International
Tables for
Crystallography
Volume F
Crystallography of biological macromolecules
Edited by M. G. Rossmann and E. Arnold

International Tables for Crystallography (2006). Vol. F, ch. 23.1, pp. 575-578   | 1 | 2 |
https://doi.org/10.1107/97809553602060000714

Chapter 23.1. Protein folds and motifs: representation, comparison and classification

C. Orengo,a J. Thornton,d L. Holmb and C. Sanderc

aBiomolecular Structure and Modelling Unit, Department of Biochemistry and Molecular Biology, University College, Gower Street, London WC1E 6BT, England,bEMBL–EBI, Cambridge CB10 1SD, England,cMIT Center for Genome Research, One Kendall Square, Cambridge, MA 02139, USA, and dBiochemistry and Molecular Biology Department, University College London, Gower Street, London WC1E 6BT, England, and Department of Crystallography, Birkbeck College, University of London, Malet Street, London WC1E 7HX, England

The assignment of protein domains from three-dimensional structure is critically important in understanding protein evolution and function. Domains are quasi-independent substructures that are thought to fold autonomously, to carry specific molecular functions, to move relative to each other as semi-rigid bodies and to speed the evolution of new functions by recombination. In the first part of this chapter, the classification of protein folds is discussed. In the second part of the chapter, the concepts underlying computational methods for locating domains in 3D structures are presented. Early algorithms focused on physical criteria to identify compact subunits. With the growth of the structural database, the focus has shifted to methods for identifying recurrent substructures that can form the basis for a consistent protein-structure classification.

23.1.1. Protein-fold classification

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C. Orengoa* and J. Thorntond

Since the first structure of myoglobin was solved in 1971, there has been an exponential growth in known protein structures with about 10 000 chains currently deposited in the Protein Data Bank (PDB; Abola et al., 1987[link]) and 200 or more solved each month. Since it is likely that the millennium will be marked by several international structural genomics projects, we can expect significant expansion of the data bank in the future. When dealing with such large numbers it is necessary to organize the data in a manageable and biologically meaningful way. To this end, several structural classifications have been developed [SCOP (Murzin et al., 1995[link]), CATH (Orengo et al., 1997[link]), DALI (Holm & Sander, 1999[link]), 3Dee (Barton, 1997[link]), HOMSTRAD (Mizuguchi et al., 1998[link]) and ENTREZ (Hogue et al., 1996[link])], differing in their methodology and the degree of structural and functional annotation for the protein families identified.

Most public classification schemes have chosen to group proteins according to similarities in their domain structures, as this is generally considered to be the important evolutionary and folding unit. However, it can be difficult to identify domain boundaries either manually or using automatic algorithms, and although there are many methods available, a recent survey of these showed that even the most reliable algorithms only give the correct answer about 80% of the time (Jones et al., 1998[link]). Methods for recognizing domains are described in Section 23.1.2[link].

Most protocols used for clustering protein domain structures into families first identify similarities in their sequences. There are many well established methods for doing this, most based on dynamic programming algorithms, and since proteins with sequence identities of 30% or more are known to adopt very similar folds (Sander & Schneider, 1991[link]; Flores et al., 1993[link]), it is relatively simple to cluster related proteins into evolutionary families on this basis. Very distant relatives (<20% sequence identity) are not easily identified by sequence alignment, but since structure is much more highly conserved during evolution, these relationships can be detected by comparing the 3D structures directly.

Various powerful algorithms have been developed for recognizing structurally related proteins (for reviews see Holm & Sander, 1994a[link]; Brown et al., 1996[link]). These build on the rigid-body superposition methods of Rossmann & Argos (1975)[link], which compare intermolecular distances after optimal translation and rotation of one protein structure onto the other. Other methods are based on the distance plots developed by Phillips (1970)[link], which enable comparison of intramolecular distances between protein structures. In comparing very distantly related proteins, there are a number of problems which must be overcome. Insertions or deletions can obscure equivalent regions, though generally these appear in the loops between secondary structures. Residue substitutions can cause shifts in the orientations of the secondary structures in order to maintain optimal hydrophobic packing in the core.

A number of strategies have been developed for handling these problems. For example, some methods only consider secondary-structure elements, as these will contain fewer insertions. Artymiuk et al. (1989)[link] represent secondary structures as linear vectors and use fast, efficient comparison algorithms based on graph theory. Others have adapted rigid-body methods to optimally superpose secondary structures, ignoring loops. Some methods chop the proteins being compared into fragments and then use various energy-minimization approaches (e.g. simulated annealing, Monte Carlo optimization) to link equivalent fragments in the two proteins. Such fragments can be identified by rigid-body superposition (Vriend & Sander, 1991[link]) or, in the case of the DALI method (Holm & Sander, 1994a[link]), by comparing contact maps for hexapeptide fragments. Several groups have modified the dynamic programming algorithms designed to cope with insertions or deletions in sequence comparison in order to compare three-dimensional (3D) information (Taylor & Orengo, 1989[link]; Sali & Blundell, 1990[link]; Russell & Barton, 1993[link]). For example, the SSAP method of Taylor & Orengo (1989)[link] uses double dynamic programming to align residue structural environments defined by vectors between Cβ atoms, whilst in STAMP (Russell & Barton, 1993[link]), dynamic programming is used in an iterative procedure, together with rigid-body superposition.

Once equivalent residues have been found, the degree of structural similarity between two proteins can be measured in a number of ways, though the most commonly used is the root-mean-square deviation (RMSD), which is effectively the average `distance' between superposed residues. However, there is still no consensus about which thresholds might imply homologous proteins or fold similarity between analagous proteins or common structural motifs. It is likely that this will become clearer as more structures are determined and the families become more highly populated, providing more information on tolerance to structural changes. These contraints will probably reflect functional requirements and/or kinetic or thermodynamic factors and will be specific to the family.

Several groups (Holm & Sander, 1999[link]; Hogue et al., 1996[link]) attempt to determine the significance of a structural match by considering the distribution of scores for unrelated proteins and calculating a Z score. These approaches are very reliable for proteins possessing unusual structural characteristics but may not be as sensitive for those with highly recurring and common structural motifs. Other groups use empirical approaches (Orengo et al., 1997[link]) to establish reasonable cutoffs for identifying homologues, though these approaches obviously suffer from the currently limited size of the structure data bank.

Because of the individual strategies used to recognize relatives, the protein-structure classifications differ somewhat in their assignments. However, most classifications group proteins having highly similar sequences (≥30%) into families. Subsequently, those families having highly similar structures and some other evidence of common ancestry [e.g. similar functions or some residual sequence identity (Orengo et al., 1999[link])] are merged into homologous superfamilies. Families adopting similar folds, but where there is no other evidence to suggest divergent evolution, are usually put into the same fold group but are described as analogous proteins, since their similarity may simply reflect the physical and/or chemical constraints on protein folding.

SCOP and CATH are currently the largest of the public classifications, each with over 1000 homologous superfamilies. In SCOP (Murzin et al., 1995[link]), these families have been very carefully manually validated using biochemical information and by consideration of special structural features (e.g. rare β-bulges, left-handed helical connections) that may constitute evolutionary fingerprints; in CATH, homologues are validated both manually and automatically (Orengo et al., 1997[link]). Other databases [HOMSTRAD (Mizuguchi et al., 1998[link]); 3Dee (Barton, 1997[link])] contain similar groupings of protein structures, and there are multiple structural alignments for the family, annotated according to residue properties.

Several studies have suggested a limited number of folds available to proteins, with estimates ranging from one thousand to several thousand (Chothia, 1993[link]; Orengo et al., 1994[link]), and this will mean an increasing number of analogous protein pairs being identified as the structural genomics initiatives continue. Recent analyses of the population of different fold families have revealed that some folds are more highly populated, perhaps because they fold more easily or are more stable. In the CATH database, ten favoured folds, described as superfolds, comprised very regular, layered architectures and were shown to contain a higher proportion of favoured motifs (e.g. Greek key, βα motif) than non-superfold structures. Similarly, analysis of SCOP (Brenner et al., 1996[link]) revealed some 40 or so frequently occurring domains (FODS), which included the superfolds. About one-third of all non-homologous structures (<25% sequence identity to each other) adopt one of these folds.

Some groups avoid explicit definition of protein families. The DALI database of Holm & Sander (1999)[link] is a neighbourhood scheme listing all related proteins for a given protein structure. Neighbours are identified using the DALI structure comparison algorithm (Holm & Sander, 1993[link]) and range from the most highly similar, homologous proteins to those sharing only motif similarities. The ENTREZ database (Hogue et al., 1996[link]) provides a similar scheme, generated by the VAST structure comparison method of Gibrat et al. (1997[link]). Both allow the user to assess significance and draw their own inferences regarding evolutionary relationships. More recently, the DALI domain database (DDD) (Holm & Sander, 1998[link]) has provided clusters of related proteins based on calculated Z scores.

Most available databases further classify the fold groups on the basis of class. These agree with the major classes recognized by Levitt & Chothia (1976)[link] (mainly α, mainly β, α/β, α + β), although in the CATH database the α/β and α + β classes have been merged (Fig. 23.1.1.1)[link]. CATH also describes an intermediate architecture level between class and fold group (Orengo et al., 1997[link]). This refers to the arrangement of secondary-structure elements in 3D, regardless of their connectivity and so defines the shape (e.g. barrel, sandwich, propeller) (Fig. 23.1.1.2[link]). There are currently 32 different architectures in CATH, with the simple barrel and sandwich shapes accounting for about 60% of the non-homologous structures.

[Figure 23.1.1.1]

Figure 23.1.1.1 | top | pdf |

Schematic representation of the (C)lass, (A)rchitecture and (T)opology/fold levels in the CATH database.

[Figure 23.1.1.2]

Figure 23.1.1.2 | top | pdf |

`CATHerine wheel' plot showing the distribution of non-homologous structures [i.e. a single representative from each homologous superfamily (H level) in CATH] amongst the different classes (C), architectures (A) and fold families (T) in the CATH database. Protein classes are shown coloured as red (mainly α), green (mainly β), and yellow (α–β). Within each class, the angle subtended for a given segment reflects the proportion of structures within the identified architectures (inner circle) or fold families (outer circle). MOLSCRIPT (Kraulis, 1991[link]) illustrations are shown for representative examples from the superfold families.

23.1.2. Locating domains in 3D structures

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L. Holmb* and C. Sanderc

23.1.2.1. Introduction

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Modular design is beneficial in many areas of life, including computer programming, manufacturing, and even in protein folding.

Protein-structure analysis has long operated with the notion of domains, i.e., dividing large structures into quasi-independent substructures or modules (Wetlaufer, 1973[link]; Bork, 1992[link]). In various contexts, these substructures are thought to fold autonomously, to carry specific molecular functions such as binding or catalysis, to move relative to each other as semi-rigid bodies and to speed the evolution of new functions by recombination (Fig. 23.1.2.1)[link].

[Figure 23.1.2.1]

Figure 23.1.2.1 | top | pdf |

The structure of diphtheria toxin (Bennett & Eisenberg, 1994[link]) beautifully illustrates domains as structural, functional and evolutionary units. Structurally, note the compact globular shape of each domain and the flexible linkers between them. Functionally, note how each domain carries out a different stage of infection by the bacterium: receptor binding, membrane penetration and ADP-ribosylation of the target protein. Evolutionarily, note the occurrence of domains homologous to the catalytic domain of diphtheria toxin in exo-, entero- and pertussis toxins, and in poly-ADP-ribose polymerase (Holm & Sander, 1999[link]). Arrows point to recurrent substructures in structural neighbours (Lionetti et al., 1991[link]; Li et al., 1996[link]; Tormo et al., 1996[link]) of each domain of diphtheria toxin. Drawn using MOLSCRIPT version 2 (Kraulis, 1991[link]).

The problem of subdividing protein molecules into structural and functional units has received the attention of numerous researchers over the last 25 years. Early algorithms focused on protein folding or unfolding pathways and aimed at identifying substructures that would be physically stable on their own. Nowadays, with bulging macromolecular databases, the focus has shifted to devise automatic methods for identifying domains that can form the basis for a consistent protein-structure classification (Murzin et al., 1995[link]; Orengo et al., 1997[link]; Holm & Sander, 1999[link]).

This review presents the concepts underlying computational methods for locating domains in 3D structures. Those interested in implementations are referred to the web services of the European Bioinformatics Institute1 and related sites.

23.1.2.2. Compactness

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A variety of ingenious techniques have been invented for locating structural domains in 3D structures. These include inspection of distance maps, clustering, neighbourhood correlation, plane cutting, interface area minimization, specific volume minimization, searching for mechanical hinge points, maximization of compactness and maximization of buried surface area (Rossmann & Liljas, 1974[link]; Rashin, 1976[link]; Crippen, 1978[link]; Nemethy & Scheraga, 1979[link]; Rose, 1979[link]; Schulz & Schirmer, 1979[link]; Go, 1981[link]; Lesk & Rose, 1981[link]; Sander, 1981[link]; Wodak & Janin, 1981[link]; Zehfus & Rose, 1986[link]; Kikuchi et al., 1988[link]; Moult & Unger, 1991[link]; Holm & Sander, 1994b[link]; Zehfus, 1994[link]; Islam et al., 1995[link]; Siddiqui & Barton, 1995[link]; Swindells, 1995[link]; Holm & Sander, 1996[link]; Sowdhamini et al., 1996[link]; Zehfus, 1997[link]; Holm & Sander, 1998[link]; Jones et al., 1998[link]; Wernisch et al., 1999[link]).

Common to most approaches are the assumptions that folding units are compact and that the interactions between them are weak. These notions can be made quantitative, for example, by counting interatomic contacts and by locating domain borders by identifying groups of residues such that the number of contacts between groups is minimized. The hierarchic organization of putative folding units can be inferred starting from the complete structure and recursively cutting it (in silico) into smaller and smaller substructures. Alternatively, one may start from the residue or secondary-structure-element level and successively associate the most strongly interacting groups. The procedure involves two optimization problems.

The first optimization problem is algorithmic and concerns finding the optimal subdivisions. This problem is complicated by the possibility of the chain passing several times between domains (discontinuous domains). Without the constraint of sequential continuity, there is a combinatorial number of possibilities for dividing a set of residues into subsets (Zehfus, 1994[link]). This hurdle has been overcome by fast heuristics (Holm & Sander, 1994b[link]; Zehfus, 1997[link]; Wernisch et al., 1999[link]).

The second optimization problem concerns formulating physical criteria that distinguish between autonomous and nonautonomous folding units, i.e., defining termination criteria for recursive algorithms. Since compactness-related criteria do not have a clear bimodal distribution, domain-assignment algorithms (Holm & Sander, 1994b[link]; Islam et al., 1995[link]; Siddiqui & Barton, 1995[link]; Swindells, 1995[link]; Sowdhamini et al., 1996[link]; Wernisch et al., 1999[link]) use cutoff parameters that have been fine-tuned against an external reference set of domain definitions.

23.1.2.3. Recurrence

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Most fold classifications use a hierarchical model where evolutionary families are a subcategory of fold type and it is natural to assume that domain boundaries should be conserved in evolution. Consistency concerns lead to a reformulation of the goals of the domain-assignment problem, away from (imprecise) physical models of stable folding units and towards recognizing such units phenomenologically in the database of known structures through recurrence. The concept of recurrence has long been the cornerstone of domain assignments by experts based on visual inspection (Richardson, 1981[link]). Recurrence means recognizing architectural units in one protein that have already been defined (named) in another.

The practical importance of domain identification is illustrated by the discoveries made by a systematic structure comparison of recurrent domains between histidine triad (HIT) proteins and galactose-6-phosphate uridylyltransferase [homodimer and internally duplicated common catalytic core, respectively (Holm & Sander, 1997[link])], and between beta-glucosyltransferase and glycogen phosphorylase [bare and heavily decorated common catalytic core, respectively (Holm & Sander, 1995[link]; Artymiuk et al., 1995[link])], even though the contours of the molecules look quite different.

Let us restate the goal of domain identification as an economic description of all known protein structures in terms of a small set of large substructures. This is an intuitive goal and conceptually related to the principle of minimal encoding in information theory. The key ingredients of the optimization problem are the gain associated with reusing a substructure and the cost associated with using many small substructures to describe a protein. An analogy in writing is that copying blocks of text is cheap, but for coherence some thought and effort is necessary for bridging the blocks.

With a suitably defined cost function, recurrence can be used to select an optimal set of substructures from the hierarchic folding or unfolding trees generated using compactness criteria. Thus, the unsatisfactorily solved problem of defining termination criteria for compactness algorithms can be turned into an optimization problem that does not rely on any external reference and leads to an internally consistent set of domain definitions.

The key difficulty is in quantifying the notion of economy so that it leads to a selection of substructures of `appropriate' size, i.e., globular folds and not, for example, supersecondary-structure motifs. One solution, which is physical nonsense but has the desired qualitative behaviour, is a heuristic objective function used in the DALI domain dictionary (Holm & Sander, 1998[link]). Recurrence is quantified in terms of the statistical significance of structural similarity for many pairs of substructures. The statistical significance is highest for structural similarities that involve large units and that completely cover a substructure unit. Exploiting these effects, a sum-of-pairs objective function is defined that favours recurrences of large substructures with distinct topological arrangements and packing of secondary-structure elements, and disfavours small substructures consisting of one or two secondary-structure elements despite their higher frequency of recurrence. Though other formulations of the optimization problem are possible, this empirically chosen objective function combined with a heuristic algorithm for optimization yields a useful set of substructures (domains).

23.1.2.4. Conclusion

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While we do not foresee that automatically delineated domains will be accepted as the gold standard of the trade, modern methods, based on a combination of recurrence and compactness criteria, yield domain definitions that are consistent within protein families and often coincide with biologically functional units, recover the well known folding topologies with many members, produce clusters with good coverage of common secondary-structure elements, and provide a useful basis for large-scale structure analysis and classification.

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