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Michaelis-Menten Kinetics

Michaelis-Menten Kinetics. Chrisantha Fernando University of Birmingham October, 2006. How fast does an Enzymatic Reaction Run? . Assume a reaction of the form… k1 is the forward rate of ES complex formation, and k1’ is the backward rate.

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Michaelis-Menten Kinetics

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  1. Michaelis-Menten Kinetics Chrisantha Fernando University of Birmingham October, 2006

  2. How fast does an Enzymatic Reaction Run? • Assume a reaction of the form… • k1 is the forward rate of ES complex formation, and k1’ is the backward rate. • We want an expression for the forward rate, i.e. k2[ES], but this cannot be solved analytically.

  3. Simplifying Assumptions • Assume that k2 << k1 and k1’, i.e. that there is a quasi-equilibrium of the state of ES, I.e. assume that there is a quasi-steady state of the ES complex, i.e. d[ES]/dt = 0 • If, initially [E] << [S], then this means that Etotal = E + ES.

  4. From the full ODEs • We have he equation… • Substituting assumption 2 (Et = E + ES), and 1.

  5. Rearranging.. Since rate = k2[ES] And dividing by k1

  6. Inhibition Competitive Un-competitive Non-competitive Substrate Inhibition

  7. Cooperativity and the Hill Equation

  8. Monod-Wyman-Changeux Kinetics

  9. Applications • Regulation of the Lac Operon in Cellerator, see CSN webpage… • Transcription Factor Regulation, see next page…

  10. TF Network AB B A Gene b Gene a D C Gene d Gene c

  11. Transcription Regulation • Bintu et al 2005. PTO.

  12. Etc…

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