1. 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

2. D. Quantitative Analysis of Coorperativity
1. The Hill equation: A measure of cooperativity
n: the binding sites, K: the dissociation constant
E + nS ESn
Y: the degree of saturation

3. The Hill plot
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
Kinetic measurements by replacing Y by the rate v

4. 2. The MWC Binding Curve: L, KR, KT, and [S]
The dissociation constant: KR (the R state), KT (the K state)
L: the allosteric constant
Y: The fraction of saturation
R: The fraction of the R state

5. 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)

6. 3. The KNF Binding Curve Many dissociation constants
cf. MWC model: two dissociation constants
No simple general equation for Y

7. 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

8. 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

9. 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

10. 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

11. 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)

12. 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

13. 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

14. 1. Glycogen Phosphorylase (GP) and Regulation of Glycogenolysis
Glycogen: a major source for energy in muscle
The rate-limiting enzyme in glycogenolysis:
glycogen phophorylase

15. 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

16. 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

17. 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

18. 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

19. 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 

20. 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 T-tight (only T is catalytically active)
Crankshaft motion of γ is mediated by F0 and energetically driven by pmf (proton motive force, H+)