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U-M CHEM 451 - Haldane Relationship

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The One-Intermediate ModelThe Haldane RelationshipThe two-intermediate modelThe “Black box” AnalogyThe Hairpin RibozymeWe measure docking rate constants by single molecule FRETCHEM 451 1st Edition Lecture 8Outline of Last Lecture I. From steady-state approximation to rate lawII. Connection between Kinetics and ThermodynamicsIII. Temperature dependence of the reaction rate constanta. Maxwell-Boltzmann Theoryb. The Arrhenius Equationc. Typical activation energiesIV. Applying our knowledge to enzymes: InvertaseV. Michaelis-MentenOutline of Current Lecture I. One-intermediate model with reversible stepsa. Haldane RelationshipII. Two-intermediate modela. The “Black Box” AnalogyIII. The Hairpin Ribozymea. Measuring docking rate constants by FRETCurrent LectureUp until now, we have assumed that enzymatic reverse reactions can be neglected. But many enzymatic reactions are highly reversible (have a small ΔG) that have products that reverse to form substrates at a considerable rate. The One-Intermediate ModelThe new rate law:These notes represent a detailed interpretation of the professor’s lecture. GradeBuddy is best used as a supplement to your own notes, not as a substitute.The Haldane RelationshipHaldane Relationship: a reversible enzymatic reaction depends on both the product and substrate, related by the equilibrium constant for the overall reaction. The reaction is still independent of the presence of the enzyme. The two-intermediate modelThis now creates six kinetic constants, yet we still have the four parameters Vfmax, Vrmax, KSM, and KPM. Steady-state kinetics cannot distinguish the number of intermediates in a reversible enzymatically-catalyzed reaction. We can only rule out some alternative mechanisms.The “Black box” AnalogyWe cannot solve for these rate constants with a system of only four equations, so we look at a “black box” containing a system of water pipes with one inlet and one drain.- Steady state: after pipes have filled with water. We may observe the relationship between pressure (which we control) and output flow (which we measure).- We do not know the construction of the plumping connecting the inlet to the drain. This requires opening the black box and tracing the pipes.- Steady-state kinetics only yield phenomenology, not mechanism. Intermediates can only be analyzed by independent means.- We can only rule out alternative mechanisms if kinetic data are not compatible with a given mechanism. We cannot unambiguously establish a mechanism.The Hairpin RibozymeExists in viroid satellite RNA. Five reversible rate step.Rueda, D., Bokinsky, G., Rhodes, M.M., Rust, M.J., Zhuang, X. and Walter, N.G. Proc. Natl. Acad. Sci. USA 101 (2004) 10066-10071We measure docking rate constants by single molecule FRETFRET = Fluorescence Resonance Energy Transfer.- Visualize single molecules in microscope- Put spectroscope probe fluorophore on RNA molecule which is excited by green light and emits reddish-greenish light- Once conformational change occurs, the donor transfers energy to accepter through space via dipole-dipole interaction. Instead of green fluorescence, we see red fluorescence from second fluorophore.- We can separate green from red fluorescence and measure both with a sensitive camera.- Immobilize RNA molecules to surface by coupling with biotin (important cofactor for glycosylation reactions)- Use total internal reflection fluorescence spectroscopy: reflect laser beam; only molecules at surface will be illuminated- Individual molecules interchange between docked and undocked forms: visualize green to red transitions- Measure time between high FRET and low FRET states to find the rate constant. (Recall that the rate constant is the average time spent in one state)Kinetic modeling then allows us to extract the unobservable reversible chemistry rate


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