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JOANNE STUBBE: OK, so
welcome to class today.
Today, I'm going to
be talking about one
of my favorite topics--
enzymes and catalysis.
And what I would like to
do is give you an outline
of where we're going today.
First, we're going to
define what a catalyst is.
And we're going to focus
on enzymes as catalysts.
Then what we're going
to do is describe
the theory of catalysis.
And we'll show how
the theory can account
for all experimental
observations or most
experimental observations.
We'll then talk about the
mechanisms of catalysis,
and we'll see that there
are three basic mechanisms.
I won't write them out,
but we'll come to them.
And then if time allows, we'll
talk about another property
of enzymes.
These are all focused with
amazing rates of reaction.
And the second
property of enzymes,
besides the fact that they
can accelerate reactions
by a million to a billion
fold, is their specificity.
So that's where we're going.
And what I'd like to do
in the very beginning
is show you why--
spend a little time
to show you why
enzymes are important.
Why do you care about enzymes?
That's why you
care about enzymes.
Look at this mess.
That's what's going
on inside your body.
There are thousands of reactions
going on inside your body.
Without enzymes, no reaction.
So you must care about enzymes.
So what we're going to see
over the course of the semester
is that we can
break down this mess
into a few basic reactions.
OK, so here is Waldo.
And over the course
of this semester,
as you've seen many times, we
walk through central metabolism
and all of the reactions.
Now, a second
thing about enzymes
that I think will be what
you guys do for a living
if you decide to become
biochemists and enzymologists
is can we take our understanding
of how these amazing catalysts
work and design our
own protein catalysts
to do any reactions we
want not involved in the 10
or 12 basic reactions we have
going on inside our body?
And we can't do that
now, but I would
argue that understanding
catalysis is a key requirement
for getting to the point
where we can actually
do catalytic design.
And the third thing that I
think is really important
is that 40% to 50% of all
the drugs we presently
use in treatment of
antibacterial infections,
anti-viral infections,
anti-cancer infections
are all inhibitors of
enzyme-based reactions.
And understanding
catalysis helps
us to design better inhibitors.
So understanding catalysis
is central to many things
that are important to
all of us in society.
So let me just tell you how
I got excited about enzymes.
So I went to graduate school.
Never had a biochemistry course.
They didn't do anything
about biochemistry
at the molecular level.
When I went to graduate
school, I went to a lecture
in the first year
of graduate school
that was given by a
faculty member at Stanford.
And he talked about an enzyme
called lenosterol cyclase that
converts a linear molecule.
So here's the linear
molecule, but I have
it folded up into four rings.
And these four rings
provide the basis
for all steroids like
estrogen and testosterone
and cholesterol.
And look at what
this reaction does.
One enzyme in a single step
converts this linear molecule
through a series of cascade
transformations in hydride
and methyl shifts
into this molecule,
putting in six
asymmetric centers
in a single step in 100%
yield at 37 degrees in a pH 7.
I said, my god, why do
I want to be a chemist?
You sweat.
There are no
blocking [INAUDIBLE].
You to sweat to put in any
kind of an asymmetric center,
and here, this little
protein has figured out
how to do all of this under
really mild conditions.
And so this was a transformative
experience for me.
I remember the lecture
clearly because I thought
it was so amazing and I'd
never seen that enzymes could
catalyze reactions like this.
So enzymes really are amazing.
So what you want
to do now is start
by defining what a catalyst is.
And a catalyst, it can
be for those of you who
have had more
chemistry, it can be
an inorganic ion for example.
It can be a small
organic molecule.
But for us, we're
going to be focused
on large macromolecules.
And the macromolecules,
we'll see
that we're getting focused
on, could be proteins or RNA.
But most of the reactions
found in our body
are catalyzed by
protein catalysts.
And these catalysts increase
the rate of the reaction
without themselves being
changed during the reaction.
And furthermore, while
they can increase
the rate of the
reaction, they don't
affect the overall
equilibrium of the reaction.
They just increase the rate
of approach to equilibrium.
So they have no effect on
equilibrium insolution,
but increase the rate of
approach to equilibrium.
So what I want to
do now is define
some of the basic
properties of the catalysts
that we'll be talking about
for the next 15 minutes or so.
So the first thing is that
the catalysts we're going
to be focused on are enzymes.
Remember, we've spent
the last few lectures
talking about proteins.
Enzymes are simply
proteins, but then we
see that they have special
regions in the protein
structure which allow
them to accelerate
rates of defined reactions.
I also will mention that
we have inside of us
a machine called the ribosome.
And the ribozome is the machine
that makes proteins, makes
polypeptide bonds.
We're not going to
talk about that in 507,
but we talk about it in 508.
And the amazing observation
was made really initially
by the seminal experiments by
Harry Knoller at UC Santa Cruz
that you don't need any
proteins to make peptide bonds.
That was heresy at the time.
In 2001, Steitz
won the Nobel Prize
for the structure of
the ribosome and Harry
didn't get the Nobel Prize.
Bad.
He's the one that made
the seminal discovery,
although the structure
of a ribosome,
which is 2.3 megadaltons, is
really sort of spectacular.
I still get goosebumps when I
think about that structure that
was published in 2001.
But Harry didn't get it.
Anyhow, so that
was a digression.
So that took a few
minutes off my 50 minutes.
Anyhow, we're
going to be focused
on enzymes as catalysts.
So why are enzymes important.
They're important because
as I already told you,
they accelerate the
rates of reaction 10
to the 6-- a million--
to 10 to the 15-fold.
Whoa.
Can you imagine that?
Essigmann always used to say
to me, give them an example.
That's a lot.
It's faster than
a speeding bullet.
Do you know where
that came from?
Faster than a speeding bullet?
See, if this is when I have a
disconnection with my audience.
It's a bird, it's a plane,
able to leap tall buildings
in a single bound.
Superman, course five.
That's where our course
five logo came from.
So let me just give
you an example of this.
And so this is taken from
an article by Wolfenden,
and this is the
expanse of reactions
that it rates that enzymes
can catalyze that also
can occur in solution.
So if you take down at this
end a half life of adding water
to CO2 is five seconds.
That's pretty fast.
Why do you need
water to hydrate CO2?
Anybody got any ideas?
Where have you seen that
in the last few lectures?
Hemoglobin.
Why do you need that?
Because in your tissues, all of
the fatty acids of the glucose
gets breakdown to CO2.
The CO2, where does it come out?
You exhale it.
Somehow it has to be carried
around and into your lungs
from your tissues.
And there's a key enzyme
called carbonic anhydrase
that accelerates even this
very fast reaction by a million
fold.
Let's look at another one
that might be familiar to you.
Let's think about
peptide bond hydrolysis.
We just told you the
ribosome makes peptides.
What about peptide
bond hydrolysis, which
plays a major role in cell media
death and blood coagulation
and controlling the levels
of proteins inside the cell?
If you look at the half
life of peptide bond
hydrolysis, 450 years.
That means if we needed this
reaction in our lifetime,
it wouldn't ever happen.
So if you actually look
at the rate acceleration,
proteases, which
hydrolyze peptide bonds,
have rate constants of
about 50 per second.
This rate constant is about
10 to the minus 9 per second.
That's the rate acceleration
of 10 to the 12.
So without these
kinds of enzymes
and many other kinds of
enzymes, we would not be alive
and we would not be
able to function.
So the description
of rate accelerations
is given by a term we're going
to derive in the next lecture--
kcat over KM.
A kcat is a turnover number.
It tells you how good your
catalyst is in terms of per
second.
KM has a concentration
dependence.
So this is a second order
rate constant-- concentration
inverse, time inverse.
And this is what we use to think
about how efficient enzymes
are, as we'll see
in the next lecture.
So what I want to show
you here is another graph
that was made by Wolfenden,
who we were talking about data
in the previous slide.
And what I want to do is
show you his comparison
of enzyme catalyzed
reactions and
non-enzyme catalyzed reactions.
And we just heard with peptide
bond hydrolysis, 450-fold rate
acceleration.
That's a lot.
What do you notice
immediately about
enzyme catalyzed reactions?
The kcat over KM is on the order
of 10 to the 6 to 10 to the 8
per molar per second.
Does that ring a
bell with anybody?
Where have you seen a number
like 10 to the 6 to 10 to the 8
per molar per second?
What that is is a diffusion
constant of any two molecules
finding each other in solution.
So what is that telling us?
That's telling us
that inside the cell,
enzymes have evolved
to be so efficient
that the rate-limiting
steps are going to be
finding each other in solution.
It's physical.
It has nothing to do
with the chemistry.
So you've had billions
of years to figure out
all this chemistry, and
what limits everything--
and we'll come back
to this in a minute--
is the enzyme and the small
molecule finding themselves.
And so that's where this
number-- of 10 to the 6 or 10
to the 8 per molar
per second comes from.
If you look at the
non-enzymatic reactions,
we just talked about
hydration of CO2
versus enzyme
catalyzed reaction,
what you see is that
they're all over the place.
So the staggering
rate accelerations
of 10 to the 6 to 10
to the 15 that you see
are really based on the rates
of the non-enzymatic reactions.
And the enzymes have
evolved-- most of them
have evolved over
billions of years
to be incredibly
effective at what they do.
So the other thing that I
wanted to say about enzymes
at this stage is that
enzymes are usually
in addition to being
great catalysts,
they're also-- you learn, I
think, if you've seen enzymes
before that they are very
specific for the substrates,
which I'll call S and we'll
come back to this in a minute.
So they only react-- you
have hundreds of metabolites
inside of our body.
That only will pick up and react
with one of those metabolites.
But in reality, I think what
we found over the last 15 years
or so is enzymes are
not all that specific.
They are specific for what
they encounter inside us.
So if you take them
out as a biochemist
and start messing
around with them,
they aren't anywhere
near as specific.
They don't have to be that
specific because they never
encounter these molecules
inside the cell.
So they are very specific
for substrates in vivo.
And in fact, many of them
are promiscuous in vitro.
And I think that's something
that's been under-appreciated.
So this is number three.
I wanted to talk
about specificity.
Number four, enzymes
in general, if you
look at that metabolic chart,
almost all those reactions
can be subdivided into
10 to 12 reactions.
And those 10 to
12 reactions, even
though it looks like
a jungle and a mess,
are found in the lexicon
that you have been
given in the first lecture.
So that lexicon provides a
framework to think about all
of primary metabolism.
Now, in reality, there are
many other kinds of reactions.
But the ones that you're
going to see in 507
can be limited to
10 to 12 reactions.
So enzymes have a limited
repertoire of reactions
in primary metabolism.
And so in this case, let me
give a plug for the chemists.
Chemists have the
whole periodic table.
Do we have a
periodic table here?
No.
We're in the wrong department.
We're in the wrong building.
Anyhow, we have
hundreds-- not hundreds--
we have 50 elements where we
can use to catalyze reactions.
We can do all kinds of
reactions catalytically,
and we can do it
with something small,
like a proton, or
something small,
like a metal with a little
organic spinach hanging off
of it.
But what are we
doing with enzymes?
We have these big
huge molecules.
So there's a playoff.
Enzymes have a very
limited repertoire
of reactions they catalyze,
while chemists actually
are limited by their imagination
to catalyze these reactions.
However, as the world
becomes more and more green,
chemists are no longer
allowed to use metals.
For example, they can
be toxic to people.
And so people are
rethinking and refocusing
on developing green catalysts.
So the question that
you can ask yourself,
is there any way
that enzymes can
enhance their
repertoire of reactions
that they can catalyze?
And they can.
They do that by using the
vitamins on the vitamin bottle.
So enzymes have a
limited repertoire,
but they increase this
repertoire using vitamins.
This is what we eat out
of our vitamin bottle that
are converted into co-factors.
So the vitamins we eat
have to be subtly modified
and then get incorporated
into the protein catalysts
and greatly expand
the repertoire.
So many of you probably-- how
many of you take vitamins?
Everybody should
be taking vitamins.
Why don't you take vitamins?
Anyhow, so you can see vitamin
B6, vitamin B2, vitamin B1.
And over the next
three weeks or so,
we talk about the chemistry
of how these vitamins interact
with the protein
catalyst to increase
the repertoire of reactions
to 10 that actual enzymes can
catalyze.
But in addition
to the vitamins, I
want to make mention of
another type of catalyst.
So most of the vitamins
are organic molecules.
One also needs to think
about inorganic molecules.
Inorganic molecules--
copper, zinc, iron,
all those if you look
at your vitamin bottle
are at the bottom and
they're labeled inorganic.
And they almost always in
introductory biochemistry
courses get swept
under the table.
And in fact, many biologists
don't think about metals
at all.
But 30% to 35% of
all the enzymes
have metals incorporated.
And these metals are essential
for the repertoire of reactions
that enzymes can catalyze.
So without going
into any details,
I just want to
whet your appetite.
Look at this guy.
Well, what are we
looking at here?
These yellow things are sulfurs.
The purple thing is molybdenum,
and the green things are iron.
And in the middle
of all these irons
is this silver thing, which is
a carbon bonded to four irons.
Most of you probably
aren't sophisticated
enough yet to think
that's amazing,
but it was only two years ago
that the x-ray crystallography
where we can look at
things at atomic resolution
was good enough so
we can see that guy.
So what does this guy do?
What's its function?
Pretty damn important.
It converts nitrogen
into ammonia.
So it turns out to be an
eight electron reduction
because not only do
you produce ammonia--
two molecules of
ammonia-- but you also
have to produce a molecule of
hydrogen during that reaction.
So this is the
basic way we control
nitrogen-- one of the
basic ways we control
nitrogen in the environment.
So chemists would
love to understand
how this spectacular
inorganic molecule can
mediate what turns out to
be a six electron reduction.
Another molecule--
co-factor molecule
that's all metal-based that
I think is equally amazing
is this one.
We recently got an atomic
resolution structure down
to 1.5 angstroms.
It has four manganese
and a calcium.
Anybody have any
idea what this does?
This is the co-factor
that takes water
in the presence of
light-- sunlight--
and converts it to oxygen gas.
Why is that important?
Because we need
oxygen gas to breathe.
So anyhow, on this one co-factor
mediates that transformation.
Pretty amazing.
And that's a major
focus of people
who want to think about how
these catalysts actually work,
but we won't be
discussing that further.
We won't be discussing
that further in 507.
So I just wanted to point
out here that, again, enzymes
have a limited repertoire.
Their repertoire is much less
than what chemists can do,
but they're amazingly
efficient at what they do.
So I would argue if we
really could understand
the basis of catalysis and
how these things evolve
to be able to do these
amazing transformations,
we might, if I was able to
come back 50 years from now,
see that we had designer
proteins all over the place
that could catalyze the
specific reactions that we're
interested in, not the ones
that are found in our bodies.
OK, so the next thing I
want to briefly mention
is that enzymes, so if
you look at an enzyme,
it's a big macro molecule.
We've looked at these in
the last few lectures.
The region where the
chemistry or catalysis occurs
is called the active site.
And we've seen this
before in the TIN barrel
superfamily of proteins.
And so there's a region
of about 10 angstroms.
We have your amino
acid side chains
that I asked you to try to
remember and think about.
We'll see those are key
to making these rate
accelerations so fantastic.
This is where the
chemistry happens.
But I think it's now
clear from studies
that have been done
in the last 15 years
or so this is not true.
One can make changes
out here or here.
One can change the amino acids
and totally turn off the enzyme
or turn on the enzyme.
So chemists use these
small little molecules,
biology uses big huge molecules.
Everybody initially focused
on this one little region
where you can see the chemical
transformation occurring.
But what about the
rest of the molecule?
The rest of the molecule
is also important.
You cannot remove, in general,
all of this spinach and come up
with a catalyst that has these
amazing rate accelerations.
So the active site
is very important.
But so are specific amino acids
outside of the active site.
And people have studied
this because of technology
of sight directed
mutagenesis, which many of you
have probably done in
either 702 or in 335.
So what implications
does that have?
And I just want to
mention one more thing.
I don't want to spend
a lot of time on this,
but our thinking about catalysis
is changing dramatically
and has changed and
continues to change.
I continue to study
this, even to teach 507.
Because it turns out,
how does change out here
govern what's going
on in this region
where you think the
chemistry happens?
And it governs that
chemistry because
of conformational
changes and movements.
So another thing
about enzymes that we
need to do more thinking
about-- and this
is a major focus of what
people are thinking about now--
is dynamics in enzyme
catalyzed reactions.
And so if you look at the
time scale-- and I made
you think about size scale
in the first few lectures.
Like how long is
a hydrogen bond?
How long is a carbon
nitrogen bond?
A carbon oxygen bond?
You also need to think
about time scales.
And this is particularly true
in the case of catalysis.
What happens on the
fantasecond time scale?
That's pretty fast.
That's a vibration of the bond.
But what are you doing during
an enzyme catalyzed reaction?
You're breaking the bond
and you're making the bond.
So we'll see that the
transition state of the reaction
happens on the
fantasecond time scale.
Yet, if you look at the
criteria kcat, which
is a turnover number,
the enzyme, which
is given in time
inverse, they're
usually on 10 per second
to 1,000 per second.
So they're on the millisecond
to second time scale.
So catalysis is
happening way up here.
Now, I've just told
you that mutations
outside the active site
can affect catalysis,
and so one also needs to
think about the time scales
in between these two extremes.
I've also told you that
finding an enzyme, finding
its substrate in solution,
can often be the slow step.
So here you have nanosecond,
microsecond time scales,
and I'm not going to
spend any time on this,
but you come back
and look at this
and think about you've
got all these side
chains of your amino acids.
You might have loops that
are moving in and out
and covering the active site.
All of this dynamic interaction
plays a key role in catalysis,
making the enzyme
as a whole important
in the overall
catalytic process.
So that's my introduction to you
for what an enzyme catalyst is.
And so now what I want to do
is look at the second bullet
we were going to talk about,
which I've already lost.
How do we describe catalysis?
How do we try to conceptualize
in a theoretical framework
all of the experimental
observations that
have been made for decades?
And there are many things that
are wrong with this theory,
but this theory has
stood the test of time,
not only for biochemists,
but for also chemists.
And I think it helps us
to think about how enzymes
are able with just the amino
acid side chains for protein
to give us these amazing rate
accelerations and specificity
that we actually observe.
So what we want is a theory
to conceptualize catalysis.
And this is transition
state theory.
And this is-- many of you
have seen this in some form
before, either in
freshman chemistry
or maybe if you've had 560.
People go through and derive
all of the rate equations.
What I'm going to
do is just show you
a picture of how
this theory helps
us think about these
catalytic transformations
and then how this picture helps
us think more specifically
about these amazing
rate accelerations
that we actually observe.
OK, so I can't remember
what's on the next slide,
but this is a picture
you often see when you're
thinking about catalysis.
So this is chemical catalysis,
but again, chemical catalysis,
biological catalysis, really
the same basic principles
hold that we have
some substrates A
and B going to products
and what's required.
So I think all of
this is intuitive,
but if you have two
things coming together,
they have to come together
in exactly the right way
to be able to make a bond.
They have to remove all the
solvent from outside them.
They have to come
together with enough force
to be able to get over the
barrier, whatever it is,
to break one bond and
to form a new bond.
So that's true of all
reactions and everybody faces
the same issues in terms
of conversion of substrate
into products.
And the highest point
along the reaction
coordinate-- so
this is what we call
a reaction coordinate diagram.
And this is energy.
So the highest point along the
reaction coordinate diagram
is called the
transition state-- TS.
This is transition state theory.
OK, TS theory.
And this is where-- this is
the point where we can ever
isolate it because
this is a point where
all the chemistry is happening.
The bonds are being
made and broken.
And the lifetime I just showed
you on the previous slide
is fast-- fentaseconds.
So you can never isolate
a transition state.
Everything needs to be aligned.
That doesn't come
free of charge.
You have to do a lot of
work to get to the stage
where you can get this
chemistry to happen.
That's what our
catalysts are doing.
And then bang, the reaction
is over at that time.
So this is another way of
describing the transition
state of the reaction.
And in reality,
this is the cartoon
you see in most introductory
textbooks that are describing
rates of reaction.
But the reaction coordinate is
much, much more complicated.
And that's true in
enzymatic reactions as well.
So it's true of
chemical reactions,
it's true enzymatic reactions.
So you might have
a plus b, and they
might form two or
three intermediates
along the reaction
pathway where you
have many transitions-- you
have many transition states
along the reaction pathway.
And each of these transitions
states would be non-isolable.
But what about these
little valleys?
These little valleys are
where you might have a chance
to see an intermediate during
the conversion of a plus
b into p plus q.
So an intermediate--
and if you're
interested in studying
catalysis and the chemistry
of the reaction and
you need to define
what these intermediates
are, they can be high
or that could be
lower in energy.
They may be easy to isolate,
not easy to isolate.
But they have all
covalent bonds intact.
So in contrast to the
transition state where
the bonds are being
made and broken,
you can never isolate this.
You have a chance to be able--
if you're clever and creative,
which people that
study mechanisms are,
you can actually look
at the intermediates
along the reaction coordinate.
So that's a reaction
coordinate diagram.
We're going to
come back to these
because I think they really help
us to conceptualize how enzymes
can go about achieving these
fantastic rate accelerations.
So from transition
state theory, one
assumes the following--
I'm not going
to go through the
details of this at all.
But the key point that
one needs to think about
in transition state
theory is that--
and this was first put
forth by Linus Pauling.
Who's Linus Pauling?
He's my hero.
OK, Linus Pauling,
he's the vitamin C guy.
He lost it when he got
old, but in the early days,
he's the one that could take
a polypeptide chain-- just
a string of amino
acids-- and he sat there
and he played with it.
And lo and behold,
he says, we're
going to have alpha
helices in proteins.
How amazing is that?
You've heard me talk
about him before.
He was the one that I think
conceptualized-- first
conceptualized-- how an enzyme
might catalyze a reaction.
What do you want to do
to catalyze a reaction?
You want to lower this barrier.
So how do you lower the barrier?
You don't want the enzyme to
bind the substrates tightly,
and I'll come back
to this in a minute.
You want to bind the
transition state tightly.
So he put forth in the
1940s that the way enzymes
might be able to catalyze
their reactions is
by tightly binding--
uniquely and tightly binding
the transition state
of the reaction.
And I think that turns out
to be a really good way
to conceptualize most
enzymatic reactions.
Now, transition
state theory tells
us, which again is
not so appealing to me
but it works to describe
most experimental data,
that the ground state-- so this
would be the ground state--
is in equilibrium with
the transition state.
So you might ask
yourself, how the heck
can you ever be in
equilibrium with something
with such a short half life?
That's a good question to ask.
But in fact, this framework--
transition state theory--
allows us to able
to explain almost
all the experimental
observations
that we make as both
chemists and biochemists.
So this goes through and
derives that equation, which
I'm not going to do today.
In the old days, I used
to spend a lot of time
deriving equations.
Nowadays, I don't derive
equations anymore.
But the key equation that
you need to think about
is shown here.
And the consequences of this
equation are quite simple.
It tells you that the rate
constant for the reaction-- so
from transition state
theory, the rate
constant for the reaction.
And where is this rate constant?
Where does this rate
constant come from?
A is going to some product p.
You can measure
it experimentally.
So k observed is an
experimentally measurable
parameter is equal to a
bunch of constants called
the transmission coefficient.
This should be a cappa.
Boltzmann's
constant, temperature
in degrees Kelvin,
Planck's constant times
e to the minus delta
g dagger over rg.
So this is the equation.
This is a constant.
This is Planck's constant,
Boltzmann's constant.
This you can measure
experimentally.
Cappa is telling you basically--
the transmission coefficient
is telling you the frequency
that this transition state
breaks down to form
products versus going back
to starting materials and in
general, is on the order of one
in most reactions.
And so the key thing to remember
from this equation, which
explains the data and helps
us to think about catalysis,
is that as you increase
the rate of the reaction,
it's inversely related to
the activation barrier.
So what you want to do,
this equation tells you,
is you lower this barrier.
The rate of your reaction
becomes faster and faster.
So the whole goal is,
then, to figure out
how to lower the barrier.
If you can lower the
barrier, this theory
predicts that the rate of
your reaction will be faster.
So that's what we
want to be able to do.
The rate constant
is inversely related
to the activation barrier.
And so now let's look at an
enzyme system specifically.
So I'm going to draw the
same kind of reaction
coordinate that we've drawn over
there for a chemical reaction.
And I'm going to use
a simple equation.
E is the enzyme, s is
the substrate forms
an enzyme substrate complex.
The substrate
binds in the region
that we call the
active site over here.
Somehow, the enzyme is able to
convert itself into product.
Now, most reactions are much
more complicated than this.
You have many substrates.
You have many products.
But it doesn't affect
anything in terms
of thinking about the problem.
And then in the end,
the product dissociates.
So that's a simple reaction.
You get something in there,
a catalyst works on it,
it gets converted to
the desired product,
and the product is released.
So what I've told you
now a couple of times
is that enzymes have
evolved to such an extent
that often the physical
steps and not the chemistry
is rate limiting.
So what are the physical steps?
Here are the physical steps.
Enzyme finding
substrate and solution,
that's a physical step.
What is limited by?
It's limited by
diffusion control.
How fast can they find
each other in solution?
That's the number 10
to the 8 per molar
per second that limits most
enzyme-based reactions that I
showed you several slides ago.
What about this?
We have product dissociation.
What about product dissociation?
That's a physical step too.
You made the product
sitting around,
but in order for the
enzyme to turn over, again,
to free up the active
site, the product
has to come off so it can
bind another substrate.
And here is the chemistry.
Ah, that's what I care about.
But what happens, now, is
that if these steps are
rate limiting, then you
can't see the chemistry.
So it's really challenging,
often really challenging,
to study the chemistry
of a reaction
because the rate limiting
steps have nothing
to do with the chemistry.
So let me just draw a diagram.
So you can draw a reaction
coordinate diagram.
And so what you have is
some enzyme plus substrate
and it can form an
enzyme substrate complex.
You have a transition
state of your reaction.
The enzyme product
complex can then
dissociate to form
enzyme plus product.
So what you need to
think about if you're
thinking about how to
accelerate the reaction is
what is the bottleneck
in the overall reaction?
You don't want to
start mucking around
with something that
doesn't control
the rate of the reaction.
So you need to know what
the rate limiting step
is in the reaction.
And the rate limiting step
is the highest barrier
along the reaction coordinate.
OK, now I've already told you
that this is a simple case.
We have one substrate getting
converted into product.
Most enzymatic reactions are
going to have many barriers.
And so in order to affect the
overall rate of the reaction,
you need to figure out
what's rate limiting,
and somehow the
enzyme has figured out
how to lower the barrier to make
this reaction easier to occur.
Remember, I just told you that
the rate constant is inversely
related to this
activation barrier.
So if we can lower
this barrier somehow,
what we're going to see, if
we can lower this barrier,
now we have a lower overall
rate of the reaction.
So this theory
allows us to think
about what we need to do to
make these catalysts actually
work with rate constants of
10 to 6 to 10 to 15 times
faster than
non-catalyzed reactions.
And I want to say one other
thing before you move on.
As with everything,
I think it's good
that we're in a field
that's rapidly changing.
Remember, I told you have
to think about dynamics.
We no longer think about
a single reaction barrier.
That's in most of
the textbooks now.
Really what we think about is
we bring dynamics into this.
I told you things
outside the active site
can modulate what's going
on inside the active site.
What we think about is
a reaction landscape.
And so one has many barriers
that one has to get over.
Almost all reactions
involve multiple barriers.
So you've got to figure out
which one is rate limiting
and lower that
activation barrier.
And enzymes, if you think
about this, they're huge.
Do they all fold
exactly the same way?
No.
So we always think we
have a homogeneous enzyme.
No.
If any of you work
in UROPs, you'll
find that out pretty fast.
You use recombinant technology
to fold things inside the cell.
They don't all fold right.
So you have all
mixtures of things.
And so you get a
reaction landscape.
And so this axis is
bringing in the dynamics
that I told you about
earlier on that you
need to think about-- the
conformational changes that
occur every step along
the reaction pathway.
The enzyme is moving
at all kinds of steps,
reorienting everything to get
the chemistry exactly right.
So what I want to do now
is-- so that gives you
a way to conceptualize
rate accelerations.
Now what I want
to do is tell you
what the major mechanisms are
that the enzyme uses to enhance
the rates of these reactions.
How do we lower these
energy barriers?
So let me see.
I need to start
erasing somewhere.
OK, so we're on the
third bullet over here.
Mechanisms of catalysis.
And what we're going
to be talking about
is multiple mechanisms
of catalysis.
We're going to be talking
about binding energy, which
is the one people have most
trouble thinking about.
We're going to be talking about
general acid, general base
catalysis.
And we're going to be talking
about covalent catalysis.
And we will see
that over the course
of the rest of
the semester, when
we start talking about
metabolic pathways,
all of these mechanisms
are used in almost
all enzyme catalyzed
reactions to give us
these tremendous
rate accelerations.
What I want to do-- that's
the first time I did that.
That wasn't too bad.
OK, so what are the
mechanisms of catalysis?
How do we get 10 to the 6 to
10 to the 15 accelerations?
And so the first
thing, and I think
the one that really is unique
to enzyme catalysts compared
to small inorganic
or organic molecules,
is the use of binding
energy in catalysis.
So this is the one--
and this is also
the one that's thought to
contribute the greatest
amount to these factors
of up to 10 to 15.
So binding energy in catalysis,
and what does that mean?
What do we need to think about?
So the enzyme binds
to a substrate.
If we take this simple
case, we need it to bind.
We need it to bind specifically.
So that's a key
part of the enzyme
that we haven't gotten
to yet-- specificity.
But what if it bound its
substrate really tightly?
Do you think that would be good?
No.
So it's not good
because what does it do?
If it took all of the spinach
changing off of your substrate
and made hydrogen bonds and
Van Der Waals interactions,
all the weak
non-covalent interactions
we spent a half
a lecture talking
about four or five lectures
ago, what would happen is you
would have type binding.
You would have lower energy.
But what does that then do
to the activation barrier?
It increases the
activation barrier.
So the binding energy is the
free energy released when
enzyme combines with substrate.
But the key is that
this bind energy is not
used to bind completely.
It's used for catalysis.
So this energy is used
both to bind substrate
and-- and this is the key
thing-- for catalysis.
So what do we want to be able
to do and how does it do this?
So if we look at this, if
we look at our reaction
coordinate diagram over here,
we don't want to bind substrate
tightly because this is the
biggest barrier-- the rate
limiting step along
the reaction pathway.
What we want to do is
lower this barrier.
So how can we lower the barrier?
We can lower the barrier by
stabilizing the transition
state.
That now makes this
barrier-- probably
can't read anything now, but
that makes this barrier lower.
How's another way you
could lower the barrier?
You could lower the barrier
by straining the substrate
to look more like
the transition state.
So you could strain the
substrate in this form,
and now, again, you would
have a lower barrier compared
to that barrier.
So you're going to use this
binding energy to stabilize
a transition state.
So we want to use binding energy
to stabilize the transition
state to de-stabilize-- any
of these or all of these
could be true-- de-stabilize
the ground state-- G-S.
Or what else do you need
to do to get a reaction
to work if you have one or
two substrates or even one
substrate?
Your molecules in
solution are all solvated.
What you need to be able to
do is get rid of the solvent.
If you have two substrates, you
have to bring them together.
You have to bring them together
at the right orientation.
That doesn't come
free of charge.
You have to get the
energy from somewhere,
and the energy is proposed to
come from this binding energy.
So the binding
energy is not used
to completely bind
the substrate,
but to do all of these
things to get your substrates
ready to form product.
So you can dissolvate and
bring reactants together.
And you can freeze out
rotational, translational
entropy.
So you're getting everything
ready for the reaction
to happen.
So in this case, then, let me
just erase this and make this
so that this is clearer.
What you could have, now, is
you can-- so in the beginning,
this is the barrier.
If you stabilize the transition
state, this becomes a barrier.
If you de-stabilize
the ground state,
then this becomes the barrier.
So what we're trying to
do is lower this barrier
to get the reaction to work.
And so the major
way that we do this
is by using the interactions
between the enzymes
of the weak non-covalent
interactions between the enzyme
and substrate to help
us do these things
to enhance catalysis.
So that's one of the major
mechanisms of catalysis.
A second-- and this
type of catalysis
is unique to proteins.
So the two types of
catalysis are used widely
in organic or
inorganic chemistry
when you're designing
your catalyst.
I mean, when you're designing
a catalyst substrate binding,
a small molecule, a big product
release is still an issue.
If you go and read the
organometallic literature,
people have trouble with
product release all the time.
So the issues in catalysis
are exactly the same
in biochemistry as they are
in organic and inorganic.
But now we have to deal
with this big protein, which
has these unique
properties, one of which
is that the whole protein is
playing a key role in catalysis
and allowing everything to
align within tenths of angstroms
to make these reactions work
really efficiently, which
chemists can't do yet.
And I don't think we'll
ever be able to design it,
but we can evolve catalysts
to become better and better
so that they can
do the same thing.
That's the beauty of proteins
is you can evolve them to become
better and better catalysts.
So the second mechanism--
so the first mechanism
is binding energy.
The second mechanism-- I can't
remember whether they're using
I's or 2's.
The second mechanism is general
acid, general base catalysis.
Now, as a chemist,
what do you learn
about catalyzing reactions?
Well, one way you could do
it is with a big fat proton.
Protons are pretty good at
helping you catalyze reactions
if you go back and think
about chemical transformations
or hydroxide ions.
What are the concentration
of protons and hydroxide ions
in aqueous solution of pH 7?
10 to the minus 7 molar.
So you don't have much
protons and hydroxide
ions in the active site.
So even though these
are very good catalysts
that organic chemists
and inorganic chemists
use all the time, they're
using them in organic solvents,
you can argue the active
site of the enzyme
is more like an organic solvent.
But anyhow, this type of
catalysis is called specific.
So when you see specific
acid or based catalysis--
where does the general acid
and base catalysis come from?
It comes from the side
chain of your amino acids.
So remember, the second
or third lecture I said,
oh, here are all
the amino acids.
Here are all the side chains.
You really shouldn't know
all of your amino acids.
It's a basic vocabulary
of all of biochemistry,
and the pKas of all
the side chains.
Why?
That's why.
Because you can't understand
anything about catalysis
without knowing what these
side chains of the enzymes
are actually doing.
So the general acid
and base catalysis
come from the side chains
of your amino acids.
So what side chains do you have?
You can have carboxylates.
Anybody know what the
pKa of a carboxylate is?
Hey, Boggin, what is it?
STUDENT: Four to five.
JOANNE STUBBE:
Good, four to five.
See, he remembers.
You could have imidazole.
This has a pKa at neutral pH.
Anyhow, you need
to go back and look
at what the groups are that
can be involved in catalysis.
And chemists, for
decades, have studied
how you can use general
acid and base catalysis
to give you rate enhancements.
Now, what I haven't told you is
the amount of rate enhancement
And so people over the
years have measured
that with binding energy, you
can get factors of 10 to the 8.
If you look at general acid
base catalysis from all
the organic and
inorganic reactions
people have studied for decades,
you get factors of 100 to 1,000
fold.
Now, we need to get to a factor
of 10 to the 15 in some cases.
We've already gotten to
the factor of 10 to 6.
So obviously,
you're going to have
to use multiple combinations
of these mechanisms
to give you these tremendous
rate accelerations.
So you will see over the course
of the rest of the semester
many active sites of enzymes
with many amino acid side
chains that are playing roles
in general acid and base
catalysis.
And the last type of catalysis
is covalent catalysis.
And again, covalent catalysis
means that you form--
and where have you already
seen covalent catalysis?
You've already seen this
when we talked about, how
do you study the structure
of the primary structure
of a protein?
We use proteases with
tripsin or kimotripsan
that can break down the big
protein into small pieces.
We went through the
mechanism of that reaction.
In the active site
of that enzyme,
there is a serine that
forms a covalent bond.
So over the course
of the semester,
you're going to
see many examples.
And I'll just put in
parentheses for those of you
who don't remember, go back
and look at serine proteases.
This is a classic example
that's in every textbook.
And how do we know how
much rate acceleration
you get from covalent
catalysis versus not having
covalent catalysis.
We know this, again, because
of organic chemists studying
the detailed chemical
mechanisms of these reactions,
and we find out
that in this case,
we get rate accelerations
of 100 to 1,000 fold.
So what you see is the enzymes.
And these are the three
general mechanisms
by which all enzymes
catalyze their reactions
in some variation.
Now, attributing out of
this 10 to 15, 10 to the 8
is associated with
this, and 10 squared
is associated with that
is extremely challenging.
And there are a lot
of people still trying
to dissect reaction
mechanisms in detail.
And I would argue
that understanding
how these different methods
work and synergize to give you
these accelerations is a
key to eventually designing
new catalysts that
can do what you
want them to do that's
distinct from biological
transformations.
And I think I'm probably over.
I just want to say
one more thing.
I just want to
give you a feeling
for what you have to do.
If you're thinking about this
reaction coordinate, what
you need to do is think
about how would you
stabilize the transition state
relative to the ground state?
So what we're talking
about is stabilization
that's unique to the transition
state and not the ground state.
If you stabilized them
both, what would happen?
If you stabilized them both--
if you stabilize this guy
and you stabilize
this guy, the barrier
would be exactly the same.
So what you need is some
way to uniquely stabilize
the transition state
over the ground state.
So the question is,
how much do you think?
How much rate
acceleration do you
think you can get
from a hydrogen bond?
Does anybody have any idea?
One hydrogen bond.
So here, you have a protein
with 1,500 hydrogen bonds.
But if you can get one
hydrogen bond that's
here in the transition
state of the reaction,
that's not over here, how
much rate acceleration
do you think you can get?
Anybody got any idea?
You can get almost 1,000 fold.
I mean, and you can do a
very simple calculation.
I can't remember whether I have
this on the-- OK, so that's it.
So we can do a very
simple calculation,
and I'll use this to
show you the calculation.
Here, we have our rate.
This should be Delta G. The
dagger should be up in the air.
So this is the
enzymatic reaction.
This is the
[INAUDIBLE] equation.
One has the same equation
for non-enzymatic reactions.
So here's a
non-enzymatic reaction.
In general, the
non-enzymatic reaction
can happen by some mechanism.
To the enzymatic reaction
is just much, much slower.
So if we assume, for example,
that the rate difference
between enzymatic and a
non-enzymatic reaction
is a factor of 10,
how much do you
get assuming that
all of these terms
are the same in the enzymatic
and the non-enzymatic reaction?
You can calculate a
Delta Delta G dagger
of 1.38 kilocalories per mole.
For those of you
who are modern, this
is 5.8 kilojoules per mole.
Sorry, I'm really
old, so I still
think in kilocalories per mole.
But a hydrogen bond, one
hydrogen bond is worth 2 to 7--
compared to no hydrogen
bond, is worth 2
to 7 kilocalories per mole.
So a factor of 10 is 1.4
kilocalories per mole.
So that shows you, then,
that if you had 2 to 7
with one hydrogen
bond, it can give you
these factors of 1,000.
So I think that's an
observation that's
something you need to keep
in the back of your mind.
Because you think about
it over and over again.
It really doesn't take
much to align everything
in exactly the right way.
And when I say hydrogen bond,
these hydrogen bond strengths
are really dependent on
how everything is aligned.
If they're exactly aligned, then
you get much stronger bonds.
They can even approach--
in the gas phase,
they could approach 30
kilocalories per mole.
So having everything
aligned, that's
the job of this
whole big protein,
to actually give you catalysis.
And I think I'm at the
end of my lecture now.
I won't have time to talk
about-- I went over already
about the question
of specificity.
But let me just say, I
think enzymes are really
quite amazing.
There's nothing like them.
Faster than a speeding bullet.
They can catalyze the rates
a million to 10 to the 12, 10
to the 15-fold.
And they use really
the simple concepts
that chemists have
developed over the years.
But the key to the enzyme
is this big huge molecule,
and the dynamics within this
molecule that gets everything
to align exactly right to be
able to lower these barriers so
that you can convert your
substrate into your product.
OK guys, see you next time.
The end.
