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`SYNGENTA EXHIBIT 1014SYNGENTA EXHIBIT 1014
`
`
`
`Syngenta v. FMC, PGR2020-00028Syngenta v. FMC, PGR2020-00028
`
`SYNGENTA EXHIBIT 1014
`Syngenta v. FMC, PGR2020-00028
`
`

`

`Cover art redrawn after D. Matthews, R. Alden, J. Bolin,
`S. Freer, R. Hamlin, N. Xuong, J. Kraut, M. Poe, M. Williams,
`and K. Hoogsteen, 1977, Science 197:452. Copyright © 1977 by
`the American Association for the Advancement of Science.
`
`Sponsoring Editor: Arthur C. Bartlett
`Manuscript Editor: Lawrence W. McCombs
`Designer: Robert Ishi
`Production Coordinator: Linda Jupiter
`fllustration Coordinator: Batyah Janowski
`Artist: Eric G. Hieber, EH Technical Services
`Compositor: The Universities Press Limited
`Printer and Binder: The Maple-Vail Book Manufacturing Group
`
`Library of Congress Cataloging in Publication Data
`
`Walsh, Christopher.
`Enzymatic reaction mechanisms.
`
`Bibliography: p.
`Includes index.
`1. Enzymes.
`QP601.W23
`ISBN 0-7167-0070-0
`
`I.
`
`Title.
`574.1'925
`
`78-18266
`
`Copyright © 1979 by W. H. Freeman and Company
`
`No part of this book may be reproduced by any mechanical,
`photographic, or electronic process, or in the form of
`a phonographic recording, nor may it be stored in a retrieval
`system, transmitted, or otherwise copied for public or
`private use, without the written permission of the publisher.
`
`Printed in the United States of America
`
`9 8 7 6 5 4 3 2
`
`

`

`Chapter 2
`
`Introductory Remarks About Enzymes and
`Enzymatic Catalysis
`
`2.A ENZYMES AND CATALYSIS
`All enzymes are proteins, but the converse is not true.* Enzymes are the one
`subset of proteins with catalytic activity-a concept established when Sumner
`(1926) isolated the enzyme urease (which hydrolyzes urea to CO2 and NH3 ) from
`jack-bean meal, crystallized it, and validated its protein nature. Proteins are large,
`linear, condensed biopolymers of a:-amino acids as monomeric units. The com(cid:173)
`mon structural linkage is the amide or peptide bond between amino group of one
`monomer and carboxyl group of another.
`
`R'
`0
`I
`II H
`H
`R-C-C-N-C-C008
`I
`H
`NHf
`peptide bond
`
`a
`H
`R-C-C008
`I
`NHf
`a -amino acid
`
`a
`H
`HC-C008
`I
`NHf
`glycine
`
`There are about 20 a:-amino acids that are the common building blocks of
`proteins. All of them except glycine have at least one asymmetric carbon (the
`a-carbon) and are thus optically active. There are enantiomeric D- and L-pairs
`(R,S-pairs in the nomenclature proposed by Cahn, Ingold, and Prelog, 1956,
`1966). Only the L-amino acids are activated enzymatically and incorporated into
`proteins (although n-isomers are observed
`in some low-molecular-weight
`polypeptide antibiotics and in bacterial cell walls).
`
`* It is recommended that readers without a recent perusal of protein chemistry read the relevant
`chapters in a general biochemistry textbook (such as those listed at the beginning of the References
`section) as an adjunct to these few comments.
`
`1'hus enzymes, ,
`reagents-unlik
`note, this is the
`For backgr
`tions (such as t
`1970).
`
`2.B AMINO-A
`
`Table 2-1 lists
`relevant pKa va
`10.0; those of
`physiological pl(cid:173)
`be represented
`
`Table 2-1
`Amino-acid struc1
`
`Acidic
`
`{3
`H H
`e
`OOC-C-C-C<
`I
`H
`~H3
`
`PK.= 3.8
`
`aspartate (Asp)
`
`{3 a
`'Y
`H H H
`e
`OOC-C-C-C(cid:173)
`I
`H H
`PK. = 4.2
`NI
`glutamate (Glu)
`
`

`

`El)
`
`coo0
`I
`H3 N-C-H
`I
`CH 3
`L-isomer of alanine (Fischer projection)
`
`25
`
`:ymes and
`
`i.- Enzymes are the one
`:ablished when Sumner
`L to CO2 and NH3) from
`1ture. Proteins are large,
`omeric units. The com(cid:173)
`een amino group of one
`
`a
`H
`HC-C008
`I
`NHf
`glycine
`
`non building blocks of
`asymmetric carbon (the
`1tiomeric D- and L-pairs
`5old, and Prelog, 1956,
`ly and incorporated into
`e
`low-molecular-weight
`
`cin chemistry read the relevant
`1e beginning of the References
`
`Thus enzymes, composed only of L-amino-acid residues, are asymmetric or chiral
`reagents-unlike most synthetic chemical reagents, which are achiral. As we shall
`note, this is the key to several features of enzymatic stereospecificity.
`For background information on stereochemistry and structural representa(cid:173)
`tions (such as the Fischer projection), see Alworth (1972) and Bentley (1969-
`1970).
`
`2.B AMINO-ACID STRUCTURES AND FUNCTIONAL GROUPS
`
`Table 2-1 lists the structures of the 20 common amino acids, along with some
`relevant pKa values. The pKa values of the o:-amino group range from 8.8 to
`10.0; those of the o:-COOH group range from 1.8 to 2.3. Thus, at neutral
`physiological pH values, o:-amino acids are dipolar, zwitterionic species and will
`be represented this way throughout the text (see top of p. 27).
`
`Table 2-1
`Amino-acid structures
`
`Acidic
`
`Basic
`
`Free amino acids
`
`(3
`H H
`8 00C-C-C-C008
`I
`H
`pKa = 3.8
`~H3
`aspartate (Asp)
`
`EB H H H H H
`H3 N-C-C-C-C-C-C008
`I
`H H H H
`pKa = 10.5
`~H3
`lysine (Lys)
`
`a-COOH: pK. = 1.8-2.3
`a-NHf: pKa = 8.8-10.0
`
`0
`
`/3 a
`'Y
`H H H
`OOC-C-C-C-C008
`H H I
`NH3
`pKa = 4.2
`glutamate (Glu)
`
`NH
`EBl
`2 HHHH
`H2 N=C-N-C-C-C-C-C008
`I
`H H H H
`pKa = 12.5
`~H3
`arginine (Arg)
`
`H H
`EB ;~-=\-s-?-CQQ0
`HNVNH
`~H3
`pKa = 6
`histidine (His)
`
`

`

`Table 2-1
`
`(continued)
`
`_________ Am_1_·d_es ____ ___________ __ s_e_c_on_d_a_rY __ i
`
`0
`II H H H
`H2N-C-C-C-C-C008
`I
`H H
`~H3
`
`asparagine (Asn)
`
`glutamine (Glu)
`
`proline (Pro)
`
`Aliphatic (hydrophilic)
`
`Aliphatic (hydrophobic)
`
`H
`HC-C008
`I
`~H3
`
`glycine (Gly)
`
`H
`H C-C-C008
`I
`a
`~H3
`
`alanine (Ala)
`
`HC
`3
`"--H H
`C-C-C008
`/
`I
`H3 C
`~H3
`
`HC
`3 "--H H H
`C-C-C-C008
`I
`/
`H
`H3C
`~H3
`
`valine (Val)
`
`Jeucine (Leu)
`
`H
`H3C-C
`H"--H H
`C-C-C008
`/
`I
`H3C
`~H3
`
`isoleucine (Ile)
`
`Aromatic
`
`Polar
`
`0-H H
`
`-
`
`C-C-C008
`I
`H
`NH
`EB
`
`3
`
`phenylalanine (Phe)
`
`H H
`HO-C-C-C008
`I
`H
`NH3
`EB
`
`K
`p a
`
`14
`serine (Ser)
`
`H("\__/\ ~-~-cooe
`~~H I
`~H3
`
`pK. = 10.1
`tyrosine (Tyr)
`
`H H
`HS-C-C-C008
`I
`H
`~H3
`
`pK. = 8
`cysteine (Cys)
`
`threonine (Thr)
`
`H H H
`H3C-S-C-C-C-C008
`I
`H H
`~H3
`
`methionine (Met)
`
`The side <
`enzymatic
`for the -y(cid:173)
`range inh
`nucleophil
`ff). Theim
`free base J
`amine) ca
`thiolate m
`and the fr
`Protei
`weights ra
`phosphata
`Given an
`chains tht
`enzyme c
`oligomeric
`Presumabl
`attainmen(cid:173)
`three-dim(
`the exact
`
`to specific
`KEl'>, NaEl'>,
`selenium :
`1971). Otl
`'•'·"'·'·'··'" coenzymei
`to form r
`
`Co-c-c-coo0
`
`H H
`I
`~H3
`
`N
`H
`tryptophan (Trp)
`
`H
`
`EB
`NH3
`I
`H
`S-C-C-C008
`
`I H H
`
`H H
`S-C-C-C008
`I
`H
`~H3
`
`cystine (Cys-S-S-Cys)
`
`

`

`Secondary
`
`proline (Pro)
`
`1ic)
`
`H H H
`C-C-C-C008
`I
`H
`~H3
`
`:eucine (Leu)
`
`:oo0
`
`OH
`I H
`:-C-C-C008
`I
`H
`~H3
`
`hreonine (Thr)
`
`H H H
`:-S-C-C-C-C008
`I
`H H
`~H3
`
`methionine (Met)
`
`:::ys)
`
`21
`
`H
`I
`R-C-C008
`I
`NH3
`EB
`
`The side chains of the amino acids provide the important functional groups for
`enzymatic catalysis. The pKa values of 3.8 for the (3-carboxyl of aspartate and 4.2
`for the y-carboxyl of glutamate imply that these are ionized in the neutral pH
`range inhabited by most proteins and thus can function as either basic or
`nucleophilic catalytic groups in catalysis (Jencks, 1969, p. 67 ff; Gray, 1971, p. 19
`ff). The imidazole group of histidine has a pKa of 6, so a high concentration of the
`free base form (a relatively good, unhindered nucleophile despite being a tertiary
`amine) can exist at neutral pH. Also of importance catalytically will be the
`thiolate anion of cysteine (pKa = 8), the phenoxide form of tyrosine (pKa = 10),
`and the free base form of the a-amino group of lysine (pKa = 10.5).
`Proteins with enzymatic activity are macromolecular catalysts, with molecular
`weights ranging from polypeptide chains of about 9,000 molecular weight for acyl
`phosphatase from brain to 155, 000 mol wt for the (3-subnit of RNA polymerase.
`Given an average molecular weight for an amino acid of ca. 150, polypeptide
`chains thus can range from 60 to about 1,000 amino-acid residues long. An
`enzyme can be composed of several polypeptides (each a subunit) to form
`oligomeric complexes of up to 5 or 6 x 106 mol wt units (Reed and Cox, 1970).
`Presumably the enormous size of these biological catalysts is related to the
`attainment of sufficient local-controlled flexibility on the one hand and precise
`three-dimensional arrangement of amino-acid side chains on the other to provide
`the exact spatial array needed to promote efficient and specific catalysis when a
`substrate molecule (as large as another protein or as small as carbon dioxide)
`binds to the active site. Some enzymes require metal cations, which will be bound
`to specific oxygen, nitrogen, or sulfur ligands of the protein. These metals include
`\ NaEB, CuEB, Mg2EB, Zn2EB, Ca2EB, Ni2EB, Fe2EB, Fe3 EB, Co3EB, Mo6EB, and inorganic
`KE1
`selenium and sulfur (Coleman, 1971; Bender, 1971; Mildvan, 1974; Eichhorn,
`1971). Other enzymes depend totally for activity on low-molecular-weight organic
`coenzymes that may either bind in dynamic equilibrium or be bound so tightly as
`to form nondissociable, stoichiometric holoenzyme complexes. Some enzymes
`require lipid bound noncovalently or covalently; others are glycoproteins.
`The in vivo milieu of an enzyme is a heterogeneous intracellular (or extracel(cid:173)
`lular) enviroment; but, for the study of catalytic mechanism, enzymes have been
`purified-often to a state of physical homogeneity to ensure that observed
`reactions depend only on the single enzyme under study. The advantages of a
`pure protein for studying catalysis are mitigated by the sometimes herculean
`
`

`

`28
`
`INTRODUCTIORY REMARKS ABOUT ENZYMES AND ENXYMATIC CATALYSIS
`
`labors needed to obtain detectable quantities. A typical purification scheme to
`isolate a specific enzyme might involve the following steps (all done in aqueous
`medium near neutral pH, and at low temperatures to minimize loss of catalytic
`activity): disruption of cells by mechanical or sonic treatment; differential cen(cid:173)
`trifugation to separate "soluble" and particulate fractions; fractionation by
`differential solubility in solutions of high salt (ammonium sulfate); ion-exchange
`chromatography to separate species of different charge; adsorption chromatog(cid:173)
`raphy (i.e., on calcium phosphate crystals); molecular sieve (gel-filtration)
`chromatography to separate species of different size; and electrophoresis (again
`separation by charge differences) on various supports.
`Analysis for purity can include crystallization, ultracentrifugal analysis, disc(cid:173)
`gel electrophoresis, amino-acid composition (and sequence) determination, and
`various molecular weight determinations. The isolated proteins are often labile
`with respect to loss of catalytic activity; even minor perturbations in the three(cid:173)
`dimensional structure of the protein, as a consequence of the purification se(cid:173)
`quence or perhaps merely due to removal from its normal milieu, can cause dramatic
`loss in catalytic function. To try to preserve the native (active) three-dimensional
`conformation of an enzyme and avoid inactive, denatured conformations, purified
`proteins are stored at low temperature, anywhere from 4° C to -196° C, and
`half-lives may range from hours to years in this state. To obtain an enzyme pure
`of other contaminating proteins, one may have to purify it anywhere from 20-fold
`to 50,000-fold from the biological starting material. In the latter case, if the
`overall yield of active enzyme were 10% of that in the crude extract, 500 g of cell
`protein would yield 1 mg of enzyme. If this enzyme has a molecular weight of
`50,000 g/mole, this amount represents 20 nmoles (2 x 10-s mole), not a large
`quantity. Indeed some enzymatic purifications result in microgram (10-6 g) quan(cid:173)
`tities. This example points out that the general method for analyzing whether a
`purification procedure is working is by analysis of enzyme activity, not of enzyme
`mass. The international definition of activity is a unit (U) and corresponds to a
`rate of conversion of one micromole (10-6 mole) of substrate to product per
`minute.* The specific activity of an enzyme is measured as U/mg, and this specific
`activity should rise during purification until a constant value, indicative of pure
`protein, is obtained. We shall discuss subsequently a number of specific irreversi(cid:173)
`ble inactivators for certain enzymes, which can then be used to titrate the number
`of active enzyme molecules in a test tube and provide a direct measure of how
`much catalyst is present.
`
`* An alternative unit is the katal (kat), defined as the amount of enzyme that converts one mole of
`substrate to product per second (1 kat = 6 x 107 units).
`
`2.C SPE
`
`To a stm
`catalysis a
`is compa1
`catalyzed
`and will b
`of the tex
`
`2.C.1 Sp
`
`Enzymatic
`(substrate)
`valent, em
`Michaelis,
`and Ment<
`not by dire
`
`The I
`the substn
`every cata
`Specif
`steps or or
`bind only 1
`one isomei
`catalytic c
`shed light
`we shall sc
`Specif
`(substrate n
`J(this is the
`As a 1
`<'.,.
`· patalysis. 1
`l'hey (almc
`lunction is
`
`

`

`2.C SPECIFICITY AND RATE ACCELERATIONS
`
`29
`
`purification scheme to
`,s (all done in aqueous
`nimize loss of catalytic
`ment; differential cen(cid:173)
`ions; fractionation by
`sulfate); ion-exchange
`adsorption chromatog(cid:173)
`' sieve (gel-filtration)
`electrophoresis (again
`
`ntrifugal analysis, disc(cid:173)
`;e) determination, and
`oteins are often labile
`1rbations in the three(cid:173)
`of the purification se(cid:173)
`.ieu, can cause dramatic
`:ive) three-dimensional
`;onformations, purified
`4° C to -196° C, and
`)btain an enzyme pure
`mywhere from 20-fold
`the latter case, if the
`le extract, 5 00 g of cell
`a molecular weight of
`)-8 mole), not a large
`:rogram (10-6 g) quan(cid:173)
`,r analyzing whether a
`::1ctivity, not of enzyme
`and corresponds to a
`,strate to product per
`U /mg, and this specific
`lue, indicative of pure
`er of specific irreversi(cid:173)
`j to titrate the number
`Jirect measure of how
`'
`
`e that converts one mole of
`
`SPECIFICITY AND RATE ACCELERATIONS
`
`To a student of enzymology, perhaps the most salient features of enzymatic
`catalysis are the specificity and the rate acceleration when the enzymatic reaction
`is compared with either the analogous uncatalyzed chemical reaction or the
`catalyzed nonenzymatic equivalent. Some aspects of these points are noted here
`and will be examined in the context of specific examples in the next four sections
`of the text.
`
`Specificity
`
`Enzymatic catalysis always involves prior complex formation between the reactant
`(substrate) and the enzyme, generally in an equilibrium, fast process; this nonco(cid:173)
`valent, enzyme-substrate complex (ES complex) is also commonly designated as a
`Michaelis complex, after Lenor Michaelis who enunciated this proposal (Michaelis
`and Menten, 1913). Subsequent catalysis occurs only from this ES complex and
`not by direct bimolecular reaction with substrate free in solution.
`
`E + S
`
`E . S
`
`catalysis, E . p
`
`E + p
`
`The ES complex does not form in a topologically random manner. Rather,
`the substrate binds to a specific region on the enzyme (the active-site region) in
`every catalytic cycle, and catalysis occurs only at the active site.
`Specificity can be imposed on the binding step or on any subsequent catalytic
`steps or on both. Thus an enzyme oxidizing a-hydroxy acids to a-keto acids may
`bind only one enantiomer (binding specificity) or may bind both but oxidize only
`one isomer. Compounds that bind to the enzyme active site but do not undergo
`catalytic conversion are common and function as enzyme inhibitors. They can
`shed light on reaction paths depending on the type of inhibition they exhibit, as
`we shall see in Chapter 4.
`Specificity can be absolute: there are enzymes for which only a single
`substrate molecule is acceptable. Or, specificity can be for broad structural types:
`this is the case, as we shall note explicitly, with the protease chymotrypsin.
`As a rule, enzymes demonstrate unerring and complete stereospecificity in
`catalysis. They can invariably distinguish between optical or geometrical isomers.
`They (almost) always use one form of an enantiomeric pair, unless their specific
`function is to interconvert isomers. Even more spectacularly, at first glance,
`enzymes always distinguish between paired chemically like substituents in cases
`such as Caabc; e.g., the two hydrogens on a meso carbon atom CH2XY, also
`
`

`

`(.'.)
`<1
`~ lii Substrate
`
`; r~~o--
`
`Lt
`
`React
`
`-2.8 kcal/mole=
`
`At chemical eq1
`substrate molecu
`at equilibrium,
`provides no info
`product. The rat£
`of substrate mole
`molecule, say at :
`conversion to p1
`substrate molecu
`energy required(cid:173)
`before being co
`sketched in Figur
`
`30
`
`INTRODUCTORY REMARKS ABOUT ENZYMES AND ENZYMATIC CATALYSIS
`
`known as a prochiral carbon. We shall examine in some detail the chemical basis
`for this stereospecificity and the mechanistic information it can impart in Section
`III (Chapter 10).
`Why are enzymes such stereospecific catalysts? Because they are asymmetric
`or chiral reagents, composed uniquely of L-amino-acid centers. Interaction of
`some normal symmetric chemical laboratory reagent with two enantiomers (e.g.,
`o- or L-lactate) generates transition states that are enantiomeric and of equal
`energy levels. When a chiral enzyme interacts with each enantiomer during
`reaction, diastereomeric transition states are formed. These will be of different
`energies, will have different reactivities, and will partition differently between
`reactants and products.
`
`2.C.2 Rate Accelerations
`
`As catalysts, enzymes do not participate in the reaction stoichiometry (are not
`consumed) and cannot affect the equilibrium position of a reaction; they can only
`hasten the rate of approach to the same equilibrium as that for an uncatalyzed
`reaction. The equilibrium ratio for a substrate S and a product P, [S]/[P], is of
`course a function of which compound is more stable-Le., which has a lower free
`energy. Most reduced organic molecules are thermodynamically unstable in an•
`oxidizing atmosphere; their oxidations are exergonic processes. For example,
`consider the oxidation of glucose to CO2 and H 20 by molecular oxygen.
`
`-686 kcal/mole
`
`-2872 kJ/mole
`
`This oxidation is favored by an enormous 686 kcal/mole (the negative /1G0
`reflecting an exergonic process). At chemical equilibrium (110° = - RT ln Keq),
`there would be essentially no glucose present. But, in fact, glucose is a stable
`organic compound that can be kept in bottles on the shelf. It is thermodynamical!
`labile but kinetically stable.
`The distinction between effect on thermodynamic stability and effect on.
`kinetic !ability of a molecule is clearly indicated in the free-energy diagram (Fig.
`2-1). The equilibrium concentrations of substrate and product are determined by
`their difference in free-energy content: 110°= -RTin Kew In Figure 2-1 the
`product is indicated to be more stable than the substrate. Suppose 110° here wer
`
`

`

`detail the chemical basis
`1 it can impart in Section
`
`mse they are asymmetric
`j centers. Interaction of
`th two enantiomers (e.g.,
`antiomeric and of equal
`each enantiomer during
`'hese will be of different
`ition differently between
`
`m stoichiometry (are not
`a reaction; they can only
`s that for an uncatalyzed
`L product P, [S]/[P], is of
`e., which has a lower free
`mamically unstable in an
`processes. For example,
`molecular oxygen.
`
`ti.G 0
`
`-686 kcal/mole
`
`- 2872 kJ/mole
`
`/mole (the negative AG0
`rium (AG0 = -RTln Keq),
`n fact, glucose is a stable
`~lf. It is thermodynamically
`
`,'
`
`ic stability and effect on
`free-energy diagram (Fig.
`Jioduct are determined by
`ln Keq. In Figure 2-1 the
`e. Suppose AG0 here were
`
`31
`
`c.:,
`<I
`
`~ iii Substrate
`jti.G0
`- - - - - - - - Product
`
`:
`I£
`1.1.
`
`Reaction coordinate
`
`Figure 2-1
`Equilibrium position determined by ti.G 0 be(cid:173)
`tween substrate and product.
`
`-2.8 kcal/mole= -11.7 kJ/mole. Then
`ln Keq = (-2.8 kcal/mole)/(-RT)
`Keq = 100 = [product]/[substrate]
`
`At chemical equilibrium, there would be 100 product molecules for every
`substrate molecule. This ratio is what would happen if the chemical system were
`at equilibrium, but this thermodynamic tendency for product to accumulate
`provides no information about how fast substrate will actually be converted to
`product. The rate at which the conversion occurs, a measure of the kinetic !ability
`of substrate molecules, is independent of AG0
`• Given that the substrate is a stable
`molecule, say at room temperature, and not instantaneously undergoing complete
`conversion to product, some energy (e.g., heat) will have to be put into the
`substrate molecules to convert them to products. That is, there is some activation
`energy required-some energy barrier that molecules of substrate must surmount
`before being converted to product. An arbitrary activation energy, AG\ is
`sketched in Figure 2-2. The highest point on the free-energy curve (surface) is the
`
`Transition state
`
`Product
`
`c.:,
`<I
`>
`e>
`Q)
`C:
`a,
`
`Q) !
`
`Substrate
`
`ti.G0
`
`t
`
`Figure 2-2
`Rate of reaction determined by ti.Gt activation
`energy barrier between substrate and product.
`
`

`

`t ~ I
`transition state for the reaction, by definition a fleeting entity, lasting perhaps for i --~
`
`32
`
`INTRODUCTORY REMARKS ABOUT ENZYMES AND ENZYMATIC CATALYSIS
`
`one molecular vibration ( ~ 10-13 sec). A simplified version of transition-state
`theory for reaction rates relates the rate of a reaction to the height of AG:J:
`through the following simple exponential expression.
`kobs = (RT/nh)e-t,,G*/RT
`This transition-state formulation, which assumes that reactants and transition
`state are in equilibrium, is extremely useful in that it allows one to evaluate
`kinetic behavior on the basis of energetic barriers, potentially predictable from
`structural data (Fersht, 1977).
`Those substrate molecules that have kinetic energy > AG:J: can pass over the
`barrier to products. Any catalyst, chemical or enzymatic, that accelerates a
`chemical reaction has its effect by lowering the energy barrier between substrate
`and transition state, reducing AG*, but having no effect on AG0 (no effect on
`equilibrium position).
`A chemical catalyst (e.g., a palladium metal catalyst for hydrogenation of an
`olefin) probably lowers AG:J: almost exclusively by selective stabilization of the
`transition state (e.g., bringing reactants together at the finely divided metal
`surface) as suggested in Figure 2-3a. An enzymatic catalyst also will probably
`
`Ji
`)J.
`
`"'
`
`selectively stabi
`transition state ,
`b.G*. thus no r:
`bound at the a
`catalysts probab
`having small A (
`catalyst shows ,
`transition state,
`and a second sh
`Truly stupei
`enzyme urease 1
`nonenzymatic n
`
`This ratio is on
`average rate inc
`these rate accele
`rate acceleration
`constant for inte
`
`In the absence
`conversion to A
`the value of Ke
`k_ 1 = 105 min-1,
`value of 102 mi1
`An average
`substrate reacte,
`high as 106 sec-
`
`temperature anc
`enzyme molecul
`
`- Chemical catalyst
`
`Product
`
`Substrate
`
`a
`
`ES complex
`
`Subs+Enz
`
`(2)
`
`Intermediate
`
`Product
`
`b
`/Figure 2-3
`(a) Action of chemical catalyst to lower b.G* and increase rate of
`reaction.
`(b) Possible action of enzymatic catalyst to lower b.G* and
`replace one large activation barrier with multiple lower barriers.
`
`

`

`2.C SPECIFICITY AND RATE ACCELERATIONS
`
`33
`
`entity, lasting perhaps for
`'ersion of transition-state
`m to the height of AG*
`
`reactants and transition
`t allows one to evaluate
`tentially predictable from
`
`> AG:J: can pass over the
`natic, that accelerates a
`barrier between substrate
`:ct on AG 0 (no effect on
`
`t for hydrogenation of an
`~ctive stabilization of the
`the finely divided metal
`1talyst also will probably
`
`2) L
`
`;e rate of
`ver AG* and
`>arriers.
`
`selectively stabilize the transition state relative to reactants (if reactants and
`transition state were stabilized to the same extent, there would be no lessening of
`b,G*, thus no rate acceleration), but may also selectively destabilize substrates
`bound at the active site by induction of strain or distortion. Also, enzymatic
`catalysts probably act to replace a single step having a large A Gt by multiple steps
`having small AG* overall. For instance, Figure 2-3b for a hypothetical enzyme
`catalyst shows destabilization of the ES complex, selective stabilization of a
`transition state, formation of a finite-lived intermediate (a local energy minimum),
`and a second shallow ti.G* to transition state (2) preceding product formation.
`Truly stupendous accelerations can be achieved over nonenzymatic rates. The
`enzyme urease hydrolyzes urea at a rate estimated to be 1014-fold faster than the
`nonenzyrnatic rate of hydrolysis.
`
`0
`
`H2NANH2 + H20
`
`-
`
`NH;r' + [H2N-C008 ]
`
`H 2 0
`
`This ratio is on the high side, with accelerations of 108 to 10 12 representing an
`average rate increase brought about by an enzyme. It's worth noting again that
`these rate accelerations cannot affect the equilibrium constant and thus represent
`rate acceleration in both directions (Segel, 1976, p. 208). Suppose the equilibrium
`constant for interconversion of compounds A and B is 103 in favor of B.
`
`A
`
`B
`
`In the absence of an enzyme, starting with compound B, the observed rate of
`• Then k 1 (A- B) must be 10-8 min- 1 given
`conversion to A might be 10-s min- 1
`the value of Keq· If an enzyme accelerates the rate of B to A by 1010
`, so that
`k_ 1 = 105 min-1, then the reverse rate must also be accelerated by 1010 up to a
`value of 102 min- 1
`•
`An average turnover number for an enzyme is 1,000 min- 1-i.e., 1,000 moles
`substrate reacted per minute per mole of enzyme active site. Some enzymes run as
`high as 106 sec- 1 (Talalay and Benson, 1972). Such a molecule of purified enzyme
`in a test tube might maintain full catalytic activity for 24 hours at room
`temperature and at its optimal pH, so that one might see 1.4 x 108 turnovers per
`enzyme molecule-emphasizing its behavior as a catalyst.
`
`2.C.3 What limits the Rate of Enzymatic Reactions?
`
`One can ask what might be the maximal turnover number for an enzyme. Is 105
`or 106 moles substrate reacted per mole enzyme per second an upper limit? As we
`
`

`

`34
`
`INTRODUCTORY REMARKS ABOUT ENZYMES AND ENZYMATIC CATALYSIS
`
`noted above, enzymatic catalysis involves 110th physical steps (binding of substrate
`and debinding of product from the active site of the enzyme) and chemical steps,
`as does any chemical reaction.
`
`X-Y···Z
`
`physical
`chemical X···Y-Z
`~ step
`
`X + Y-Z
`
`chemical
`step
`
`E·P
`
`physical
`step
`
`E + p
`
`E·S -
`
`chemical
`reaction
`
`enzymatic
`reaction
`
`X-Y
`
`+ z
`
`E+ s
`
`physical
`
`step
`
`physical
`step
`
`Because few chemical reactions in solution (except some proton transfers) are
`limited by the rate at which two species diffuse together, the physical steps are
`rarely important in rate determination. However, because enzymatic rates are so
`much accelerated, the diffusional steps can reasonably put an upper limit on
`catalytic rates. The bimolecular rate constant for diffusional approach of small
`molecules with each other (e.g., H 30EB+ ye) is about 1010
`1 sec-1; for small
`M-
`molecules with macromolecules such as enzymes, the diffusion limit may be ca.
`108 to 109
`1 sec-1 (Hammes and Schimmel, 1970; Fersht, 1977). One can then
`M-
`state that the diffusion limit might constrain the rate of enzymatic reactions and
`examine if this is the fact. First, however, we note that this 109 value is
`109 M- 1 sec- 1
`, whereas a turnover number of an enzyme equals k0 bJ[Enz], which
`is expressed in units of sec- 1
`• One can look at an appropriate bimolecular rate
`constant for the enzymatic case at low substrate/enzyme ratios in the following
`simple case.
`
`E + S
`
`E·S
`
`E + p
`
`Here k 2 is the observed rate of product formation, and K8 = k_ifk1 is the
`dissociation constant from E · S. The ratio k 2 /Km is essentially an apparent
`bimolecular rate constant for reaction of enzyme and substrate (in a collisional
`process corrected for partitioning of E · S forward to product or back to sub(cid:173)
`strate), and the upper limit should be ca. 109 M- 1 sec- 1.* Thus, the important factor
`is the ratio k 2 /Km rather than the absolute size of k 2 • Analysis of this (rate
`constant)/(equilibrium constant) ratio shows that certain enzymes are close to the
`diffusion-controlled limit. The enzyme triose phosphate isomerase (interconvert(cid:173)
`ing glyceraldehyde-3-phosphate and dihydroxyacetone phosphate) as a turnover
`
`* This is so if, in this most simplified kinetic mechanism, k2 » k_ 1. More generally, one can write .
`
`kl
`kcat
`E+S ,== E·S----' E+P
`._,
`The kcat can be a complex catalytic rate constant containing several elementary steps. An
`additional useful constant, as will be discussed explicitly in the next chapter, is Km (the Michaelis
`constant); here Km= (kcat + k_ 1)/k1 • Now if kcat » k_ 1 , then kca,/Km = k 1 , the association rate constant,
`which has the diffusion-controlled upper limit of 108 to 109 M_, sec- 1 (Fersht, 1977). In the prototypic
`this does not hold in all cases (Fersht, 1977, p.96).
`case chosen, k2/Ks=kca.fK,,,, although
`
`number (kca,) of
`under special ki1
`phosphate of ca
`
`Qn the other hi
`first enzyme in
`GTP of 2x10-
`(kca1) for this en
`actual observed
`that would exce
`
`Two points
`differ enormom
`essentially at t
`generally), not !
`
`enzyme can do r
`an enzyme has
`(Albery and Kn
`achieve high tu
`enzyme must p~
`fraction oJ
`limit. An additi<
`step is much slo,
`limited not by 1
`i::atalysis.
`
`e major types
`combinatior
`ctions II thrc
`
`

`

`)S (binding of substrate
`ae) and chemical steps,
`
`-Z
`
`X + Y-Z
`
`physical
`step
`
`E + p
`
`~ proton transfers) are
`, the physical steps are
`enzymatic rates are so
`put an upper limit on
`mal approach of small
`010 M- 1 sec- 1
`; for small
`fusion limit may be ca.
`1t, 1977). One can then
`mzymatic reactions and
`that this 109 value is
`:quals k0 bJ[Enz], which
`,priate bimolecular rate
`ratios in the following
`
`p
`
`.nd Ks= k_tfk 1 is the
`essentially an apparent
`1bstrate (in a collisional
`,roduct or back to sub(cid:173)
`ms, the important factor
`. Analysis of this (rate
`enzymes are close to the
`isomerase (interconvert(cid:173)
`h.osphate) as a turnover
`
`2.D TYPES OF ENZYMATIC CATALYSIS
`
`35
`
`number (kcat) of ca. 103 sec- 1 and an affinity constant (Km, which equals Ks only
`under special kinetic circumstances, as shown in Chapter 3) for glyceraldehyde-3-
`phosphate of ca. 10-s M (Trentham et al., 1964; Reynolds et al., 1971).
`
`-1
`103
`sec
`10-s M =
`
`108
`
`-1
`M
`
`-1
`sec
`
`On the other hand, the bacterial enzyme GTP-cyclohydrolase (Yim, 1975), the
`first enzyme in formation of the folate coenzymes, has an affinity constant for
`GTP of 2 x 10-3 M, extremely tight binding. This argues that the turnover rate
`(kcat) for this enzyme might be in the range of ten catalytic events per second (the
`actual observed value) but could not be in the range of 103 to 104 sec-1, because
`that would exceed the diffusion limit. For example,
`
`Two points emerge from this brief consideration. First, two enzymes may
`differ enormously in catalytic turnover numbers even though each may be
`essentially at the diffusion-controlled limit, because it is k2/K8 (or kcatlKm
`generally), not simply kikcat), that is relevant. In these cases, the enzymes are
`operating at maximal catalytic efficiency: a physical step, not a chemical step, is
`the slow step in catalysis. If the physical step occurs at the diffusion limit, then the
`enzyme can do nothing to increase catalytic efficiency. It has been stated that such
`an enzyme has reached the end of its evolutionary development as a catalyst
`(Albery and Knowles, 1976). Second, an enzyme that binds substrate loosely can
`achieve high turnover rates; the tighter the substrate is bound, the more the
`enzyme must pay in rate of achievable turnover. It should be noted that only a
`small fraction of known enzymes appear to be operating at a diffusion-controlled
`limit. An additional subset of enzymes have a physical rate-limiting step, but that
`step is much slower than the diffusion limit. The majority of enzymes probably are
`limited not by physical steps but by the rate of one or more chemical steps in
`catalysis.
`
`,re generally, one can write
`
`2.D TYPES OF ENZYMATIC CATALYSIS
`
`,everal elementary steps. An
`chapter, is Km (the Michaelis
`l, the association rate constant,
`'ersht, 1977). In the prototypic
`cases (Fersht, 1977, p. 96).
`
`Clearly, anyone concerned with how enzymatic catalysis is achieved must give
`thought to the enabling mechanisms