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Transcript
Enzyme Kinetics II Nov. 11, 2008 Robert Nakamoto 2-0279 380 Snyder [email protected] Studying the photograph of a racehorse cannot tell you how fast it can run. Jeremy Knowles Eadweard Muybridge, 1878 Why bother with kinetics? The rates at which a reaction occurs, compared to other reactions in a pathway, will determine the rate limiting and controlling reaction A→B→C→D→E if the reaction C→D is the slowest then regulating the enzyme carrying out this reaction will control the amount of E made [C] will accumulate A→B→C→D→E If only the production of E is followed then one cannot tell which enzyme is controlling the overall rate Or if only the disappearance of A were followed, then one cannot tell how fast E is made Lots of information in a reaction time course If only one time point is taken, then many important aspects may be missed. A non-linear rate A lag before the steady state Running out of substrate A competing activity or build up of product inhibition [product] time Enzyme velocity at steady stateMichaelis-Menton considerations E+S V = Ks ES kcat E+P [E]o [S] kcat Ks + [S] Where kcat[E]o = Vmax, then Valid when binding is much faster than kcat V = The [S] at which v=1/2 Vmax is the Km [S] Vmax Km + [S] v = Vmax = kcat [E]o Vmax/2 Km [S] Linear vs Log activity plots Vmax is estimated from asymptote of maximal measured binding v/Vmax 1.0 0.5 Km at ½ saturating Km at ½ saturating [S] -1 0 +1 log [S] Linear plot is hyperbolic. In log plot, it takes two orders of magnitude in [S] to go from 10-90% saturation. Note: you use the same mathematical considerations for ligand binding to a receptor What does the Km mean? E+S E+S Km = Ks k+1 k-1 ES ES k+2 + k-1 k+1 kcat k+2 E+P Valid when if k+2 << k-1 E+P More general form Ks approximates Km if k+2 << k-1 Elementary rate constants depend on the energy and entropy of activation Transition state theory: temperature and the activation energy activated complex enthalpy EA forward reaction transition state E’A reverse reaction reactants DH of reaction products Reaction coordinate EA is the activation energy for the forward reaction. E’A is the activation energy for the reverse reaction. EA- E’A = DH, enthalpy change for the reaction. Temperature and activation energy: the Arrhenius relationship d lnK dT d lnk dT P DH° = RT2 EA = P RT2 Van’t Hoff equation shows the change with temperature of an equilibrium constant. A similar relationship holds for a reaction rate constant. This equation is rearranged to give: d lnk = And integrated to give: lnk = lnA - EA EA dT R T2 and finally k = A e RT A = integration factor -EA RT What does the Arrhenius eq. mean? -EA k = A e RT A is the frequency of collisions with the proper orientation to produce a chemical reaction. Can be as fast as 1013sec-1, which is about the frequency of collision in liquids. Thus, Arrhenius theory says that the rate constant is determined by i) the ratio of EA to T and ii) by the frequency of collisions The Arrhenius plot slope = log v - EA R DH‡ = EA - RT 1/T DS‡=Rln(ANh/RT)-R DG‡ = DH‡ + T(DS‡) Note that a lower slope means a lower activation energy EA and that the reaction goes faster. The “better enzyme” will reduce EA to a greater extent. Example: amino acid substitutions can affect EA, better or worse catalyst. The Assay If you want to understand the kinetics of a reaction, like the binding of a ligand to a receptor, or an enzymatic reaction, like a phosphorylation or dephosphorylation of a signaling protein, or transport of an ion across a membrane, or transcriptional activation of a gene, You need an assay with the proper “time constant” Time domains of various techniques Laser scatter Dielectric relaxation and electric dichroism Fl polarization Pressure jump EPR and NMR Ultrasound absorption and electric field jump Spectroscopic methods 10-10 Stopped flow and continuous flow Flash and T jump 10-5 seconds Hand mixing 100 102 Specificity of the reaction Is the reaction you are measuring carried out by only one enzyme? Temperature? Co-factors? Competing activities? Are there “non-enzymatic” pathways to the products? Controls, controls, controls. Example of kinetic analysis of a chemical reaction: ATP hydrolysis Detection of ATP hydrolysis Pi production: How? “Coupled” assays Colorimetric or Chromogenic assay Radioactivity What are the variables? Sensitivity Time domain Background Chromogenic reactions for Pi production Acid Molybdate Taussky and Shorr (Fe2+ at acid pH) Fiske and SubbaRow (1-amino-2-naphthol-4sulfonic acid with sulfite buffer Lin and Morales (Vanadate at alkaline pH) Malachite Green These assays stop the reaction, one time point per sample. Luciferase assay hn ATP + luciferin ADP + luciferase Enzyme coupled assay YFE ATP ADP + Pi Pyruvate kinase ADP + Phosphoenol pyruvate Pyruvate + ATP Lactate dehydrogenase Pyruvate + NADH Lactate + NAD+ Follow absorbance change at 340 nm in the spectrophotometer. Radioactivity detection of ATP hydrolysis Labels: [g-32P]ATP OR a or b labels or 14C (3H) labels on adenine Separation of labeled Pi from labeled ATP Acid molybdate Organic extraction Selective precipitation Extraction of ATP by charcoal Norit TLC to separate ATP, ADP and Pi For fast reactions, rapid mixing and quench of the reaction is needed Assay for production of radioactive Pi from [g-32P]ATP Reactions are prepared by having an enzyme solution and a substrate solution. [g-32P]ATP is isotopically diluted with non-radioactive ATP. Reactions are carried out. The reaction stopped with acid. One or more samples for each time point. An acid molybdate solution is added to precipitate the Pi Samples are centrifuged to sediment precipitate, supernatants are removed The pelleted precipitates are dissolved in alkali solution Radioactivity each sample is determined by scintillation counting The amount (moles) of Pi is determined by comparison to standards. Fluorescence assay for Pi production Phosphate binding protein modified with coumarin Fluorescence increase upon binding of Pi Detects release of Pi from enzyme Fluorescence change can be followed continuously in stopped flow Mechanical mixing-spectroscopic observation Usual deadtime ~ 1 ms; time resolution is less than 1 ms Stopped-flow spectrometers Pre-steady state measurements ATP hydrolysis: production of 32Pi from [g-32P]ATP (rapid acid quench) •Syringe A •1 mM F1 •25 mM TES-KOH •0.244 mM MgCl2, •0.20 mM EDTA Syringe B 25 mM TES-KOH 0.46 mM MgCl2 0.20 mM EDTA 0.50 mM [g32P]ATP Final 49 mM Mg2+free 107 mM Mg·ATP 0.5 mM F1 pH 7.5 25 °C Quench 0.3 N PCA 1 mM Pi Pi release: fluorescence signal from MDCC-labeled PBP (stopped flow) •Syringe A •1 mM F1 •25 mM TES-KOH •0.244 mM MgCl2, •0.20 mM EDTA •10 mM MDCC-PBP •“Pi mop” Syringe B 25 mM TES-KOH 0.46 mM MgCl2 0.20 mM EDTA 0.50 mM ATP 10 mM MDCC-PBP “Pi mop” Final 49 mM Mg2+free 107 mM Mg·ATP 0.5 mM F1 pH 7.5 25 °C PMT hn Pi mop: purine nucleoside phosphorylase (PNPase), phosphodeoxiribomutase (PDRM), 100 mM 7-methylguanosine, 0.1 mM a-D-glucose 1,6-bis-phosphate Pre-steady state: addition of 107 mM ATP·Mg to F1 ATPase E+ATP↔E·ATP↔E·ADP·Pi→E·ADP+Pi 1. ATP hydrolysis by production of 32Pi from [g-32P]ATP (rapid quench) 2. Pi release by coumarin labeled Pi binding protein (stopped flow) Fit requires a slow step after hydrolysis and before Pi release E+ATP↔E·ATP↔E·ADP·Pi ↓ krotation E’·ADP·Pi→E”·ADP+Pi