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visit MIT OpenCourseWare at ocw.mit.edu. 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.
