Structural Mechanisms
for Domain Movements in Proteins †

Mark Gerstein 1,‡, Arthur M Lesk 2, & Cyrus Chothia 1,3
1 MRC Laboratory of Molecular Biology
2 Department of Haematology, Cambridge University,
3 Cambridge Center for Protein Engineering
Hills Road, Cambridge CB2 2QH, UK

‡ Present address:	Beckman Center for Structural Biology, Department of Cell Biology, 
Stanford Medical School, Stanford, CA 94305
† Supported by:		Damon Runyon-Walter Winchell Fellowship DRG-1272 
Running Title: 	Domain Movements 
Key Words:	Domain Closure, Protein flexibility, 
Hinge Mechanism, Shear Mechanism
Revised manuscript (BI19034C) sent to Biochemistry  on 29 March 1994. 

Abstract: We survey all the known instances of domain movements in proteins for which there is crystallographic evidence for the movement. We explain these domain movements in terms of the repertoire of low-energy conformation changes that are known to occur in proteins. We first describe the basic elements of this repertoire, hinge and shear motions, and then show how the elements of the repertoire can be combined to produce domain movements. We emphasize that the elements used in particular proteins are determined mainly by the structure of the domain interfaces. 

	Nearly all large proteins are built from domains (Wodak & Janin, 1981), and large relative movements of domains provide spectacular examples of protein flexibility. Domain motions are important for a variety of protein functions, including catalysis, regulation of activity, transport of metabolites, formation of protein assemblies and cellular locomotion. Domains often close around a binding site between them. Generally, the presence of bound substrates stabilizes a closed conformation, and their absence favours an open conformation. Consequently, domain motions illustrate induced-fit in protein recognition (Koshland, 1958).
	Most of our information on the mechanisms of domain movements has come from X-ray crystal structures of open and closed conformations of particular proteins. The results of early investigations were reviewed by Janin & Wodak (1983) and by Bennett & Huber (1984). Since then, a considerable amount of new information has become available, and we review here the portion of this information that concerns structural mechanisms of domain closure.
	In catalysis, domain closure often excludes water from the active site and helps position catalytic groups around the substrate. It also traps substrates and prevents the escape of reaction intermediates (Anderson et al., 1979; Knowles, 1991). Domain closure, therefore, must be fast, and the transition between open and closed forms cannot involve high energy barriers. Protein interiors, however, have features that place strong constraints on their possible conformational changes: they are close-packed with main chains and side chains in preferred conformations and with buried polar groups hydrogen bonded. In the first part of this review, we discuss the repertoire of possible low energy conformational changes that are available to proteins, i.e. their intrinsic flexibility. In the second part we describe how this repertoire of low energy conformational changes are used to produce domain movements in particular proteins.
I.	The Intrinsic Flexibility of Proteins
	The intrinsic flexibility of proteins is taken here to mean the ability of different segments of the protein to move in relation to one another with only small expenditures of energy. Analysis of protein crystal structures has shown that this intrinsic flexibility can take two forms: hinge motions in strands, b-sheets and a-helices that are not constrained by tertiary packing interactions and shear motions between close-packed segments of polypeptide (Figure 1).
A.	Hinge motions in strands, sheets, and helices not constrained by packing interactions. 
(1) b-Strands.	The most basic motion of a polypeptide chain is a few large changes in mainchain torsion angles in a localized region, i.e. at a hinge. The deformation of an extended strand is the simplest hinge motion because its only constraint is that the torsion angles of the strand remain in the allowed regions of the Ramachandran diagram. Consequently, its torsion angle changes can be very large and the resulting motion can rotate the polypeptide chain up to 60°. As shown in figure 2A, in lactate dehydrogenase two adjacent torsion angle changes rotate a strand by ~35° in a direction not accessible by a single change (Gerstein & Chothia, 1991). 
(2) b-Sheets: Two strands connected in a b-sheet can move together like the hinges on a door. However, the necessity that the strands remain hydrogen-bonded together provides an additional structural constraint beyond the limitations of the Ramachandran diagram. As shown in figure 2B, for the hinged sheet in lactoferrin this additional constraint means that in both strands the rotation axes of the principal torsion angle changes must be nearly parallel to each other and to the axis of the overall rotation of the sheet (Gerstein et al., 1993b). Three large (>30°) torsion angle changes produce the bulk of the motion, rotating the sheet by 53°. 
(3) a-Helices:	Hinges in a-helices present a contrasting story. Because residues in helices are subject to more severe hydrogen-bonding and steric constraints than those in sheets, their torsion angles are restricted to a smaller region of the Ramachandran diagram. Thus, if residues are to remain in a helical conformation, the possible changes in their torsion angles are correspondingly smaller than residues in an extended conformation, and the deformation of helices must be spread over more residues than the deformation of sheets. Such spread-out helical deformations can produce bending motions: eight torsion angles changes between 9° and 15° in the C-terminus of a helix in a mutant lysozyme bend its end to produce a shift of 3.3 Å (Dixon et al., 1992; figure 2C). Similar deformations can also stretch a helix: six torsion angle changes over 4 residues at the N-terminus of a helix in lactate dehydrogenase tighten the helix up from an a to a 310 conformation and stretch it by 3.3 Å  (Gerstein & Chothia, 1991).
	A different situation occurs in those helices that contain kinks, which often involve prolines. The disruption in the normal pattern of hydrogen bonding, and hence in the constraints on the helix, allows larger torsion angle changes. As shown in figure 2D, such large torsion angle changes have been found in the proline-kinked helix in adenylate kinase.
	The interconversion of helical and extended conformations is also possible and has been found in calmodulin (Ikura et al., 1992; Meador et al., 1992, 1993) and triglyceride lipase (Derewenda et al., 1992). While such an interconversion may involve crossing energy barriers somewhat higher than those in the motions discussed above, it permits large torsion angle changes and large deformations. In calmodulin, torsion angles changes in 5 residues in the middle of a long helix split it into two smaller helices, separated by 4 residues of extended strand. These two small helices are inclined at an angle of ~100°. 
B.	Limited shear motions of close-packed segments of polypeptide.  The preceding discussion of hinges considered only the effects of structural constraints intrinsic to b-strands, b-sheets and a-helices — i.e. constraints arising from the requirements of secondary structure. The interactions that stem from tertiary structure provide even more severe structural constraints. Most of the atoms in a protein are partially buried and close packed — in particular, most of the mainchain is buried beneath layers of sidechains. This close packing precludes large torsion angle changes and hence hinges. Indeed, a structural requirement for a residue to act as a hinge is that it have few tertiary structure packing constraints on its mainchain.
	As shown in figure 3, we can divide movements of close-packed segments of polypeptide into those that are perpendicular to an interface and those that are parallel. Hinges from outside the region of the interface can produce a motion perpendicular to the plane of an interface (so the interface exists in one conformation but not in the other, as in the opening and closing of a book). As discussed below, this sort of motion can be driven by ligands stabilizing a closed conformation. Motions parallel to the plane of the interface are limited by the packing contacts involving the interdigitation of sidechains. Large shifts of close-packed segments of polypeptide would require switching between different interdigitating configurations. Although such packing changes are seen at the subunit interfaces of allosteric proteins (Perutz, 1989), they have not been observed, so far, in domain closure. This is probably because such motions involve crossing high energy barriers and would not occur with sufficient rapidity.
	Small shear motions (figure 3) that do not involve repacking the interface are commonly involved in domain closure and have the following characteristics:
(1)	 Interdigitating sidechains accommodate shear motions, mostly, by small (<15°) changes in sidechain torsion angles. They keep the same overall rotomer configuration and move among conformational states of nearly the same energy without crossing large energy barriers. Occasionally, they may change to a different rotomer conformation (i.e. to a different local minimum) with large rotations (>100°).
(2)	The mainchain of each segment in a shear motion does not deform appreciably. In the case of helices, the r.m.s. difference in the positions of their main chain atoms in the open and closed forms is typically 0.15-0.25 Å; for loops the difference is slightly larger. This rigidity, combined with “rocking” movements of sidechains, implies that the interface itself shears.
(3)	 The segments shift and rotate relative to each other by no more than 2 Å and 15°, an amount likely to be the limit of low-energy conformational adjustments. Except at very small interfaces, larger movements than this require the combination of several shear motions.
	These characteristics were initially deduced from the analysis of protein crystal structures (Chothia et al., 1983; Lesk & Chothia, 1984). A similar, and in some ways more detailed, picture of shear motions has recently emerged through physical studies and computational simulations (Elber & Karplus, 1987; Rojewska & Elber, 1990; Frauenfelder et al., 1991).
II.	Shear and Hinge Motions Underlie Domain-Motion Mechanisms 
	The characteristics of the two basic mechanisms of protein flexibility, hinge and shear motions, are summarized in figure 1. These two mechanisms constitute a repertoire of conformational changes that can be used in a great variety of protein motions. Here we describe their use in the motions of whole protein domains, i.e.  in the relative motion of discrete linked units that consist, in most cases, of at least a hundred residues. Hinge and shear mechanisms are also involved in the motion of small protein fragments, for example, when individual loops or helices move relative to each other. In Table 1 we summarize the current crystallographic evidence for hinge and shear mechanisms in both domain motions and smaller motions. 	 It is important to realize that hinge and shear motions are ideal paradigms for describing large domain motions. A real domain motion will often have a combination of both motions, i.e. hinges in one part of the protein and shearing interfaces elsewhere. Nevertheless, many domain motions can be described as occurring predominantly by a hinge or a shear mechanism.
	As shown in figure 1, proteins that have a predominantly hinged domain motion usually have two domains connected by linking hinge regions that are relatively unconstrained by packing. A few large torsion angle changes are sufficient to produce almost the whole domain motion. The rest of the protein rotates essentially as a rigid body, with the axis of the overall rotation passing through the linking hinge regions.
	Since an individual shear motion is small, a single one is usually not sufficient to produce a large domain motion. Usually, a number of shear motions combine to give a large effect — in a similar fashion to each block in a stack sliding slightly to make the whole stack lean considerably. (The peptides that link the shearing segments have small mainchain torsion angle changes to accommodate the relative movements.)
	Proteins with shear motions tend to have certain architectural features. First, they often have layered architectures with one layer sliding over another. Second, though shear motions have been found at many different interfaces (i.e. helix-helix, sheet-helix, loop-sheet, and loop-helix), helix-helix interfaces are most commonly used. The helices involved in shear motions are usually crossed. That is, they are usually oriented in a more perpendicular than parallel fashion (interhelical angle 60° to 90°). Such crossed geometries are unusual in that helix-helix packings tend to be more parallel. Crossed helices will obviously have a smaller and more accommodating interface than parallel helices, and this is perhaps the reason for their preferential involvement in shear motions. 
	Table 1A lists all instances of crystallographically resolved domain motion, i.e., proteins that have been solved in two or more conformations. With the notable exception of the immunoglobulins, almost all large domain motions can be understood in terms of hinge and shear motions. Table 1B lists proteins for which a domain closure mechanism can be inferred. The structures of these proteins have been determined in only one conformation. However, they are similar to that of a protein with a well-characterized domain motion, i.e. one listed in Table 1A, and are expected to move using the same mechanisms.   
III.	Examples of Shear Domain Movements 
A.	Citrate Synthase. Citrate synthase is one of the clearest examples of a domain closure occurring through  shear motions. The molecule is a dimer, and each monomer comprises a large domain, containing 15 helices, and a small domain, containing 5 helices, with the active site cleft between them (figure 4). The domain closure involves the small domain closing over the large one, burying the substrates in the active site (Remington et al., 1982). An extensive interface between the large and small domains prevents closure taking place through a hinge mechanism. As shown in figure 4, closure is produced by the summation of many small shear motions between pairs of packed helices (Lesk & Chothia, 1984). The overall motion results in a helix on the far side of the small domain shifting by 10 Å and rotating by 28°, thereby moving an adjacent loop over the active site. Each local shear motion involves one helix moving relative to another by main-chain rotations and shifts of up to 13° and 1.8 Å. To a good approximation, the main chain of each helix moves without deformation as a rigid body. The shear motions are facilitated by small deformations in the loops linking the helices.
	There are over 50 distinct helix-helix interfaces in the citrate synthase dimer. Depending on the angle between neighboring helices these interfaces can be categorized as having roughly parallel helices, roughly perpendicular ones, or orientations in between. The interfaces between many of the moving helices tend to be roughly perpendicular, or “crossed,” while the helices that are relatively motionless tend to have a more parallel packing.
B.	Aspartate Amino Transferase.  In citrate synthase the domain closure is the cumulative result of many shear motions. In aspartate amino transferase (AAT), the domain motion is mainly the result of just two shear motions, which occur in perpendicular directions (McPhalen et al., 1992). AAT has an active site situated between a large and a small domain, and on substrate binding the small domain closes over the active site. The major shear motion involves a 13° rotation of the core of the small domain relative to the large one. A secondary shear motion moves a helix on one side of the small domain in a direction perpendicular to both the interdomain interface and the direction of the other shear motion. With a 1.2 Å shift and a 10° rotation, it “drops down” to cover the active site.
	The shear motions in AAT are facilitated by a hinge motion in a long interdomain helix. This helix is kinked by 17° in the open form and changes its kink angle by 12° on closure.
C.	Glyceraldehyde-3-phosphate Dehydrogenase, Alcohol Dehydrogenase and Hexokinase. In the previous two examples, domain closure involved motions spread throughout a domain. Here we describe three examples where the major shear motion occurs at the interface between the domains with subsidiary motions on one or both sides of this region.
	Because the enzymes hexokinase, glyceraldehyde-3-phosphate dehydrogenase (GAPDH), and alcohol dehydrogenase (ADH) share many common architectural features, their domain movements proceed through similar mechanisms (see Table 1 detailed references). These enzymes have 3 moving layers in one domain that shift relative to 3 rigid layers in the other domain. This distinctive layering pattern is of the form XBAabx, where abx are the 3 moving layers and XBA the rigid layers (figure 5). The interface between the two middle layers is where the major shear motion occurs. One layer of helices from the mobile domain (a) slides over a layer of helices from the motionless domain (A). Helices in these two layers, which in a sense form gears upon which the domains slide, are often “crossed,” as is dramatically illustrated for the case of hexokinase in figure 5. Near to the a and A layer helices, the ligand binds in the interdomain cleft . Packed onto either side of the central layers of helices (a and A) are sheets (b and B) from the mobile and motionless domains, respectively. The mobile sheet (b) forms a second moving layer, which slides over the helices, and packed onto the other face of this sheet is a third layer (x) which moves with the sheet. Symmetrical to this third moving layer (x), a third motionless layer (X) is packed onto one side of the static sheet (B). (Layer x is made up of helices in hexokinase and GAPDH, and helices and a sheet in ADH, and layer X is made up of helices in hexokinase and ADH, and a sheet from another subunit in GAPDH.)
	In addition to its shear motion, ADH also has two well defined hinge points (Eklund et al., 1981; Colonna-Cesari et al., 1986). 
	As discussed in table 1B, a number of other proteins have XBAabx architectures similar to those of hexokinase, GAPDH, and ADH but have not yet been solved in multiple conformations. These proteins include phosphoglycerate kinase (PGK), actin, and heat-shock protein. There is experimental evidence that these proteins may undergo domain movements (e.g., for PGK, see Mas et al., 1987, 1988), and they would be expected to use mechanisms similar to those of hexokinase, GAPDH, and ADH. Moreover, a model-building study done on PGK (Blake et al., 1986) predicts that the domain movement will involve the shearing of the two central helices, a conclusion similar to that implied by our comparisons. 
D.	trp Repressor.  In the previous sections we described examples of domains closing around substrates. In the trp  repressor, the binding of a ligand stabilizes a more open conformation. The trp repressor is a small protein that regulates three operons involved in the synthesis of tryptophan. It is a dimer, and each subunit contains six helices, divided between two domains. The central core of the molecule is formed from four helices from each subunit. On either side of this core, helix-turn-helix motifs form two symmetrically arranged DNA “reading head” domains. Between the central core and the reading-head domains, there are two binding sites for L-tryptophan, which need to be filled for trp repressor to recognize DNA (Zhang et al., 1987). Comparison of the holo and apo forms of the repressor (Lawson et al., 1988) shows that the binding of L-tryptophan shifts Ca atoms in the reading head domain by up to 4 Å. These shifts are produced by separate shear motions of the two helices in the reading-head domain (0.75 to 1.5 Å, 5° to 20°). These helix motions move the reading-head domains further apart than they are in the apo form so they are correctly separated to bind DNA. 
IV.	Examples of Hinged Domain Movements
A.	Tomato Bushy Stunt Virus. An example of a very simple hinge motion is found in the coat protein of tomato bushy stunt virus (Olsen et al., 1983). This spherical virus contains 180 subunits arranged with icosahedral symmetry on a T=3 lattice. Each subunit, in turn, contains two major domains, the shell (S) and projection (P) domains that are linked by a peptide in an extended conformation. The symmetry of the virus requires each subunit to fit into one of three different packing environments. One of the principal mechanisms for accommodating the different environments is a relative movement of the two domains by ~22°. This movement involves a simple hinge in the peptide connecting the S and P  domains (Olsen et al., 1983). 
B.	Calmodulin.  Like the TBSV coat protein, the motion in calmodulin involves a single deformation. The unligated form of calmodulin contains two globular domains, connected by a long helix (Babu et al., 1985). NMR and X-ray structures of ligated calmodulin show the molecule binding to peptide helices with different sequences and the two domains closing around the peptide far enough to make contact with each other (Ikura et al., 1992; Meador et al., 1992, 1993). As discussed above (§ I.A.3), in this motion, the long interdomain helix, which is known to have only marginal stability in solution (Ikura et al., 1992), partly unfolds to break into two helical segments connected by a hinge region in an extended conformation. The angle between the axes of the two helical segments is ~100°. As there is an additional twist around the helix axes, the total rotation of one domain relative to the other is upwards of 150°. Calmodulin can bind peptides with different sequences because of flexibility in the side chains that make contact with the peptide and by slightly shifting the relative placement of the domains through changes in the extent of the hinge region, which has consequently been dubbed “a variable expansion joint” (Meador et al., 1993).
C.	T4 Lysozyme Mutants.  Like calmodulin, two mutants of T4 lysozyme (Ile 3ÆPro and Met 6ÆIle) have a hinge motion involving a long interdomain helix. Crystals of these mutants grow in a number of different forms. Depending on the crystal form, their structures are either very similar to that of the wild-type or differ from it by a range of rigid-body domain rotations up to 32° (Dixon et al., 1992; Faber & Matthews, 1990). There are two main hinge points for the domain motion. They occur at the ends of the long helix that spans the domains. As discussed above, the second hinge involves small torsion angle changes spread throughout the C-terminal part of the helix (figure 2C). As the location of the mutation is next to the hinge, the domain motion appears to be a consequence of the loss of close-packing created by the mutation and is an example of hinged motion created by reducing the number of steric constraints. 
D.	Lactoferrin and the Periplasmic Binding Proteins.  Unlike the TBSV coat protein, lysozyme, and calmodulin, lactoferrin and the periplasmic binding proteins have two or three interdomain linkages, containing hinges. These proteins proteins are examples of transport proteins that use domain closure to recognize and sequester small molecules.  
	Lactoferrin has two similar lobes, and each lobe, in turn, has two domains with an iron-binding site between them. Analyses of the open and closed forms of one of lobes gives a detailed picture of the domain movements (Anderson et al., 1990; Gerstein et al., 1993b). Upon binding iron, the two domains move together, rotating 53° essentially as rigid bodies. The axis of rotation passes through the two b-strands linking the domains (Figure 6). As discussed previously (§ I.A.2 and figure 2B), these strands contain distinct hinges, and as the rotation axes of principal torsion angle changes are nearly parallel to the axis of the overall 53° rotation, the local motion in the hinges can be directly related to the overall domain closure. 
	The two domains make different packing contacts in the open and closed forms. In the open form the contacts are on one side of the hinges and in the closed form they are on the other side. Pivoting about the hinges produces a see-saw motion between the two interfaces: when the domains close, residues in the interface on one side of the hinges become buried and close-pack, and residues on the other side become exposed. The situation is reversed on opening.
	Lactoferrin shares a similar structure, topology, and binding-site construction with the group-II periplasmic binding proteins (Baker et al., 1987). For two of these binding proteins, the maltodextrin-binding protein and LAO-binding protein (Sharff et al., 1992; Spurlino et al., 1991; Oh et al., 1993), structures have been determined for both the open and closed forms and the mechanism of domain movement appears to be similar to that in lactoferrin. The domain motion in the maltodextrin-binding protein is a 35° rotation about an axis through the hinge region, and there are large, localized torsion angle changes in the three peptides linking the domains. The positions of two of the hinges are structurally equivalent to the lactoferrin hinges. In the LAO binding protein there is a 52° rotation of the two domains, which involves only a few large torsion angle changes in a region structurally equivalent to the lactoferrin hinge.
E.	Adenylate Kinase.  A more complex and extensive hinge motion is seen in the large variants of adenylate kinase. This enzyme has two nucleotide binding sites, and crystal structures have been solved with both sites, a single site, and no sites filled (Schultz et al., 1974, 1990; Diederichs & Schulz, 1991; Müller & Schulz, 1992). The major conformational change, which occurs when the second substrate binds, involves the smaller of the two domains rotating ~90° relative to the larger one and shifts main chain atoms up to 32 Å. The small and large domains are linked by two helices and, on closure, conformational changes take place in four hinges at the N and C termini of these linking helices (Gerstein et al., 1993b). Two of these hinges have simple motions; a third hinge requires motion throughout an extended loop; and a fourth hinge (§ I.A.3 and figure 2D) occurs in the middle of a proline-kinked helix. The four hinges have few packing constraints on their main-chain. One pair of hinges is responsible for one-third of the total rotation, and the other pair for two-thirds.   
F.	cAMP-dependent protein kinase.  Like ADK, the catalytic subunit of cAMP-dependent protein kinase has an elaborate multi-part hinged motion, which involves at least five distinct hinges, split into the two sets. Containing two domains, one large and one small, the structure of the catalytic subunit has been solved in binary and ternary complexes with an inhibitory peptide and in an apo form (Knighton et al., 1991; Karlsson et al., 1993). In comparing the apo and either complex form, the core of the small domain rotates ~12° relative to that of the large one. The small domain is principally connected to the large domain through three roughly parallel peptide linkages, which deform as hinges upon closure. In addition, through the deformation of two more hinges a loop in the small domain near the binding pocket rotates a further 6° down into the interdomain cleft. Partly because of the size of the interdomain cleft, which has to accommodate a 15 residue peptide, the protein kinase motion does not involve an extensive interdomain interface. There is, however, one helix in the small domain which moves in a shear fashion to maintain its contacts with the large domain throughout the motion.
V.	The Ball-and-socket Motion in the Immunoglobins
	The domain motion observed in the immunoglobulins involves, so far as is known at present, a unique combination of hinge and shear motions. In the immunoglobulins the VL domain is linked by an extended peptide to the CL domain, and VH  is similarly linked to CH1. VL and VH pack together, as do CL and CH1. The VL-VH dimer can freely rotate, relative to the CL-CH1 dimer, over a range of ~50° in a manner described as “elbow motion.”
	Elbow motion involves localized deformations in the two peptides that link the V and C dimers (Bennett & Huber, 1984). These deformations are similar to those in the hinged domain closures described in the previous sections. However, the elbow motion also involves an unusual type of shear motion: two large residues in CH1,  a Pro and Phe, pack closely together, forming a “ball,” and three residues in VH  spread out as part of a b-sheet, forming a “socket”  (figure 7). The three VH and two CH1 residues are packed together and move relative to each other in a manner similar to a socket moving over a ball (Lesk & Chothia, 1988).
	Unlike the shear motions discussed above, which are characterized by close-packed interfaces of interdigitating sidechains, the ball-and-socket joint has a “smooth” interface, in which the side chains do not interdigitate. This interface facilitates motion over a wide range of relative orientations. It also permits greater flexibility than found in shear motions: the “socket” residues can move up to 4.5 Å relative to those in the “ball,” rather than the 1.5 to 2.0 Å displacement usually found at an interface undergoing shear motion. 
VI.	The stability of the closed and open states	
	The evidence currently available suggests that the open and closed states are only slightly different in energy and at room temperature are in dynamic equilibrium. This small energy difference between the open and closed states is most directly suggested by the discovery that relatively weak crystal packing forces can stabilize the unliganded closed forms of lactoferrin and the binding-proteins (Baker et al., 1991; Sharff et al., 1992 and references therein). It is also suggested by simulations of loop closure (Wade et al., 1993, 1994). 
	The relative stabilities of the open and closed states depend on the presence or absence of the substrate. A likely progression is that the substrate first binds to one domain, then thermal fluctuations bring the second domain in contact with it, and the newly formed contacts stabilize the closed conformation. The ability of a ligand to bind to a single domain has, in fact, been observed in transferrin (Lindley et al., 1993). Inspection of the structures of liganded closed states invariably shows that the ligand makes numerous interlocking salt bridges, hydrogen bonds, and packing interactions with both domains (references in Table 1), and these interactions account for the stability and specificity of the closed state. Catalytic transformation of the substrate destroys, at least in part, the interactions made with the protein and so makes the open form more stable. The rate of domain movements, consequently, is governed to a degree by the catalytic efficiency of the protein. This may be particularly relevant to domain movements involved in locomotion. 
	The main function of the open form is to allow access to the active site. By itself, this function does not require the open form to have a unique conformation, as opposed to a range of conformations. Experimental evidence for a unique open form is sketchy and mixed. On the one hand, there is clear evidence that the open form has a unique conformation in certain proteins. As discussed above (§IV.C), in lactoferrin the interdomain interface formed in the open form appears to uniquely fix its conformation. Likewise, within particular species, AAT has the same open conformation in different crystal forms, which have very different intermolecular contacts (McPhalen et al., 1992). On the other hand, there is also evidence that the open form of other proteins can have a range of conformations. T4 lysozyme has been found to have a number of different “open” conformations in various crystal forms (Faber & Matthews, 1991; Dixon et al., 1992). The leucine/isoleucine/valine-binding protein has been solved in a “more-opened” form (Sharff et al.,  1992 and references therein). A variety of different orientations have been found for the two domains of E. coli  NADP+-dependent glutamate dehydrogenase; this hexameric protein has been solved in a crystal form where all six subunits are in the asymmetric unit (D Rice, personal communication). 
	The crystallographic evidence relating to the uniqueness of the open state must be treated with care as there is a possibility that the intermolecular contacts in the crystal may fix domains in orientations not preferred in solution. Also, by necessity, crystallography forces one to think in terms of discrete, rigid conformational states, which may be an erroneous model altogether for open and closed conformations. 	
VII.	Conclusions
	We have shown how hinge and shear motions, which constitute the repertoire of low-energy conformation changes available to proteins, can be combined to describe most of the known instances of domain movements. We emphasize the importance of the architecture of the interdomain interface in determining the relative mix of hinge and shear motions. While our hinge and shear mechanisms do not describe domain motions precisely enough for accurate energy calculations, they provide a conceptual framework for understanding complicated structural transformations and can be used as a guide for more quantitative formulations. As more data becomes available, the descriptions of hinge and shear mechanisms should be refined and extended so that they can be applied to the complex large-scale motions that occur in structures such as that of myosin (Rayment et al., 1993).

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Figure 1:	Hinged vs. Shear Mechanisms for Domain Closure
	Shear Mechanism	Hinged Mechanism	
Simple Example:	Citrate Synthase	Lactoferrin	
Mainchain Packing:	Constrained by close packing	Free to kink	
Mainchain Torsions: 	Many small changes	A few large changes	
Motion Overall:	Concatenation of small local motions	Identical to twisting at hinge	
Motion at Interface:	Parallel to plane of interface (shear)	Perpendicular to plane of interface, exposing & burying surfaces.	
Sidechain Packing:	Same packing in both forms	New contacts created; Packing at base of hinge crucial.	
Sidechain Torsions:	Mostly small changes	Some large changes	
Figure 2:	Hinge Motions in Strands, Sheets, and Helices
(A, FAR LEFT) A hinge in lactate dehydrogenase is an example of a isolated hinge in a strand. Changes in two torsion angles (∆f(96) = 36° and ∆f(97) = 40°) are responsible for rotating the polypeptide chain ~35°. (B, MIDDLE LEFT) The hinges in lactoferrin are an example of the coupling of two simple hinges together in a sheet. The hinges move through 3 large torsion angle changes and the rotation axes for these torsion angle changes are inclined less than 20° with respect to the axis of the overall motion. (In the strand on the left ∆y(250) = -33° and ∆f(249) = 30°, in the strand on the right ∆y(90) = 49°.) Small conformational changes in adjacent residues help maintain the integrity of the b-sheet structure. As evident in figure 6, the hinges have few mainchain packing constraints on them. (C, MIDDLE RIGHT) The interdomain helix in lysozyme is an example of a bending helix. It bends through the coordinated action of 8 torsion angle changes between 9° and 15°, shifting the Ca atom at the C-terminal end of the helix by 3.3 Å. (D, FAR RIGHT) The helix linking the two domains in ADK is an example of kinking helix. A torsion angle change in the residue three before Pro177 (∆f = -53°) causes the helix to deform in a direction perpendicular to its original kink  (Gerstein et al., 1993a).

Figure 3:	Shear Motions Involve Interfaces
Two examples taken from citrate synthase show helix-helix interfaces undergoing a shear motion. The 2 labelled axes show the direction of parallel and perpendicular motion at an interface. (left) The QP helix-helix interface illustrates how small hinges in linking peptides function in shear motions. Helix Q shifts 1.4 Å and rotates 13° relative to helix Q. (right) The NQ helix-helix interface shows a crossed helix packing and a slightly larger motion than at the QP interface. Helix N shifts 1.8 Å and rotates 11° relative to helix Q. There are many close-packed sidechains forming the N-Q interface, which just rock slightly in the shear motion.
Figure 4:	Shear Motions in Citrate Synthase
(TOP Left) Cartoon of one subunit of citrate synthase. a-helices are represented by cylinders. The small domain contains helices N, O, P, Q, and R. (Top Right) Schematic  showing the relative movements of the principal helices in citrate synthase. (This figure is adapted in part from Lesk & Chothia, 1984.) Each helix is represented by its letter, and the lines indicate the existence of helix-helix packings in both the open and closed form. The shifts and rotations show local changes in the positions of pairs of packed helices (i.e. the movement in one helix in a pair relative to the other). (BOTTOM RIGHT) The overall effect of the helix movements. The same conventions as in the top right schematic apply, but the shifts and rotations shown now are those required to superimpose equivalent pairs of helices after the open and closed forms have been superimposed on the core of the large domain. Many small motions add up to shift helix O by 10.1 Å and rotate it by 28°. (BOTTOM LEFT) Incremental motion in shear domain closure is shown by Ca traces of the OP loop. BLACK is the apo form; WHITE, holo form; GRAY, cumulative effect of motion over the K, P, and then Q helix-helix interfaces. (The apo form was fit to the holo form, first on the core, and then on the K, P, and Q helices.) 
Figure 5:	XBAabx Layering in Hexokinase and Other Proteins
XBAabx layering (see § III.C) is shown graphically by schematics of GAPDH (left) and hexokinase (right). Helices are drawn as narrow cylinders (radius 1.0 Å); sheets are represented as sheets as opposed to collections of strands; and substrates are drawn in CPK representation. (GAPDH is shown in its closed form with its actual ligand. Hexokinase, however, is shown in its open form with the inhibitor ortho-toluoylglucosamine.) 
Figure 6:	Hinge Motion in Lactoferrin
(LEFT) Cartoon of the two domains of lactoferrin  (N1 and N2)  in the open form (drawn with MOLSCRIPT, Kaulis, 1991). The origin of the rotation axis for the domain movements (§ IV.A) lies at the center of the figure. The view is down the rotation axis, which is indicated by a circle with a dot in it. N2 is shown in darker shading than N1, and the two antiparallel b-strands with the hinges are highlighted with bold line. The Ca atoms of the residues with the largest movements (90 and 251) are indicated by empty circles. They lie in the middle of these strands and are very near the rotation axis in the open form.  (MIDDLE and RIGHT) Slices through the van der Waals envelope of the open and closed forms, respectively. N1 is shown by a thin black line; N2, by a dotted black line; the mainchain atoms of the hinge (89-92 and 249-252), by a bold black line; the sidechain of Tyr 92, by light gray line; and the iron, by a dark gray line. Note the absence of packing constraints on the mainchain atoms of the hinge in the open form, and the tight packing at the base of hinge in the closed form. 
Figure 7:	The Ball and Socket Motion in the Immunoglobulins
Domain Movements in the Immunoglobulins. (Left) The conserved VH to CH1 contacts and the switch (hinge) peptides. Three VH residues (11, 110, and 112) form a “socket” and two CH1 residues, 149 and 150, form a “ball.” The view is such that the motion of the V dimer relative to the C dimer is in and out of the page. (Middle and Right) The movement of the ball-and-socket joint. The five side chains in the joint are represented by spheres drawn at half van der Waals radius. White spheres indicate the socket, and black ones, the ball. The orientation is roughly perpendicular to that in the left figure (see the eye symbol there). The middle figure shows the packing that occurs when the domains are fully extended (i.e., 180° elbow angle), and the right figure shows the packing that occurs when the domains are close enough to be in contact (135° elbow angle).