Unformatted text preview: e high affinity inhibitors with good “drug-like properties”. Basic Kinetic Measurements
[A]0 [S] P Step 1. Write the reaction with
the k's (rate constants)
indicating the process.
Step 2. Write how the
compounds change with
time: [P] d[S]/dt = - k1[S]
d[P]/dt = k1[S]
So, d[P]/dt = - d[S]/dt
Velocity of the reaction is v
v = d[P]/dt = - d[S]/dt = k1[S]
(Units of k1 = sec-1) Enzyme Kinetic Experiment: S P 1. Use constant amount of enzyme, [ET].
2. Measure amount of product P formed as a function of time with several initial
concentrations of substrate S.
3. Calculate initial slopes from the graph of [P] vs. time to get initial rates,
d[P]/dt = vo.
4. Plot the initial velocities as function of [S] [S]4 [P] [S]3 [S]2
[S]1 Concentration of Product P with time as
function of increasing substrate
concentrations [S]1, [S]2, [S]3, [S]4 Enzymes often form an Enzyme:Substrate complex
E+S k1 k2
ES E+P k-1
E is enzyme; S is substrate; P is product; ES is the “Michaelis complex” For many enzyme-catalyzed reactions:
● Acceleration is very fast (µsec to msec)
while the time scale is in minutes. ● d[ES]/dt = 0 means a “steady state
condition” applies to most of the
reaction progress. Total enzyme concentration [E]T is:
[E]T = [E] + [ES]
Vvp f12.02 Towards the Michaelis-Menten Equation
E+S k2 k1 ES E+P (VVP eqn. 12-12) k-1
ES k2 Indicates the breakdown of ES.
Indicates the buildup of ES. Assuming “steady state conditions”
d[ES]/dt = 0
(VVP Eqn. 12-16)
and defining the Michaelis constant KM:
KM = (k-1+k2)/k1 (VVP Eqn. 12-20)
one obtains for the initial velocity vo:
vo = k2[ES] = k2 [ET][S]/(KM + [S]) (VVP eqn. 12-23) The Michaelis-Menten Equation
The maximal velocity of a reaction, Vmax,
occurs at high [S] when the enzyme is saturated,
that is, when it is entirely in the [ES] form:
Vmax = k2[ET] (VVP eqn 12-24).
Subsituting this into :
vo = k2[ET][S]/(KM + [S]) (VVP eqn. 12-23)
( i.e. the last eqn. at the previous slide) gives:
vo = Vmax[S]/(KM + [S]) (VVP eqn. 12-25)
this is the Michaelis-Me...
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