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Concentrations as optimized parameters
Initial or total concentrations can be treated as adjustable parameters, subject to the optimization limits given by the parameter ConcError explained in Chapter 11. A given concentration can be optimized globally or locally. Global optimization means that the same best-fit value of an optimized concentration applies to all datasets analyzed together.
Example 1: Global optimization. Four sets of initial velocity measurements (data file names f1 through f5) were conducted by varying the concentration of a tight-binding inhibitor I, while keeping the concentration of the substrate constant in each set. The concentration of the enzyme was identical in all measurements, but it is not known exactly. In fact, one of the purposes of the experiment was to determine it (active site titration). Here the best-fit concentration of the enzyme applies to the entire superset of experimental data.
[mechanism] E + S <==> ES : K(s) dissoc ES --> E + P : k(cat) E + I <==> EI : K(i) dissoc [constants] K(s) = 100, k(cat) = 10, K(i) = 0.01 [concentrations] E = 0.010 ? [responses] P = 1 [velocities] variable I ; in the first column of each datafile file f1 | conc S = 10 file f2 | conc S = 20 file f3 | conc S = 40 file f4 | conc S = 80 [end]
Example 2: Local optimization. Four sets of progress curve data (data file names f1 through f5) were obtained by varying the concentration of a tight-binding inhibitor I, while keeping the concentration of the substrate and enzyme constant. The concentration of the enzyme is not known exactly, and is subjected to least squares fit. Here each of the best-fit concentrations of the enzyme applies to four of the five individual dataset (progress curve).
[mechanism] E + S <==> ES : k ks ES --> E + P : kr E + I <==> EI : k ki [constants] k = 100, ks = 10, ki = 0.01, kr = 20 [concentrations] S = 10 [responses] P = 1 [progress] file f1 | concentration I = 1, E = 0.01 file f2 | concentration I = 2, E = 0.01 ? file f3 | concentration I = 4, E = 0.01 ? file f4 | concentration I = 8, E = 0.01 ? [end]
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Petr Kuzmic | Jul 12 2005