Understanding Allosteric Proteins & Protein Function in Biophysics

1. Absorption Spectroscopy/Protein Function Topic 4 Part 2 Biophysics

2. C t Chemical KineticsZero Order • Rate independent of concentrations • -dC/dt = k • C(t) = C0 – kt Reaction of nitrite with deoxyhemoglobin

3. ln(CA) t Chemical KineticsFirst Order • -dCA/dt = kCA , CA = CA0 e-kt • t1/2 = ln(2)/k; t = 1/k = lifetime NO binding to Hb

4. Chemical KineticsSecond Order • -dCA/dt = -dCB/dt = kCACB • Make one species in excess so get pseudofirst order kinetics, kobs = kCB so CA = CA0 exp(-kobst)

5. Hemoglobin • Cooperative Binding of Oxygen • Linked to quaternary structure • Explained by MWC Model

6. On the Nature of Allosteric Transitions:A Plausible Model Jacques Monod, Jeffries Wyman, Jean-Pierre Changux J. Mol. Biol. 1965

7. “Molecular Amplifiers”

8. ATCase The goal is control – want a switch. “Indirect interactions between distinct specific binding sites (allosteric effects)”

9. Definitions and Generalizations • Homotrophic effects – identical ligands (eg. for Hb: O2, CO, NO) • Heterotrophic effects –different ligands (eg. for Hb: DPG, IHP, Cl-, NO as SNO, NEM) • Most allosteric proteins are oligomers (several subunits or protomers) • Allosteric changes often involve quaternary stucture • Heterotrophic - positive or negative, Homotrophic – only positive (exception of Hg reductase?)

10. Model in English • Allosteric proteins are oligomers where the protomers are arranged symmetrically • There is one and only one identical ligand-binding site on each protomer • Tertiary structure of protomers affected by quaternary structure • There are two quaternary states (R and T) which dictate ligand affinities on all protomers • Transitions between states preserve symmetry

11. Model in Math • T0 = L R0, , L is the allosteric constant, (Big L = Big allostery) • Only also define • c defines relative affinities of quaternary states and a defines absolute affinity of one • When L is small

12. Compare Hill Equation vs Q is a constant, n is the number of ligand sites, n is Hill coefficient

13. Hb, L, c …

14. Hb Sigmoidal See satsimple.mw and sat.mw

15. Heterotrophic effectors Affect L Activators decrease L (push to R) and Inhibitors increase it

16. See sat.mw

17. Hb – microstate predictions (vs sequential) Unlike in sequential model, no R2 or T2 – see states.mw

18. ATCase and inhibitor • At low concentrations of substrate, low concentrations of analogue activate (by promoting R-state) upper curve • Desensitized enzyme (quaternary interactions suppressed) shows no increase in activity by analoque (maleate) • Generally, desensitized enzymes lose cooperativity. Hb dimers are R-state like and like Mb. Homotrophic ligands promote tetramer stabilization (hard to dissociate oxyHb), as predicted

19. Activators can decrease cooperativity Fig 6a is theoretical (see yf.mw ) Fig 6b and c show activations in real systems

20. Confirmations of MWCATCase • Model predicts fraction in R-state > fraction ligand bound. Schachman lab (1966) shows this using sedimentation to examine quaternary state (size) and spectroscopy for ligation. • They also showed (like Gerhart lab) low concentration of inhibitor activate ATCase

21. Confirmations - Hb • MWC’s prediction of concomitant changes in tertiary structure in protomers with known symmetry of tetramer confirmed by more refined X-ray structures. • Perutz provides mechanism of allosteric transitions • Szabo and Karplus show quantitative agreement of MWC/perutz model with equilibrium data (Eg Lc4 constant after all salt bridges broken). • Equilibrium oxygen binding to Hb trapped in T-state crystal non-cooperative (Eaton lab). • CO rebinding following photolysis of HbCO (R-state) much faster than CO binding to Hb (T-state) – Gibson.