Post on 12-Mar-2018
Previous Class
•Michaelis – Menten equation
•Steady state vs pre-steady state
Today
Review derivation and interpretation
Graphical representation
Michaelis – Menten equations and parameters
The Michaelis – Menten Equation
v = Vmax [S]Km + [S]
Km = Michaelis constant: Concentration of Substrate needed to reach half maximum velocity – measure of substrate affinity
Vmax = maximum velocity – directly proportional to enzyme concentration
The Michaelis – Menten Equation
Km
Ef + S ES Ef + P k1 k2
k-1
[E][S][ES]
= k-1 + k2 = Km Eqn 1k1
Km is an apparent dissociation constant (Ks) and represents the [S] when v = ½ Vmax
Therefore, a lower Km value indicates a higher affinity for the substrate
The Michaelis – Menten Equation
Interpretation
Obtain kinetic behaviour of an enzyme
E + S ES E + P k1 k2
k-1
k2 = kcat Catalytic constant of the reaction (first order) when k2 is fast (saturating kinetics)
(When EP → E + P is fast)kcat is also known as the turnover number of the enzyme –defining the maximum number of substrate molecules converted to product per unit of time
kcat = Vmax/[ET]
Units
v0 = initial velocity of Product formation = moles Product formation (moles substrate loss)/litre x time
= mM s-1
Vmax = represents the maximum rate the enzyme reaction can achieve. Vmax occurs when all of the enzyme is in the ES complex.
Km = [S] at Vmax/2 = µM
kcat = first order rate constant = s-1
# of catalytic cycles active site undergoes per unit of time
The Michaelis – Menten Equation
kcat/KmAt any [S] including:
At very low [S] ([S]→0) : pre-steady state conditions
v0 = Vmax [S]
Km + [S]becomes v0 = Vmax[S] = kcat[E][S]
Km Km
The second order rate constant kcat/Km indicates the catalytic efficiencyof the enzyme:
A direct measure of the efficiency of the enzyme in transforming Subst.
kcat/Km combines: the effectiveness of transformation of bound product
the effectiveness of productive substrate binding
Unitsv0 = initial velocity of Product formation = moles Product formation (moles substrate loss)/litre x time
= mM s-1
Vmax = represents the maximum rate the enzyme reaction can achieve. Vmax occurs when all of the enzyme is in the ES complex.
Km = [S] at Vmax/2 = µM
kcat = first order rate constant = s-1
# of catalytic cycles active site undergoes per unit of time
kcat/Km = second order rate reaction of E and S = M-1 s-1
Lineweaver-Burke transformation of the Michaelis-Menton equation.
•Velocity vs substrate plots are useful for visually estimating kinetic parameters
•Hyperbolic curves cannot properly determine the upper limit of the curve (Vmax)
•Transforming the data to a form that can be plotted as a line.
Lineweaver-Burke transformation of the Michaelis-Menton equation.
v = Vmax [S]Km + [S]
Reciprocal of the equation is:
1
v Vmax [S]
Km + [S]=
Express reciprocal in the familiar form y = mx + b
1 V Vmax [S]
Km= + 1 Vmax
y = mx + b
Lineweaver-Burke transformation of the Michaelis-Menton equation.
Lineweaver-Burke equation represents a straight line with slope = Km/Vmax, y intercept = 1/Vmax, and x intercept = -1/Km
1 V Vmax [S]
Km= + 1 Vmax
1/[S] (mM)
1/v (mM/min)
0.3 0.25 0.20 0.15 0.10 0.1 0.15 0.2 0.25 0.30 0.35
0.6
0.5
0.4
0.3
0.2
0.1
A
B
Lineweaver-Burke transformation of the Michaelis-Menton equation.
•Most commonly used
•Magnitude of errors can become distorted
•Furthest point to the right (lowest [S]) influences where line is drawn
•e.g. small error in v = large error in 1/v
•Good for observing enzyme inhibition
Eadie-Hofstee Plot
•Multiply both sides of L.B. by Vmax
•Multiply both sides by v
•Rearrange for v
v0
[S]Km = -Vmax v0
Plot v0 vs v0[S]
Eadie-Hofstee Plot
•Best for controlling slight deviations from linearity
•One disadvantage is that the least precise parameter (v0) is expressed in both sides of the equation and plot
Plotting kinetic data
Michaelis-Menten kinetics (steady state kinetics)
Measure Initial rates (v0) at different substrate concentrations by detecting the absorbance difference over time and obtaining the slope of the line
Obtain various initial rates at different substrate concentrations and plot
Use Lineweaver-Burke plots to obtain kcat, Km, kcat/Km
Plotting kinetic data
Measuring initial rates:
•The initial velocity is the amount of product produced per minute
•Assay involves adding all of the components including substrate first
•Once enzyme is added the absorbance is continually monitored andrecorded with respect to time
•Abs vs time can be plotted
•Determine slope of tangentA
bsor
.
time
Enzyme added
Plotting kinetic data
Measuring initial rates:
•The slope of tangent = ∆Abs/unit of time (min)
•Recall A = εcl, therefore ∆A = ε∆cl (change in conc of Product)
•When ∆c occurs in a known time period then ∆c min-1 = v0
•v0 = ∆A min-1/ εl = ∆c min-1
•Has M/min after multiplying by vol. of enzyme assay solution theunits change to mol/min.