TABLE 7-6. TORSION ANGLES (dz, w) FOR RESIDUES 24 T0 73 or HEN EGG WHITE
`LYSOZYME
`
`Residue
`Number
`
`Amino
`Acid
`
`dz (deg)
`
`Residue
`
`Number
`
`Amino
`
`Acid
`
`([2 (deg)
`
`I]! (deg)
`
`Problems
`
`189
`
`Source: lmoto, T., Johnson, L.N., North, A.C.T., Phillips, D.C., and Rupley, J.A., in Boyer, P.D. (Ed.), The
`Enzymes (3rd ed.), Vol. 7, pp. 693 -695, Academic Press (1972).
`
`probable identity of residue 54? (d) What is the secondary
`structure of residues 69 — 7 1? (e) What additional information
`besides the torsion angles, (I) and 1//, of each of its residues are
`required to define the three-dimensional structure of a pro-
`tein?
`
`. Hair splits most easily along its fiber axis, whereas fingernails
`tend to split across the finger rather than along it. What are the
`directions of the keratin fibrils in hair and in fingernails? Ex-
`plain your reasoning.
`
`. What structural features are responsible for the observations
`that 0: keratin fibers can stretch to over twice their normal
`
`length, whereas silk is nearly inextensible?
`
`. What is the growth rate, in turns per second, ofthe ct helices in
`a hair that is growing 15 cm -year"?
`
`. Can polyproline form a collagenlike triple helix? Explain.
`
`. As Mother Nature’s chief engineer, you have been asked to
`design a five-tum a helix that is destined to have half its cir-
`Cumference immersed in the interior ofa protein. Indicate the
`helical wheel projection of your prototype (X helix and its
`amino acid sequence (see Fig. 7-45).
`
`- B.-Aminopropionitrile is effective in reducing excessive scar
`tissue formation after an injury (although its use is contraindi-
`cated by side effects). What is the mechanism of action of this
`lathyrogen?
`
`11. Proteins have been classified as oz, B, a/B, or 0: + fl proteins
`depending on whether their tertiary structures, respectively,
`consist of mostly oz helices, mostly B sheets, alternating a
`helices and B sheets, or some 0: helices and /3 sheets that tend to
`aggregate together rather than alternate along the polypeptide
`chain. By inspection, classify the following proteins according
`to this nomenclature and, where possible, identify their super-
`secondary structures: carboxypeptidase A (Fig. 7-19a), triose
`phosphate isomerase (Fig. 7- 1 9b), myoglobin (Fig. 7-42), con-
`canavalin A (Fig. 7-43), carbonic anhydrase (Fig. 7-44), gly-
`ceraldehyde-3-phosphate dehydrogenase (Fig. 7-47), and
`prealbumin (Fig. 7-59).
`
`. The coat protein of tomato bushy stunt virus consists of 180
`chemically identical subunits, each of which is composed of
`~386 amino acid residues. The probability that a wrong
`amino acid residue will be biosynthetically incorporated in a
`polypeptide chain is 1 part in 3000 per residue. Calculate the
`average number ofcoat protein subunits that would have to be
`synthesized in order to produce a perfect viral coat. What
`would this number be if the viral coat were a single polypep-
`tide chain with the same number of residues that it actually
`has?
`
`. State the rotational symmetry of the following objects: (a) a
`starfish, (b) a square pyramid, (c) a rectangular box, and (d) a
`
`trigonal bipyramid. NPS EX. 2029
`Part 3
`CFAD v. NPS
`
`IPR2015-00990
`
`page 51
`
`Page 51
`
`NPS EX. 2029
`Part 3
`CFAD v. NPS
`IPR2015-00990
`
`

`
`
`
`190 Chapter 7. Three-Dimensional Structures OfProteins
`
`14.
`
`15.
`
`16.
`
`17.
`
`Myoglobin and the subunits of hemoglobin are polypeptides
`of similar size and structure. Compare the expected ratio of
`nonpolar to polar amino acid residues in myoglobin and in
`hemoglobin.
`Why are London dispersion forces always attractive?
`Membrane-bound proteins are generally closely associated
`with the nonpolar groups of lipid molecules (Section 1 1-3A).
`Explain how detergents affect the structural integrity of mem-
`brane bound proteins in comparison to their effects on normal
`globular proteins.
`
`Sickle-cell hemoglobin (HbS) differs from normal human
`adult hemoglobin (HbA) by a single mutational change, Glu
`B6 —> Val, which causes the HbS molecules to aggregate under
`proper conditions (Section 6-3A). Under certain conditions,
`the HbS filaments that form at body temperature disaggregate
`when the temperature is lowered to 0°C. Explain.
`
`18.
`
`19.
`
`Indicate experimental evidence that is inconsistent with the
`hypothesis that urea and guanidinium ion act to denature
`proteins by competing for their internal hydrogen bonds.
`Proteins in solution are often denatured if the solution is
`shaken violently enough to cause foaming. Indicate the mech-
`
`20.
`
`*21.
`
`*22.
`
`anism of this process. (Hint: The nonpolar groups of deter-
`gents extend into the air at air—water interfaces.)
`An oligomeric protein in a dilute buffer at pH 7 dissociates to
`its component subunits when exposed to the following agents.
`Which ofthese observations would not support the contention
`that the quaternary structure ofthe protein is stabilized exclu-
`sively by hydrophobic interactions? Explain. (a) 6M guanidi-
`nium chloride, (b) 20% ethanol, (c) 2M NaCl, (d) tempera-
`tures below 0°C, (e) 2-mercaptoethanol, (f) pH 3, and (g)
`0.01M SDS.
`
`What are the relative amounts of each isozyme formed when
`equimolar amounts ofpure heart and muscle lactate dehydro-
`genase (H4 and M,,) are hybridized?
`The SDS—polyacrylamide gel electrophoresis of a protein
`yields two bands corresponding to molecular masses of 10 and
`17 kD. After cross-linking this protein with dimethylsuberi-
`midate under sufficient dilution to eliminate intermolecular
`cross-linking, SDS—polyacrylamide gel electrophoresis of the
`product yields 12 bands with molecular masses 10, 17, 20, 27,
`30, 37, 40, 47, 54, 57, 64, and 74 kD. Assuming that dimethyl-
`suberimidate can cross-link only contacting subunits, dia-
`gram the quaternary structure of the protein.
`
`
`
`
`
`‘-:l.n.I|—...|.:uni-nun.-J-n,..>==.-_-.....
`
`'.;n-‘lg
`
`Page 52
`
`Page 52
`
`

`
`CHAPTER
`
`
`
`1
`
`Enzymatic Catalysis
`
`1. Catalytic Mechanisms
`A. Acid—Base Catalysis
`B. Covalent Catalysis
`C. Metal Ion Catalysis
`D. Electrostatic Catalysis
`E. Catalysis through Proximity and Orientation Effects
`F. Catalysis by Preferential Transition State Binding
`
`2. Lysozyme
`A. Enzyme Structure
`B. Catalytic Mechanism
`C. Testing the Phillips Mechanism
`3. Serine Proteases
`
`A. Kinetics and Catalytic Groups
`B. X-Ray Structures
`C. Catalytic Mechanism
`D. Testing the Catalytic Mechanism
`E. Zymogens
`4. Glutathione Reductase
`
`Enzymes, as we have seen, cause rate enhancements that
`are orders of magnitude greater than those of the best
`chemical catalysts. Yet, they operate under mild conditions
`and are highly specific as to the identities of both their
`substrates and their products. These catalytic properties are
`so remarkable that many nineteenth century scientists con-
`cluded that enzymes have characteristics that are not
`shared by substances of nonliving origin. To this day, there
`are few enzymes for which we understand in more than
`cursory detail how they achieve their enormous rate accel-
`erations. Nevertheless, it is now abundantly clear that the
`catalytic mechanisms employed by enzymes are identical
`
`371
`
`to those used by chemical catalysts. Enzymes are simply
`better designed.
`In this chapter we consider the nature of enzymatic catal-
`ysis. We begin by discussing the underlying principles of
`chemical catalysis as elucidated through the study of or-
`ganic reaction mechanisms. We then embark on a detailed
`examination of the catalytic mechanisms of several of the
`best characterized enzymes: lysozyme, the serine proteases,
`and glutathione reductase. Their study should lead to an
`appreciation of the intracacies of these remarkably elficient
`catalysts as well as of the experimental methods used to
`elucidate their properties.
`
`1. CATALYTIC MECHANISMS
`
`Catalysis is a process that increases the rate at which a
`reaction approaches equilibrium. Since, as we discussed in
`Section 13-1C, the rate of a reaction is a function of its free
`energy of activation (AG T ), a catalyst acts by lowering the
`height of this kinetic barrier; that is, a catalyst stabilizes the
`transition state with respect to the uncatalyzed reaction.
`There is, in most cases, nothing unique about enzymatic
`mechanisms of catalysis in comparison to nonenzymatic
`mechanisms. What apparently make enzymes such power-
`ful catalysts are two related properties: their specificity of
`substrate binding combined with their optimal arrangement
`of catalytic groups. An enzyme’s arrangement of binding
`and catalytic groups is, of course, the product of eons of
`evolution: Nature has had ample opportunity to “fine
`tune” the performances of most enzymes.
`
`Page 53
`
`Page 53
`
`

`
`372 Chapter 14. Enzymatic Catalysis
`
`The types of catalytic mechanisms that enzymes employ
`have been classified as:
`
`In aqueous solvents, the initial rate of mutarotation of(1-1)-
`glucose, as monitored by polarimetry (Section 4-2A), is ob-
`served to follow the relationship:
`
`v:
`
`_ d[a-D-glucose]
`dt
`
`= obs [oz-D-glucose]
`
`[l4. 1]
`
`where kob, is the reaction’s apparent first-order rate con-
`stant. The mutarotation rate increases with the concentra-
`
`tions of general acids and general bases; they are thought to
`catalyze mutarotation according to the mechanism:
`
`H—/ls
`H
`
`H)F\'.B—
`_/
`0L-D-Glucose
`
`H‘A
`—O{ ’{1‘H :B"
`
`J \H
`
`B-D-Glucose
`
`A /
`
`H :l-\'
`
`CH —/via‘ H - B
`_/
`
`Linear form
`
`This model is consistent with the observation that in aprotic
`solvents such as benzene, 2,3,4,6-0-tetramethyl-a-I)-glu-
`cose (a less polar benzene-soluble analog)
`
` H
`
`OCH3
`2,3,4,6-0-Tetramethy1- oi-D-glucose
`
`. Acid—base catalysis.
`
`. Covalent catalysis.
`
`Metal ion catalysis.
`
`. Electrostatic catalysis.
`
`Proximity and orientation effects.
`
`Preferential binding of the transition state complex.
`
`In this section, we examine these various phenomena. In
`doing so we shall frequently refer to the organic model
`compounds that have been used to characterize these cata-
`lytic mechanisms.
`
`A. Acid - Base Catalysis
`
`General acid catalysis is a process in which partial proton
`transfer from a Bronsted acid (a species that can donate
`protons; Section 2-2A) lowers thefree energy ofa reaction ‘s
`transition state. For example, an uncatalyzed keto—enol
`tautomerization reaction occurs quite slowly as a result of
`the high energy of its carbanionlike transition state (Fig.
`14-la). Proton donation to the oxygen atom (Fig. 14-lb),
`however, reduces the carbanion character of the transition
`state, thereby catalyzing the reaction. A reaction may also
`be stimulated by general base catalysis ifits rate is increased
`by partial proton abstraction by a Bransted base (a species
`that can combine with a proton; Fig. 14-1 c). Some reactions
`may be simultaneously subject to both processes: a con-
`certed general acid— base catalyzed reaction.
`
`Mutarotation Is Catalyzed by Acids and by Bases
`The mutarotation of glucose provides an instructive ex-
`ample of acid—base catalysis. Recall that a glucose mole-
`cule can assume either of two anomeric cyclic forms
`through the intermediacy ofits linear form (Section 10- 1 B):
`
`
`
`H
`
`OH
`
`H
`
`OH
`
`oc-D-Glucose
`[0c]]2)° = 112.2°
`
`\‘
`argon
`
`1/
`
`B-D-Glucose
`[0(,]]2)0 = 1s.7°
`
`does not undergo mutarotation. Yet, the reaction is cata-
`lyzed by the addition of phenol, a weak benzene-soluble
`acid, together with pyridine, a weak benzene-soluble base,
`according to the rate equation:
`
`v = k[phenol] [pyridine] [tetramethyl-oz-D-glucose]
`
`[l4.2]
`
`Moreover, in the presence of oz-pyridone, whose acid and
`base groups can rapidly interconvert between two tauto-
`
` H
`
`OH
`Linear form
`
`Page 54
`
`Page 54
`
`

`
`Keto
`
`R
`
`Transition state
`
`Enol
`
`R
`
`5_
`I
`1
`(a) foe» (ll:-=0
`cH2
`CH3"
`H
`H5+
`
`(b)
`
`c=o+ H"-A —> Q--—-O5-H---A_T> c—o—H + A"
`ll
`H.
`CH2
`1’.
`‘EH2
`R
`H
`1118+
`
`
`
`HQ
`
`2
`
`H—A + OH-
`
`R
`
`R
`
`(c)
`
`C=O+:B ——> cl-=0
`
`(IJH2
`H
`
`CH2
`Hm
`156+
`
`FIGURE 14-1. Mechanisms of keto—eno1 tautomerization: (a) uncatalyzed, (b) general acid
`catalyzed, and (c) general base catalyzed.
`
`meric forms and are situated so that they can simulta-
`neously catalyze mutarotation,
`
`on-Pyridone / \
`H/1:‘ Q.)
`jg
`
`H
`
`/C\
`Glucose
`
`/ \
`4/ (Cl)
`TO)
`
`the reaction follows the rate law
`
`v = k’[oz-pyridone][tetramethyl-oz-D-glucose]
`
`[l4.3]
`
`where k’ = 7000M X k. This increased rate constant indi-
`
`cates that at-pyridone does, in fact, catalyze mutarotation in
`a concerted fashion since 1M a-pyridone has the same cata-
`
`
`
`lytic effect as impossibly high concentrations of phenol and
`pyridine (e.g., 70M phenol and 100M pyridine).
`Many types of biochemically significant reactions are
`susceptible to acid and/or base catalysis. These include the
`hydrolysis ofpeptides and esters, the reactions ofphosphate
`groups, tautomerizations, and additions to carbonyl groups.
`The side chains of the amino acid residues Asp, Glu, His,
`Cys, Tyr, and Lys have pK’s in or near the physiologicalpH
`range (Table 4-1) which, we shall see, permits them to act in
`the enzymatic capacity ofgeneral acid and/or base catalysts
`in analogy with known organic mechanisms. Indeed, the
`ability ofenzymes to arrange several catalytic groups about
`their substrates makes concerted acid- base catalysis a
`common enzymatic mechanism.
`
`The RNase A Reaction Incorporates General Acid—Base
`Catalysis
`Bovine pancreatic ribonuclease A (RNase A) provides an
`illuminating example of enzymatically mediated general
`acid—base catalysis. This digestive enzyme functions to hy-
`drolyze RNA to its component nucleotides. The isolation
`of 2’,3’-cyclic nucleotides from RNase A digests of RNA
`
`Page 55
`
`Page 55
`
`

`
`
`
`FIGURE 14-2. The pH dependence of V(m /K,1, in the RNase
`A-catalyzed hydrolysis of cytidine-2’,3’-cyclic phosphate where
`Vfm /Kj, is given in units of M"s“. Analysis of this curve
`(Section 13-4) suggests the catalytic participation of groups with
`pK’s of 5.4 and 6.4. [After del Rosario, E.J. and Hammes, G.G.,
`Biochemistry 8, 1887 (1969).]
`
`in Fig. 8-2). Evidently, the RNase A reaction is a two-step
`process (Fig. 14-3):
`
`1. His 12, acting as a general base, abstracts a proton from
`an RNA 2’-OH group, thereby promoting its nucleo-
`philic attack on the adjacent phosphorus atom while His
`119, acting as a general acid, promotes bond scission by
`protonating the leaving group.
`
`2. The 2’,3’-cyclic intermediate is hydrolyzed through
`what is essentially the reverse of the first step in which
`water replaces the leaving group. Thus His 12 acts as a
`general acid and His 119 as a general base to yield the
`hydrolyzed RNA and the enzyme in its original state.
`
`B. Covalent Catalysis
`
`Covalent catalysis involves rate acceleration through the
`transient formation of a catalyst—substrate covalent bond.
`The decarboxylation of acetoacetate, as chemically cata-
`lyzed by primary amines, is an example of such a process
`(Fig. 14-4). In the first stage of this reaction, the amine
`nucleophilically attacks the carbonyl group of acetoacetate
`to form a Schifl‘ base (imine bond).
`
`374 Chapter 14. Enzymatic Catalysis
`
`indicates that the enzyme mediates the following reaction
`sequence:
`
`
`
`0i
`
`-0 — II’ = 0
`0
`!
`
`(I)
`-0 —l“°—O-—CH2
`0
`H
`
`H
`
`0
`
`Base
`
`H
`
`H
`
`1)‘?/ft)
`-0" wt)
`
`2',3'-Cyclic nucleotide
`
`H20
`H+
`
`
`
`The RNase A reaction exhibits a pH rate profile that peaks
`near pH 6 (Fig. 14-2). Analysis of this curve (Section 13-4),
`together with chemical derivatization and X-ray studies,
`indicates that RNase A has two essential His residues, His
`12 and His 1 19, which act in a concerted manner as general
`acid and base catalysts (the structure ofRNase A is sketched
`
`H
`
`H
`H
`+ \(‘=O —‘—lE1"—é-Gin —“*—IL'+— r‘;
`—N‘’
`"\r--19" V "
`I
`E H \ +
`E‘
`{V
`Schiff
`:13
`H—A
`base
`
`I‘:
`
`H
`
`Page 56
`
`Page 56
`
`

`
`Section 14- 1. Catalytic Mechanisms 375
`
`The protonated nitrogen atom ofthe covalent intermediate
`then acts as an electron sink (Fig. 14-4, bottom) so as to
`reduce the otherwise high-energy enolate character of the
`transition state. The formation and decomposition of the
`Schifi" base occurs quite rapidly so that it is not rate deter-
`mining in this reaction sequence.
`
`Covalent Catalysis Has Both Nucelophilic and
`Electrophilic Stages
`As the preceding example indicates, covalent catalysis
`may be conceptually decomposed into three stages:
`
`1. The nucleophilic reaction between the catalyst and the
`substrate to form a covalent bond.
`
`2. The withdrawal of electrons from the reaction center by
`the now electrophilic catalyst.
`
`3. The elimination of the catalyst, a reaction that is essen-
`tially the reverse of stage 1.
`
`Reaction mechanisms are somewhat arbitrarily classified as
`occurring with either nucleophilic catalysis, or electrophilic
`catalysis depending on which of these effects provides the
`greater driving force for the reaction, that is, which cata-
`lyzes its rate-detennining step. The primary amine-cata-
`lyzed decarboxylation of acetoacetate is clearly an electro-
`philically catalyzed reaction since its nucleophilic phase,
`Schiff base formation, is not its rate-determining step. In
`other covalently catalyzed reactions, however, the nucleo-
`philic phase may be rate determining.
`The nucleophilicity of a substance is closely related to its
`basicity. Indeed, the mechanism of nucleophilic catalysis
`resembles that of general base catalysis except that, instead
`of abstracting a proton from the substrate, the catalyst nu-
`cleophilically attacks it so as to fonn a covalent bond. Con-
`sequently, if covalent bond formation is the rate-determin-
`ing step of a covalently catalyzed reaction, the reaction rate
`tends to increase with the covalent catalyst’s basicity (pK).
`An important aspect of covalent catalysis is that the more
`stable the covalent bond formed, the less facilely it will
`decompose in the final steps of a reaction. A good covalent
`catalyst must therefore combine the seemingly contradic-
`tory properties of high nucleophilicity and the ability to
`form a good leaving group, that is, to easily reverse the bond
`formation step. Groups with high polarizabilities (highly
`mobile electrons), such as imidazole and thiol functions,
`have these properties and hence make good covalent cata-
`lysts.
`
`Certain Amino Acid Side Chains and Coenzymes Can
`Serve as Covalent Catalysts
`Enzymes commonly employ covalent catalytic mecha-
`nisms as is indicated by the large variety of covalently
`linked enzyme— substrate reaction intermediates that have
`been isolated. For example, the enzymatic decarboxylation
`ofacetoacetate proceeds, much as described above, through
`Schifl base formation with an enzyme Lys residue’s
`
`Page 57
`
`
`
`FIGURE 14-3. The bovine pancreatic RNase A-catalyzed
`hydrolysis of RNA is a two-step process with the intermediate
`formation of a 2’,3’-cyclic nucleotide.
`
`Page 57
`
`

`
`376 Chapter 14. Enzymatic Catalysis
`
`FIGURE 14-4. The uncatalyzed reaction
`mechanism for the decarboxylation of
`acetoacetate (top) and the reaction
`mechanism as catalyzed by primary amines
`(bottom).
`
`0 l
`
`l
`CH3— c— CH3
`
`Acetone
`
`1
`(.03
`
`C O-
`/‘v
`I
`CH3— c= CH2
`
`Enolate
`
`+
`
`H
`I
`
`RNH,
`
`R
`
`II
`
`+
`
`2
`
`I
`
`i
`
`C?‘
`CH3— c =k-EH2
`
`L.
`
`CH3—C—CH3
`
`/0
`“if
`/"'—"'\
`[
`GIL — {‘. — C1-l'.-.-- (I
`.5
`-
`\,10
`
`Acetoacetate
`
`R N I I .3
`
`on "
`
`|.-
`
`,1:
`N.
`ll
`/
`cH_.,—c—”cii._.\—c
`
`o
`
`’1o
`
`I \
`
`chapters in conjunction with discussions of specific enzyme
`mechanisms.
`
`Metal Ions Promote Catalysis through Charge
`Stabilization
`
`In many metal ion—catalyzed reactions, the metal ion
`acts in much the same way as a proton to neutralize nega-
`tive charge, that is, it acts as a Lewis acid. Yet, metal ions are
`often much more eflective catalysts than protons because
`metal ions can be present in high concentrations at neutral
`pH ‘s and can have charges > + I . Metal ions have therefore
`been dubbed “superacids.”
`The decarboxylation of dimethyloxaloacetate, as cata-
`lyzed by metal ions such as Cu“ and Ni“ , is a nonenzyma-
`tic example of catalysis by a metal ion:
`
`'Ml1+
`
`—o'
`0 CH 0
`\C <7 é 3//
`//
`KW v'\
`0
`CH3 0-
`
`Dimethyloxaloacetate
`
`Schiff base
`
`oz-amino group. The covalent intermediate, in this case, has
`been isolated through NaBH4 reduction ofits imine bond to
`an amine, thereby irreversibly inhibiting the enzyme. Other
`enzyme functional groups that participate in covalent ca-
`talysis include the imidazole moiety of His, the thiol group
`of Cys, the carboxyl function of Asp, and the hydroxyl
`group of Ser. In addition, several coenzymes, most notably
`thiamine pyrophosphate (Section 16-3B) and pyridoxal
`phosphate (Section 24-IA), function in association with
`their apoenzymes mainly as covalent catalysts.
`
`C. Metal Ion Catalysis
`
`Nearly one third ofall known enzymes require the presence
`of metal ions for catalytic activity. There are two classes of
`metal ion-requiring enzymes that are distinguished by the
`strengths of their ion — protein interactions:
`
`1. Metalloenzymes contain tightly bound metal ions, most
`commonly transition metal ions such as Fe“, Fe”,
`Cu“, Zn“, Mn“ or C0”.
`
`2. Metal-activated enzymes loosely bind metal ions from
`solution, usually the alkali and alkaline earth metal ions
`Na+, K+, Mg“ , or Ca“.
`
`Metal ions participate in the catalytic process in three
`major ways:
`
`1 . By binding to substrates so as to orient them properly for
`reaction.
`
`2. By mediating oxidation—reduction reactions through
`reversible changes in the metal ion’s oxidation state.
`
`3. By electrostatically stabilizing or shielding negative
`charges.
`
`In this section we shall be mainly concerned with the
`third aspect of metal ion catalysis. The other forms of en-
`zyme-mediated metal ion catalysis are considered in later
`
`co,
`
`CH
`
`3
`
`CH3
`
`_
`
`MIl+
`
`-o
`
`'o
`
`\c C/:50/I
`
`//
`0
`
`U \
`
`H+
`
`CH3
`
`0
`"0
`/
`ll
`\
`c— c — OH
`//
`\
`0
`
`CH3
`
`+ M~+
`
`Page 58
`
`Page 58
`
`

`
`
`
`Section 14- 1. Catalytic Mechanisms 377
`
`in a process facilitated through general base catalysis
`most probably by His 64 (Fig. 14-5). Although His 64 is
`too far away from the Zn“-bound water to directly re-
`move its proton, these entities are linked by two inter-
`vening water molecules to form a hydrogen bonded net-
`work that is thought to act as a proton shuttle.
`
`2. The resulting Zn“-bound OH‘ nucleophilically attacks
`the nearby enzymatically bound CO2, thereby convert-
`ing it to HCO§.
`
`Im
`|
`Im—z|n4+~-<|,~
`Im ll
`
`O
`||
`(If
`(0
`
`+
`
`P“
`Im—Zn2'+'
`|
`Im
`
`0//
`C
`\
`
`0‘
`
`0
`|
`I-I
`
`Wk H20
`
`Im
`0
`I
`,+
`//
`Im—Z|n—(‘)“ + H+ + H " O "C\
`Im H
`
`0-
`
`Im = imidazole
`
`3. The catalytic site is then regenerated by the binding and
`ionization of another H20 to the Zn“, possibly before
`the departure of the HCO; ion, so as to transiently form
`a 5-coordinated Zn“ complex.
`
`Metal Ions Promote Reactions through Charge Shielding
`Another important enzymatic function of metal ions is
`charge shielding. For example, the actual substrates of ki-
`nases (phosphoryl-transfer enzymes utilizing ATP) are
`Mg2+—ATP complexes such as
`
`\l:_'_{
`
`Adenine
`
`Ribose
`
`if
`0 fl’
`O
`
`O
`
`if
`fl’
`O
`
`O
`
`(I)-
`E O’
`0
`
`rather than just ATP. Here, the Mg“ ion’s role, in addition
`to its orienting effect, is to shield electrostatically the nega-
`tive charges of the phosphate groups. Otherwise,
`these
`charges would tend to repel the electron pairs of attacking
`nucleophiles, especially those with anionic character.
`
`D. Electrostatic Catalysis
`
`The binding of substrate generally excludes water from an
`enzyme’s active site. The local dielectric constant of the
`active site therefore resembles that in an organic solvent,
`where electrostatic interactions are much stronger than
`
`Page 59
`
`Here the metal ion (M"+), which is chelated by the dimethy-
`loxaloacetate, electrostatically stabilizes the developing en-
`olate ion of the transition state. This mechanism is sup-
`ported by the observation that acetoacetate, which cannot
`form such a chelate, is not subject to metal ion—catalyzed
`decarboxylation. Most enzymes that decarboxylate oxalo-
`acetate require a metal ion for activity.
`
`Metal Ions Promote Nucleophilic Catalysis via Water
`Ionization
`
`A metal ion ‘s charge makes its bound water molecules
`more acidic than free H20 and therefore a source of OH‘
`ions even below neutral pH ‘s. For example, the water mole-
`cule of (NH3)5Co3+(H2O) ionizes according to the reaction:
`
`(NH3)5Co3+(H2O) :‘ (NH3)5Co3+(OH‘) + H’“
`
`with a pK of 6.6, which is some 9 pH units below the pK of
`free H2O. The resulting metal ion — bound hydroxyl group is
`a potent nucleophile.
`An excellent example of this phenomenon occurs in the
`catalytic mechanism of carbonic anhydrase (Section 9- 1 C),
`a widely occurring enzyme that catalyzes the reaction:
`
`C0, + H20 : Hco; + H+
`
`Carbonic anhydrase contains an essential Zn“ ion that is
`implicated in the enzyme’s catalytic mechanism as follows:
`
`1. The crystal structure of human carbonic anhydrase (Fig.
`7-44) reveals that its Zn“ lies at the bottom of a 15-A-
`deep active site cleft, where it is tetrahedrally coordi-
`nated by three evolutionarily invariant His side chains
`and a H20 molecule. This Zn“-polarized H20 ionizes
`
`
`
`
`
`Glu 106
`
`GIU 117
`
`FIGURE 14-5. The active site of human carbonic anhydrase.
`The light grey ligand to the Zn“ indicates the probable fifth
`211“ coordination site. The arrow points towards the opening of
`the active site cavity. [After Sheridan, R. P. and Allen, L. C.,
`1- Am. Chem. Soc. 103, 1545 (1981).]
`
`Page 59
`
`

`
`Here k}, the pseudo-first-order rate constant, is 0.0018 s“‘
`when [imidazole] = 1M (d) = phenyl). However, for the
`intramolecular reaction
`
`3?
`C—t': ~ ¢N0._,
`
`N:
`
`l
`./_
`‘QR; _,.N‘l-l
`
`k2
`—?>
`
`‘H’
`C
`\
`N1;
`W
`:1’
`\\_/N1-I
`
`.
`+ IJr-
`
`,
`£L‘iVL|._.
`
`the first-order rate constant k, = 0.043 s”‘.; that is, k2 =
`24 kg. Thus, when the 1M imidazole catalyst is covalently
`attached to the reactant, it is 24-fold more efl‘ective than
`when it is free in solution; that is, the imidazole group in the
`intramolecular reaction behaves as if its concentration is
`24M. This rate enhancement has contributions from both
`
`proximity and orientation.
`
`Proximity Alone Contributes Relatively Little to Catalysis
`Let us make a rough calculation as to how the rate of a
`reaction is affected purely by the proximity of its reacting
`groups. Following Daniel Koshland’s treatment, we shall
`make several reasonable assumptions:
`
`1. Reactant species, that is, functional groups, are about
`the size of water molecules.
`
`2. Each reactant species in solution has 12 nearest-neigh-
`bor molecules, as do packed spheres of identical size.
`
`3. Chemical reactions occur only between reactants that
`are in contact.
`
`4. The reactant concentration in solution is low enough so
`that the probability of any reactant species being in si-
`multaneous contact with more than one other reactant
`
`molecule is negligible.
`
`Then the reaction:
`
`A + B “—'> A—B
`
`obeys the second-order rate equation
`
`_ d[A—B]
`_
`dt
`
`v
`
`=
`
`= k2[A9B]pairs
`
`where [A,B],,,,,-,3 is the concentration of contacting mole-
`cules of A and B. The value of this quantity is
`
`[A9B]pairs
`
`_ 12[A][B]
`‘ 55.5M
`
`[
`
`since there are 12 ways that A can be in contact with B, and
`[A]/55.5M is the fraction of sites occupied by A in water
`solution ([H2O] = $5.5M in dilute aqueous solutions) and
`hence the probability that a molecule of B will be next to
`one of A. Combining Eqs. [14.5] and [l4.6] yields
`
`v = k.(%§)[A,B1,,..»,. = 4.6k.[A,B1,..,.
`
`£14.71
`
`Page 60
`
`378 Chapter 14. Enzymatic Catalysis
`
`they are in aqueous solutions (Section 7-4A). The charge
`distribution in a medium of low dielectric constant can
`greatly influence chemical reactivity. Thus, as we have
`seen, the pK’s of amino acid side chains in proteins may
`vary by several units from their nominal values (Table 4-1)
`because of the proximity of charged groups.
`Although experimental evidence and theoretical analy-
`ses on the subject are still sparse, there are mounting indica-
`tions that the charge distributions about the active sites of
`enzymes are arranged so as to stabilize the transition states
`of the catalyzed reactions. Such a mode of rate enhance-
`ment, which resembles the form of metal ion catalysis dis-
`cussed above, is termed electrostatic catalysis. Moreover,
`in several enzymes, these charge distributions apparently
`serve to guide polar substrates towards their binding sites so
`that the rates ofthese enzymatic reactions are greater than
`their apparent diflusion-controlled limits (Section I3-2B).
`
`E. Catalysis through Proximity and
`Orientation Eflects
`
`Although enzymes employ catalytic mechanisms that re-
`semble those of organic model reactions, they are far more
`catalytically eflicient than these models. Such efliciency
`must arise from the specific physical conditions at enzyme
`catalytic sites that promote the corresponding chemical re-
`actions. The most obvious efl'ects are proximity and orien-
`tation: Reactants must come together with theproper spatial
`relationship for a reaction to occur. For example, in the
`bimolecular reaction of imidazole with p-nitropheny1ace-
`tate,
`
`.'-!|J',
`
`Un
`
`CH;}T(1
`
`/1
`ll‘
`(' p-Nitrophenylacetate
`
`-"~'..
`
`.
`1r
`\\
`‘— H
`[midazole
`
`CH3\C +
`N
`
`II
`
`5:
`
`N--.
`
`V+E
`
`-—- NH
`
`p-Nitrophenolate
`
`N-Acetylimidazolium
`
`the progress of the reaction is conveniently monitored by
`the appearance ofthe intensely yellowp-nitrophenolate ion:
`
`61 [I7-N02¢0']
`dt
`
`= k,[imidazole][p-NO2d>Ac]
`= k{[p-NO2d>Ac]
`
`[l4.4]
`
`Page 60
`
`

`
`‘T
`
`
`
`Section 14 — I . Catalytic Mechanisms 379
`
`Thus, in the absence of other effects, this model predicts
`that for the intramolecular reaction,
`
`TABLE 14-1. RELATIVE RATES OF ANIIYDRIDE
`FORMATION FOR ESTERS POsEssING DIFFERENT DEGREES
`OF MOTIONAL FREEDOM IN THE REACTION:
`
`I3 2
`A 13::-A B
`
`1;:
`
`k2 = 4.6k, , which is a rather small rate enhancement. Fac-
`tors that will increase this value other than proximity alone
`clearly must be considered.
`
`Arresting Reactants’ Relative Motions and Properly
`Orienting Them Can Result in Large Catalytic Rate
`Enhancements
`
`The foregoing theory is, of course, quite simple. For ex-
`ample, it does not take into account the motions of the
`reacting groups with respect to one another. Yet, in the
`transition state complex, the reacting groups have little rel-
`ative motion. In fact, as Thomas Bruice demonstrated, the
`rates of intramolecular reactions are greatly increased by
`arresting a molecule’s internal motions (Table 14-1). Thus,
`when an enzyme brings two molecules together in a bimo-
`lecular reaction, as William Jencks pointed out, not only
`does it increase their proximity, but it freezes out their rela-
`tive translational and rotational motions (decreases their
`entropy), thereby enhancing their reactivity. Table 14-1 in-
`dicates that such rate enhancements can be enormous.
`
`Another efl"ect that we have neglected in our treatment of
`proximity is that of orientation. Molecules are not equally
`reactive in all directions as Koshland’s simple theory as-
`sumes. Rather, they react most readily only ifthey have the
`proper relative orientation (Fig. 14-6). For example, in an
`SN2 (bimolecular nucleophilic substitution) reaction, the
`incoming nucleophile optimally attacks its target along the
`direction opposite to that of the bond to the leaving group
`(backside attack). The approaches of reacting atoms along a
`trajectory that deviates by as little as 10 ° from this optimum
`direction results in a significantly reduced reactivity. It has
`been estimated that properly orientating substrates can in-
`crease reaction rates by a factor of up to ~100. In a re-
`lated phenomenon, a molecule may be maximally reactive
`only when it assumes a conformation that aligns its various
`orbitals in a way that minimizes the electronic energy of
`
`
`
`Productive
`
`Unproductive
`
`FIGURE 14-6. Molecules are susceptible to chemical attack
`over only limited regions of their surfaces (represented by the
`colored areas). Without the proper relative orientation (left),
`reactions do not occur (right).
`
`0
`ll
`R,—C--O
`
`R —C—O“
`2
`ll
`O
`
`Br
`
`0
`
`/
`R,—C\
`
`R -—
`2
`
`\0
`
`Reactants"
`
`Relative Rate Constant
`
`CH3COO<t>Br
`+
`
`CH3COO“
`COO¢>Br
`
`:§
`
`s-E
`
`0
`
`CO0‘
`
`C00:;llBr
`
`C00"
`
`COO</>Br
`
`CO0’
`
`1.0
`
`~1 X 103
`
`~2.2 X 10-‘
`
`~5 X 107
`
`" Curved arrows indicate rotational degrees of freedom.
`Source: Bruice, T.C., Annu. Rev. Biochem. 45, 353 (1976).
`
`its transition state, an elfect
`assistance.
`
`termed stereoelectronic
`
`Enzymes, as we shall see in Sections 14-2 and 14-3, bind
`substrates in a manner that both immobilizes them and
`
`aligns them so as to optimize their reactivities. The free
`energy required to do so is derivedfrom the specific binding
`energy ofsubstrate to enzyme.
`
`F. Catalysis by Preferential Transition State
`Binding
`
`The rate enhancements effected by enzymes are often
`greater than can be reasonably accounted for by the cata-
`lytic mechanisms so far discussed. However, we have not
`yet considered one of the most important mechanisms of
`enzymatic catalysis: The binding ofthe transition state to an
`enzyme with greater aflinity than the corresponding sub-
`strates or products. When taken together with the previ-
`ously described catalytic mechanisms, preferential transi-
`tion state binding rationalizes the observed rates of
`enzymatic reactions.
`The original concept of transition stat