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 Y: the degree of saturation

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

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

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