§
`
`164 Chapter 7. Three-Dimensional Structures OfProteins.
`
`a topographic map. A stack of such sections, drawn on
`transparencies, yields a three-dimensional electron density
`map (Fig. 7-37b). Modern structural analysis, however, is
`often carried out with the aid of graphics computers, on
`which electron density maps are contoured in three dimen-
`sions (Fig. 7-37c).
`
`Protein Crystal Structures Exhibit Less Than Atomic
`Resolution
`The molecules in protein crystals, as in other crystalline
`substances, are arranged in regularly repeating three-di-
`mensional lattices. Protein crystals, however, differ from
`those of most small organic and inorganic molecules in
`being highly hydrated; they are typically 40 to 60% water by
`volume. The aqueous solvent ofcrystallization is necessary
`for the structural integrity of the protein crystals as J. D.
`Bernal and Dorothy Crowfoot Hodgkin first noted in 1934
`when they carried out the original X-ray studies of protein
`crystals. This is because water is required for the structural
`integrity of native proteins themselves (Section 7-4).
`The large solvent content of protein crystals gives them a
`soft, jellylike consistency so that their molecules lack the
`rigid order characteristic ofcrystals ofsmall molecules such
`as NaCl or glycine. The molecules in a protein crystal are
`typically disordered by a few angstroms so that the corre-
`sponding electron density map lacks information concern-
`ing structural details of smaller size. The crystal is therefore
`said to have a resolution limit of that size. Protein crystals
`typically have resolution limits in the range 2 to 3.5 A,
`although a few are better ordered (have higher resolution,
`that is, a lesser resolution limit) and many are less ordered
`(have lower resolution).
`Since an electron density map of a protein must be inter-
`preted in terms of its atomic positions, the accuracy and
`even the feasibility of a crystal structure analysis depends
`on the crystal’s resolution limit. Figure 7-38 indicates how
`the quality (degree of focus) of an electron density map
`varies with its resolution limit. At 6—A resolution, the pres-
`ence ofa molecule the size ofdiketopiperazine is difficult to
`
`discern. At 2.0-A resolution, its individual atoms cannot
`yet be distinguished, although its molecular shape has be-
`come reasonably evident. At 1.5-A resolution, which
`roughly corresponds to a bond distance, individual atoms
`become partially resolved. At 1.1-A resolution, atoms are
`clearly visible.
`Most protein crystal structures are too poorly resolved
`for their electron density maps to reveal clearly the posi-
`tions of individual atoms (e.g., Fig. 7-37). Nevertheless, the
`distinctive shape of the polypeptide backbone usually per-
`mits it to be traced, which, in turn, allows the positions and
`orientations of its side chains to be deduced (e.g., Fig.
`7-37c). Yet, side chains of comparable size and shape, such
`as those of Leu, Ile, Thr, and Val, cannot be differentiated
`with a reasonable degree of confidence (hydrogen atoms,
`having but one electron, are not visible in protein X-ray
`structures), so that a protein structure cannot be elucidated
`from its electron density map alone. Rather, the primary
`structure ofthe protein must be known, thereby permitting
`the sequence of amino acid residues to be fitted, by eye, to
`its electron density map. Mathematical refinement can
`then reduce the errors in the crystal structure’s atomic posi-
`tions to around 0.1 A (in contrast, the errors in small mole-
`cule X-ray structure determinations may be as little as
`0.001 A).
`
`Most Crystalline Proteins Maintain Their Native
`Conformations
`What is the relationship between the structure of a pro-
`tein in a crystal and that in solution where most proteins
`normally function? Several lines of evidence indicate that
`crystalline proteins assume very nearly the same structures
`that they have in solution:
`
`1. A protein molecule in a crystal is essentially in solution
`because it is bathed by solvent of crystallization over all
`of its surface except for the few, generally small patches
`that contact neighboring protein molecules. In fact, the
`40 to 60% water content of typical protein crystals is
`similar to that of many cells (e.g., see Fig 1-13).
`
`(a) 6.043 resolution
`
`(12)
`
`2.0-A resolution
`
`(c)
`
`1.5-A resolution
`
`(d)
`
`1.1-A resolution
`
`
`
`FIGURE 7-38. A section through the electron density map of diketopiperazine calculated at the
`indicated resolution levels. Hydrogen atoms are not apparent in this map because of their
`low electron density. [After Hodgkin, D.C., Nature 188, 445 (1960).]
`
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`
`2_ A pl-otgin may crystallize in one of several forms or
`“habits,” depending on crystallization conditions, that
`differ in how the protein molecules are arranged in space
`relative to each other. In the numerous cases in which
`different crystal forms of the same protein have been
`independently analyzed, the molecules have virtually
`identical conformations. Similarly, in the several cases
`that both the X-ray crystal structure and the solution
`NMR structure of the same protein have been deter-
`mined, the two structures are, for the most part, identical
`to within experimental error (see below). Evidently,
`crystal packing forces do not greatly perturb the struc-
`tures of protein molecules.
`
`3. The most compelling evidence that crystalline proteins
`have biologically relevant structures, however, is the ob-
`servation that many enzymes are catalytically active in
`
`Section 7-3. Globular Proteins
`
`165
`
`the crystalline state. The catalytic activity of an enzyme
`is very sensitive to the relative orientations of the groups
`involved in binding and catalysis (Chapter 14). Active
`crystalline enzymes must therefore have conformations
`that closely resemble their solution conformations.
`
`Protein Structure Determination by 2D-NMR
`The determination ofthe three-dimensional structures of
`
`small globular proteins in aqueous solution has become
`possible, since the mid 1980s, through the development of
`two-dimensional (2D) NMR spectroscopy (and, more re-
`cently, of 3D and 4D techniques), in large part by Kurt
`Wiithrich. Such NMR measurements, whose description is
`beyond the scope of this text, yield the interatomic dis-
`tances between specific protons that are <5 A apart in a
`protein of known sequence that has no more than ~200
`residues. The interproton distances may be either through
`space, as determined by nuclear Overhauser eifect spectros-
`copy (NOESY, Fig. 7-39a), or through bonds, as deter-
`mined by correlated spectroscopy (COSY). These dis-
`
`
`
`NC
`
`(b)
`
`FIGURE 7-39. The 2D proton NMR structures of proteins.
`(a) A NOESY spectrum of a protein presented as a contour plot
`with two frequency axes, co, and col. The conventional 1D-
`NMR spectrum of the protein, which occurs along the diagonal
`flfthc plot (co, = coz), is too crowded with peaks to be directly
`interpretable (even a small protein has hundreds of protons).
`The off-diagonal peaks, the so-called cross peaks, each arise
`from the interaction of two protons that are <5 A apart in space
`and whose 1D-NMR peaks are located where the horizontal
`and vertical lines through the cross peak intersect the diagonal
`[a nuclear Overhauser effect (NOE)]. For example, the line to
`the left of the spectrum represents the extended polypeptide
`chain with its N- and C-terminal ends identified by the letters N
`and C and with the positions of four protons, a to d, represented
`by small circles. The dashed arrows indicate the diagonal NMR
`peaks to which these protons give rise. Cross peaks, such as i, j,
`and k, which are each located at the intersections of the
`§0r}z0ntal and vertical lines through two diagonal peaks, are
`Indicative of an NOE between the corresponding two protons,
`
`indicating that they are <5 A apart. These distance relationships
`are schematically indicated by the three circular structures
`drawn below the spectrum. Note that the assignment of a
`distance relationship between two protons in a polypeptide
`requires that the NMR peaks to which they give rise and their
`positions in the polypeptide be known, which requires that the
`polypeptide’s amino acid sequence has been previously
`determined. [After Wiithrich, K., Science 243, 45 (1989).]
`(b) The NMR structure of a 64-residue polypeptide comprising
`the Src protein SH3 domain (Section 34-4B). The drawing
`represents 20 superimposed structures that are consistent with
`the 2D- and 3D-NMR spectra of the protein (each calculated
`from a different, randomly generated starting structure). The
`polypeptide backbone, as represented by its connected C“
`atoms, is white and its Phe, Tyr, and Trp side chains are yellow,
`red, and blue, respectively. It can be seen that the polypeptide
`backbone folds into two 3-stranded antiparallel 5 sheets that
`form a sandwich. [Courtesy of Stuart Schreiber, Harvard
`University.]
`
`
`
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`

`
`166 Chapter 7. Three-Dimensional Structures OfProteins
`
`tances, together with known geometric constraints such as
`covalent bond distances and angles, group planarity, chira-
`lity, and van der Waals radii, are used to compute the pro-
`tein’s three-dimensional structure. However, since inter-
`proton distance measurements are imprecise,
`they are
`insufficient to imply a unique structure. Rather, they are
`consistent with an ensemble of closely related structures.
`Consequently, an NMR structure of a protein (or any other
`macromolecule with a well-defined structure) is often
`presented as a representative sample of structures that are
`consistent with the constraints (e.g., Figure 7-39b). The
`“tightness” of a bundle of such structures is indicative both
`ofthe accuracy with which the structure is known, which in
`the most favorable cases is roughly comparible to that of an
`X-ray crystal structure with a resolution of2 to 2.5 A, and of
`the conformational fluctuations that the protein undergoes
`
`(Section 8-2).
`In most of the several cases in which both the NMR and
`X-ray crystal structures of a particular protein have been
`determined, the two structures are in good agreement.
`There are, however, a few instances in which there are real
`differences between the corresponding X-ray and NMR
`structures. These, for the most part, involve surface resi-
`dues that, in the crystal, participate in intermolecular con-
`tacts and are thereby perturbed from their solution confor-
`mations. NMR methods, besides providing mutual
`crosschecks with X-ray techniques, can determine the
`structures of proteins and other macromolecules that fail to
`crystallize. Moreover, since NMR can probe motions over
`
`time scales spanning 10 orders of magnitude, it can be used
`to study protein folding and dynamics (Chapter 8).
`
`Protein Molecular Structures Are Most Effectively
`Illustrated in Simplified Form
`The several hundred nonhydrogen atoms of even a small
`protein makes understanding the detailed structure of a
`protein a considerable effort. The most instructive method
`ofstudying a protein structure is the hands—on examination
`of its skeletal (ball-and-stick) model. Unfortunately, such
`models are rarely available and photographs ofthem are too
`cluttered to be of much use. A practical alternative is a
`computer-generated stereo diagram in which the polypep-
`tide backbone is represented only by its C0, atoms and only a
`few key side chains are included (Fig. 7-40). Another possi-
`bility is an artistic rendering of a protein model that has
`been simplified and slightly distorted to improve its visual
`clarity (Fig. 7-41). A further level of abstraction may be
`obtained by representing the protein in a cartoon form that
`emphasizes its secondary structure (Fig. 7-42; also see Fig.
`7-19). Computer-generated drawings of
`space-filling
`models, such as Figs. 7-12 and 7-18, may also be employed
`to illustrate certain features of protein structures.
`
`B. Tertiary Structure
`
`The tertiary structure (3° structure) ofa protein is its three-
`dimensional arrangement; that is, the folding of its 2 ° struc-
`tural elements, together with the spatial dispositions of its
`
`
`
`FIGURE 7-40. A computer-drawn stereo diagram of sperm
`whale myoglobin in which the Cu, atoms are represented by balls
`and the peptide groups linking them are represented by solid
`bonds. The 153-residue polypeptide chain is folded into eight oz
`helices (highlighted here by hand-drawn envelopes), connected
`by short polypeptide links. The protein’s bound heme group
`
`(purple) in complex with an 02 molecule (orange sphere) is
`shown together with its two closely associated His side chains
`(light blue). Hydrogen atoms have been omitted for the sake
`of clarity. Instructions for viewing stereo diagrams are given in
`the appendix to this chapter. [Figure copyrighted © by Irving
`Geis.]
`
`Page 28
`
`Page 28
`
`

`
`side chains. The first protein X-ray structure, that of sperm
`wha1e myoglobin, was elucidated in the late 1950s by John
`Kendrew and coworkers. Its polypeptide chain follows such
`a tortuous, wormlike path (Figs. 7-40 through 7-42), that
`these investigators were moved to indicate their disappoint-
`
`ment at its lack of regularity. In the intervening years, well
`over 500 protein structures have been reported. Each of
`them is a unique, highly complicated entity. Nevertheless,
`their tertiary structures have several outstanding features in
`common as we shall see below.
`
`Section 7-3. Globular Proteins
`
`167
`
`Amino end of chain
`
`FIGURE 7-4]. An artist’s rendering of sperm whale
`ml/Oglobin analogous to Fig. 7-40. One of the heme group’s
`Dropionic acid side chains has been displaced for clarity. The
`
`amino acid residues are consecutively numbered, starting from
`the N-terminus, and the eight helices are likewise designated
`A through H. [Figure copyrighted © by Irving Geis.]
`
`Page 29
`
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`
`

`
`Page 30
`
`

`
`FIGURE 7-43. The jack bean protein concanavalin A largely
`consists of extensive regions of antiparallel ,8 pleated sheet, here
`represented by arrows pointing towards the polypeptide chain’s
`C-terminus. The balls represent protein-bound metal ions. The
`back sheet is shown in a space-filling representation in Fig. 7-18.
`[After a drawing by Jane Richardson, Duke University.]
`
`
`
`Section 7-3. Globular Proteins
`
`169
`
`2. The charged polar residues Arg, His, Lys, Asp, and Glu
`are largely located on the surface ofa protein in contact
`with the aqueous solvent. This is because the immersion
`of an ion in the virtually anhydrous interior ofa protein
`results in the uncompensated loss of much of its hydra-
`tion energy. In the instances that these groups occur in
`the interior of a protein, they often have a specific chem-
`ical function such as promoting catalysis or participating
`in metal ion binding (e.g., the metal ion—liganding His
`residues in Figs. 7-41 and 7-44).
`
`3. The uncharged polar groups Ser, Thr, Asn, Gln, Tyr,
`and Trp, are usually on the protein surface but fre-
`quently occur in the interior of the molecule. In the
`latter case, these residues are almost always hydrogen
`bonded to other groups in the protein. In fact, nearly all
`buried hydrogen bond donorsform hydrogen bonds with
`buried acceptor groups; in a sense, the formation of a
`hydrogen bond “neutralizes” the polarity of a hydrogen
`bonding group.
`
`FIGURE 7-44. Human carbonic
`anhydrase in which at helices are
`represented as cylinders and each
`strand of ii sheet is drawn
`as an arrow pointing towards the
`polypeptide’s C-terminus. The gray
`ball in the middle represents a Zn“ ion
`that is coordinated by three His side
`chains (blue). Note that the C-terminus
`is tucked through the plane of a
`surrounding loop of polypeptide
`chain so that carbonic anhydrase is one
`of the rare native proteins in which a
`polypeptide chain forms a knot. [After
`Kannan, K.K., Liljas, A., Waara, 1.,
`Bergsten, P.-C., Lovgren, S., Strandberg,
`B., Bengtsson, J., Carlbom, U.,
`Friedborg, K., Jarup, L., and Petef,
`M., Cold Spring Harbor Symp. Quant.
`Biol. 36, 221 (1971).]
`
`Page 31
`
`Page 31
`
`

`
`170 Chapter 7. Three-Dimensional Structures 0fProteins
`
`(a)
`
`
`
`Residues
`facing
`protein
`interior
`
`Residues
`exposed
`to surface
`
`(b)
`
`
`
`FIGURE 7-45. The H helix of sperm whale myoglobin. (a) A
`helical wheel representation in which side chain positions about
`the oz helix are projected down the helix axis onto a plane. Here
`each residue is identified both according to its sequence in the
`polypeptide chain, and according to its position in the H helix.
`The residues lining the side of the helix facing the protein’s
`interior regions are all nonpolar. The other residues, except Leu
`137, which contacts the protein segment linking helices E and
`F (Figs. 7-40 and 7-41), are exposed to the solvent and are all
`more or less polar. (b) A skeletal model, viewed as in Part a, in
`which the main chain is white, nonpolar side chains are yellow,
`and polar side chains are purple. (c) A space-filling model,
`viewed from the bottom of the page in Parts at and b and
`colored as in Part b. Compare these diagrams with the drawing
`of the H helix in Fig. 7-42.
`
`Page 32
`
`Page 32
`
`

`
`Section 7-3. Globular Proteins
`
`171
`
`oil drop; that is, it is efliciently packed. The ability of most
`hydrogen bonding donors to find acceptors under such
`constrained conditions is explained by the observation that
`most hydrogen bonding partners reside on residues that are
`close in sequence (which is, in turn, explained by the facts
`that backbone N—H groups comprise the majority of the
`hydrogen bonding donors in proteins and that most protein
`residues are members of secondary structural elements).
`The bonds of protein side chains, including those occu-
`pying protein cores, almost invariably have low-energy
`staggered torsion angles (Fig. 7-5b). Evidently, interior side
`chains adopt relaxed conformations despite their profusion
`of intramolecular interactions (Section 7-4).
`
`Large Polypeptides Form Domains
`Polypeptide chains that consist of more than ~200 resi-
`dues usually fold into two or more globular clusters known
`as domains, which give these proteins a bi- or multilobal
`appearance. Most domains consist of 100 to 200 amino
`acid residues and have an average diameter of~25 A. Each
`subunit of glyceraldehyde-3-phosphate dehydrogenase, for
`example, has two distinct domains (Fig. 7-47). A polypep-
`tide chain wanders back and forth within a domain but
`
`neighboring domains are usually connected by one, or less
`commonly two, polypeptide segments. Domains are there-
`fore structurally independent units that each have the char-
`acteristics ofa small globular protein. Indeed, limited pro-
`teolysis of a multidomain protein often liberates its
`domains without greatly altering their structures. Never-
`theless, the domain structure of a protein is not always
`obvious since its domains may make such extensive con-
`tacts with each other that the protein appears to be a single
`globular entity.
`An inspection of the various protein structures dia-
`grammed in this chapter reveals that domains consist of
`two or more layers of secondary structural elements. The
`reason for this is clear: At least two such layers are required
`to seal off a domain’s hydrophobic core from the aqueous
`environment.
`
`Domains often have a specific function such as the bind-
`ing of a small molecule. In Fig. 7-47, for example, nicotin-
`amide adenine dinucleotide (NAD+) binds to the first do-
`main of glyceraldehyde-3-phosphate dehydrogenase. Small
`molecule—binding sites in multidomain proteins often
`occur in the clefts between domains; that is, the small mole-
`cules are bound by groups from two domains. This arrange-
`ment arises, in part, from the need for a flexible interaction
`between the protein and the small molecule that the rela-
`tively pliant covalent connection between the domains can
`provide.
`
`Supersecondary Structures Have Structural and
`Functional Roles
`
`Certain groupings of secondary structural elements,
`named supersecondary structures or motifs, occur in many
`unrelated globular proteins:
`
`FIGURE 7-46. A space-filling model of an antiparallel /3 sheet
`from concanavilin A in side view with the interior of the protein
`(the surface of a second antiparallel fl sheet; see Fig. 7-43) to
`the right and the exterior to the left. The main chain is white,
`nonpolar side chains are brown, and polar side chains are purple.
`
`This side chain distribution is apparent in Figs. 7-42 and
`7-45, which show the surface and interior exposures of the
`amino acid side chains of myog1obin’s H helix. This ar-
`rangement is likewise seen on the covers of this textbook,
`which show the distributions of polar (front cover) and non-
`polar (back cover) residues of cytochrome c, as well as in
`Fig. 7-46, which shows one of the antiparallel ,6’ pleated
`sheets of concanavilin A.
`
`Globular Protein Cores Are Efficiently Arranged With
`Their Side Chains in Relaxed Conformations
`
`Globular proteins are quite compact; there is very little
`Space inside them so that water is largely excluded from
`their interiors. The micellelike arrangement of their side
`chains (polar groups outside, nonpolar groups inside) has
`led to their description as “oil drops with polar coats.” This
`generalization, although picturesque, lacks precision. The
`Packing density (ratio ofthe volume enclosed by the van der
`Waals envelopes ofthe atoms in a region to the total volume
`Of the region) of the internal regions of globular proteins
`averages ~0.75, which is in the same range as that ofmo1ec-
`ular crystals of small organic molecules. In comparison,
`equal-sized close-packed spheres have a packing density of
`0.-7_4, whereas organic liquids (oil drops) have packing den-
`Sltles that are mostly between 0.60 and 0.70. The interior of
`0 Protein is therefore more like a molecular crystal than an
`
`Page 33
`
`

`
`172 Chapter 7. Three-Dimensional Structures 0fProteins
`
`FIGURE 7-47. One subunit of the enzyme g1yceraldehyde-3-
`phosphate dehydrogenase from Bacillus stearothermophilus.
`The polypeptide folds into two distinct domains. The first
`domain (red, residues 1- 146) binds NAD+ (black) near the C-
`
`terminal ends of its parallel B strands, and the second domain
`(green) binds glyceraldehyde-3-phosphate (not shown). [After
`Biesecker, G., Harris, J.I., Thierry, J.C., Walker, J.E., and
`Wonacott, A., Nature 266, 331 (1977).]
`
`Page 34
`
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`
`

`
`
`
`Section 7-3. Globular Proteins
`
`173
`
`
`
`(b)
`
`(c)
`
`(a)
`
`FIGURE 7-48. Schematic diagrams of (a) a Ba/1‘ motif, (b) a B i
`hairpin motif, and (c) an ozoz motif.
`
`
`
`
`
`FIGURE 7-49. Comparisons of the backbone folding patterns
`of protein B barrels (right) with geometric motifs commonly
`used to decorate Native American and Greek weaving and
`pottery (left). (a) Native American polychrome cane basket and
`the polypeptide backbone of rubredoxin from Clostridium
`pasteurianum showing its linked B meanders. [Museum of the
`American Indian, Heye Foundation.] (b) Red figured Greek
`amphora with its Greek key border area showing Cassandra and
`Ajax (about 450 B.C.) and the polypeptide backbone of human
`prealbumin with its “Greek key” pattern. [The Metropolitan
`Museum of Art, Fletcher Fund, 1956.] (c) Early Anasazi
`redware pitcher from New Mexico and the polypeptide
`backbone of chicken muscle triose phosphate isomerase showing
`its “lightning” pattern of overlapping BozB units. This so-called
`oz/B barrel is also diagrammed in Fig. 7-19b. [Museum of the
`American Indian, Heye Foundation.] [After Richardson, J.S.,
`Nature 268, 498 (I977).]
`
`Page 35
`
`. The most common form of supersecondary structure is
`the [MB motif, in which the usually right-handed cross-
`over connection between two consecutive parallel
`strands of a B sheet consists of an or helix (Fig. 7—48a).
`
`. Another common supersecondary structure, the B hair-
`pin motif, consists of an antiparallel B sheet formed by
`sequential segments of polypeptide chain that are con-
`nected by relatively tight reverse turns (Fig. 7-48b).
`
`. In an aa motif, two successive antiparallel a helices
`pack against each other with their axes inclined so as to
`permit energetically favorable intermeshing of their
`contacting side chains (Fig. 7—48c). Such associations
`stabilize the coiled coil conformation of oz keratin (Sec-
`tion 7-2A).
`
`. Extended B sheets often roll up to form B barrels (e.g.,
`Fig. 7- 1 9b). Three different B barrel topologies (the ways
`in which the strands and their interconnections are
`
`arranged) have been named in analogy with geometric
`motifs found on Native American and Greek weaving
`and pottery (Fig. 7-49).
`
`Supersecondary structures may have functional as well as
`structural significance. A BozBozB unit, for example, in which
`the B strands form a parallel sheet with right-handed oz heli-
`cal crossover connections (two overlapping BozB units), was
`shown by Michael Rossmann to form a nucleotide-binding
`site in many enzymes. In most proteins that bind dinucleo-
`tides, two such BozBaB units combine to form a motif alter-
`natively known as a dinucleotide-binding fold or a Ross-
`mann fold (Fig. 7-50). In some cases, the second or helix in a
`BaBaB unit is replaced by a length of nonhelical polypep-
`tide. This occurs, for example, between the BE and BF
`strands ofglyceraldehyde-3-phosphate dehydrogenase (Fig.
`7-47).
`
`Page 35
`
`

`
`174 Chapter 7. Three-Dimensional Structures OfProteins
`
`FIGURE 7-50. An idealized representation of the coenzyme-
`binding domain from various dehydrogenases. This domain
`consists of two structurally similar fiozfiot/3 units, drawn here with
`one yellow and the other blue, each of which binds a nucleotide
`portion of NAD*' so as to form a dinucleotide-binding or
`
`Rossmann fold. Compare this figure with the NAD+-binding
`domain of glyceraldehyde-3-phosphate dehydrogenase (Fig. 7-
`47). [After Rossmann, M.G., Liljas, A., Branden, C.-1., and
`Banaszak, L.J., in Boyer, P.D. (Ed.), The Enzymes, Vol. 11 (3rd
`ed.), p. 68, Academic Press (1975).]
`
`4. PROTEIN STABILITY
`
`A. Electrostatic Forces
`
`Incredible as it may seem, thermodynamic measurements
`indicate that native proteins are only marginally stable enti-
`ties under physiological conditions. The free energy re-
`quired to denature them is ~0.4 kJ-mol" of amino acid
`residues so that 100-residue proteins are typically stable by
`only around 40 kJ - mol“. In contrast, the energy required
`to break a typical hydrogen bond is ~20 kJ-mol“. The
`various noncovalent
`influences to which proteins are
`subject— electrostatic interactions (both attractive and re-
`pulsive), hydrogen bonding (both intramolecular and to
`water), and hydrophobic forces— each have energetic mag-
`nitudes that may total thousands of kilojoules per mole
`over an entire protein molecule. Consequently, a protein
`structure is the result ofa delicate balance among powerful
`countervailing forces. In this section we discuss the nature
`of these forces and end by considering protein denatura-
`tion: that is, how these forces can be disrupted.
`
`Molecules are collections of electrically charged particles
`and hence, to a reasonable degree of approximation, their
`interactions are determined by the laws of classical electro-
`statics (more exact calculations require the application of
`quantum mechanics). The energy of association, U, of two
`electric charges, q, and q2, that are separated by the distance
`r, is found by integrating the expression for Coulomb’s law,
`Eq. [2. 1], to determine the work necessary to separate these
`charges by an infinite distance:
`
`_ kqlq2
`Dr
`
`U
`
`[7.l]
`
`Here k = 9.0 X 109 J - m-C‘? and D is the dielectric con-
`stant of the medium in which the charges are immersed
`
`(recall that D = 1 for a vacuum and, for the most part,
`increases with the polarity of the medium; Table 2-1). The
`dielectric constant of a molecule-sized region is difficult to
`
`Page 36
`
`Page 36
`
`

`
`estimate. For the interior of a protein, it is usually taken to
`be in the range 3 to 5 in analogy with the measured dielec-
`tric constants ofsubstances that have similar polarities such
`as benzene and diethyl ether.
`
`Ionic Interactions Are Strong but Do Not Greatly
`Stabilize Proteins
`The association of two ionic protein groups of opposite
`Charge is known as an ion pair or salt bridge. According to
`}3q_ [7 . 1 ], the energy of a typical ion pair, say the carboxyl
`group of Glu and the ammonium group of Lys, whose
`charge centers are separated by 4.0 A in a medium ofdielec-
`tric constant 4, is— 86 kJ - mol'1 (one electronic charge =
`1.60 )< 10"” C). Free ions in aqueous solution are highly
`solvated, however, so that the free energy of solvation of
`two separated ions is about equal to the free energy of for-
`mation of their unsolvated ion pairs. Ion pairs therefore
`contribute little stability towards a protein’s native struc-
`ture. This accounts for the observations that although
`~7 5% of charged residues occur in ion pairs, very few ion
`pairs are buried (unsolvated) and that ion pairs that are
`exposed to the aqueous solvent tend to be but poorly con-
`served among homologous proteins.
`
`Dipole—Dipole Interactions Are Weak but Significantly
`Stabilize Protein Structures
`
`The noncovalent associations between electrically neu-
`tral molecules, collectively known as van der Waals forces,
`arise from electrostatic interactions among permanent
`and/or induced dipoles. These forces are responsible for
`numerous interactions of varying strengths between non-
`bonded neighboring atoms. (The hydrogen bond, a special
`class of dipolar interaction, is considered separately in Sec-
`tion 7-4B.)
`Interactions among permanent dipoles are important
`structural determinants in proteins because many of their
`groups, such as the carbonyl and amide groups of the pep-
`tide backbone, have permanent dipole moments. These in-
`teractions are generally much weaker than the charge-
`charge interactions of ion pairs. Two carbonyl groups, for
`example, each with dipoles of 4.2 X l0‘3° C - m (1.3 debye
`units) that are oriented in an optimal head-to-tail arrange-
`nient (Fig. 7-51a) and separated by 5 A in a medium of
`dielectric constant 4, have a calculated attractive energy of
`Only ‘ 9.3 kJ - mol‘ ‘. Furthermore, these energies vary with
`V3 so they rapidly attenuate with distance. In or helices,
`however, the dipolar amide and carbonyl groups of the
`polypeptide backbone all point in the same direction (Fig.
`7-1 1) so that their interactions are associative and tend to be
`additive (these groups, ofcourse, also form hydrogen bonds
`but here we are concerned with their residual electric fields).
`The carbonyl groups all have their oxygen atoms pointing
`towards the C terminal end ofthe or helix, giving it a signifi-
`cant dipole moment that is positive towards the N tenni-
`nus and negative towards the C terminus. Consequently, in
`
`Section 7-4. Protein Stability 175
`
`(a)
`
`Interactions between permanent dipoles
`
`(b,) Dipole—induced dipole interactions
`
`+ j-+
`
`T.-
`
`(c) London dispersion forces
`
`+
`
`T _
`
`+
`
`FIGURE 7-51. Dipole—dipole interactions. The strength of
`each dipole is represented by the thickness of the accompanying
`arrow. (a) Interactions between permanent dipoles. These
`interactions, here represented by carbonyl groups lined up head
`to tail, may be attractive, as shown here, or repulsive, depending
`on the relative orientations of the dipoles. (b) Dipole—induced
`dipole interactions. A permanent dipole (here shown as a
`carbonyl group) induces a dipole in a nearby group (here
`represented by a methyl group) by electrostatically distorting its
`electron distribution (shading). This always results in an
`attractive interaction. (c) London dispersion forces. The
`instantaneous charge imbalance (shading) resulting from the
`motions of the electrons in a molecule (left) induce a dipole in a
`nearby group (right); that is, the motions of the electrons in
`neighboring groups are correlated. This always results in an
`attractive interaction.
`
`the low dielectric constant core of a protein, dipole—dipole
`interactions significantly influence protein folding.
`A permanent dipole also induces a dipole moment on a
`neighboring group so as to form an attractive interaction
`(Fig. 7-5 lb). Such dipole—induced dipole interactions are
`generally much weaker than are dipole—dipole interac-
`tions.
`
`Although nonpolar molecules are nearly electrically neu-
`tral, at any instant they have a small dipole moment result-
`ing from the rapid fluctuating motion of their electrons.
`This transient dipole moment polarizes the electrons in a
`
`Page 37
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`
`fl
`
`3i '
`
`1
`
`176 Chapter 7. Three-Dimensional Structures OfProteins
`
`neighboring group, thereby giving rise to a dipole moment
`(Fig. 7-51c) such that, near their van der Waals contact
`distances, the groups are attracted to one another (a quan-
`tum mechanical effect that really cannot be explained in
`terms of only classical physics). These so—called London
`dispers