Download Bi-Substrate Enzyme Kinetics

Phosphoryl Transfer
•
O
HO
P
O
OH
OH
Phosphoric acid
HO
P
OH
OH
•
In biological systems, the element
phosphorous almost always exists as
phosphate. Phosphorous is stable in several
different oxidation states, but in phosphate,
the oxidation state is +5. Therefore, the
phosphorous atom in phosphate will always
behave as an electrophile.
Phosphorous can form more than four
covalent bonds. As a second-row element, it
has low lygin d orbitals into which additional
electron pairs can be put to form a fifth bond.
In the phosphate group, the unshared electron
pair on one of the oxygen atoms can be shared
with a d orbital of the phosphorous to form a
d-pp bond.
Examples of Phosphoryl Groups in
Biochemistry
OR
O
P
OR
O
Ad
O
P
O
O
O
O
O
Ad
O
O
H
P
NH2
Adenosine Triphosphate (ATP)
O
O
O
O
Cyt
P
OH
O
O
P
O
Cyt
O
H
P
O
O
O
O
Phosphoediester
bonds
Phosphoanhydride bonds
Phosphoester bonds
O
O
O
O
O
O
P
Ad
O
OH
O
Deoxyribonucleic Acid
P O
O
CH2
O
Adenosine
Adenosine monophosphate
O
Ad
O
H
P O

O
N
N
OH OH
O
O
O
N
N
O
Adenosine diphosphate
OH
Ribonucleic Acid
Small Phosphoryl-Containing Molecules
O
H OH
O
H O
HO
HO
H
OH
H
H
O
O
P
O
P
O
H3C
HO
H O
HO
HO
H
H
O
Glucose 1-phosphate
O
OH
P
O
O
O
Acetyl phosphate
H
O
OH
Glucose 6-phosphate
C
O
O
P
O
O
O
P
O
O
Pyrophosphate
O
O
+
H3N
O
O
P
O
OH
O
O
COO
H H
C C
C
H2
Phosphatidyl ethanolamine
H2C
C
O
O
P
O
O
Phosphoenol pyruvate
Phosphoryl Amino Acids
TYR
SER
O
CH2
O
O
O
O
O
P
P
P
THR
O
OH
CH
CH3
O
OH
O
OH
LYS
ARG
HIS
O
P
HN
C
NH
O
P
OH
NH2
HN
O
O
P
O
N
O
O
OH
NH
Classes of Phosphoryl Transfer
O
R
O
O
P
O
+
H2O
R
+
OH
Phosphatases
O
HO
P
O
O
R
O
O
P
O
+
R'
R
H2O
O
P
RO
P
O
O
O
+
O
Y
Y
Kinases
O
P
+
HO
P
O
+
O
X
O
In kinases, X is almost
always ADP. However,
GDP is known to
substitute i some cases.
O
O
ROR'
+
OH
Phosphodiesterases
O
X
O
RO
O
Phosphorylases
P
O
O
+
R'OH
Kinases
•
•
•
Kinases are phosphotransferases that catalyze the transfer of a phosphoryl group to an acceptor
molecule. Most often, the phosphoryl group comes from the terminal (gamma) position of adenosine
triphosphate.
There is high negative charge associated with the triphosphate group of ATP, which shields each
phosphorus against reaction with incoming nucleophiles. This property makes ATP kinetically stable
int he cell, although thermodynamically, its hydrolysis is favorable. In enzyme catalysis, these
charges are typically neutralized in order to facilitate nucleophilic attack.
– Coordination with metal ions. Most often magnesium. In the cell, ATP is frequently found
associated with magnesium, and the true substrate is MgATP.
– Ion pairing with positively charged amino acids such as the guanidinium of arginine, or the
lysine ammonium group.
From the structure of ATP, chemical precedent would indicate that the -bond would be cleaved via a
dissociative transition state, while the  and -bonds would be cleaved via associative transition
states.
Adenylate Kinase
NH2
N
N
O
NH2
O
O
O
O
OH OH
O
O
O
O
O
OH OH
Mg 2+
enzyme
P+Q
•
E+A+B
EAB
EPQ
•
E+P+Q
This is a sequential or single-displacement mechanism
•
•
E+A
EA
E*P
P
E*
E*B
EQ
O
ADP
•
A+B
O
N
N
OH OH
MgATP
AMP
O
O P O P O
NH2
N
N
N
N
O P O P O P O
O
O
N
N
N
N
O P O
NH2
E+Q
B
This is a Ping-Pong or double-displacement mechanism
N
N
O
O
O
O
Mg 2+
N
N
O P O P O
O
OH OH
MgADP
The transfer of phosphoryl groups between different
nucleotides, as well as other small molecules is important for
utilizing and replenishing the cellular pool of energy-rich
phosphate compounds. Adenylate kinase is a classic example
of enzymes in this class.
Adenylate kinase was formerly known as myokinase because
it is found in high concentrations in muscle tissue.
The adenylate kinase reaction is isoenergetic. A
phosphoanhydride is cleaved and formed on both sides of the
equation.
Adenylate kinase displays sequential kinetics, in which both
substrates must be bound before any product is released.
This is distinguished from what is termed ping-pong
kinetics, in which one reactant modifies the enzyme, and then
a second reactant interacts with the modification.
Bi-substrate Enzyme Kinetics
Sequential
B
A
1. ordered
2. random
E
EA
P
EAB
Ping-pong
P
A
E
EPQ
EA
E*P
Q
EQ
B
E*
E
Q
E*B
EQ
E
Equations for Bi-substrate Kinetics
[B]
1/v
v=
Vmax[A][B]
Ka[B] + Kb[A] + [A][B]
1/[A]
v=
Vmax[A][B]
[B]
1/v
[A][B] + Ka[B] + Kb[A] + KaKb
1/[A]
Sequential Kinetics
•
•
•
•
•
Sequential kinetics can be distinguished from ping-pong kinetics by
initial rate studies.
In practice, measure initial rates as a function of the concentration of
one substrate while holding the concentration of the second constant.
Next, vary the concentration of the second substrate and repeat.
Lineweaver-Burk (double-reciprocal) analysis should yield a family
of lines that intersect at the left of the y-axis of the graph.
Within the realm of sequential reactions lies ordered sequential and
random sequential at the extreme ends. The equations for the two are
identical; therefore, simple initial rate studies cannot differentiate
between the two.
In ordered sequential reactions, one substrate is obligated to bind to
the enzyme before a second substrate. In random sequential
mechanisms there is no preference. In practice, there is usually some
degree of order in binding.
Ordered- vs. Random- Sequential
Random Sequential
E+A
EA
B
P
EAB
QE
E+Q
EQP
Q
E+B
EB
A
EP
E+P
B
EAB
EA
A
Ordered Sequential
E
Q
EQP
EQ
P
Adenylate Kinase Kinetic Pathway
Adenylate kinase displays a random ordered kinetic mechanism. In this case, the two
substrates are bound randomly, and are in equilibrium with the “ternary complex”
(E•MgATP•AMP). As in our derivation, this necessitates that the off rate for each of the
substrates is less than the forward rate constant for the chemical step. This allows us to
replace Km with Ks. However, it would not be incorrect to use Km values. Below is
typical shorthand notation for kinetic schemes.
MgATP
AMP
KsMgATP
ADP
Ks'AMP
Ks'ADP
E
E • MgATP • AMP
E
E • MgADP • ADP
E • AMP
AMP
KsMgADP
E • MgADP
E • MgATP
KsAMP
MgADP
E • ADP
Ks'MgATP
MgATP
Ks'MgADP
MgADP
KsADP
ADP
Nucleoside Diphosphate Kinase
•
•
Nucleoside diphosphate kinase (NDP Kinase) catalyzes the transfer of the terminal
phosphoryl group of ATP to a nucleoside diphosphate.
NDP Kinase displays a steady state kinetic pattern that is distinctly different from that of
adenylate kinase. If one substrate is varied while the other is fixed at several different
concentrations, a family of parallel lines is obtained by Lineweaver-Burk analysis. This
is reminiscent of a Ping-Pong reaction.
NH2
NH2
N
O
O
O
O
O
N
N
O P O P O P O
N
O
N
O
O
O
Mg
N
O
OH OH
MgATP
MgADP
O
O
N
O
O P O P O
O
N
O
O
Mg2+
O
OH OH
MgGDP
N
O
Mg2+
OH OH
2+
O
O P O P O
N
N
NH
N
NH2
O
O
O
N
O P O P O P O
O
O
O
Mg2+
O
OH OH
MgGTP
NH
N
NH2
Economy in the Evolution of Binding
Sites
• Since adenylate kinase and nucleoside diphosphate kinase catalyze
very similar reactions, why don’t they proceed by similar mechanisms?
• NDP kinase catalyzes a symmetrical reaction, whereas adenylate
kinase does not. For NDP kinase, the product of the ping (MgADP) is
similar in structure to the substrate for the pong (MgGDP). The only
difference involves the purine rings of each nucleotide.
• By using a ping-pong reaction, the enzyme can use just one binding
site for the phsphoryl transfer.
UDP-Glucose Pyrophosphorylase
O
H OH
HN
H O
HO
HO
H
H
Mg
H
OH
O
O
O
P
O
O
O
P
O
O
O
P
O
O
O
O
P
O
O
O
H
MgUTP
Glucose 1-phosphate
H
H
OH
H
OH
MgPPi
O
H OH
This is a special type of
sequential mechanism in
which MgUTP must bind
firs, before glucose-1phosphate. There is no
degree of randomness.
Ordered binding also
implies ordered product
release.
H O
HO
HO
H
H
HN
H
OH
O
O
P
O
O
O
O
P
O
N
O
O
H
N
H
H
OH
H
OH
UDP-Glucose Pyrophosphorylase
•
•
Steady State kinetic equation is similar to adenylate kinase. Therefore
Lineweaver-Burk plots cannot distinguish the two forms of sequential
reactions. Must do product inhibition studies.
Stereochemistry indicates inversion; however, incubation of the enzyme with
radiolabeled UTP, followed by gel-filtration shows a radiolabeled
intermediate. Be careful! This is because UTP or UDP-glucose binds very
tightly to the enzyme. In fact, the enzyme is isolated with UTP and UDPglucose tightly bound, and will catalyze an exchange reaction, which is
characteristic of Ping-pong reactions.
Ping-Pong Reaction
O
H OH
H O
HO
HO
OH
HO
H
H
OH
O
H
H O
HN
O
P
O
O
O
O
P
H
HO
N
H
H
O
H
OH
O
O
O
H
O
P
O
H
H
OH
H
OH
O
galactose 1-phosphate
UDP -Glucose
HO
O
OH
H O
H
HO
H
H
H
OH
O
H OH
HN
O
P
O
O
O
O
P
O
N
O
O
H
UDP -Galactose
H O
HO
HO
H
H
H
H
OH
H
OH
H
OH
O
O
P
O
O
glucose 1-phosphate
Galactose-1-P Uridylytransferase
O
H OH
H O
HO
HO
H
H
OH
O
H
O
P
O
O
O
O
P
O
H O
N
HO
HO
Ping
O
O
H
E
H OH
HN
His
H
H
OH
O
H
H
H
OH
H
OH
O
P
O
O
glucose 1-phosphate
O
UDP-Glucose
HN
+
HO
H O
H
HO
H
H
E
O
OH
HN
H
OH
O
O
P
O
O
O
O
P
O
HO
N
O
O
H
H
UDP-Galactose
OH
H
H
OH
O
O
Pong
His P
O
H
H O
H
HO
H
H
O
O
OH
H
OH
O
O
P
O
O
galactose 1-phosphate
N
H
H
OH
H
OH