure and function in the small heat-shock protein superfamily, was determined in the context of the lens protein alphaA-crystallin by systematic application of site-directed spin labeling. The sequence-specific secondary structure was assigned primarily from nitroxide scanning experiments in which the solvent accessibility and mobility of a nitroxide probe were measured as a function of residue number. Seven beta-strands were identified and their orientation relative to the aqueous solvent determined, thus defining the residues lining the hydrophobic core. The pairwise packing of adjacent strands in the primary structure was deduced from patterns of proximities in nitroxide pairs with one member on the exposed surface of each strand. In addition to identifying supersecondary structures, these proximities revealed that the seven strands are arranged in two beta-sheets. The overall packing of the two sheets was determined by application of the general rules of protein structure and from proximities in nitroxide pairs designed to distinguish between known all beta-sheet folds. Our data are consistent with an immunoglobulin-like fold consisting of two aligned beta-sheets. Comparison of this folding pattern to that of the evolutionary distant alpha-crystallin domain in Methanococcus jannaschii heat-shock protein 16.5 reveals a conserved core structure with the differences sequestered at one edge of the beta-sandwich. A beta-strand deletion in alphaA-crystallin disrupts a subunit interface and allows for a different dimerization motif. Putative substrate binding regions appear to include a buried loop and a buried turn, suggesting that the chaperone function involves a disassembly of the oligomer.     

Standard conformations of beta-arches in beta-solenoid proteins

Strand-turn-strand motifs found in beta-helical (more generally, beta-solenoid) proteins differ fundamentally from those found in globular proteins. The latter are primarily beta-hairpins in which the two strands form an antiparallel beta-sheet. In the former, the two strands are relatively rotated by approximately 90 degrees around the strand axes so that they interact via the side-chains, not via the polypeptide backbones. We call the latter structures, beta-arches, and their turns, beta-arcs. In beta-solenoid proteins, beta-arches stack in-register to form beta-arcades in which parallel beta-sheets are assembled from corresponding strands in successive layers. The number of beta-solenoids whose three-dimensional structures have been determined is now large enough to support a detailed analysis and classification of beta-arc conformations. Here, we present a systematic account of beta-arcs distinguished by the number of residues, their conformations, and their propensity to stack into arcades with other like or unlike arches. The trends to emerge from this analysis have implications for sequence-based detection and structural prediction of other beta-solenoid proteins as well as for identification of amyloidogenic sequences and elucidation of amyloid fibril structures.     

1H NMR-based determination of the secondary structure of porcine pancreatic spasmolytic polypeptide: one of a new family of "trefoil" motif containing cell growth factors.

Two-dimensional 1H NMR spectroscopy has been used to obtain comprehensive sequence-specific resonance assignments for the putative cell growth factor porcine pancreatic spasmolytic polypeptide, which is a 106-residue protein containing two "trefoil" domains. The patterns of sequential (i,i+l), medium-range (i,i less than 5), and long-range NH to NH, alpha CH to NH, and alpha CH to alpha CH nuclear Overhauser effects clearly show that the protein's two trefoil domains adopt essentially the same secondary structure in solution. The main feature of each domain is a seven-residue helix followed by a short antiparallel beta-sheet formed from two strands of four amino acids each. This is a novel supersecondary structure, which clearly identifies the trefoil motif as a new class of growth factor associated module, distinct from other types of highly disulfide cross-linked domains, such as those found in epidermal growth factor and insulin-like growth factor I.     

On the significance of alternating patterns of polar and non-polar residues in beta-strands

A common assumption about protein sequences in beta-strands is that they have alternating patterns of polar and non-polar residues. It is thought that such patterns reflect the interior/exterior geometry of amino acid residue side-chains on a beta-sheet. Here we study the prevalence of simple hydrophobicity patterns in parallel and antiparallel beta-sheets in proteins of known structure and in the sequences of amyloidogenic proteins. The occurrence of 32 possible pentapeptide binary patterns (polar (P)/non-polar (N)) is computed in 1911 non-homologous protein structures. Despite their tendency to aggregate in experimentally designed proteins, the purely alternating hydrophobic/polar patterns (PNPNP and NPNPN) are most frequent in beta-sheets, typically occurring in antiparallel strands. The overall distribution of the pentapeptide binary patterns is significantly different in strands within parallel and antiparallel sheets. In both types of sheets, complementary patterns (where the hydrophobic and polar residues pair with one another) associate preferentially. We do not find alternating patterns to be common in amyloidogenic proteins or in short fragments involved directly in amyloid formation. However, we do note some similarities between patterns present in amyloidogenic sequences and those in parallel strands.     

1H nuclear-magnetic-resonance studies of the three-dimensional structure of the cardiotoxin CTXIIb from Naja mossambica mossambica in aqueous solution and comparison with the crystal structures of homologous toxins

Using the previously reported sequence-specific 1H-NMR assignments, structural constraints for the cardiotoxin CTXIIb from Naja mossambica mossambica were collected. These include distance constraints from nuclear Overhauser enhancement measurements both in the laboratory and in the rotating frame, dihedral angle constraints derived from spin-spin coupling constants, and constraints from hydrogen bonds and disulfide bridges. Structure calculations with the distance geometry program DISMAN confirmed the presence of the previously identified antiparallel beta-sheets formed by residues 1-5 and 10-14, and by 20-27, 35-39 and 49-55, and established the nature of the connections between the individual beta-strands. These include a right-handed crossover between the two peripheral strands in the triple-stranded beta-sheet, and a type I tight turn immediately preceding the beta-strand 49-55. The spatial arrangement of the polypeptide backbone in the solution structure of CTXIIb is closely similar to that in the crystal structure of the homologous cardiotoxin VII4 from the same species. In an Appendix the origin of the large pH dependence of two amide proton chemical shifts in CTXIIb is explained.     

Alanine-scanning mutagenesis of the beta-sheet region of phage T4 lysozyme suggests that tertiary context has a dominant effect on beta-sheet formation

In general, alpha-helical conformations in proteins depend in large part on the amino acid residues within the helix and their proximal interactions. For example, an alanine residue has a high propensity to adopt an alpha-helical conformation, whereas that of a glycine residue is low. The sequence preferences for beta-sheet formation are less obvious. To identify the factors that influence beta-sheet conformation, a series of scanning polyalanine mutations were made within the strands and associated turns of the beta-sheet region in T4 lysozyme. For each construct the stability of the folded protein was reduced substantially, consistent with removal of native packing interactions. However, the crystal structures showed that each of the mutants retained the beta-sheet conformation. These results suggest that the structure of the beta-sheet region of T4 lysozyme is maintained to a substantial extent by tertiary interactions with the surrounding parts of the protein. Such tertiary interactions may be important in determining the structures of beta-sheets in general.     

Intestinal fatty acid binding protein: the folding mechanism as determined by NMR studies

The intestinal fatty acid binding protein is composed of two beta-sheets surrounding a large interior cavity. There is a small helical domain associated with the portal for entry of the ligand into the cavity. Denaturation of the protein has been monitored in a residue-specific manner by collecting a series of two-dimensional (1)H-(15)N heteronuclear single-quantum coherence (HSQC) NMR spectra from 0 to 6.5 M urea under equilibrium conditions. In addition, rates for hydrogen-deuterium exchange have been measured as a function of denaturant concentration. Residual, native-like structure persists around hydrophobic clusters at very high urea concentrations. This residual structure (reflecting only about 2-7% persistence of native-like structure) involves the turns between beta-strands and between the two short helices. If this persistence is assumed to reflect transient native-like structure in these regions of the polypeptide chain, these sites may serve as nucleation sites for folding. The data obtained at different urea concentrations are then analyzed on the basis of peak intensities relative to the intensities in the absence of urea reflecting the extent of secondary structure formation. At urea concentrations somewhat below 6.5 M, specific hydrophobic residues in the C-terminal beta-sheet interact and two strands, the D and E strands in the N-terminal beta-sheet, are stabilized. These latter strands surround one of the turns showing residual structure. With decreasing urea concentrations, the remaining strands are stabilized in a specific order. The early strand stabilization appears to trigger the formation of the remainder of the C-terminal beta-sheet. At low urea concentrations, hydrogen bonds are formed. A pathway is proposed on the basis of the data describing the early, intermediate, and late folding steps for this almost all beta-sheet protein. The data also show that there are regions of the protein which appear to act in a concerted manner at intermediate steps in refolding.     

Conformational energy studies of beta-sheets of model silk fibroin peptides. I. Sheets of poly(Ala-Gly) chains

A new model structure is proposed for the silk I form of the crystalline domains of Bombyx mori silk fibroin and the corresponding crystal form of poly(L-Ala-Gly). It was deduced from conformational energy computations on stacked sheet structures of poly(L-Ala-Gly). The novel sheet structure contains interstrand hydrogen bonds but is composed of anti-parallel polypeptide chains whose conformation differs from that of the antiparallel beta-sheets that constitute the silk II structure. The strands of the new sheet have a two-residue repeat, in which the Ala residues adopt a right-handed and the Gly residues a left-handed sheet-like conformation. The computed unit cell is orthorhombic, with cell dimensions a = 8.94 A, b = 6.46 A, and c = 11.26 A. The model accounts for most spacings in the observed fiber x-ray diffraction patterns of silk I and of the silk-I-like form of poly(L-Ala-Gly), and it is consistent with nmr and ir spectroscopic data. As a test of the computations, the well-established beta-sheet structure of silk II and the corresponding form of poly(L-Ala-Gly) have been reproduced. The computed energies for the two forms of poly(L-Ala-Gly) indicate that the silk-II-like form is more stable, by about 1.0 kcal/mol per residue. The main difference between the two structures is the orientation of the Ala side chains of neighboring strands in each sheet. In the Pauling-Corey beta-sheet and in the silk II form, referred to as an "in-register" structure, the Ala side chains of every strand point to the same side of a sheet. In the silk I structure, referred to as "out-of-register," the side chains of Ala residues in adjacent strands point to opposite sides of the sheet.     

Tachylectin-2: crystal structure of a specific GlcNAc/GalNAc-binding lectin involved in the innate immunity host defense of the Japanese horseshoe crab Tachypleus tridentatus

Tachylectin-2, isolated from large granules of the hemocytes of the Japanese horseshoe crab (Tachypleus tridentatus), is a 236 amino acid protein belonging to the lectins. It binds specifically to N-acetylglucosamine and N-acetylgalactosamine and is a part of the innate immunity host defense system of the horseshoe crab. The X-ray structure of tachylectin-2 was solved at 2.0 A resolution by the multiple isomorphous replacement method and this molecular model was employed to solve the X-ray structure of the complex with N-acetylglucosamine. Tachylectin-2 is the first protein displaying a five-bladed beta-propeller structure. Five four-stranded antiparallel beta-sheets of W-like topology are arranged around a central water-filled tunnel, with the water molecules arranged as a pentagonal dodecahedron. Tachylectin-2 exhibits five virtually identical binding sites, one in each beta-sheet. The binding sites are located between adjacent beta-sheets and are made by a large loop between the outermost strands of the beta-sheets and the connecting segment from the previous beta-sheet. The high number of five binding sites within the single polypeptide chain strongly suggests the recognition of carbohydrate surface structures of pathogens with a fairly high ligand density. Thus, tachylectin-2 employs strict specificity for certain N-acetyl sugars as well as the surface ligand density for self/non-self recognition.