Transcript Chap 7. Detection of Intermediates in Enzymatic Reactions

C. Negative Cooperativity and Half-of-the-Sites
Reactivity
• Successive binding with decreasing affinity
• KNF: suitable model
• Half-of-the-sites or half-site reactivity
Example
• Thyrosyl-tRNA synthetase:
dimer
binding only 1 mol of tyrosine tightly
• Glyceraldehyde 3-phosphate dehydrogenase:
KD = <10-11, <10-9, 3×10-7, 3×10-5 M
D. Quantitative Analysis of Coorperativity
1. The Hill equation: A measure of cooperativity
n: the binding sites, K: the dissociation constant
E + nS
ESn
[ E ][S ]n
K
[ ESn ]
[ ESn ]
Y
[ E ]0
Y: the degree of saturation
[E]
1 Y 
[ E ]0
log
Y
 n log[S ]  log K
1 Y
The Hill plot
Y
log
 h log[ S ]  log K
1 Y
•
•
•
•
log
Fig 10.7
h: the Hill constant (a measure of cooperativity)
The higher h: the higher the cooperativity
At the upper limit, h = the number of binding sites
If h = 1, no cooperativity,
If h > 1, positive cooperativity
If h < 1, negative cooperativity
v
Vmax  v
 h log[S ]  log K
Kinetic measurements by
replacing Y by the rate v
2. The MWC Binding Curve: L, KR, KT, and [S]
c
KR
KT
[T0 ]
L
[ R0 ]
The dissociation constant: KR (the R state), KT (the K state)
L: the allosteric constant
([R1 ]  2[ R2 ]      n[ Rn ])  ([T1 ]  2[T2 ]      n[Tn ])
Y
n([R0 ]  [ R1 ]      [ Rn ]  [T0 ]  [T1 ]      [Tn ])
[S ]

KR
Y: The fraction of saturation
Lc (1  c ) n 1   (1   ) n 1
Y
L(1  c ) n  (1   ) n
(1   ) n
R
L(1  c ) n  (1   ) n
R: The fraction of the R state
The dependence of the Hill constant on L and c
• Y  h value
• a plot of h against L at a constant c:
a bell-shaped curve
• If L >> c or L << c then h = 1
• When L is very low, sufficient protein in R state
(no cooperativity)
When L is very high, too small concentration of the R state
• L is maximal when L=c-n/2 (n is number of binding sites)
3. The KNF Binding Curve
• Many dissociation constants
cf. MWC model: two dissociation constants
• No simple general equation for Y
4. Diagnostic Tests for Cooperativity,
and MWC versus KNF Mechanisms
Determination of cooperativity
• The value of h in the Hill plot
• Characteristic deviations
• MWC model cannot have negative cooperativity
• MWC and KNF models can be consistent with positive
cooperativity
• Differences in measurement of the rates of ligand binding:
fewer relaxation times because of fewer stated involved
E. Molecular Mechanism of Cooperative
Binding to Hemoglobin
• The physiological importance:
A means of lowering the oxygen affinity
over a very narrow range of pressures
• The binding of oxygen:
the structural change
– the change from 5 to 6 coordination
(high spin to low spin)
– a small movement of the iron
– triggering the change in quaternary
structure
• Remarkable agreement with MWC model
Chemical Models of Hemes
• Fe-O2 bond is bent while Fe-CO
bond is linear, and linear ligand
causes steric hindrance
• H-bond between terminal
oxygen of Fe-O2 and His-NH
F. Regulation of Metabolic Pathways
• Mass action ratio:
- the ratio of the concentrations of its products to those of its
substrates
- useful to identify the rate-limiting step
• Two principle means of controlling the activity of an enzyme
- binding of allostric effectors
- covalent modification by phosphorylation/de-phosphorylation
of Ser, Thr, and Tyr –OH groups
G. Phosphofructokinase (PFK) and Control
by Allosteric feedback
Fructose 6-phosphate + ATP
fructose 1,6-diphosphate + ADP
• Inversion process: a direct attack, Asp-127 as a general base
• Fructose 6-phophate with a positive cooperativity
• In eukaryotes, PFK activated by AMP, ADP, and 3’,5’-cAMP
inhibited by high concentrations of ATP and citrate
• In prokaryotes, PFK activated by ADP and GDP
inhibited by phosphoenolpyruvate (PEP)
Phosphofructokinase (PFK) from
B. stearothermophilus
• An α4 tetramer of subunit Mr 33900
• An MWC two-state model: a K system - both R and T states
have same kcat, but R state binds fructose 6-phosphate more
tightly than does T state
cf. V system:
• same affinity, but one state has higher kcat
• An effector (not substrate) binds preferentially to one
H. Glycogen Phosphorylase and Control
by Phosphorylation
• Importance of the phosphoryl group:
- a source of steric repulsion
- electrostatic effects (a dianion)
- a network of hydrogen bond
• Protein kinases catalyze the phosphorylation
• Phosphatases remove the phosphoryl group
• Phosphoryl kinase/phophatase: exquisitely regulated
1. Glycogen Phosphorylase (GP) and
Regulation of Glycogenolysis
• Glycogen: a major source for energy in muscle
• The rate-limiting enzyme in glycogenolysis:
glycogen phophorylase
Glycogen phosphorylase
• Tow interconvertible forms, a and b
• An α2 dimer of Mr 97,333 (841 amino acid residues) per subunit
• Inactive b form: activated by allostreic effectors AMP and IMP,
inhibited by ATP and ADP
• a form: an active tetramer,
converted by phosphorylation of b form at Ser14 by
phosphorylase kinase
at low [Pi], activated by AMP and inhibited by glucose
• The key faction in a/b interconversion:
the activity of the phosphoryl kinase
Control mechanisms of the activity of phophorylase kinase
• Neural control: PK is, in turn, activated by Ca2+ ion release
in muscle that results from electrical stimulation
• Hormonal control: PK is also activated by secondary
messenger 3’,5’-cAMP that is produced as a result of
hormonal stimulation
I. G Proteins: Molecular Switches
• G protein-GTP complexes: binding to and activating various
targets during signal transduction
• A common core domain of Mr ~ 21,000: G domain
• The phosphate binding loop (G1 loop): absolutely conserved
region, binding to α,β-phosphate groups
• Thr in G2 loop and Gly in G3 loop : binding to γ-phosphate
• G1 loop: a Walker A consensus found in molecular motors
(loops is positioned between β-strand and α-helix)
cf. Table 10.4
Binding to targets
J. Motor Proteins
• Motor proteins: using the free E
of hydrolysis of ATP to move
• Three superfamilies: myosin,
kinesin, and dynein
myosin – moves along actin
filaments
kinesin and dynein – move along
microtubules
• Myosin•ATP and myosin•ADP•Pi bind to actin ~10000 times
more weakly compared to myosin•ADP
• Sequence similarity between the loops (N1-N4) in motor proteins
and those (G1-G4) in G proteins
• Procession along actin (or microtublues) is believed to occur from
successive bind/release steps that involve hydrolysis of ATP
K. ATP Synthesis by Rotary Catalysis: ATP
Synthase and F1-ATPase
• Proton chemical potential ∝ RT ln (pH)
• ATP synthetase has F0 and F1 components that are joined
together by long subunit
• F0 component is in membrane and F1 component is in cytosol
• The flow of hydrogen ion across the membrane: by the F0 part
• F 1 complex: ----- around the 
• F1 component makes ATP but is driven by “crankshaft
motion of γ subunit that induces conformational “switching”
change of β subunits
• Three alternating conformations: L-loose, O-open, and Ttight (only T is catalytically active)
• Crankshaft motion of γ is mediated by F0 and energetically
driven by pmf (proton motive force, H+)