Practical Enzyme Kinetics

1. Practical Enzyme Kinetics • There are many ways to assay an enzyme! • Assays differ in their features and in their uses and limitations. It is important to understand the terminologies used in describing an enzyme assay and to keep the limitations in mind when you read papers reporting values obtained using enzyme kinetics or when you seek to assay an enzyme for yourself. • The following methods are described for assays designed to measure initial velocities. Recall that working under initial velocity conditions greatly simplifies the interpretation of the kinetic data. The most satisfactory method of determining kcat, kcat/Km and Km is to measure initial rates (≤ 5% of the reaction).

2. Direct Assay • Direct measurement of [P] or [S] as a function of time • eg. cytochrome c oxidase cyt c (Fe2+) cyt c (Fe3+)

3. Coupled Assay • Enzymatic reaction of interest is paired with a 2nd enzymatic reaction which may be easily followed. • eg. Hexokinase • Caveats: • 1st enzyme MUST be rate limiting (product of 1st rxn must be immediately turned over by the second enzyme) • It is often difficult to match ideal conditions for 2 distinct enzymes • Inhibitors (or substrates) may affect both enzymes 3 NAD+ NADH

4. Continuous vs. End-point assays • Continuous assay: The signal is measured at discrete intervals over the entire linear range of the reaction. The initial velocity is measured from the slope of the linear range of the curve. • Discontinuous (End-point) assay: the signal is measured at a specific time point on the linear range of the assay. Disadvantage: won’t notice deviations from linearity!

5. Detection Methods • Spectrophotometry Abs = e  l  c (Beer’s law) vi = dc = dAbs (1/(e  l)) dt dt • Spectrofluorimetry • Radioactivity

13. Transcription 2-10 nM 9-12 nt synthesis 1x108 M-1s-1 30s-1 150s-1 bent

17. Fobs = Fo(1- e-kt)+Fb

20. Expected results fluorescence time Measurement of the dissociation rate constant chase 2-AP High fluorescence No fluorescence excess No fluorescence low fluorescence 2-AP

21. Measurement of the dissociation rate constant 0.05 mM p-dsDNA-T7 RNAP complex (0.05 mM T7 RNAP + 0.1 mM -4T 2-AP p-dsDNA) with 2 mM non-fluorescent p-dsDNA in a standard fluorescence cuvette. Time-dependent fluorescence decrease at 370 nm (upon excitation at 315 nm) was monitored (circles). The fluorescence decrease was fit to Eqn. 6 that provided koff of 0.00034 s-1 (solid line). Thus the overall Kd (= koff/kon) of T7 RNAP-p-dsDNA complex is 1.3 pM.

22. kcat k1 k-1 Kd = k-1/k1

23. P1 E + S ES EI E+P2 P1 EI P2

26. 0.1

27. P1 E + S ES EI E+P2 P1 EI P2

28. Observed rate = k1x[A] = 4 x 106 M-1s-1 x 100 x 10-6 M = 400 s-1 = 20 s-1