Chapter 4:
Structural Mechanisms for Protein Motions 

Mark Gerstein 1, Arthur M Lesk 2, & Cyrus Chothia 3
1 Structural Biology Department
Stanford University, Stanford, CA 94305
2 Department of Haematology, Cambridge University,
3 MRC Laboratory of Molecular Biology
Hills Road, Cambridge CB2 2QH, UK

	In this chapter, we describe two basic mechanisms for conformational change in proteins: hinge and shear. These mechanisms underlie, either individually or in combination, most large-scale protein motions. This is evident in the comprehensive listing of protein motions in chapter 5.	Most of our information on protein movements has come from X-ray crystal structures of open and closed conformations of particular proteins. The results of early investigations have been thoroughly reviewed 1, 2.  Ranked in order of their size protein movements fall into four categories: the motions of subunits, of domains, of fragments smaller than domains, and of individual sidechains. The protein motions we are predominately interested in are in the second and third categories, the motion of domains and fragments smaller than domains. As nearly all large proteins are built from domains, domain motions provide perhaps the most common examples of protein flexibility. The motion of fragments smaller than domains usually refers to the motion of surface loops, but it can also refer to the motion of secondary structures, such as of the helices in insulin. For convenience, we will often refer to the motions of these small fragments simply as loop motions. As we shall see, the motions of domains and loops require surmounting similar energy barriers and consequently involve essentially the same hinge and shear mechanisms. In contrast, the largest and smallest protein motions, those involving subunits and individual sidechains, are distinctly different. Subunit motion affects two large sections of polypeptide that are not covalently connected. Furthermore, it is often part of an allosteric transition, which requires the extensive repacking of interfaces and surrmounting much higher energy barriers than domain or loop motions.  Conversely, the motion of sidechains, while often essential for catalysis, involves much smaller-scale motions and smaller energy barriers than domain or loop motions.  
	Domain and loop 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 and loops often close around a binding site. Generally, the presence of a bound substrate stabilizes a closed conformation, and its absence favors an open conformation. Consequently, domain and loop motions provide mechanisms for induced-fit in protein recognition 3, 4.
	In catalysis, domain or loop 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 5, 6. It, 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 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 chapter, 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 movements in particular proteins.
The Intrinsic Way Proteins Can Move
	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 usually takes 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 4.1).
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 4.2a, in lactate dehydrogenase two adjacent torsion angle changes rotate a strand by ~35° in a direction not accessible by a single change 7. 
(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 4.2b, 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 8. 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 (figure 4.2c) 9. 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 up the helix from an a to a 310 conformation and stretch it by 3.3 Å  7.
	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 4.2d, 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 10-12 and triglyceride lipase 13. 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 4.3, 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 closing and opening 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 14, 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 rotamer configuration and move among conformational states of nearly the same energy without crossing large energy barriers. Occasionally, they may change to a different rotamer 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 RMS 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.
Hinge and Shear Mechanisms Underlie Protein Motions 
	The characteristics of the two basic mechanisms of protein flexibility, hinge and shear motions, are summarized in figure 4.1. These mechanisms constitute a repertoire of conformational changes that can be used in a great variety of protein motions. It is important to realize that they are ideal paradigms for describing protein motions. A large domain motion, for instance, will often have a combination of both motions, i.e. hinges in one part of the protein and shearing interfaces elsewhere. Nevertheless, most protein motions can be described as occurring predominantly by a hinge or a shear mechanism.
	As shown in figure 4.1, proteins that have a predominantly hinged motion usually have two domains (or fragments) 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 overall 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 usually tend to be more parallel 15. Crossed helices will obviously have a smaller and more accommodating interface than parallel helices, and perhaps this is the reason for their preferential involvement in shear motions. 
	One can rapidly and almost semi-automatically differentiate between shear and hinge motions by re-expressing the overall protein motion as a screw-axis transformation 8. As shown in figure 4.4, this transformation relocates the location of the rotation axis so that the total translation is minimal and occurs only along this axis. If one finds, after performing a screw-transformation, that the translation is nearly zero and that the rotation axis passes close to the polypeptide backbone, near a reasonable hinge point, then the motion almost certainly occurs by a single hinge mechanism. Otherwise, the motion involves shear motions or, perhaps, a complicated sequence of hinge motions. 
An Example of a Shear Domain Movement: 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 4.5). The domain closure involves the small domain closing over the large one, burying the substrates in the active site 16. An extensive interface between the large and small domains prevents closure taking place through a hinge mechanism. As shown in figure 4.5b, closure is produced by the summation of many small shear motions between pairs of packed helices 17. 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. As shown in figure 4.5c, the interfaces between many of the moving helices tend to be roughly perpendicular, or “crossed,” whereas the helices that are relatively motionless tend to have a more parallel packing.
An Example of a Hinged Domain Movement: Lactoferrin
	Lactoferrin and the periplasmic binding proteins have two or three interdomain linkages, containing hinges. These 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 the lobes gives a detailed picture of the domain movements 8, 18. 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 4.6). As discussed previously (figure 4.2b), these strands contain distinct hinges, and as the rotation axes of the principal torsion angle changes are nearly parallel to the axis of the overall 53° rotation, the local motion in the hinges can be related directly 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 become close-packed, 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 19. For two of these binding proteins, the maltodextrin-binding protein and LAO-binding protein 20-22, 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.
An example of a hinged loop closure: Triose Phosphate Isomerase
	Triose Phosphate Isomerase is one of the most extensively studied examples of loop closure. Three different variants of the enzyme have been analyzed crystallographically (chicken, yeast, and trypanosome) and the enzyme has been solved in both open and closed conformations 23-31. The loop closure has also been studied by techniques including site-directed mutagenesis 32, 33 and molecular dynamics 34-37.  TIM is a b-barrel enzyme that contains 8 helices packed onto a barrel of 8 sheets. An 11-residue loop running from an inner strand to an outer helix is flexible (Figure 4.7). When the enzyme binds its substrate the loop closes over the active site, shielding the substrate from water. It may also act as a gate, regulating the rate of the enzyme 34, 35. The loop appears to close as a rigid lid 37, stabilized by internal hydrogen bonds. Some alpha carbons in the loop move up to 8 Å. The closure involves the filling of a cavity near the base of the helix to which the loop is connected 24 and the formation of new hydrogen bonds and contacts. 
	Changes in the conformation of  about five residues are responsible for the bulk of the motion 37. (This is evident in the appreciable changes seen in five a-angles, which are the pseudo-dihedral angles connecting a-carbons). Furthermore, as shown in the figure 4.7, changing four mainchain torsion angles, two on either side of the loop, can achieve most of the effect of the loop closure. Achieving the motion through so few torsion angles changes is not that easy. Loop motion, especially that of a short loop, is in a way, much more constrained than domain motion. The positions of the termini of the loop are fixed in space, and if the loop is short, this constraint often means that large torsion changes at the N-terminal end can not be compensated by any combination of torsion angle changes at the C-terminal end. 
The stability of the closed and open states	
	The currently available evidence suggests that the open and closed states are only slightly different in energy and so are in dynamic equilibrium at room temperature. This small energy difference between the open and closed states is most consistent with the discovery that relatively weak crystal packing forces can stabilize the unliganded closed forms of lactoferrin and the binding-proteins 21, 38.
	The relative stabilities of the open and closed states depend on the presence or absence of the substrate. For domain closure, 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 39. 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, and these interactions account for the stability and specificity of the closed state. Catalytic transformation of the substrate destroys, at least in part, the favorable 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. There is clear evidence that the open form has a unique conformation in some proteins — e.g. lactoferrin and aspartate amino transferase 40 — but there is also evidence that the open form of other proteins can have a range of conformations — e.g. T4  lysozyme 9, 41 and leucine/isoleucine/valine-binding protein 21.  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 that are 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. 	
Conclusion
	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 many of the known instances of protein movements. We emphasize the importance of the architecture of the interface in determining the relative mix of hinge and shear motions. While our hinge and shear mechanisms do not describe 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 42.

Acknowledgements
MG received support from a Damon Runyon-Walter Winchell Fellowship (DRG-1272). AML thanks the Kay Kendall foundation for generous support. 

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Figure 4.1:	Hinged vs. Shear Mechanisms 
	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	
{ The above table is meant to be the caption for figure 4.1 } 

{ The above figure is meant to be the graphic for figure 4.1 } 

Figure 4.2:	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 4.6, 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 adenylate kinase 43 is an example of a 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.

Figure 4.3:	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. (A, 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. (B, 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 rocks slightly in the shear motion.

Figure 4.4:	The screw transformation
If a set of points x, (i.e.  the atoms in a protein domain) moves as a rigid body to the points x´, the transformation xÆx´ is can be expressed as a rotation R about the origin followed by a translation T : 
	x´ = R x + T
Up to a difference in sign, the rotation R has a unique axis n and magnitude k (e.g. Goldstein, 1980). ( By convention, n is a normalized vector along the rotation axis, and the rotation k is positive if it increases in a counterclockwise direction when viewed looking down n towards the origin. ) However, the translation T depends on the origin of the coordinate system. As shown in the figure, an origin x0 can always be chosen (up to arbitrary translation along n) so that the translation is minimal and parallel to the axis of rotation. If the initial and final coordinates refer to this origin, the entire transformation is referred to as a “screw motion”:
	(x´ – x0) = R (x - x0) + T|| ,
where the parallel component of the translation is T|| = n ( n • T ), the perpendicular component is T^ = T – T||, and the origin is
	x0 = F(1,2) B( T^ + n ¥ T^ cot F(k,2) ) .
The derivation of this formula for the value of x0 is shown geometrically in the figure. The view is down the rotation axis n, which is coming out of the page. In the plane perpendicular to this axis, there are two perpendicular directions, T^ and n ¥ T^. Shifting the origin to x0 requires a translation of  F(1,2) T^ in the first direction and a translation of  F(T^,2) cot F(k,2)  in the second.

Figure 4.4 (continued)

Figure 4.5:	Shear Motions in Citrate Synthase
(A) Cartoon of one subunit of citrate synthase, 1CTS. Adjacent one is related by two-fold axis shown.  Small two-stranded sheet is omitted to improve clarity. a-helices are represented by cylinders. The small domain contains helices N, O, P, Q, and R. Figure is adapted from Lesk & Chothia (1984) with loops removed.
(B) The overall effect of the helix movements.  Many small motions add up to shift helix O by 10.1 Å and rotate it by 28°. The incremental motion in shear domain closure is shown by Ca traces of the whole protein and of a closeup 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.) 
(C)	Schematic of principal helixes in citrate synthase. The orientation is perpendicular to the twofold axis. Selected helixes from both subunits are shown. (Upper-case letters are one subunit and lower-case letters are the other.) The helices shown with white lettering on a black background are motionless, while those shown in black on white move appreciably. Edges represent indicate the existence of helix-helix packings in both the open and closed form. Double edges are nearly parallel packing (0-30°); single edges, intermediate packing (30°-60°); and dotted edges, crossed packing (60°-90° and on-end packing). There is no packing between helixes L and N because helixes L,M,G, and F are much higher (coming out of page) than O,N,Q,P,R,K. S and I are long and make contacts with both sets. Note in the diagram how the dimer neatly divides into six layers with the active site, indicated by a star, at the intersection between layers. Part of one subunit is enlarged at the bottom of the diagram and shows the relative movements of the principal helices in citrate synthase. 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). Clearly, larger relative movements tend to be associate with more crossed helix-helix packings. 
Figure 4.5a
{ Insert from 

Figure 4.5b

Figure 4.5c

Figure 4.6	Hinge Motion in Lactoferrin
(A, LEFT) Cartoon of the two domains of lactoferrin  (N1 and N2)  in the open form (drawn with MOLSCRIPT 44). The origin of the rotation axis for the domain movements 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.  (B, MIDDLE and C, 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 the hinge in the closed form. 

Figure 4.7:	Hinge Motion in Triose Phosphate Isomerase
(A)	Location of the flexible loop in TIM. Only the helices and sheets in the barrel are shown. (B) Closeup of the loop motion. The closed conformation is shown with a dotted line and the open conformation with a solid black line. (C) A different view of the loop is shown. The closed and open conformations are again shown with dotted and solid lines. In addition, the closed conformation of the loop is split at residue 174 into N and C terminal halves, which are individually fit onto the open conformation. (The carbonyl oxygen of residue 174 is highlighted by a circle.) Then in the N-terminal half, which is shown with a thick light gray line, f(167) is changed by 18° and f(172), by 39° . Likewise, in the C-terminal half, which is shown with a thick dark gray line, f(177) is changed by 67° and f(179), by 59°. After making these torsion angle changes individually in the two halves, the loop is nearly still in one piece: Residue 174, the point of breakage, from either half nearly matches up with residue 174 of the open conformation. 

Figure 4.7a

Figure 4.7b

Figure 4.7c