#10 Biochemistry Enzymes II Lecture for Kevin Ahern's BB 450/550

Uploaded by oharow on 17.10.2011

Kevin Ahern: Tailgating is always fun.
The beautiful thing about tailgating is,
it doesn't matter if you win or lose.
Before the game even starts, you're ready.
It doesn't matter, right?
Last time I got started talking about enzymes,
and I'll be talking about enzymes today
and in the lecture on Wednesday.
I've had a couple of questions about where the material's
going to go and I haven't decided yet.
It will almost certainly go through the exam on Wednesday,
but it all depends on how far I get.
So I don't have a set place, I just like to see how things
are going and decide according to that.
But it will probably go through the exam on Wednesday.
I will announce on Wednesday where the exam will go to.
In anticipation of a couple of other questions about the exam,
number one, I will do a review session and that
will likely be on the weekend.
I haven't decide on a time for that yet,
but I will announce that, as well.
Yes, I will videotape the review session,
so if you can't be there you'll have
a chance to watch it, et cetera.
Let's see, what else?
How to study for the exam.
My strong recommendation is that you use my highlights
as an outline for your studying.
It doesn't mean you should only look at the highlights
but you should use the highlights as an outline.
That lets you sort of broaden from there.
I definitely do not recommend you study old exams.
That's just a dumb idea.
So study the material.
The old exams that I provide are there
for you to see the format of my exam,
and it's very important you understand the format.
So you don't waste too much time on a question,
you don't waste too much time on a section,
you need to understand that format.
The format will not change from the way you see it on the exam,
and I'll have more to say about that as we get closer to it.
Those are just some general guidelines for you.
A lot of you are coming and asking questions,
and I think that's great.
I love to answer questions.
If you have questions, please come see me.
Please come see the TAs.
If you want a tutor, I can help you get a tutor.
Remember that the TAs are free tutoring
during their office hours.
You don't have to go to just your TA's office hours.
You can go to any TA's office hours and have,
essentially, a free tutor, so take advantage of that.
You're paying for it.
You should get it.
Last time, I think I finished at about this point,
where I talked about maximum velocity and I talked about Kcat.
Let me just briefly refresh what I said on that,
and that is that maximum velocity is dependent on enzyme,
on how much enzyme that we use, just like maximum car production
is dependent upon how many factories I have producing cars.
So it's a relative thing.
I use more enzyme, I get a higher maximum velocity.
I use a lower amount of enzyme, I have a lower maximum velocity.
We need to take maximum velocity
and turn it into a quantity that is independent
of the amount of enzyme, and that's why we take the maximum
velocity that we determine and divide it by
the concentration of enzyme that we used to get that.
So the maximum velocity divided by the concentration
of enzyme gives us a very important quality called Kcat.
Kcat is a quantity that is linked to the enzyme.
It's a characteristic of the enzyme.
It is not dependent upon the quantity of the enzyme that I use.
So Kcat is also called "turnover number" or identical things,
and they represent a number.
So if I had a Kcat of 100,000,
then it means that my enzyme is converting 100,000
molecules of substrate into product per second.
Each molecule of enzyme is doing that, okay?
So the turnover number gives me a relative measure
of how fast the enzyme is working.
If we think about an enzyme, there's a couple of terms
that I want to define for you.
One, I keep talking about substrate,
and I sort of briefly mentioned it as an aside,
but you should know that a substrate is a molecule
that the enzyme is acting upon.
A substrate is a molecule that the enzyme is acting upon.
The place where the enzyme acts upon the substrate
is known as the "active site."
This is the place where the reaction is catalyzed.
So the active site is a portion of the enzyme,
a specific place in the enzyme,
where it catalyzes the reaction.
Now, commonly, the active site is internal to the enzyme.
We'll see some examples of that actually next week,
not this week.
Molecules that will fit into the active site
have a fairly specific shape.
This is why enzymes, as I said earlier,
will not work on all molecules.
They work on specific molecules of specific shapes
that will fit into their active site.
Some enzymes have more flexibility than others
do to accommodate other molecules.
Some are extraordinarily specific.
So there are some big differences between them.
What you see here is an enzyme and it has some various
side chains that are here.
This enzyme probably works on a couple of substrates.
Some enzymes may put two things together and make one.
Some enzymes may transfer something from one substrate
to the other inside of it, and some enzymes may simply
take a substrate and rearrange it.
So there's all kinds of possibilities for what
an enzyme can do.
Student: Are enzymes typically bigger than the substrate?
Kevin Ahern: Are enzymes typically bigger than the substrate?
Absolutely, absolutely.
Well, let me back up on that.
Yes and no, alright?
So, yes, you should always think of them in those terms.
But there are some enzymes that work on other enzymes.
So if we define that other enzyme as a substrate,
then I would say, well, not necessarily, but, in each case,
when it's working on a another enzyme,
it's working on a specific portion of that other enzyme.
So, in essence, the answer is, yes,
they will always be bigger than their substrates.
Other questions?
I got off on a big roll, there, didn't I?
Student: Does substrate usually bind to the active site,
is that...
Kevin Ahern: So the substrate binds
and will be held in at the active site, right.
So we can think of a binding site, and people say,
"What's the difference between a binding site
and the active site?"
Well, we can almost think of them interchangeably.
The substrate has to bind and a portion of it is going to stick
into the active site where the reaction's catalyzed.
That's really what's going on.
So I use the terms essentially interchangeably,
"active site" and "binding site."
Yes, sir?
Student: You said that commonly the active site is internal,
like inside the enzyme.
Does that mean that there has to be a very
specific molecule to go inside the enzyme?
Kevin Ahern: So his question is, do you have to have
a very specific molecule to get in the enzyme?
And the answer is, yes, absolutely.
That's why enzymes have very,
very strong structure specificity, yes.
So that is the sort of overview of them.
Not surprisingly, one of the things that we see
is that the binding of the substrate to the enzyme
commonly occurs as a result of hydrogen bonds.
Here we see some hydrogen bonds that are helping
to hold this substrateóin this case,
uracilóin the active site of an enzyme.
That's not at all uncommon.
What we will see next week is that,
when we look at enzyme mechanisms, that some enzymes,
as a result of their catalysis,
transiently become linked covalently to their enzyme.
I emphasize "transient" because if it becomes covalently
linked and it doesn't come off, we just destroyed the enzyme.
We'll talk about that next week.
For right now, when we think of binding,
the binding occurs essentially by hydrogen bonds.
Hydrogen bonds are the most common bonds we see in nature.
Now I need to just introduce a couple of concepts to you
with respect to how enzymes work.
How do enzymes do what they do?
There are two common models that are used to describe mechanisms
of enzymatic action, and these two models that are there,
usually you've only heard of one of them.
In basic biology classes one of the things
that you're almost always taught is that the enzyme binds
to the substrate very much like a lock fits a key.
I see people shaking their heads before I even start to say that.
That there's a relationship.
The key, not all keys will fit into an enzyme.
I mean, not all keys will fit into a lock and not
all substrates will fit into an enzyme.
That relationship and that metaphor actually works
very well to describe substrate binding.
It does not, understand "not," do a very good job
of describing how an enzyme accomplishes what it accomplishes.
So the first modelóit's called the "lock and key model"
it's also called the "Fischer model"óis shown here.
There is your lock.
There is your key.
There is a perfect relationship between them,
and it explains why enzymes only bind
and act on specific molecules.
Only certain keys will fit into the lock.
So it's nice at explaining that.
By the way, when you see this thing that says
"ES complex" that's just the enzyme bound
to the substrate before the reaction has occurred.
So binding has to occur before the reaction occurs,
and we call this thing the ES complex.
Well, that's very nice about explaining specificity,
but it doesn't do a very good job of telling us how
it is that the enzyme catalyzes the reaction that it does.
As a result of that, peopleóa man named Daniel Koshland,
for exampleósaid that we're not thinking about this
in the right way, and the reason that we're not thinking
about it in the right way is this assumes a rigid enzyme.
Enzymes really aren't rigid.
You saw hemoglobin had very tiny shape changes,
for example, that happened.
It tells us that proteins, of which enzymes are included,
proteins have flexibility, and that flexibility turns out
to be very important for understanding how an enzyme works.
So Daniel Koshland proposed this, and he proposed that,
instead of a lock and key model for explaining enzymatic action,
that an induced fit was a better descriptor.
The induced fitóand this is not the best figure,
but you get an idea hereónotice that here's the enzyme
before it has bound to substrate.
You'll see that there's something that resembles a,
and there's something that resembles b,
and there's something that resembles c.
But it's not exactly what it ends up being over here.
It's not exactly that.
So what this tells us is, first of all, the enzyme is flexible.
It has to be.
But that the binding of the substrate actually
induces the enzyme to change shape.
It induces the enzyme to change shape.
You think, "Well, how does that happen?"
We could imagine that there's quite a few ways it might happen,
even for something as simple as this.
Imagine, if you will, that a fits a very well.
When a binds to a over here, this causes a conformational change,
not unlike the conformational change we saw with
oxygen binding to hemoglobin.
And now this starts getting to shape more like b,
and changing of b makes it more like c,
andóbang!óthe enzyme has bound to the substrate.
So this induced fit is a fundamental difference
from the Fischer lock and key model.
The Fischer lock and key modelóand I'll explain the significance
of that in a secondóbut the Fischer lock and key model says
that enzymes bind to substrates, and then magic happens.
It doesn't explain catalysis.
On the other hand, the induced fit model tells us
that the enzyme binds to the substrate,
this causes a change in the enzyme,
and this change in the enzyme may bring regions together
that weren't together before,
and this new structure favors catalysis.
Very much like we saw in hemoglobin,
where this new structure favored binding of additional oxygens.
So the flexibility of the enzyme,
and we'll see several examples of it this term,
the flexibility of the enzyme is critical
for how enzymes function.
It turns out that when I talked the other day
about the Kcat of enzymes that had a Kcat
of a millionówe saw carbonic anhydrase
had a Kcat of a millionóand I said there's no way
that we'd get that with a chemical catalyst,
we realize that the flexibility is what differs
between an enzyme and a chemical catalyst,
and that flexibility facilitates all of
the properties of the enzyme.
So the induced fit model does a very nice job
of explaining how catalysis happens.
The induced fit model, if we were to summarize it,
says that not only does an enzyme change a substrate,
but it says that a substrate also
transiently changes the enzyme.
That's a very, very key point in understanding
how enzymes function.
Not only does the enzyme change the substrate,
but the substrate also transiently changes the enzyme.
Yes, sir?
Student: Could that explain how some enzymes
can bind to an entire class of substrates...
Kevin Ahern: Yes.
Student: ...by catalyzing the activity at different
rates for each one?
Kevin Ahern: Yes, his question is a very good one.
His question is, does that explain how some enzymes
can bind different substrates and have different Kcats
for those individual substrates?
And the answer is, yes, it can be a factor, absolutely.
It explains, as you could imagine,
why some enzymes are more flexible, bind different substrates.
They may have more flexibility of binding in that region.
We'll... oh I'm sorry.
Student: The change done to the enzyme would have
to be less permanent, though, otherwise...
Kevin Ahern: That's why I said "transient."
Student: Oh, meaning...
Kevin Ahern: It's transient, yeah.
It's not a permanent change.
If it's a permanent change,
if we make a permanent change to an enzyme,
I don't care what it is, the enzyme works one time.
One time.
So we don't want to make permanent changes because,
again, by the definition of a catalyst,
remember your definition of a catalyst from
freshman chemistry is a catalyst speeds
a reaction without itself being changed.
If when I finish with this enzyme it has been changed,
then I don't have a catalyst anymore.
But the difference between an enzyme
and a chemical catalyst is that transient change.
That change can happen to an enzyme
and actually enhance its ability to function,
and that's why we see such an increase in activity.
Student: Yeah, just as a follow-up, if a enzyme generally
is able to bind to a wider class of substrates...
Kevin Ahern: Yep.
Student: ... a larger, broader range, does that lack
of specificity for a single target give
it less catalytic activity?
Kevin Ahern: So his question is,
if an enzyme binds a bunch of substrates does that basically
make it less functional or less effective as an enzyme?
The answer is, as I'll talk about in a little bit,
there's not a direct relationship between
the binding of the affinity of the enzyme
and the rate of the enzyme reaction.
So there's not, no.
Okay, you guys are thinking about this.
I'm very pleased to see that.
That's good.
The induced fit model is a very interesting model
as we think about it, and it really does explain
how enzymes function differently from chemical catalysts.
Well, at this point, I need to introduce
and say a few words about the Michaelis-Menten model
of explaining or studying enzymatic reactions.
This is simply a way that we do our experiments.
There are some reasons why we do experiments the way
that we do to study enzymatic reactions.
Let's imagine that I'm interested in studying
carbonic anhydrase, and carbonic anhydrase catalyzes
a reaction that goes very, very, very fast.
I'm interested in how fast this enzyme can make product.
So I start with my enzyme.
I start with my substrate.
I let the reaction go and I start measuring
how much product that there is.
There's a problem with this,
and the problem is that this becomes an issue
when we think about equilibrium.
Equilibrium happens when we have reactions
going forwards and backwards at the same rate.
Now, I'm interested in understanding how fast this
enzyme is making product.
I really don't want to see the backwards rate, right?
Because that's going to make it look like my enzyme
isn't going as fast as it possibly could go.
So one of the considerations I have in doing
my experiments is I want to measure what are called
"initial velocities," Initial velocities.
Initial velocities are done on a fairly short time scale,
before the amount of product starts to accumulate.
Once the amount of product starts to accumulate,
I get way up here in this range, actually,
up here in this range, once the product starts to accumulate,
now the backwards reaction starts going
and I'm going to see a less accurate measure of velocity.
I'm really only interested in the conversion
of substrate to product, not product back to substrate.
So one of the considerations is that I should be working
at initial velocity...
fairly short time frames to do those measurements.
There are a lot of considerations in the Michaelis-Menten
and I'm not going to go through all of them,
nor am I going to require you to do the derivation.
There is some sophisticated math that we would have
to do to derive Michaelis-Menten,
and I'm not really interested in having you understand that.
But there are some things that I want you to understand
that arise from Michaelis-Menten.
You've seen maximum velocity is one of those.
Kcat derives from maximum velocity,
and I'm going to illustrate another one to you in just a second.
Now, what am I showing you on the screen?
I haven't even told you this.
Here's that V-versus-S that we did before.
You'll notice that little zero right there.
That zero means, initial velocity means measure
that velocity very quickly.
Don't let things accumulate.
How would I do this experiment that you see
on the screen right here?
I think it's important for students to understand
how we perform experiments in a lab.
These points didn't just come out of the air,
but, in fact, somebody had to do the work to do those.
So how would I do that experiment?
Well, when I do an experiment,
I always want to have one variable,
one thing that is changing and I keep everything else,
as much as I can, constant, because I can't determine
how the two variables are affecting an experiment.
If I were to do this experiment, I want to generate my curve,
I'm interested in velocity versus substrate concentration.
Well, one of my variables is obviously going to be
varying concentrations of substrate.
Let's say I take 20 tubes.
I put into those 20 tubes the same amount
and the same concentration of buffer.
I put into those 20 tubes the same amount
and the same concentration of enzyme.
I measure each reaction, ultimately,
for the same amount of time, a fairly short period of time.
But the difference is, in each tube I have a different
concentration of substrate that I'm adding.
Well, higher concentrations of substrate, way out here,
are going to give higher velocities
than low concentrations of substrate.
Higher concentrations of substrate are going
to give higher velocities.
Student: That initial velocity,
is that also going to be a max velocity?
Is that the fastest it's going to be going at any point?
Kevin Ahern: Well, maximum velocity is what I determine
when I get the enzyme saturated with substrate out here.
Initial velocity, every one of these is done
at the same time point.
So, no, not everyone is going to be maximum velocity,
because that's way out up here.
I'm trying to determine maximum velocity.
So to determine maximum velocity,
I have to do this experiment I've just told you.
Clearly, if I'm way down here in terms of concentration,
that is not going to be maximum velocity
because, again, the analogy to the factory,
where I've got this factory that doesn't have enough
supplies to keep things going as fast
as I want to keep the workers working.
Okay, makes sense?
Other questions there?
I want to introduce, at this point,
another parameter that we can learn by doing
Michaelis-Menten kinetics.
This parameter is an important one.
It might seem at the surface like it's related to Vmax,
but, in fact, it's not.
This parameter that we're interested in,
not only are we interested in how fast an enzyme works,
but we're also interested in how much affinity
the enzyme has for its substrate.
How much affinity do you have for your significant other?
Some of you have high affinity.
Maybe, if you're not getting along real well,
maybe you have low affinity.
But affinity is a desire to, shall we say, grasp.
Why is that funny?
I knew it would be, but why is that funny?
It's always nice to think of real world examples
for what are actually fairly abstract molecular concepts,
and affinity is one of those that always generates giggles.
So an enzyme's affinity for its substrate is very much
like your affinity for your significant other.
That's a real world example.
Well, the measure of that affinity is called Km.
It's called the "Michaelis constant,"
and you don't need to know that.
Just Km is fine.
Let's think about what Km is.
Let's imagine I have an enzyme, and we'll come back to this
graph in a second, so I'll explain the graph to you,
what I'm telling you, in a second,
let's imagine that I have an enzyme
and it has a very high affinity for its substrate.
That means when that enzyme is out there it's going
to grab that substrate.
You see your significant other all the way across campus
and you go racing over to grab the significant other.
Or maybe you have several significant others.
I don't know if you have.
And that actually becomes important
for the other consideration.
Let's say I have an enzyme that doesn't have much
affinity for its substrate.
They don't really feel like running all the way
across campus to go grasp the significant other.
But, hey, there's one over here.
Let me grab them.
If I start flooding the enzyme,
if I have an enzyme that has low affinity for its substrate,
I have to flood it with significant others before
it will start grasping.
I have to flood it.
Well, what does that mean?
It means if I go to saturating amounts of substrate,
way up here at Vmax,
everything at saturating amounts is going
to have substrate bound to it.
So the amount of substrate it takes to get to Vmax
doesn't really tell me anything,
because everything that's saturated with gigantic
amounts of substrate is going to have that.
So if I want to measure the affinity,
I don't want to be way up here in this region.
I actually use something called the Vmax over 2.
Now Vmax over 2, I don't actually have to have
the saturating amount to be up here to get to that amount.
Instead, what I have to have is enough substrate
to get it to this point.
If I do this for all enzymes,
then I have a comparator for each one.
That comparator turns out to be the Michaelis constant.
Now, based on what I've just told you,
does an enzyme that has high affinity for substrate
have a high Km or a low Km?
It has a low Km.
It takes very little substrate to get to half maximum velocity.
Something that has low affinity
for substrate will have a high Km.
It's important in science to be precise.
One of the ways that students in this class learn
this message the hard way is I'll ask them on an exam,
"What is Km?"
If I didn't tell you anything else,
over half of you would say,
"Km is Vmax over 2."
Now, I will ask you, is that point the same as that point?
Km is the substrate concentration
that it takes to get an enzyme to Vmax over 2.
They are not the same thing.
That's like saying 60 miles per gallon
is 30 miles per hour.
It doesn't make any sense.
It doesn't make any sense.
So Km is a substrate concentration.
Pound that into your heads.
High Km, low affinity.
Low Km, high affinity.
Does that make sense?
So Km is not the Vmax over 2.
Now I know there'll probably be some questions at that point.
Let me stop and ask if there are any questions.
Was I that clear?
Yes, question?
Student: [unintelligible]
Kevin Ahern: If an enzyme has multiple sites,
multiple binding sites where it can catalyze a reaction,
we study it in exactly the same way... exactly the same way.
Good question, and I'll actually show you,
when I talk about mechanism for that next week,
that there are some interesting things that happen as a result
of enzymes having multiple sites where we could actually
change one site and that affects the whole enzyme.
But let me save that for then.
Wow, okay that's good.
We're moving right along here.
Everything I've shown you so far has been a very simple plot,
and that simple plot has shown you velocity
and how did I define velocity, again?
Was it that big of a weekend, guys?
Student: Yes.
Student: Concentration of the product over time.
Kevin Ahern: Concentration of product over time.
So I plotted velocity versus substrate concentration.
So everything I've shown you has been that,
and you can see from this plot right here that, well,
it's kind of hard to tell exactly where Vmax is, right?
I mean, I have to kind of make a guess about where
this is going to eventually run in up here.
So because I have to make a guess in this,
I have to make a guess in thisóbecause that's just half
of itówhich means that I have to make,
ultimately, a guess in this.
I'd like to have a way of determining
these values that are more precise and easier to do.
So to do this, people have come up with other ways
of plotting the same data...
other ways of plotting the same data.
In that example I gave you, I had 20 tubes.
I had 20 concentrations and each one had a different velocity,
which meant I had 20 different velocities that were there.
What if I took and I simply inverted the numerical
value of each one of those?
Instead of velocity, I take 1 over the velocity.
If the velocity is 4 micromolar per second,
then 1 over it would be 1/4 micromolar per second.
That would correspond to a substrate concentration
that might have been 2 micromolar,
so that when I invert that, it becomes 1/2.
I take and I invert every value
and then plot the inverted values.
If I do that, I create a different kind of a plot.
It's the same information.
I don't have to do the experiment any differently.
I'm just inverting the values of these,
and I create something called a Lineweaver-Burk plot.
You can see from this that there's some real
advantages to plotting the data in this way.
I'll point out the advantages and then I'll point out
a couple of other things to you.
The advantages are that the place where the line intersects
the y-axis is known as 1 over Vmax.
I have a much more precise way of determining where Vmax is
and I can see this thing is getting ready to jump, isn't it?
Hehe, Alright.
[class laughing]
I feel like I accomplished something there, that I beat it!
I beat the system here!
Isn't that cool?
So the y-intercept is 1 over Vmax.
I now have a precise way of saying what that is.
I take whatever this value is and I say, all right,
if I want to know Vmax, then whatever this value is,
I invert it.
Bang, I've got Vmax.
The x-intercept has a value of minus 1 over Km.
I take whatever this value is, I take minus 1 over it,
and I get Km.
Now, these give me very nice and simple ways
of making these determinations.
Don't worry about the slope.
You can memorize that if you want,
but I think if you know the intercepts
you're in much better shape.
The beauty of this is I get a straight line.
Notice that all of the points that I did before
are all in this quadrant.
Why is that?
Student: They're all positive.
Kevin Ahern: They're all positive.
I can't have a negative substrate concentration.
I can only draw a theoretical line to that.
So by drawing the line, after I align my points,
to that, I get that value.
So Lineweaver-Burk plots are very,
very useful because these two intercepts,
this one right here and this one right here,
are consistent with the line that we see there,
and these two intercepts give me very,
very valuable information for me about
an enzyme and how the enzyme works.
We're just sailing through stuff.
Other comments or questions?
Student: You said that the Vmax was just a guess?
So [unintelligible] on this plot?
Kevin Ahern: Well, it's really not,
because this is an extrapolation back from here.
I can actually, if I do a least-fit square of this line,
I get a precise value there.
So, in essence, no, it's not.
Student: So, in essence, this is more precise
than guessing you would do...
Kevin Ahern: Yeah, yeah.
And this is very commonly done with data,
we use a Lineweaver-Burk plot.
The other plot doesn't have a name.
It's called a V-versus-S.
That's what it's called.
Don't forget that that's concentration of S.
So those little brackets mean concentration of S.
In fact, that's what it means right here,
1 over the concentration of S.
Brackets always refer to concentration.
And, again, we're plotting 1 over the initial velocity.
Student: The concentration for all of these is in molarity?
Kevin Ahern: Concentration can be in
whatever you want it to be, but it's generally molarity, yes.
Okay, good.
Now let's look at a variety of enzymes.
We see that enzymes can have very different Km values,
very, very different Km values.
Here's the Km value for chymotrypsin in micromolar, again,
micromolar is a measure of concentrationó5,000.
So high Km means low affinity,
so this guy has relatively low affinity.
Whereas, here's lysozyme which has very high affinity
for its substrate.
Here's an arginine-tRNA synthetase,
very high affinity for its substrate.
Like the question that the gentleman in front
asked earlier about what if an enzyme
has multiple substrates that it can bind,
it's not restricted to just binding one,
there are different Km values that will
be associated with those, different Km values.
How could I explain that with an induced fit model?
Well, we could imagine that the very first thing that
makes contact could actually be a limiting factor, right?
If that very first a that bound to a was more like
an a-prime and it didn't exactly fit,
it might have less likelihood of getting in there
and making those other changes necessary for the enzyme
to have the proper configuration for a reaction.
So the induced fit model still fits multiple substrate
interaction and how an enzyme works with that.
Look at carbonic anhydrase here.
It has a relatively high Km.
But, boy!
Once we flood that sucker with substrate, it takes off and goes.
Now, carbonic anhydrase is an odd enzyme.
I'm going to talk about it in just a minute,
because it has a very interesting property associated
with it that I'll tell you about.
So we don't see a direction relationship between
Km values and Kcat values.
They're not the same.
There's not a relationship, as such.
We see fluctuation with those.
Here are the turnover numbers.
This turnover number 600,000, we will see variation
in turnover numbers a little bit based
upon different conditions that we might use.
If I did it a different pH, I'd get a different Kcat value.
But as long as we specify the conditions,
we will get the same Kcat value from one batch
of enzyme to the next.
We see quite a wide range of velocities.
Here's lysozyme.
Lysozyme had a very low Km,
but it doesn't have much turnover number.
There's not a relationship between these two quantities.
Multiple substrates.
Well, if we talk about an enzyme that'll bind to multiple things,
here's chymotrypsin.
Chymotrypsin will act on different amino acids.
Remember chymotrypsin is a protease,
so it's recognizing and binding to specific amino acids in
a protein and then cutting their peptide bond.
Here are the different things that it will bind to and cut,
and here is a measure of the Kcat over the Km.
We see very wide range of these two.
I'm going to talk about the significance
of Kcat over Km in just a second,
but we see that there's quite a fluctuation.
The enzyme behaves differently with
some substrates than others.
Something like phenylalanine it really likes.
Something like glycine it doesn't like so much.
There's a millionfold difference between these two.
Let's think about enzymes, in general.
We've got parameters now for how fast an enzyme works,
and we've got a parameter for how much grasping affinity
the enzyme has for its substrate.
If we were to define a perfect enzyme,
what qualities would it have?
In terms of Kcat, would it have a high Kcat or a low Kcat?
High, right?
We like efficiency.
We like speed.
So it would have a high Kcat.
How about Km?
Students: Low.
Kevin Ahern: Low.
So a perfect enzyme would have a high Kcat.
It works very fast, but it doesn't take
very much substrate to get to Vmax over 2.
It likes its substrate.
We can get this sucker going pretty readily.
That's what they're plotting in this thing here.
They're plotting the value of Kcat divided by Km.
The most efficient enzymes will have a very high Kcat over Km,
because the Kcat will be high and the Km will be low.
The Kcat will be high and the Km will be low.
I'm going to tell you something that's going to surprise you.
There's very few things in nature that we describe as
"perfect" but there's a certain category of enzymes
that clearly are.
Perfect enzymes.
What is a perfect enzyme?
Well, we talked about the ideal enzyme.
Here's the ideal qualities.
It's got a high Kcat and it's got a low Km value.
But a perfect enzyme, when we study all the enzymes
that are out there, we discover that there's a group
of enzymes that get a very high Kcat over Km
and they sort of hit a brick wall.
They don't get that value much beyond a certain point.
It doesn't go infinitely high.
They get to a certain point and it gets no higher.
And you think, "Why is that?"
The reason that happens is that
when an enzyme is perfect, two things occur.
One, any changes to the enzyme will result
in a less efficient enzyme.
It'll have a lower Kcat over Km.
So it has evolved to the point where it's going as rapidly
as it can go.
Well, what limits the rapidity of an enzyme?
It turns out that what limits the rapidity of an enzyme
is how fast a substrate can diffuse into the active site.
We didn't think about this before.
Think of carbonic anhydrase.
If it's catalyzing a million molecules of product per second,
that means a million molecules of substrate have got
to bind in there per second.
That's why it's really hard to think about how an enzyme works,
compared to something in the macroscopic world.
That's how fast that that substrate has to diffuse in there
and get that reaction going.
For perfect enzymesóthis is importantófor perfect enzymes,
the limiting factor is the rate of diffusion
of the substrate in water.
If they could diffuse faster, that value would get higher.
But the reason that they all get to that same point
and have basically the same Kcat over Km value, is because water,
things can't diffuse any faster in it than that.
Student: Is that just for perfect enzymes or all enzymes?
Kevin Ahern: That's for a perfect enzyme.
These are what we call "diffusion controlled enzymes."
You'll see their values do fluctuate a bit,
but basically 10 to the 8th is about where they get stuck.
The substrate can't diffuse any faster in water.
And, yes, you could imagine some substrates will have
different diffusion rates in water than others will,
which is why we see a little bit of fluctuation,
but basically they're all in that range.
Now, these guys are perfect.
I say that they're perfect because if we mutate anything
in these enzymes we get something less efficient.
The selection process of evolution is remarkable
in terms of what it has produced.
The common question I get at this point is,
"How come all enzymes aren't perfect?
"If we have an evolutionary process driving this,
"why aren't all enzymes perfect?"
And I answer that question very simply,
"Why doesn't everybody have a Maserati
"to drive to Fred Meyer?
"And why don't they go there at 110 miles an hour?"
There would be consequences, right?
Enzymes that are capable of doing things
a million per second are dangerous to a cell.
Because if a cell makes too much of product
and it can't be controlled, all of a sudden,
"Oh my god, I made too much carbonic acid."
That's a problem.
In the case of carbonic acid, the cell kicks it out
and it's fine.
But there are other things that we could imagine.
Let's say it's an enzyme that breaks down our glycogen.
We'll talk about that later this term.
It breaks down our glycogen.
Our body needs sugar.
It's nice to break down glycogen quickly.
But I want to have it slow enough that I can control
it so it doesn't overdo the breaking down of glycogen.
Otherwise, I'm going to waste a lot of energy.
In the case of the Maserati going to Fred Meyer,
the consequences are you run over people.
In the case of the cell, we're running over
the needs of the cell.
So why do we have any perfect enzymes?
There are several reasons for this, as well.
We'll talk about a couple of them later in the term,
but one of the reasons that enzymes have evolved to being
perfect is because the speed of the reaction actually
prevents an unstable reaction from occurring.
Some of the intermediates are unstable,
so if we can make that reaction go blindingly fast,
the likelihood we have things that we don't want get lower.
There's other reasons, as well, but that's one of
the reasons we have perfect enzymes.
That's pretty cool!
There's not a large number of them,
but there's a decent number of enzymes that are perfect.
Questions about that?
I do have a song.
We're maybe a little ahead for the song,
but it's kind of fun and I think we've mostly covered this stuff,
so let's do it.
You'll see something that I'll talk about next time.
The song is to the tune of an old song from the '60s
called "Downtown."
Anybody know the song?
So with this song, when we get to the point with the
"downtown" part, I want everybody to just jump up
and throw your hands in the air and say the word "enzymes."
Let's start.
[Singing "Enzymes"]
Lyrics: Reactions alone could starve your cells to the bone.
Thank God we all produce...
Units arrange to make the chemicals change,
because you always use... enzymes!
Sometimes mechanisms run like they are at the races.
Witness the Kcat of the carbonic anhydrases.
How do they work?
Inside of the active site it just grabs
onto a substrate and squeezes it tight in an ENZYME!
CAT-al-y-sis in an ENZYME!
V versus S in an ENZYME!
All of this working for you... enzyme, enzyme.
Energy peaks are what an enzyme defeats in its catalysis.
Transition state is what an enzyme does great,
and you should all know this.
Catalytic action won't run wildódon't get hysteric.
Cells can throttle pathways with an enzyme allosteric.
You know it's true.
Kevin Ahern: Not yet, but you will.
Lyrics: Well, when an effector fits,
it will just rearrange all the subunits, inside an ENZYME!
Flipping from R to T, ENZYME!
Slow catalytically, ENZYME!
No change in Delta G... enzyme, enzyme.
You should relax when seeking out the Vmax
though there are many steps.
Lineweaver-Burk can save a scientist work,
with just two intercepts.
Plotting all the data from kinetic exploration,
lets you match a line into a best-fitting equation.
Here's what you do.
Both axes are inverted then you can determine Vmax
and establish Km for your ENZYMES!
Sterically holding tight, ENZYMES!
Substrates positioned right, ENZYMES!
Inside the active site, enzymes, enzymes.
Thank you.
Student: All right, now you have to tell me
what musical "Downtown" is from because it's...
Kevin Ahern: What musical, I don't know.
I don't think it's from a musical.
Student: [unintelligible]
Kevin Ahern: Is it?
Student: [unintelligible]
Kevin Ahern: I'm not sure it's originally from a musical, but...
Student: Okay, I feel like there's a musical it's in and I can't...
Kevin Ahern: Maybe, I don't know.
Student: Hi, is there a way to make up a recitation?
Kevin Ahern: No, no.
Missing one recitation won't kill you.
So hang in there.
Student: I'm two hours away.
Kevin Ahern: Oh, that's a bummer.
Yeah, sorry about that.
Student: Hi, I have a question.
So, I saw the table [unintelligible] side chains.
Does that come from the value of the Kcat over Km?
Kevin Ahern: No, the enzyme shape does that.
Student: Oh, really?
Kevin Ahern: Yeah.
Student: Okay.
Kevin Ahern: Uh-huh.
Excuse me, guys.
Squeeze in here.
Student: When would be a good time to talk to you aboutó