Module 6: Enzyme kinetics &
inhibition
Video 2: Michaelis-Menten model
Lauren Parker Jackson, Ph.D.
Dept. of Biological Sciences
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Will introduce Michaelis Menten model in this video
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Kinetics depend on rate constants
Rate constants quantify the rate of a general chemical reaction
k1
AàB
k2
A+BàC
rate= k1[A]
First order
rate= k2[A][B]
Second order
How do we describe an enzymatic reaction in cells?
One model: Michaelis-Menten model for single substrate reactions
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• First recall that all chemical reactions exhibit kinetics, and enzyme-catalyzed
reactions are no different
• kinetics depend on how many reactants and products are involved, and on a rate
constant
• Zero order reactions (not shown here) are independent of [reactant] and depend
only on the rate constant
• First and second order reactions depend on concentrations of reactants and on a
rate constant, because there is only one product
• What about enzymatic reactions in cells? They are really complicated!
• There are almost always more components than this: we have multiple reactants
AND multiple products
• So in biochemistry, we need to figure out a way to study enzyme kinetics and to
measure enzyme rates, which means we need a model
• One useful model is the Michaelis Menten model for single substrate reactions
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Michaelis-Menten model
k1
E+S
k-1
k2
ES à P + E
E: enzyme
S: substrate
ES: enzyme-substrate complex
P: product
First order reaction
Multiple rate constants: k1, k-1, k2
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• We will start with a general description of an enzymatic reaction
• E is enzyme, S is substrate, ES is enzyme-substrate complex, P is product
• This is a first order reaction: formation of product from ES, enzyme E is
regenerated
• We have several rate constants
• k1 is forward rate constant for ES formation
• k-1 is reverse rate constant for ES breakdown into enzyme and substrate
• k2 is rate constant for ES breakdown into P
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Michaelis-Menten model
k1
E+S
k-1
k2
ES à P + E
We can write a dissociation constant for ES:
Kd = [E][S] / [ES] = k-1/k1
assumes k-1 >>k2 (ie, binding reaches equilibrium)
Be careful about dissociation constants (big K) and rate constants (little k)!!
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• We can write a dissociation constant for ES formation
• Kd= [E][S]/[ES]= k-1/k1 (called Ks in your text)
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Michaelis-Menten kinetics
E+S
k1
k-1
k2
ES à P + E
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How can one derive a model that will allow us to use measurable
properties to learn about enzyme kinetics?
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Leonor Michaelis and Maud Menten proposed a mathematical model for
mechanism of invertase (1913)
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This model makes specific assumptions
1. Product does not convert back into substrate (2nd step irreversible)
2. Reaction is at steady-state: [ES] remains constant during reaction
3. [S] is infinitely large (present in great excess)
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• To study enzymes in labs, we need to derive a mathematical model to evaluate
enzyme behaviour
• We could write a rate equation that describes the rate of ES formation but it’s
complicated and we can’t integrate it easily
• We need to get to a formula that is easier to deal with and that will allow us to
plug in numbers that we can measure experimentally
• In the lab, we can often purify or isolate enzymes
• We can add specific and measurable amount of substrate (and cofactors if
required)
• In the lab, we cannot easily measure free [enzyme] or [ES] over the course of a
reaction
• In the lab, we can often measure product formation
• It’s easier to see product forming from nothing, as opposed to substrate
disappearing
• In BSCI2520, we look at one model of enzyme kinetics, based on a model proposed
by Leonor Michaelis and Maud Menten
• Based on studies of invertase, which hydrolyzes sucrose into glucose and fructose
• To tackle these problems, they made a few assumptions to derive a useful
mathematical model
• Many models make assumptions! It is critical to understand these
1. Product doesn’t convert back into substrate; the second reaction is irreversible
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2. Reaction is at steady-state: [ES] remains constant; this is more specific from being
at equilibrium; we set d[ES]/dt=0
3. Our substrate concentration is infinitely large or there is much much more of it
than enzyme (our enzyme is likely to be saturated)
• Each of these assumptions means we can do some simplifying math!
• But remember these assumptions: if you are studying an enzyme reaction that
DOES NOT OBEY one of these, you CANNOT use this MODEL
• Or you can use it with certain caveats
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Michaelis-Menten kinetics
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Let’s understand how simple enzymatic reaction would proceed in a graph
Graph assumes substrate is in great excess over enzyme (saturation)
[S] starts at [S0] and decreases over course of reaction (purple)
[P] increases over course of reaction until we have used up all substrate (green)
Total enzyme= [free enzyme] + [enzyme-substrate]
[free enzyme] decreases and is then regenerated (blue)
[ES] increases and then decreases
In boxed area, [E] and [ES] remain constant for a time (orange and blue)
Why? steady state approximation for ES; saturation for E
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