handbook of biochemical kinetics a guide to dynamic processes in the molecular life sciences

Handbook of
Biochemical
Kinetics
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Handbook of
Biochemical
Kinetics
Daniel L. Purich
R. Donald Allison
Department of Biochemistry
and Molecular Biology
University of Florida
College of Medicine
Gainesville, Florida
ACADEMIC PRESS
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/>Library of Congress Catalog Card Number: 99-63958
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Table of Contents
Preface vii
Abbreviations
& Symbols xi
Abbreviated
Binding Schemes xxi
Source Words 1
Wordfinder 717
Handbook of Biochemical Kinetics v
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Preface
T
he biotic world is doubtlessly the best known exam-
ple of what Nobelist Murray Gell-Mann has termed
‘‘complex adaptive systems’’—a name given to those
systems possessing the innate capacity to learn and
evolve by utilizing acquired information. Those familiar
with living systems cannot but marvel at each cell’s ability
to grow, to sense, to communicate, tocooperate, to move,
to proliferate, to die and, even then, to yield opportunity
to succeeding cells. If we dare speak of vitalism, espe-
cially as the new millennium is eager to dawn, we only
do so to recognize that homeostatic mechanisms endow
cells with such remarkable resilience that early investiga-
tors mistook homeostasis as a persuasive indication that
life is self-determining and beyond the laws of chemistry

and physics. A shared goal of modern molecular life
scientists is to understand the mechanisms and inter-
actions responsible for homeostasis. One approach for
analyzing the mechanics of complex systems is to deter-
mine the chronology of discrete steps within the overall
process—a pursuit called ‘‘kinetics.’’ This strategy allows
an investigator to assess the structural and energetic de-
terminants of transitions from one step to the next. By
identifying voids in the time-line, one considers the possi-
bility of other likely intermediates and ultimately identi-
fies all elementary reactions of a mechanism.
Kinetics is an analytical approach deeply rooted in chem-
istry and physics, and biochemists have intuitively and
inventively honed the tools of chemists and physicists
for experiments on biological processes. Biochemical ki-
netics first began to flourish in enzymology—a field
which has gainfully exploited advances in physical or-
ganic chemistry, structural chemistry, and spectroscopy
in order to dissect the individual steps comprising en-
zyme mechanisms. No apology is offered, nor should any
be required, for our strong emphasis on chemical kinetics
and enzyme kinetics. Scientists working within these dis-
Handbook of Biochemical Kinetics vii
ciplines have enjoyed unparalleled success in dissecting
complex multistage processes. Mechanisms are tools for
assessing current knowledge and for designing better
experiments. As working models, mechanisms offer the
virtues of simplicity, precision, and generativity. ‘‘Sim-
plicity’’ arises from the symbolic representation of the
interactions among the minimal number of components

needed to account for all observed properties of a system.
‘‘Precision’’ emerges by considering how rival models
have nonisomorphic features (i.e., testable differences)
that distinguish one from another. ‘‘Generativity’’ results
from the recombining of a model’s constituent elements
to admit new findings, to predict new properties, and to
stimulate additional rounds of experiment. For chemical
and enzyme kineticists, the goal of this recursive enter-
prise is to determine a mechanism (a) that accounts for
responses to changes in each component’s concentration,
(b) that explains the detailed time-evolution of all chemi-
cal events, (c) that defines the concentration and struc-
ture of transient intermediates, (d) that makes sense of
relevant changes in positional properties (i.e., conforma-
tion, configuration, and/or physical location), and (e)
that reconciles the thermodynamics of all reactions steps
and transitions. In this respect, the rigor of chemical and
enzyme kinetics teaches us all how best to invent new
approaches that appropriately balance theory and exper-
iment.
The inspiration for this H
ANDBOOK
stemmed from our
shared interest in teaching students about the logical and
systematic investigation of enzyme catalysis and meta-
bolic control. We began twenty-five years ago with the
teaching of graduate-level courses (‘‘Chemical Aspects
of Biological Systems’’; ‘‘Enzyme Kinetics and Mecha-
nism’’) at the University of California Santa Barbara as
well as a course entitled ‘‘Enzyme Kinetics’’ at the Cor-

nell University Medical College. More recently, we have
Preface
taught undergraduate students (‘‘A Survey of Biochem-
istry and Molecular Biology’’) as well as graduate stu-
dents (‘‘Advanced Metabolism’’; ‘‘Physical Biochemistry
and Structural Biology’’; ‘‘Dynamic Processes in the Mo-
lecular Life Sciences’’) here at the University of Florida.
Our lectures have included material on the theory and
practice of steady-state kinetics, rapid reaction kinetics,
isotope-exchange kinetics, inhibitor design, equilibrium
and kinetic isotope effects, protein oligomerization and
polymerization kinetics, pulse-chase kinetics, transport
kinetics, biomineralization kinetics, as well as ligand
binding, cooperativity, and allostery. Because no existing
text covered the bulk of these topics, we resorted to
developing an extensive set of lecture notes—an activity
that encouraged us to consider writing what we initially
had envisioned as a short textbook on biochemical ki-
netics.
What also became clear was that, before and during any
detailed consideration of a molecular process, teachers
must always take pains to explain the associated termi-
nology adequately. In 1789, the French chemist Antoine
Lavoisier aptly declared: ‘‘Every branch of physical sci-
ence must consist of the series of facts that are the objects
of the science, the ideas that represent these facts, and
the words by which these ideas are expressed. And, as
ideas are preserved and communicated by means of
words, it necessarily follows that we cannot improve the
science without improving language or nomenclature.’’

We recognized that there was no published resource to
help students come to grips with the far-ranging termi-
nology of biochemical kinetics. Furthermore, as the dis-
tinction between scientific disciplines becomes blurred
by what may be called ‘‘the interdisciplinary imperative,’’
students and practicing scientists from other disciplines
will require a reliable sourcebook that explains terminol-
ogy. Far too much time is wasted when students trace a
finger over many pages of a textbook, only to find a
partial definition for a sought-after term. Moreover, as
more bioscientists come from countries not using English
as a working language, there is an even greater need for
a reliable and clearly written sourcebook of definitions.
A dictionary format became an appealing possibility for
our H
ANDBOOK
, but we also wished to treat many terms
in greater depth than found in any dictionary. This led
us to adopt the present word-list format which in many
viii Handbook of Biochemical Kinetics
respects resembles the ‘‘Micropaedia’’ section of the
E
N-
CYCLOPAEDIA
B
RITANNICA
. One loses the seamless orga-
nization that can be realized in multichapter expositions
that systematically develop a series of topics. We have
accordingly attempted to mitigate this problem by in-

cluding longer tracts on absorption and fluorescence
spectroscopy, biomineralization, chemical kinetics, en-
zyme kinetics, Hill and Scatchard treatments, ligand
binding cooperativity, kinetic isotope effects, and protein
polymerization. Likewise, we have extensively inserted
cross-references at appropriate locations within many
entries. One intrinsic advantage of a mini-encyclopedia,
however, is that in subsequent printings we should be
able to make corrections and additions, or even deletions
of an entire term, without upsetting the overall format.
We also felt that readers should be encouraged to consult
the most authoritative sources on particular topics. For
this reason, we developed a collection of over 5000 litera-
ture references and, in many cases, our citations credit
the original papers on a given topic. We have included
the names of nearly 1000 enzymes, along with chemical
reactions, EC numbers, and, in many instances, their
biochemical and catalytic properties. The references
cited are not intended to be comprehensive; rather, they
serve to guide the reader to further interesting and help-
ful reading on subjects we have discussed. Where possi-
ble, at least one reference is included to provide informa-
tion on assay protocols for the listed enzyme. We also
urge readers to use the Wordfinder (included at the back
of the Handbook) to take fullest advantage of the text
and reference material. The nearly 8000 entries in the
Wordfinder represent all listed source words as well as
other subheadings, keywords, or synonyms. Each entry
is immediately followed by the recommended source
entries, and many source words are also cross-referenced

to guide the reader to other related source words.
One of us (D.L.P.) has been a member of the
M
ETHODS
IN
E
NZYMOLOGY
family of editors for well over two de-
cades. The volumes in this series on ‘‘Enzyme Kinetics
and Mechanism’’ have become a standard for those inter-
ested in biological catalysis. As the form of this book
began to emerge, we quickly recognized that
M
ETHODS
IN
E
NZYMOLOGY
could serve as an additional source for
annotations on recommended theories and practices for
kinetic studies on a wide range of topics. The Handbook
contains nearly 6000
M
ETHODS IN
E
NZYMOLOGY
cita-
Preface
tions, and we have indicated the topic, volume, and be-
ginning page for each at the foot of many of the source
words. We trust that users of our Handbook will benefit

from improved access to the first 280 volumes of
M
ETH-
ODS IN
E
NZYMOLOGY
.
For the derivations presented in this Handbook, we have
assumed that the reader is familiar with the fundamentals
of differential and integral calculus. To those who are
loathe to engage in the rigor of mathematics, we say
‘‘Take heart!’’ The successful study of kinetics requires
only that students work out a considerable number of
problems which are both theoretical and numerical in
character. We are reminded that Mithridates VI, the
Grecian king of Pontus, is said to have acquired a toler-
ance to poison by taking gradually increasing doses. To
aid those seeking their own intellectual mithridate (i.e.,
acquired antidote), we provide scores of step-by-step
derivations and practical advice on how to derive
particular rate expressions. Likewise, we have included
detailed protocols for H. J. Fromm’s systematic ‘‘the-
ory-of-graphs’’ method as well as W. W. Cleland’s net
reaction rate method. We are also greatly indebted to
Dr. Charles Y. Huang for permitting us to include
entire tracts from his chapter (which originally appeared
in Volume 63 of
M
ETHODS IN
E

NZYMOLOGY
) on the
derivation of initial velocity and isotope exchange rate
equations. We immediately recognized how daunting
the task would be to attempt to surpass Dr. Huang’s
truly outstanding treatment.
The success of our
H
ANDBOOK OF
B
IOCHEMICAL
K
INET-
ICS
can only be judged by those using this manual for
some period of time. We have come to recognize that
we could not possibly represent all of the topics falling
within the realm of biochemical kinetics—and certainly
not within a first edition. We are also certain that, despite
a determined effort to cover the terminology of chemical
Handbook of Biochemical Kinetics ix
and enzyme kinetics, we have still overlooked some im-
portant issues. We had also hoped to include additional
kinetic techniques applied in pharmacokinetics, cell biol-
ogy, electrophysiology, and metabolic control analysis.
Time constraints also prevented our developing mathe-
matical sections on Laplace transforms, vector algebra,
distribution functions, and especially statistics. Eventu-
ally, we aspire to create a compact disk version of this
Handbook, appropriately presented as hyperlinked text;

that same CD should have room for selected problems/
exercises along with step-by-step solutions, as well as
down-loadable programs for kinetic simulation, algo-
rithms for symbolic derivation of rate equations, mo-
lecular dynamics and related modeling techniques, and
tried-and-true statistical methods. We also hope that our
readers will not hesitate to advise us of shortcomings,
missed terms, as well as techniques meriting definition,
mention, or further explanation. We shall be forever
grateful for such guidance.
We thank our students and colleagues for reading earlier
drafts of our manuscript, and we are especially grateful
to both Shirley Light and Dolores Wright of Academic
Press for their insights, help, and thorough editing of the
text. We also thank Academic Press for allowing us to
incorporate the numerous annotations to
M
ETHODS IN
E
NZYMOLOGY
.
Finally, as first- and second-generation disciples of Pro-
fessor Herbert J. Fromm, we dedicate this book to him,
in recognition of his germinal and indelible contributions
to the field of enzyme kinetics and mechanism.
Daniel L. Purich
R. Donald Allison
January, 1999
ThisPageIntentionallyLeftBlank
Abbreviations

& Symbols
Roman Letters and Symbols
A Molecule in the ground state
Acceptor molecule (in fluorescence)
A* Molecule in the excited state
A SI symbol for absorbance (unitless)
SI symbol for Helmholtz energy(J)
SI symbol for the pre-exponential
term in Arrhenius equation
(mol
Ϫ
1
m
3
)
n
Ϫ
1
s
Ϫ
1
⌬A Change in absorbancy
%A Percent absorption of light
(100 Ϫ %T)
[A] Concentration of A
A, B, C, . . . Substrate A, B, C, . . .
A, B, C, . . . Coulombic contributions to the
potential energy of interaction
Moments of inertia of transition-state
complex

A
ij
Amplitude of kinetic decay
A
˚
Angstrom unit (10
Ϫ
10
m)
a
i
Thermodynamic activity of species i
a
o
Bohr radius
B Generalized base
B e
2
ͱ/2␧kT or [e
3
/(␧kT)
2/3
](2ȏN
o
/
1000)
1/2
, a constant in the Debye-
Hu
¨

ckel limiting law
B
i,j
Second virial coefficient for the
mutual interactions of species i and j
Bq Becquerel (unit of radioactivity ϭ 1
disintegration per second)
C Coulomb
Handbook of Biochemical Kinetics xi
C or c Molar concentration (M or moles/L)
C SI symbol for heat capacity(JK
Ϫ
1
)
⌬C
p
Њ Constant pressure standard heat
capacity per mole
C
ˆ
i
or c
ˆ
i
Weight concentration of the ith
species
c or Ci Symbol for Curie (old unit of
radioactivity)
c
o

SI unit for speed of light in a vacuum;
(value ϭ 2.998 ϫ 10
8
ms
Ϫ
1
)
c SI unit for speed of light in a medium
(m s
Ϫ
1
)
Concentration
D SI symbol for debye (unitless)
Donor molecule (in fluorescence)
D SI symbol for translational diffusion
constant (m
2
s
Ϫ
1
)
Spectroscopic energy of dissociation
of a diatomic molecule in the Morse
equation
⌬D
o
o
Difference in dissociation energies of
products and reactants measured from

zero-point energies
Da Dalton
D
rot
Rotational diffusion constant
d
20,w
Density extrapolated to 20ЊC, water
d Density
Collision diameter
E Free or uncomplexed enzyme
General symbol for enzyme
Effector molecule
Abbreviations & Symbols
E Energy
Initial kinetic energy of relative
motion of reactants
E Electric vector of light
E
a
Activation energy
[E
o
]orE
o
Total enzyme concentration
Eq or eq Equivalent
Equilibrium
EЊ Standard electromotive force
E

s
Energy of molecule in excited singlet
state
E
tor
Torsional potential energy
e Exponential function
e Charge on an electron (value ϭ
1.602 ϫ 10
Ϫ
19
coulombs)
Equatorial position of a substituent on
a molecule
eЈ Pseudo-equatorial position of a
substituent on a molecule
F Modified enzyme form in ping pong
mechanisms
F Force
F Free energy (archaic)
Fluorescence
Rotational-vibrational energy
distribution function
Momentum distribution function
F Faraday
f Fugacity
Number of sites for acceptor on
ligand (so-called ‘‘ligand valence’’)
Oscillator strength
Translational frictional coefficient

f Fractional attainment of isotopic
equilibrium
F
rel
Fluorescence
sample
/Fluorescence
standard
G Gibbs free energy
Gravitational constant
xii Handbook of Biochemical Kinetics
⌬G Њ Standard Gibbs free energy change
per mole
⌬
‡
GЊ Standard Gibbs free energy of
activation
g Gram
g
e
Degeneracy of the lower state
g
u
Degeneracy of the upper state
H Henry (unit of self-inductance and
mutual inductance)
H Enthalpy
Hamiltonian
H
local

Magnetic field strength at nucleus of a
molecule
⌬HЊ Standard enthalpy change per mole
⌬
‡
HЊ Standard enthalpy of activation
H Magnetic field
H
res
Magnetic field intensity at which
resonance takes place
Hz Hertz (unit of frequency cycles per
second)
h Planck’s constant ϭ 6.626 ϫ 10
Ϫ
34
Jиsec or 6.626 ϫ 10
Ϫ
27
ergиsec
ប h/2ȏ ϭ 1.055 ϫ 10
Ϫ
34
Jиsec or 1.055 ϫ
10
Ϫ
27
ergиsec
I Nuclear spin quantum number
Inhibitor

I Intensity of radiation
Ionic strength
Light transmittance
I
50
or I
0.5
Inhibitor yielding 50% inhibition or
0.5 the uninhibited rate
I(
␭
) Intensity of light at wavelength
␭
I(
␭
)
f
Intensity of emitted light at
wavelength
␭
i Square root of (Ϫ1)
J Joule
Abbreviations & Symbols
J Nuclear magnetic resonance coupling
coefficient
Flux density (units ϭ particles area
Ϫ
1
time
Ϫ

1
)
j Apparent order of a binding reaction
K Symbol for Kelvin
K or K
eq
Macroscopic equilibrium constant
K
a
Acid dissociation constant
K
A
, K
B
, . . . Dissociation constant for ligand A, B,
C,
K
ap
Apparent equilibrium constant
K
D
Dissociation constant
K
F
Formation constant (synonym of
association constant)
Dissociation constant for ligand F for
an allosteric protein
K
i

Macroscopic inhibition constant
Macroscopic ionization constant
K
ia
, K
ib
, . . . Dissociation constants in enzyme
kinetics
K
R
Dissociation constant for ligand that
binds to R-state of allosteric protein
K
S
Equilibrium constant for dissociation
of ES complex
K
T
Dissociation constant for ligand that
binds to T-state of an allosteric
protein
K
w
The constant equal to the product of
[H
ϩ
] (or, [H
3
O
ϩ

]) and [OH
Ϫ
]inan
aqueous solution
K
1
, K
2
, K
3
, . . . Stepwise binding or dissociation
constants for successive attachments
of ligand to an oligomeric receptor
k or k
B
Boltzmann constant
k Rate constant
Microscopic equilibrium constant
k
cat
Catalytic constant; turnover number
k
cat
/K
m
Specificity constant
Handbook of Biochemical Kinetics xiii
k
d
Intrinsic dissociation constant

(reciprocal of k
i,j
)
k
iH
, k
iD
, k
iT
A rate constant for isotopic isomers
containing H, D, or T
k
H
/k
D
Kinetic isotope effect
k
i,j
Intrinsic association or binding
constant (reciprocal of k
d
) for
interaction between sites on species i
and j
KE Kinetic energy
L Liter
L Avogadro’s number
L Angular momentum
L Allosteric constant equal to [T
o

]/[R
o
]
M Molecular weight
Molar
M
‡
Transition-state complex
M Magnetization
M
n
Number average molecular weight
M
r
Relative molecular mass
M
w
Weight average molecular weight
m Meter
m
e
Mass of electron at rest value ϭ
9.1094 ϫ 10
Ϫ
28
g
N Newton (unit of force)
N
o
Avogadro’s number ϭ 6.0221 ϫ

10
23
mol
Ϫ
1
n Refractive index
Number of moles
n Ǟ ȏ* Electronic transition
n Ǟ
␴
* Electronic transition
n
H
or n
Hill
Hill coefficient
P Generalized symbol for product
P or p Pressure
pK
a
Ϫlog
10
K
a
pO
2
Oxygen partial pressure
Abbreviations & Symbols
(pO
2

)
0.5
Oxygen partial pressure at 0.5
saturation
Q Coulomb (unit of electrostatic charge)
Q Heat absorbed by a defined system
Q
CO
2
Amount CO
2
released by tissue
Q
syn
Synergism quotient
q Quantum yield
q
o
Unquenched quantum yield
R Universal gas constant
Electric resistance
Gross rate of isotopic exchange
R
ȍ
Rydberg constant
R Fraction of allosteric protein in the
R-state
R
G
Radius of gyration

r Radius
Distance of separation
r Polymer end-to-end vector
S Svedberg unit (10
Ϫ
13
s)
S
A
Partial molal entropy
S
A
Ј Unitary part of the partial molal
entropy
⌬SЊ Standard entropy change
⌬
‡
SЊ Standard entropy of activation
S Scattering vector
S
1
Singlet state
s Second (unit of time)
s Sedimentation coefficient
Equilibrium constant for helix growth
s
20,w
Sedimentation coefficient corrected to
20ЊC, water
s

ˆ
Unit vector along scattered radiation
T Temperature
%T Percent transmission of light
T
m
Melting temperature
xiv Handbook of Biochemical Kinetics
T
1
Longitudinal relaxation time
T
2
Transverse relaxation time
t Time
t
1/2
Half-life
U Internal energy
V Volume
⌬V
‡
Volume of activation
V
h
Hydrated volume
V
m
or V
max

Maximal velocity
V
m,f
or V
max,f
Maximal velocity in the forward
direction
V
m,r
or V
max,r
Maximal velocity in the reverse
direction
V/K Ratio of V
max
to K
m
v Speed
Initial velocity of enzyme-catalyzed
reaction
Vibrational frequency
X
˙
dX/dt
(X
i
) Equilibrium concentration of
substance X
i
⌬(X

i
) Difference between temporal and
equilibrium concentration of X
i
z Charge on a macromolecule or ion in
units of e
Greek Letters and Symbols
Ͱ Degree of association
Alpha particle
Electric polarizability
Reduced concentration ([F]/K
F
) for
allosteric protein
Ͱ
H
Hill coefficient
ͱ Reduced concentration ([I]/K
I
) for
allosteric protein
ͱ
e
Bohr magneton
Abbreviations & Symbols
⌫ Surface concentration (mol m
Ϫ
2
)
Parameter affecting relaxation

amplitude
Ͳ Reduced concentration ([A]/K
A
) for
allosteric protein
ͳ
Phase shift
Chemical shift in nuclear magnetic
resonance
Ѩ Torque
␧ Molar absorptivity
Dielectric constant
⌬␧ Ellipticity in circular dichroism
␩
Solution viscosity
␩
o
Solvent viscosity
[
␩
] Intrinsic viscosity
␪
i
Fraction of ligand saturation of ith
site
[
␪
] Molar ellipticity
␬
Transmission coefficient for transition

state
Inverse screening length
␭
Wavelength
Kinetic decay time
Ȑ
i
Chemical potential of ith species per
mole
Ȑ
i
o
Standard chemical potential per mole
Ȑ
m
Magnetic moment
Ȑ Ionic strength
Electric dipole moment operator
Reduced mass, Ȑ ϭ m
A
m
B
/(m
A
ϩ m
B
)
␯
Frequency
␯

Fractional saturation of ligand binding
sites
⌶ Grand partition function in the
Wyman treatment
⌸ Product algorithm
Osmotic pressure
␳
Density (mass per unit volume)
Handbook of Biochemical Kinetics xv
␳
(r) Electron density
⌺ Summation algorithm
␶
Relaxation time (t)
Lag time (s)
⌽ Phi relation in enzyme kinetics
Electrical potential
␾
Quantum yield (unitless)
␹
Mole fraction of component I
⍀ Solid angle
⍀
n,i
Statistical factor for ligand-i binding at
n sites on a macromolecule
Ͷ Angular momentum
Circular frequency (Hz)
Ionic strength (archaic)
Ͷ

o
Larmor frequency (Hz)
Ͷ Angular velocity (rad s
Ϫ
1
or s
Ϫ
1
)
Mathematical Symbols
Ͱ,ͱ,Ͳ Directional angles
f Ј First derivative
f Љ Second derivative
Ѩ Partial derivative, Jacobian
͐ Integral
ϽϾ Average
Ͻ͉Ͼ Overlap interval
Ͻ͉͉Ͼ Expectation value integral
* Superscript designating radioactive
substance
Superscript designating excited state
Subscript designating complex
conjugate
‡
Superscript for transition state
(Ѩx/Ѩt)
y
Partial differential of x with respect to
time at constant y
ٌ Vector differential or gradient,

i
Ѩ
Ѩx
ϩ j
Ѩ
Ѩy
ϩ k
Ѩ
Ѩz
Abbreviations & Symbols
ٌ
2
Second derivativeoperator,
Ѩ
2
Ѩx
2
ϩ
Ѩ
2
Ѩy
2
ϩ
Ѩ
2
Ѩz
2
⌬ Constant time interval
( ) Activity of a solute
( , ) Open interval

[ ] Concentration of a solute
[ , ] Closed interval
ȍ Infinite dilution, typically as a
subscript
Multiples/Submultiples
10
12
Tera (symbol ϭ T)
10
9
Giga (symbol ϭ G)
10
6
Mega (symbol ϭ M)
10
3
Kilo (symbol ϭ k)
10
Ϫ
1
Deci (symbol ϭ d)
10
Ϫ
2
Centi (symbol ϭ c)
10
Ϫ
3
Milli (symbol ϭ m)
10

Ϫ
6
Micro (symbol ϭ m)
10
Ϫ
9
Nano (symbol ϭ n)
10
Ϫ
12
Pico (symbol ϭ p)
10
Ϫ
15
Femto (symbol ϭ f)
10
Ϫ
18
Atto (symbol ϭ a)
10
Ϫ
21
Zepto (symbol ϭ z)
Biochemical Abbreviations
A Adenine
Alanine or alanyl
aa Amino acid
aaRS Aminoacyl-tRNA
ACAT Acyl-CoA:cholesterol acyltransferase
ACES N-(2-Acetamido)-2-

aminoethanesulfonic acid
ACh Acetylcholine
xvi Handbook of Biochemical Kinetics
ACP Acyl carrier protein
ADA Adenosine deaminase
Ade Adenine
ADH Alcohol dehydrogenase
ADP Adenosine 5Ј-diphosphate
Ala Alanine or alanyl
ALA
ͳ
-Aminolevulinic acid or
ͳ
-
aminolevulinate
AMP Adenosine 5Ј-monophosphate
amu Atomic mass unit (1.66 ϫ 10
Ϫ
27
kg or
1.66 ϫ 10
Ϫ
24
g)
Arg Arginyl or arginyl
Asn Asparagine or asparaginyl
Asp Aspartic acid, aspartate, or aspartyl
Asx Aspartate ϩ asparagine or aspartyl ϩ
asparaginyl
ATCase Aspartate transcarbamoylase

ATP Adenosine 5Ј-triphosphate
B Aspartate ϩ asparagine (or
aspartyl ϩ asparaginyl)
BES N,N-Bis(2-hydroxyethyl)-2-
aminoethanesulfonic acid
Bi Two-substrate enzyme system
bp Base pair
BPG
D
-2,3-Bisphosphoglycerate
BPTI Bovine pancreatic trypsin inhibitor
Bq Becquerel
C Cytosine
Cysteine or cysteinyl
CaM Calmodulin
cAMP Cyclic AMP
CAP Catabolite gene activating protein
cAPK Protein kinase A (or cyclic AMP-
stimulated protein kinase)
CAPS 3-(Cyclohexylamino)propanesulfonic
acid
Abbreviations & Symbols
Cbz- Benzyloxycarbonyl-
cDNA Complimentary strand DNA
CDP Cytidine 5Ј-diphosphate
CHES 3-(Cyclohexylamino)ethanesulfonic
acid
Chl Chlorophyll
CM Carboxymethyl
cmc Critical micelle concentration

CMP Cytidine 5Ј-monophosphate
CoA Coenzyme A
CoASH Coenzyme A
CoQ Coenzyme Q
CTP Cytidine 5Ј-phosphate
Cys Cysteine or cysteinyl
D Dalton
Aspartic acid, aspartate, or aspartyl
d Deoxy
dd Dideoxy
DEAE Diethylaminoethyl
DFP Diisopropyl fluorophosphate
DG sn-1,2-Diacylglycerol
DHAP Dihydroxyacetone phosphate
DHF Dihydrofolate
DHFR Dihydrofolate reductase
DMF Dimethylformamide
DMS Dimethyl sulfate
DMSO Dimethylsulfoxide
DNP 2,4-Dinitrophenyl
Dol Dolichol
L
-DOPA
L
-3,4-Dihydroxyphenylalanine
DPN
ϩ
see recommended abbreviation NAD
ϩ
DSC Differential scanning calorimetry

E Glutamic acid, glutamate, or glutamyl
Handbook of Biochemical Kinetics xvii
EDTA Ethylenediaminetetraacetic acid or its
conjugate base
EF Elongation factor
EGTA Ethylene glycol bis(ͱ-aminoethyl
ether)-N,N,NЈ,NЈ-tetraacetic acid or
its conjugate base
EPPS N-2-Hydroxyethylpiperazinepropane-
sulfonic acid (also known as HEPPS)
EPR or ESR Electron paramagnetic resonance or
Electron spin resonance
F Phenylalanine or phenylalanyl
FAD Oxidized flavin adenine dinucleotide
FADHи Radical form of reduced flavin
adenine dinucleotide
FADH
2
Reduced flavin adenine dinucleotide
FBP Fructose 1,6-bisphosphate
Fd Ferredoxin
fMet N-Formylmethionine
FMN Flavin mononucleotide
F1P Fructose 1-phosphate
F6P Fructose 6-phosphate
G Guanine
Glycine or glycyl
GABA Ͳ-Aminobutyric acid
Gal Galactose
GalNAc N-Acetylglucosamine

GAP Glyceraldehyde 3-phosphate
GDP Guanosine 5Ј-diphosphate
Gla 4-Carboxyglutamic acid or
4-carboxyglutamyl
Glc Glucose
Gln Glutamine or glutaminyl
Glu Glutamic acid, glutamate, or glutamyl
Gly Glycine or glycyl
GMP Guanosine 5Ј-monophosphate
Abbreviations & Symbols
G1P Glucose 1-phosphate
G6P Glucose 6-phosphate
GSH Glutathione (sometimes referred to as
reduced glutathione)
GSSG Glutathione disulfide (sometimes
referred to as oxidized glutathione)
GTP Guanosine 5Ј-triphosphate
H Histidine or histidyl
HA Hemagglutinin
Hb Hemoglobin
HbA Adult hemoglobin
HbCO Carbon monoxide hemoglobin
HbO
2
Oxyhemoglobin
HbS Sickle cell hemoglobin
HbF Fetal hemoglobin
HDL High density lipoprotein
HEPES N-2-Hydroxyethylpiperazine-NЈ-2-
ethanesulfonic acid (also written as

Hepes)
HEPPS See EPPS
HGPRT Hypoxanthine:guanine
phosphoribosyltransferase
His Histidine or histidyl
HMG-CoA ͱ-Hydroxymethylglutaryl-CoA
hnRNA Heterogenous nuclear RNA
hsp Heat shock protein
Hyp Hydroxyproline
I Isoleucine or isoleucyl
IDL Intermediate density lipoprotein
IF Initiation factor
IgG Immunoglobulin
Ile Isoleucine or isoleucyl
IMP Inosine 5Ј-monophosphate
IPTG Isopropylthiogalactoside
xviii Handbook of Biochemical Kinetics
IR Infrared
IS Insertion sequence
ITP Inosine 5Ј-triphosphate
K Lysine or lysyl
kb Kilobase pair
kD or kDa Kilodalton
KF Klenow factor
L Leucine or leucyl
LCAT Lecithin:cholesterol acyl transferase
LDH Lactate dehydrogenase
LDL Low density lipoprotein
Leu Leucine or leucyl
Lys Lysine or lysyl

M Methionine or methionyl
MALDI-MS Matrix-assisted laser desorption
ionization-mass spectroscopy
Man Mannose
Mb Myoglobin
MbCO Carbon monoxide myoglobin
MbO
2
Oxymyoglobin
MES 2-(N-Morpholino)ethanesulfonic acid
Met Methionine or methionyl
MetHb Methemoglobin (or, Fe(III)Hb)
MetMb Metmyoglobin (or, Fe(III)Mb)
MOPS 3-(N-Morpholino)propanesulfonic acid
MS Mass spectroscopy/spectrometry
N Asparagine or asparaginyl
NAD
ϩ
Oxidized nicotinamide adenine
dinucleotide
NADH Reduced nicotinamide adenine
dinucleotide
NAG N-Acetylglucosamine
NAM N-Acetylmuramic acid
NANA N-Acetylneuraminic acid
Abbreviations & Symbols
NMN Nicotinamide mononucleotide
NMR Nuclear magnetic resonance
NOESY Nuclear Overhauser effect
spectroscopy

NTP Nucleoside 5Ј-triphosphate
P Proline or prolyl
P (or p) Phosphate
PEP Phosphoenolpyruvate
PFK Phosphofructokinase
PG Prostaglandin
2PG 2-Phosphoglycerate
3PG 3-Phosphoglycerate
PGI Phosphoglucoisomerase
PGM Phosphoglucomutase
Phe Phenylalanine or phenylalanyl
PIP
2
Phosphatidylinositol 4,5-bisphosphate
PIPES Piperazine-N,NЈ-bis(2-ethanesulfonic
acid)
PK Pyruvate kinase
PKA Protein kinase A (or cyclic AMP-
stimulated protein kinase)
PKC Protein kinase C
PKU Phenylketonuria
PLP Pyridoxal 5-phosphate
Pol DNA polymerase
PP
i
Inorganic pyrophosphate
Pro Proline or prolyl
PrP Prion protein
PRPP 5-Phosphoribosyl-Ͱ-pyrophosphate
PS Photosystem

Q Glutamine or glutaminyl
Ubiqinone (Coenzyme Q or CoQ)
Handbook of Biochemical Kinetics xix
Q
CO
2
The amount (in microliters) of CO
2
given off (under standard conditions
of pressure and temperature) per
milligram of tissue per hour
QELS Quasi-elastic laser light scattering
QH
2
Ubiqinol
Quad Four substrate enzyme system
R Arginine or arginyl
r Ribo
R5P Ribose 5-phosphate
RPC Reverse phase chromatography
RT Reverse transcriptase
RTK Receptor tyrosine kinase
Ru1,5P
2
Ribulose 1,5-bisphosphate
Ru5P Ribulose 5-phosphate
S Serine or seryl
Svedberg constant
SAM S-Adenosylmethionine
Ser Serine or seryl

T Threonine or threonyl
Thymine
TAPS Tris(hydroxymethyl)methylamino-
propanesulfonic acid
TCA Tricarboxylic acid
Ter Three-substrate enzyme system
TES N-Tris(hydroxymethyl)methyl-2-
aminoethanesulfonic acid
THF Tetrahydrofolate
Thr Threonine or threonyl
TIM or TPI Triose-phosphate isomerase
TPP Thiamin pyrophosphate (or thiamin
diphosphate)
Tris Tris(hydroxymethyl)aminomethane
TS Thymidylate synthase
Transition state
TX Transition state intermediate
Abbreviations & Symbols
Tyr Tyrosine or tyrosyl
U Uridine
Uni One-substrate enzyme system
V Valine or valyl
Val Valine or valyl
X Nonstandard or unknown amino acid
or amino acyl
xx Handbook of Biochemical Kinetics
Xaa Unspecified amino acid or amino acyl
residue
XAFS X-ray analysis for structure
Y Tyrosine or tyrosyl

YADH Yeast alcohol dehydrogenase
Z Glutamate ϩ glutamine or glutamyl ϩ
glutaminyl
Abbreviated Binding
Schemes
T
he following diagrams indicate the binding interac-
tions for enzyme kinetic mechanisms. To conserve
space, the notation used in this Handbook is a compact
version of the diagrams first introduced by Cleland
1
. His
diagram for the Ordered Uni Bi Mechanism is as follows:
Throughout this handbook, we have used the following
single-line, compact notation:
E
Aȇ (EA}EPQ) ȇ P (EQ) ȇ Q
E
This convention offers the advantage that it can be
readily reproduced on virtually all word processors and
typesetting devices without creating any special artwork.
The enzyme surface is represented by the underline, in
this case preceded by a subscript E to indicate the un-
bound (or free) enzyme before any substrate addition
and after all products desorb. An arrow pointing to the
line indicates binding, and the reader should understand
that reversible binding is taken for granted. Moreover,
unlike the original Cleland diagram, product release al-
ways is indicated by a downward arrow, because this
systematic usage emphasizes the symmetry of certain

mechanisms. The symbol ‘‘Aȇ’’ indicates that substrate
A adds; the symbol ‘‘A or Bȇȇ’’, ‘‘A or B or Cȇȇȇ’’,
etc., indicates random addition of two or three substrates,
respectively. Interconversions of enzyme-bound re-
actants can be reversible (}) or irreversible (Ǟ).
Taking the Ordered Uni Bi mechanism as an example,
we can consider several additional possibilities:
Handbook of Biochemical Kinetics xxi
EA-to-EX and EX-to-EPQ reversible:
E
Aȇ (EA}EX}EPQ) ȇP (EQ) ȇQ
E
EA-to-EX reversible and EX-to-EPQ irreversible:
E
Aȇ (EA}EX ǞEPQ) ȇP (EQ) ȇQ
E
EA-to-EX irreversible and EX-to-EPQ irreversible:
E
Aȇ (EA ǞEX ǞEPQ) ȇP (EQ)ȇQ
E
For the case of so-called iso mechanisms, the compact
diagrams are as follows:
E
Aȇ(EA}EX ǞEPQ)ȇPȇQ
F
}
E
where F}E represents the reversible isomerization step.
Other examples of one-substrate and two-substrate ki-
netic mechanisms include:

Ordered Uni Bi Mechanism
E
Aȇ (EA}EPQ) ȇP (EQ) ȇQ
E
Random Uni Bi Mechanism
E
Aȇ (EA}EPQ ) ȇȇ PorQ
E
Random Bi Uni Mechanism
E
AorBȇȇ (EAB}EP) ȇP
E
Ordered Bi Uni Mechanism
E
Aȇ (EA)Bȇ(EAB}EP) ȇP
E
Ordered Bi Bi Mechanism
E
Aȇ (EA) Bȇ (EAB}EPQ) ȇP (EQ) ȇQ
E
Ordered Bi Bi Theorell-Chance Mechanism
E
Aȇ (EA) BȇȇP (EQ) ȇQ
E
Abbreviated Binding Schemes
Ping Pong Bi Bi Mechanism
E
Aȇ (EA}FP) ȇP (F) Bȇ (FB}EQ) ȇQ
E
1

W. W. Cleland (1963) Biochem. Biophys. Acta. 67, 104.
xxii Handbook of Biochemical Kinetics
Random Bi Bi Mechanism
E
AorBȇȇ (EAB}EPQ ) ȇȇ PorQ
E
Source Words
A
A, B, C, . . ./P, Q, R, . . .
Symbols for substrates and products, respectively, in
multisubstrate enzyme-catalyzed reactions. In all or-
dered reaction mechanisms, A represents the first sub-
strate to bind, B is the second, etc., whereas P denotes
the first product to be released, Q represents the second,
etc.
See Cleland Nomenclature
AB INITIO MOLECULAR-ORBITAL
CALCULATIONS
A method of molecular-orbital calculations for de-
termining bonding characteristics and other structural
information about a wide variety of compounds and mo-
lecular configurations, including those that may not be
directly observable (e.g., transition state configurations
with partial bonds). Although ab initio calculations are
typically applied to systems with a small number of
atoms, these computationally intensive calculations can
be helpful in providing insights about the enzyme-cata-
lyzed reactions. Related methods, known as semiempiri-
cal methods, use simplifying assumptions in the calcula-
tions and are determined more quickly than standard ab

initio methods.
W. J. Hehre, L. Radom, P. von R. Schleyer & J. A. Pople (1986) Ab
Initio Molecular Orbital Theory
, Wiley, New York.
T. Clark (1985)
A Handbook of Computational Chemistry, Wiley,
New York.
W. G. Richards & D. L. Cooper (1983)
Ab Initio Molecular Orbital
Calculations for Chemists
, 2nd ed., Oxford Press, Oxford.
W. Thiel (1988)
Tetrahedron 44, 7393.
ABM-1 & ABM-2 SEQUENCES IN
ACTIN-BASED MOTORS
Consensus docking sites
1
for actin-based motility, de-
fined by the oligoproline modules in Listeria monocyto-
genes ActA surface protein and human platelet vasodila-
tor-stimulated phosphoprotein (VASP). Analysis of
Handbook of Biochemical Kinetics 1
known actin regulatory proteins led to the identification
of distinct
Actin-
Based Motility (or
Actin-Based-
Motor)
homology sequences:
ABM-1: (D/E)FPPPPX(D/E) [where X ϭ PorT]

ABM-2: XPPPPP [where X ϭ G, A, L, P, or S]
Actin-based motility involves a cascade of binding inter-
actions designed to assemble actin regulatory proteins
into functional locomotory units. Listeria ActA surface
protein contains a series of nearly identical EFPPPP
TDE-type oligoproline sequences for binding vasodila-
tor-stimulated phosphoprotein (VASP). The latter, a tet-
rameric protein with 20-24 GPPPPP docking sites, binds
numerous molecules of profilin, a 15 kDa regulatory
protein known to promote actin filament assembly
2
.
Laine et al.
3
recently demonstrated that proteolysis of
the focal contact component vinculin unmasks an
ActA homologue for actin-based Shigella motility. The
ABM-1 sequence (PDFPPPPPDL) is located at or near
the C-terminus of the p90 proteolytic fragment of vin-
culin. Unmasking of this site serves as a molecular switch
that initiates assembly of an actin-based motility complex
containing VASP and profilin. Another focal adhesion
protein zyxin
4
contains several ABM-1 homology se-
quences that are also functionally active in reorganizing
the actin cytoskeletal network.
1
D. L. Purich & F. S. Southwick (l997) Biochem. Biophys. Res.
Comm.

231, 686.
2
F. S. Southwick & D. L. Purich (1996) New Engl. J. Med. 334, 770.
3
R. O. Laine, W. Zeile, F. Kang, D. L. Purich & F. S. Southwick
(1997)
J. Cell Biol. 138, 1255.
4
R. M. Golsteyn, M. C. Beckerle, T. Koay & E. Friedrich (1997) J.
Cell Sci.
110, 1893.
ABORTIVE COMPLEXES
Nonproductive reversible complexes of an enzyme with
various substrates and/or products. The International
Union of Biochemistry
1
distinguishes dead-end complex
from abortive complex, and the latter term is regarded
Abscissa
as a synonym for ‘‘nonproductive complex’’. Complexes
that fail to undergo further reactions along the catalytic
pathway are called dead-end complexes, and the reac-
tions producing them are called dead-end reactions.
Some ambiguity exists in the literature regarding the
usage of ‘‘abortive complex’’. For example, the term
has been used to describe the nonproductive complex
formed between an enzyme and a competitive inhibitor
2
or to describe that inhibition of depolymerases resulting
from shifted registration of the substrate within the en-

zyme’s set of subsites
2,3
. Still others have used the term
interchangeably with dead-end complexes
4
. The term
abortive complexes formation is treated as a special case
of dead-end complexation and is restricted to nonpro-
ductive complexes involving the binding of substrate(s)
and/or product(s) to one or more enzyme forms. Thus,
nonproductive complexes that culminate in substrate in-
hibition are abortive complexes. For a discussion con-
cerning formation of EB and EP complexes in rapid-
equilibrium ordered Bi Bi reactions, see the section on
the Frieden Dilemma. Enzyme-substrate-product com-
plexes that often form with multisubstrate enzymes are
also abortive complexes.
Early product inhibition studies of Aerobacter aerogenes
ribitoldehydrogenase
5
demonstratedtheformationofthe
E-NAD
ϩ
-
D
-ribulose and E-NADH-
D
-ribitol complexes.
In the lactate dehydrogenase reaction, the E-NADH-lac-
tate and E-NAD

ϩ
-pyruvate complexes are stable
6
, and
determination of the K
d
values indicates that the E-
NAD
ϩ
-pyruvate ternary complex is physiologically rele-
vant
7
. Abortive complexes have been reported for a wide
variety of enzymes. Isotope exchange at equilibrium is
used to identify the E-NADH-malate abortive with bo-
vine heart malate dehydrogenase
7
. Creatine kinase forms
an E-MgADP-creatine complex
8
. Inhibition at high sub-
strate-product concentrations may arise from factors
other than abortive complexes; for example, the inhibi-
tionobserved inan equilibrium exchange experiment may
be related to high ionic strength of reaction solutions
9
.
Wong and Hanes
10
pointed out that equilibrium ex-

change studies can be useful in detecting the presence
of abortive species. Although abortive complexes can
complicate exchange kinetic behavior, the Wedler-Boyer
protocol
11
minimizes the influence of abortives on equi-
librium exchange studies.
2 Handbook of Biochemical Kinetics
Different abortives may be formed with alternative prod-
ucts or substrates. Such procedures can be useful in help-
ing to distinguish Theorell-Chance mechanisms from or-
dered systems with abortive complexes
12
. In the case
of lactate dehydrogenase, the E-pyruvate-NAD
ϩ
and E-
lactate-NADH abortive complexes may play a regula-
tory roles in aerobic versus anaerobic metabolism.
Computer simulations
13
also point to the regulatory po-
tential of these non-productive complexes.
See Deadend
Complexes; Inhibition; Nonproductive Complexes;
Product Inhibition; Substrate Inhibition; Isotope Trap-
ping; Isotope Exchange at Equilibrium; Enzyme Regu-
lation
1
International Union of Biochemistry (1982) Eur. J. Biochem. 28,

281.
2
M. Dixon & E. C. Webb (1979) Enzymes, 3rd ed., Academic Press,
New York.
3
J. D. Allen (1979) Meth. Enzymol. 64, 248.
4
H. J. Fromm (1975) Initial Rate Enzyme Kinetics, Springer-Verlag,
New York.
5
H. J. Fromm & D. R. Nelson (1962) J. Biol. Chem. 231, 215.
6
H. J. Fromm (1963) J. Biol. Chem. 238, 2938.
7
H. Gutfreund, R. Cantwell, C. H. McMurray, R. S. Criddle &
G. Hathaway (1968)
Biochem. J. 106, 683.
8
E. Silverstein & G. Sulebele (1969) Biochemistry 8, 2543.
9
J. F. Morrison & W. W. Cleland (1966) J. Biol. Chem. 241, 673.
10
J. T F. Wong & C. S. Hanes (1964) Nature 203, 492.
11
F. C. Wedler & P. D. Boyer (1972) J. Biol. Chem. 247, 984.
12
C. C. Wratten & W. W. Cleland (1965) Biochemistry 4, 2442.
13
D. L. Purich & H. J. Fromm (1972) Curr. Topics in Cell. Reg. 6,
131.

Selected entries from
Methods in Enzymology [vol, page(s)]:
Formation, 63, 43, 419-424, 432-436; chymotrypsin, 63, 205; iso-
tope exchange, 64, 32, 33, 39-45; isotope trapping, 64, 58; limita-
tion, 63, 432-436; multiple, one-substrate system, 63, 473, 474;
pH effects, 63, 205; practical aspects, 63, 477-480; substrate inhi-
bition, 63, 500, 501; two-substrate system, 63, 474-478; in prod-
uct inhibition studies, 249, 188-189, 193, 199-200, 205; identifica-
tion of, 249, 188-189, 202, 206, 208-209.
ABSCISSA
The x-coordinate axis for a graph of Cartesian coordi-
nates [x,y]or[x, f (x)] or the x-value for any [x,y] ordered
pair. This corresponds to the [Substrate Concentration]-
axis in v versus [S] plots or the 1/[Substrate Concentra-
tion]-axis in so-called double-reciprocal or Lineweaver-
Burk plots.
ABSOLUTE CONFIGURATION
A method for designating the stereoisomeric configura-
tion of a chiral carbon atom within a molecular entity.
The designation
D
was arbitrarily assigned to (ϩ)-glycer-
aldehyde, and (Ϫ)-glyceraldehyde was assigned the label