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CMU BSC 03231 - Lecture

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Biochemistry I Lecture 15 Oct 5, 20051Lecture 15: Hill Plot & Introduction to Enzyme KineticsAssigned reading in Campbell: Chapter 6.1-6.5, 7.3, 7.4Key Terms:• Hill Plot & Hill coefficient nh• Active site, catalytic groups• Transition state theory• Transition state stabilization: Enthalpic• Transition state stabilization: Entropic15.1 Hill Equation:† logY(1 -Y )Ê Ë Á ˆ ¯ ˜ = logKp+ nhlog[L]Hill Plot:1. Define: † q= Y 1 - Y2. Plot of log† q versus log[L]3. Slope at † logq= 0 (Y=0.5) is the Hill coefficient, nh.4. Intercept at † logq= 0 (Y=0.5) gives log KDAve, or the average dissociation constant. Thiscan be seen from the following:At † logq= 0 (Y=0.5):† 0 = logKp+ nhlog[L]† -1nhlogKp= log[L]† logKp-1 / n= log[L]† 1 Kpn= [L]† KDAve= [L]Qualitative interpretation of Hill Plot:nhA. Hill Plot for a non-cooperative system: KD1 = KD2B. Hill Plot for a positive cooperative system: KD1 > KD2C. Hill Plot for a negative cooperative system: KD1 < KD2At low ligand concentrations, the binding measures essentially KD1 because most of themacromolecule is in the [M] form. At high ligand concentrations, KD2 is measured because mostof the macromolecule is in the [ML] form.Biochemistry I Lecture 15 Oct 5, 20052 A. B. C.15.2 Enzyme Kinetics:For the simple enzyme-catalyzed reaction:† SEnzymeæ Æ æ æ PThe enzyme forms a complex with the substrate (S) (similar to a protein-ligand complex) andperforms some chemical reaction/transformation of the bound substrate. The resultant product(P) is released.15.3 Important Features of Enzyme Catalysis:1. Enzymes increase the rate of reactions.2. Enzymes do not change the equilibrium point of reactions.3. Enzymes are not changed by the overall reaction (although they may be reversiblymodified during the reaction).4. Catalysis occurs at the “active site”, which is specific for certain substrates. The activesite has the following with respect to its substrate:• Geometric complementarity• Energetic complementarity5. Enzyme activity is regulated:• by abundance (the number of copies of the enzyme in the cell)• by concentration of substrate(s) and product(s)• by the presence of allosteric activators and inhibitors• by post-translational modification, e.g. phosphorylation• by proteolytic cleavage of zymogens15.4 Transition State Theory:The transition state is a high energy intermediate in the reaction, a distorted substrate on its wayto becoming product. For example, in the hydrolysis of a peptide bond by hydroxide ion, thetransition state is the oxyanion:Log [L]0log (Y/1-Y)Log [L]0log (Y/1-Y)Log [L]0log (Y/1-Y)Biochemistry I Lecture 15 Oct 5, 20053Transition state theory states that the rate or velocity (v) of the reaction is directly proportional tothe concentration of molecules in the transition state:† v µ[X‡]The key assumption made in transition state theory is that the substrates and products are inequilibrium with the transition state. We can then write an equilibrium constant, e.g. for theforward reaction:K‡=[X‡]/[ES]Therefore the velocity of the reaction is: † v µ K‡[ES].Using the relationship between free energy and the equilibrium constant gives the following forthe enzyme catalyzed reaction:† vEµ exp(-DGE‡RT)[ES]For the uncatalyzed reaction:† v µ exp(-DG‡RT)[S]The rate enhancement by the enzyme (assuming all of the substrate is bound to the enzyme; i.e.[S] in the uncatalyzed reaction = [ES] in the catalyzed reaction):† vEv=e-DGERT[ES]e-DG RT[S]= e(DG -DGE) RTFrom the above equation it is clear how enzymes increase the rate of the reaction – they must doso by lowering the energy of the transition state in the enzyme substrate complex. Note theexponential dependence on the activation free energy: small changes in † DG‡ lead to largechanges in rates.Biochemistry I Lecture 15 Oct 5, 20054The transition state of the enzyme substrate complex is stabilized in two ways:1. Enthalpic - The enzyme transition-state complex is stabilized by direct interactions (e.g. H-bonds, electrostatic interactions) between the enzyme and the transition state. This reduces thefree energy of the transition state due to † DH (enthalpy).2. Entropic – Formation of the transition state requires a precise geometric arrangement ofsidechain groups. In the case of a reaction occurring in solution, this would require considerableordering of these chemical groups, i.e., a reduction in the entropy of the system, which isunfavorable.In an enzyme, these groups are already in the correct position because of the way the proteinfolded, therefore there is no loss of entropy in the complex. For example, the serine proteasesutilize a serine, histidine, and aspartic acid to catalyze peptide bond hydrolysis. Consider thefollowing changes in entropy between the initial state and the transition


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