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This article explores the principles of chemical kinetics as they relate to protein function, focusing on hemoglobin and its allosteric behavior. Essential concepts such as zero-order, first-order, and second-order kinetics are examined along with mathematical models like the MWC model of cooperative binding. Key aspects, including the influence of homotrophic and heterotrophic effects on enzyme activity and structure, are discussed with examples from hemoglobin's function in oxygen transport. Insights into molecular amplification and ligand binding affinities in oligomeric proteins are also presented.
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Absorption Spectroscopy/Protein Function Topic 4 Part 2 Biophysics
C t Chemical KineticsZero Order • Rate independent of concentrations • -dC/dt = k • C(t) = C0 – kt Reaction of nitrite with deoxyhemoglobin
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
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)
Hemoglobin • Cooperative Binding of Oxygen • Linked to quaternary structure • Explained by MWC Model
On the Nature of Allosteric Transitions:A Plausible Model Jacques Monod, Jeffries Wyman, Jean-Pierre Changux J. Mol. Biol. 1965
ATCase The goal is control – want a switch. “Indirect interactions between distinct specific binding sites (allosteric effects)”
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?)
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
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
Compare Hill Equation vs Q is a constant, n is the number of ligand sites, n is Hill coefficient
Hb Sigmoidal See satsimple.mw and sat.mw
Heterotrophic effectors Affect L Activators decrease L (push to R) and Inhibitors increase it
Hb – microstate predictions (vs sequential) Unlike in sequential model, no R2 or T2 – see states.mw
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
Activators can decrease cooperativity Fig 6a is theoretical (see yf.mw ) Fig 6b and c show activations in real systems
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
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.