- [Voiceover] Enzyme kinetics is a high-yield topic.
We give it a four out of five.
You really need to understand this
before you go into your boards.
Enzyme kinetics is the study of
enzyme-catalyzed reactions.
It's important to understand because it helps to explain how
enzymes work and also predict enzyme behavior in the body.
The Michaelis-Menten model of enzyme kinetics
is also very high-yield.
It is one of the best-known models of enzyme kinetics that
we have, and it is the basis for most of our understanding
and the way that we teach single-substrate enzyme kinetics.
Let me introduce what we're talking about.
There is a picture on the right that shows
three different reactions, each one of them
with varying concentrations of substrate
but a constant concentration of enzyme.
What we want to know is how does this enzyme
perform under different situations,
such as with a change in substrate.
This is what enzyme kinetics is all about.
How will the reaction on the far left
differ from the reaction on the far right?
So this is a graph that is going to demonstrate
the relationship between substrate concentration
and reaction velocity, and we're going to do it
using the Michaelis-Menten model.
From the curve that we're going to graph,
we will be able to deduce things about properties
that the enzyme and the reaction has, such as what is the
affinity of the enzyme for the substrate,
what is the potency of this enzyme,
how will the reaction change with the addition
of a competitive or non-competitive inhibitor.
So the first point to understand is that
enzyme-catalyzed reactions are saturable.
What that means is that the enzymes
can only do so much work.
There can be such a large increase
in substrate concentration that the enzymes can't keep up.
That means that we do not get a linear response
to the reaction velocity from an increase
in substrate concentration, so let me demonstrate
what's not happening.
Let me demonstrate what a linear reaction would look like.
These red dots represent individual reactions.
Remember, we're not dealing with one reaction
and watching it chronologically with a change
in substrate concentration.
We're actually sampling multiple reactions
in multiple test tubes with a sequential increase
in substrate concentration, and we're only really measuring
the very initial phase, or the very first part
of that reaction, and then we plot those numbers
and draw a curve.
So here is four separate reactions.
Each one of these reactions would've had
a different substrate concentration in the test tube.
You can see that in this false example,
there would be a linear relationship between increasing
substrate concentration and how fast the reaction occurs
or the reaction velocity.
This is not the case. This is false.
What we actually see in real life is a curve that tapers
as the substrate concentration increases,
and the slope of that curve eventually levels out
so that it doesn't matter how much more substrate you add.
The reaction will not go any faster than that point,
and that is called the Vmax or the maximum velocity.
Vmax is important because it helps us understand
the efficacy of the enzyme or the drug if we're using
this model for pharmacokinetics, but we also need to know
the Vmax so that we can calculate half Vmax.
Half Vmax is as simple as it sounds.
It is located halfway between
the value or the rate or the reaction velocity
that is Vmax and zero,
so halfway between those two we have half Vmax.
Sounds easy, right?
If we were to put a point on the curve on our graph
at half Vmax and then draw an x-intercept
or a line straight down from that point,
we would find another important value.
This would be the Michaelis constant or Km.
So now that we've defined these terms,
let's change graphs and play with these values,
move them up and down and see what happens.
So now that we've defined and talked about some concepts,
let's relabel our graph with those things
that we've talked about.
What is Vmax and where is it on this new graph?
It is a line that intercepts the y-axis.
It is a reaction velocity or a rate, and it is placed
such that our curve or our graph never quite reaches it.
It approaches it but never quite reaches it.
What about half Vmax?
Yeah, so half Vmax is exactly halfway between
that rate, which we call Vmax, and zero.
What do we use half Vmax for?
Well, we use it to find the Michaelis constant or Km,
and we do that by placing a point on the graph or on
the curve and then running straight down to the x-intercept.
The Km represents the affinity of the enzyme
for the substrate or the potency of a drug.
An enzyme with a very high affinity for its substrate will
have a very small Km,
so they're inversely proportional.
The larger the Km, the lower the affinity
or the lower the potency, so basically we're saying
the closer Km is to zero,
the faster that enzyme takes off.
So this is interesting.
Look what happens when we move the Km back and forth.
As the, and maybe this will make more sense
if you can see it move, as the Km moves away
from the y-axis, again, the potency is decreasing,
the affinity is decreasing.
Can you see that?
Can you see how the steepness of the curve
of our graph decreases, how the reaction just isn't
taking off quite as fast?
However, Vmax doesn't change, so you can still approach
Vmax if you add enough substrate,
but the speed with which it takes off,
with which the reaction explodes
out of the box, so to say, is slower.
It still reaches top speed. It still reaches Vmax.
It just takes off slower.
So now we're gonna start talking about inhibiting the system
with a competitive inhibitor.
Take just a second to think about how
competitive inhibition works.
Competitive inhibitors directly interfere
with the substrate for binding sites on the enzyme,
so the enzyme has to work a little bit harder
to find the correct substrate.
Well, this is going to increase the Km
and decrease the affinity as we've already seen.
However, think about it.
If you add enough substrate, if you just keeping pouring it
into the test tubes, eventually you will still approach Vmax
just because you'll drown out all the inhibitor.
Vmax does not change with competitive inhibition.
However, the Km does, right,
because that very low substrate concentrations.
The inhibitor is really gonna mess with the enzymes.
It's gonna confuse them.
Does that make sense?
It's pretty cool, huh?
Okay, moving on.
Efficacy, I mentioned this before.
What is it?
Efficacy is or describes the relationship between
a ligand and a receptor or an enzyme and a substrate
and is also related to the maximum response.
So what is the relationship with the graph or the curve
that we have here and efficacy?
Efficacy is demonstrated by the Vmax in this graph,
so as the Vmax goes up,
the efficacy also goes up.
As Vmax comes down, efficacy or efficiency
or maximum response also comes down.
Another thing to make mention of, another thing to note,
is that Vmax is proportional to enzyme concentration.
That's what I mean there by enzyme in brackets,
enzyme concentration.
As the enzyme concentration increased
in our little experiments, in our test tubes,
the Vmax would also increase.
There would be more enzyme to do the work.
It would almost be like sharing the load
amongst more workers.
However, the Michaelis constant would not change.
So, again, let's talk about inhibition.
Non-competitive inhibitors decrease the Vmax
and decrease the efficacy.
However, a non-competitive inhibitor does not change
the Km or the Michaelis constant,
and it really does make sense if you just think about
how non-competitive inhibitors work.
They just cause a general slowing down of the enzymes
without directly interfering with the enzyme
and it's substrate binding to the active site,
so the graph looks something like what you see on the right.
One more thing to think about
in the inhibitor category.
What would a non-reversible inhibitor
look like on our graph?
It would look a lot like the non-competitive inhibitor.
Vmax and efficacy would go down with no change in the Km.
How far down it goes really just depends on
how much of the inhibitor is given and/or how long
the enzymes are exposed and also if their is some source
to replenish the enzymes.
So what would it look like if we replenished the enzymes?
It would go back up, Km would stay the same,
Vmax would go up, and efficacy would go up.
Lineweaver-Burk plots are another fun thing
we can do with Michaelis-Menten kinetics
because I know that you're having fun right now.
Basically, we take the same plot that we're used to,
the same axes and the same concepts,
but we apply them to a graph that looks different.
So on the right you'll see a picture of what you're used to.
On the x-axis is the substrate concentration.
On the y-axis is the reaction velocity.
The Lineweaver-Burk plot is kind of similar.
We're still talking about substrate concentration
on the x-axis and velocity on the y-axis,
but the values are inverted.
Okay.
So instead of the x-axis
being substrate concentration,
it's now one over substrate concentration.
What does that do for the way we interpret this graph?
Well, as the substrate concentration gets bigger,
the fraction gets smaller,
so we actually approach zero
as the substrate concentration gets larger
or the velocity gets larger.
Okay. So keep that in mind.
So let's use the Lineweaver-Burk plot and go over
some examples so that we understand it.
The current graph that you see with this black line
represents our starting point, but I'm gonna add
two new lines to this Lineweaver-Burk plot,
and they are actually going to represent the previous
two graphs that we did, the two curved lines.
So here's the first one,
and here is the second one.
So, first, let's talk about what we're looking at.
Where on this Lineweaver-Burk plot is the Vmax?
Well, think about what Vmax is.
Vmax is a point on the velocity axis,
and that would be the y-axis.
It represents a reaction rate or a reaction velocity
that cannot be exceeded no matter how much
substrate we pour into the system,
so as the substrate approaches infinity,
the Vmax cannot get any larger.
So where on this graph does
the substrate approach infinity?
That happens at the X value of zero,
so the red dot depicts Vmax.
What about the Michaelis constant?
Well, the km, or the Michaelis constant,
is a substrate concentration that represents the affinity
of the enzyme for its substrate.
That is represented on the y-axis at the green dot.
So the slope of this line is actually
Km over Vmax.
Let's shift some of these things around
and see what happens.
So the first thing that we're going to manipulate
is going to be the affinity or the potency.
Do you remember how that looked
on the previous type of graph?
So look at our first example, the red example.
The affinity or the potency was directly related
with the Km, and as the Km moved farther away from zero
or as the Km became larger,
the affinity or the potency of that enzyme
or that drug decreased.
How would that be depicted on the Lineweaver-Burk plot?
Remember, the Vmax did not change,
but the Km got larger.
See how that works?
The Km approaches zero
because we're dealing with inversed numbers.
This is what the addition of a competitive inhibitor
would look like.
Now how about the efficacy?
What if we play around with the efficacy
of the same system?
And, again, this is the same thing that we did
to the previous graph.
What did that look like?
Well, we decreased the Vmax
without changing the Km.
So how will a decreasing Vmax with a constant Km,
how will that look on the Lineweaver-Burk plot?
There you have it.
Does that make sense?
So this is what a competitive inhibitor would look like
if we were to add it to our system
on the Lineweaver-Burk plot.
Pretty cool, huh?
Great way to spend a Friday night.