michaelis-menten kinetics
DESCRIPTION
Michaelis-Menten kinetics Michaelis-Menten equation Km = [S] at which reaction rate is ½ Vmax Michaelis curveTRANSCRIPT
Michaelis-Menten kinetics
• Michaelis-Menten equation
– Km = [S] at which reaction rate is ½ Vmax
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Michaelis curve
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))
E + S ES E + Pk1
k-1
k2
Michaelis-Menten Equation
• Vo and [S] are experimental values (ie. measurable and/or defined by experimenter)
• Run experiments to determine Km and Vmax
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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
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kkkKm
E + S ES E + Pk1
k-1
k2
Km
• At low [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
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)
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
• Units: – Vmax mol/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
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tcat
EVk
Comparing kinetics
Which enzyme is more efficient?Which substrate is preferred?
• Km → Lower = “better”
• Vmax/kcat → Higher = “better”
• “Specificity constant”
– Units: M-1s-1
m
cat
Kk
How do you determine Km/Vmax?
• From Michaelis-Menten (saturation) plot][][max
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Estimate Km/Vmax
ORUse computer analysis
Vo and [S] are “raw” data
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
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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
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Enzyme inhibition
• Drugs • Natural toxins • Natural regulators of enzyme function
• Use kinetic analyses to determine– Potency of inhibition– Mechanism of inhibition
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