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Michaelis-Menten kinetics

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Presentation on theme: "Michaelis-Menten kinetics"— Presentation transcript:

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2 Michaelis-Menten kinetics
Michaelis-Menten equation Km = [S] at which reaction rate is ½ Vmax Michaelis curve

3 Michaelis-Menten Kinetics
Subset of enzymes can be assumed to follow these kinetics Fairly simplified way to model kinetics Two-step reaction Assume steady-state [ES] doesn’t change k2 is rate limiting (ie. S→P (actual catalysis) not E + S → ES (substrate binding to enzyme))

4 Michaelis-Menten Equation
Vo and [S] are experimental values (ie. measurable and/or defined by experimenter) Run experiments to determine Km and Vmax

5 Km Conglomerate of rate constants
If k2 << k-1 (ie. k2 is slow/rate-determining step), Km = k-1/k1 ( = Kd) How tightly does enzyme bind substrate? Lower Km → stronger affinity

6 Km At low [S], Km doesn’t matter At high [S], Km doesn’t matter
Vo is well below Vmax Vo increases proportionally as [S] increases (pseudo-first order) At high [S], Km doesn’t matter Vo ≈ Vmax Typically, Km will jive with [S] In vivo and in experiments

7 Vmax How quickly does the enzyme ‘do the chemistry’?
ie. If the substrate is not limiting ([S]>>Km), the reaction’s rate depends on k2 and [Et] Vmax = k2[Et] so Vmax gives a measure of k2 (rate of ES → E + P)

8 Vmax vs kcat kcat derived from Vmax, but more general usage
Vmax ~ k2 for one-step reaction One-step reactions: very simple case kcat ~ rate constant for rate-determining step in multi-step reaction

9 kcat ~ rate constant for slowest step kcat = turnover number
Units: Vmax mmol/min (for example) kcat s-1 (so you also have to change min to s) kcat ~ rate constant for slowest step kcat = turnover number How many substrate molecules are “turned over” per unit time by each enzyme molecule

10 Comparing kinetics Which enzyme is more efficient
Comparing kinetics Which enzyme is more efficient? Which substrate is preferred? Km → Lower = “better” Vmax/kcat → Higher = “better” “Specificity constant” Units: M-1s-1

11 How do you determine Km/Vmax?
From Michaelis-Menten (saturation) plot Vo and [S] are “raw” data Estimate Km/Vmax OR Use computer analysis

12 How do you determine Km/Vmax?
‘Linearize’ M-M curve Lineweaver-Burk plot Reciprocal of both sides of MM equation y = mx + b Y-intercept= 1/Vmax X-intercept= -1/Km Problem: Small errors at low [S] (ie. to the right) have major effects

13 How do you determine Km/Vmax?
‘Linearize’ M-M curve (part 2) Eadie-Hofstee plot Multiply both sides of MM equation by Km + [S] & simplify Plot Vo vs. Vo/[S] Slope = -Km y-int = Vmax Equal weight to points from whole range of [S] Problem: both axes are dependent on Vo So any experimental error will be magnified

14 Enzyme inhibition Drugs Natural toxins
Natural regulators of enzyme function Use kinetic analyses to determine Potency of inhibition Mechanism of inhibition

15 Enzyme inhibition Two simple/idealized ways an inhibitor can ‘slow down’ an enzyme Interfere with substrate binding “Competitive” inhibitor Increase the Km Apparent Km > Intrinsic Km Slow down catalysis “Non-competitive” inhibitor Decrease the Vmax “Real” reversible inhibitors often work by a combination of the two “Mixed” inhibitor


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