CLASS: Fundamentals I 10:00-11:00
DATE: 8/20/2010
PROFESSOR: Deivanayagam
I.
II.
III.
IV.
V.
Enzyme Kinetics
Scribe: Caleb Landrum
Proof: Jordan Ridgeway
Page 1 of 6
Virtually all reactions in cells are mediated by enzymes [S3]
a. Enzymes catalyze many mechanisms by making them more thermodynamically favorable. In simple terms, if
you take the simple glucose molecule and put it on the countertop in a test tube and put oxygen into it,
nothing will happen. It’ll stay there forever. Glucose is a very stable molecule. You can let oxygen flow into it
for years, but nothing will happen. A bottle of glucose stays as a bottle of glucose forever because it is such a
stable molecule
b. . But on the other hand, when enzymes catalyze these reactions, in no time glucose is being broken down
into carbon dioxide and oxygen. So how do enzymes do these things? It’s very fascinating to look at
enzymes. If they lose their potential to perform certain functions, there are a number of diseases that can
arise. Enzymes themselves are very interesting, and studying their characteristics is even more interesting.
Why do we want to know if one enzyme is more efficient or less efficient? (Question to class) How many of
you have worked with polymerases? DNA polymerase is required for any type of cloning, and vendors will tell
you that their enzyme is better than the other vendor’s, and that’s a selling point. But how do you sell it? Just
by saying it works? It’s impossible to sell anything just by saying “mine is better than yours” and so you have
to be able to define it with numbers.
c. These numbers that we must define are what makes up enzyme kinetics. Enzyme kinetics define the
enzyme in a way that one can readily look into it and say “yes, this is a better enzyme than the others.”
“Reaction energy profile” [S4]
a. Without the enzyme, the free energy requirement of the glucose oxidation reaction is pretty high. Enzymes
generally reduce the energy of activation for a reaction. For example, the glucose molecule being broken
down. There are pathways in our cells that break down glucose because we need energy.
b. Enzymes enable these reactions to be carried out in a more rapid, efficient, and spontaneous manner
because they lower the activation energy of the reaction. Enzymes act as catalysts, we’ll come back to that in
a little bit.
What characteristic features define enzymes? [S5]
a. There are some numbers that we must have to define some things. Enzymes are defined in three specific
ways. The first one is catalytic power, the second is specificity, and the third is regulation.
Catalytic power [S6]
a. Catalytic power is defined as the ratio of the enzyme-catalyzed rate of a reaction compared to the
uncatalyzed rate.
b. Urease is a good example, and if you look at the catalyzed rate of 3x10 4 per second and the uncatalyzed rate
of 3x10-10 per second, and you take the ratio of these, it is 1x1014. This is one of the fastest enzymes.
c. Catalytic power is important because it tells how fast an enzyme can catalyze a particular substrate.
Specificity [S7]
a. All enzymes are extremely specific.
b. For example, there are extracellular matrix molecules on every epithelial cell, like hyaluronans and
glycosaminoglycans. And If you look closer at the glycosaminoglycans, there are heparin sulfates and
hyaluronans, etc. So you can see that there are many types of polymers present on the cell surface.
c. Sometimes enzymes are brought in to cut these molecules. These enzymes are so specific that they will
recognize their substrate. Substrate recognition is very important for an enzyme to be active. If it didn’t
recognize a particular enzymes, it would become a “universal enzyme” which will just cut anything, but one
doesn’t call that an enzyme.
d. In the definition of an enzyme, we have a very specific term called “specificity.” In general, any enzyme is
very specific, but there are also non-specific enzymes. To every clause that we create, there is always a subclause. For example, if you take some chondroitin sulfates lyases (used to cut chondroitin sulfates), they can
also cut hyaluronans because chondroitin sulfates and hyaluronans look very similar. When two molecules
are very similar, an enzyme may cut both of them, but it will cut one to a greater extent than the other.
e. So most enzymes are specific, but they can also be nonspecific sometimes. But if you look at the substrates,
it makes sense why it can cut both of them.
VI. Regulation [S8]
a. The third characteristic is regulation. We’ll be looking at this much more closely later, because I’ll be teaching
you about the synthesis of purines and pyrimidines – basically about how nucleotides are synthesized.
b. These things have to be produced in a very controlled fashion. If the cell suddenly starts producing a lot more
of a particular substrate or enzyme, then the cell begins to die because there is an overproduction of
something.
CLASS: Fundamentals I 10:00-11:00
Scribe: Caleb Landrum
DATE: 8/20/2010
Proof: Jordan Ridgeway
PROFESSOR: Deivanayagam
Enzyme Kinetics
Page 2 of 6
c. A certain amount of regulation is required.
d. To emphasize the point, there are three main characteristics of enzymes: one is specificity, the second is
regulation, and the third is catalytic power.
VII. Enzyme nomenclature provides a systematic way of naming metabolic reactions [S9]
a. The system of enzyme nomenclature is something that evolved over time, particularly in the early days when
people named things as they liked, or after what they thought a particular enzyme was doing. Usually the
suffix “-ase” is added to the enzyme’s name.
b. For example, phosphatase is one that would be cutting off a phosphate group; a protease is one that cuts into
a protein chain. However, there are outliers to this, like trypsin, pepsin, and catalase. But now the
International Commission has come in and as usual they have a way of naming these things.
VIII. Table 13.1 [S10]
a. There are six classes of enzymes they have developed, which are oxidoreductases, transferases, hydrolases,
lyases, isomerases, and ligases. It’s very simple. For example, transferases transfer things, and there are
subgroups of them depending on what they transfer. So “transferase” always has to have something in front
of it to define what kind of tranferase it is.
b. If you know the six types of enzymes and what they do, you can look in front of the name to determine the
specific function of that enzyme.
IX. Coenzymes and cofactors are non-protein components essential to enzyme activity [S11]
a. Most enzymes need some help to function. This help comes in the form of coenzymes and cofactors.
b. Cofactors are generally metal ions and there are a number of metal ions that are required in our system to
carry out function. Cofactors are generally required to carry out certain reactions.
c. Sometimes a cofactor is very tightly bound, and is then called a prosthetic groups. Such a combination of a
tight-bound enzyme and cofactor is called a “haloenzyme.” In the absence of the coenzyme, it is called an
“apoenzyme.”
d. So it’s a plus and minus situation. Plus cofactor = haloenzyme, minus cofactor = apoenzyme.
e. So if you look at several of these enzymes that are tightly regulated, they always have cofactors and
coenzymes. That will be discussed in detail in later lectures.
X. Can the rate of an enzyme-catalyzed reaction be defined in a mathematical way? [S12]
a. Now comes the difficult part. Now we have to define what kinetics is. We have said an enzyme has a
specificity, and a catalytic rate, but can these things be defined in a mathematical way? Kinetics is a branch
of science dealing with the rates of reactions.
b. The most important thing enzyme kinetics seeks to determine is the maximum reaction velocity that enzymes
can attain and one can also determine the binding affinities of substrates and inhibitors.
c. Why is this very important? There are a lot of enzymes that do bad things, and if you want to be able to
control them, you need to design inhibitors.
d. With the presence of inhibitors, you can see how the enzymes rate of reaction has been reduced, and you
want to be able to see this in numerical terms. This is important in the design of drugs, because when you
apply an inhibitor to cells you want to see how the cells survive or how the metabolism is controlled, and it
becomes an important issue.
XI. Several kinetics terms to understand [S13]
a. There are several kinetic terms you need to understand, not necessarily for this course, but if you were to be
an enzymologist someday you would need to know what a rate law, rate constant, etc is.
XII. Exploring enzyme kinetics [S14]
a. If one wants to look in mathematical terms, you start with a product A, and then over time the product A
becomes product P.
b. How can this be determined in terms of velocity? Velocity is classically defined as distance traveled divided
by time. In this case, it is not distance traveled, but it is instead the amount of product that is being produced
over time.
c. For example, you start with a glucose molecule, and how many carbon dioxide and water molecules are
being produced. So distance traveled divided by time is usually represented as (x 2 – x1)/(t), and that can
always be defined as dx/dt. In this case, we can define this as the amount of product produced over time. It
can also look at how much the initial product has gone down, which can be represented by –d[A]/dt. So you
start with a certain amount of [A], and the direction of [A] can also be figured out. In this case, we can simply
call it a function of a constant, so this (k[A]) is the constant, which we call the velocity of a rate constant. So
the rate is proportional to the [A]. If you start with [A] and the reaction proceeds and keeps on producing P,
you can either look at [P] or the amount of A that has been reduced.
d. But whenever you perform an experiment, you start with a known amount of enzyme, and a known amount of
substrate. It’s better to start with what you know so you can measure what’s coming out. That’s what kinetics
is all about.
CLASS: Fundamentals I 10:00-11:00
Scribe: Caleb Landrum
DATE: 8/20/2010
Proof: Jordan Ridgeway
PROFESSOR: Deivanayagam
Enzyme Kinetics
Page 3 of 6
XIII. Enzyme Kinetics [S15]
a. If you plot the graph, you can see that the concentration of A starts at 100% and falls down over time.
b. At any given time, d[A]/dt is the slope of that line.
c. This is for a unimolecular reaction, but if you have a bimolecular where there are two things that are involved,
A & B, then the rate is proportional to both A & B. So the velocity is equal to v = k[A][B].
d. One important thing I want to mention is that kinetics cannot prove a reaction mechanism. It can only rule out
various hypotheses.
XIV.
Catalysts lower the free energy of activation for a reaction [S16]
a. This is something I have already shown you regarding the free energy of activation, so I’m going to skip it. But
you can go through it again. Catalysts lower the activation energy of reaction and this is something you must
keep in mind.
XV. What equations define the kinetics of enzyme catalyzed reactions? [S17]
a. Equations have orders, like the zero order, first order, etc. And most of the time kinetics, is usually defined as
the first order reaction or the zero order, and that depends on the substrate.
b. The main idea here is that the enzyme first has to react with the substrate. So the enzyme and the substrate
have to come together.
c. Not only that, but the enzyme has to release itself also because when the substrate comes it is being cut.
Once it is cut, it has done its job and has to release, and an equilibrium is established to where the substrate
is rapidly coming in and going out.
d. When there are free enzymes and you introduce a substrate, all of the enzymes have to bind to all the
substrates, so there is a time lag. After a little bit of time lag, there is saturation, and you get the asymptotic
curve on the graph here. Here it reaches its maximum velocity.
e. Theoretically, a maximum velocity of an enzyme can never be reached because there is always a time lag
between the release and the coming back together. If the enzyme and substrate were always stuck together,
the enzyme could always be cutting. But the time lag between the substrate being released from the enzyme
and a new substrate binding prevents maximum velocity from actually being achieved. However, one can still
assess what the theoretical maximum velocity would be.
f. So at higher concentrations of substrate, the enzyme reaction approaches zero order kinetics, while [audio
unclear] it becomes a very straight line.
g. On the other hand, when you have a parabolic or a hyperbolic equation, then you know it is not a simple
straight line equation with just X & Y. It’s going to involve a square or a cube or whatever, it’s just a higher
order equation that you’ll have to deal with.
XVI.
[ES] Remains Constant Through Much of the Enzyme Reaction…[S18]
a. I’m going to skip this because I’m coming back to it later.
XVII. The Michaelis-Menten Equation is the Fundamental Equation of Enzyme Kinetics [S19]
a. In 1928, Michaelis and Menten came up with this brilliant idea about how to deduce these constants,
particularly with enzymes, and they came up with a bunch of equations. Today these equations are the gold
standard model in which they define how enzyme kinetics can be derived.
b. “ES” with brackets ([ES]) denotes the concentration, and as I’ve told you, the enzyme and substrate have to
come together to form an enzyme-substrate complex before the reaction can occur.
c. The idea Michaelis and Menten introduced was that this particular reaction is always at equilibrium (E + S ↔
ES). With this, they defined the constant for the forward reaction as k1, and the constant for the reverse
reaction as –k1.
d. They wanted to define the entire thing based on what we know – enzyme and substrate. Experimental
physicists, chemists, and biologists try to solve these equations so they can put these numbers into these
equations and then deduce them.
e. So here we know the concentration of the enzyme and the concentration of the substrate being used in the
reaction, and then it forms a complex [ES], which is an unknown.
f. But it always gives rise to a product, P + E, with a rate constant of k2. So this reaction gives rise to product P,
and the enzyme is now free. The free enzyme is then ready to bind the next substrate and then proceed on.
g. It was with this basic idea that Michaelis and Menten derived all the constants.
XVIII.
XIX.
“Michaelis-Mention equation continued” [S20]
a. There are two constants in the Michaelis-Menten equation. One is the rate constant Km that we have looked
at.
b. The other one is Vmax, or the maximum velocity at which an enzyme can react. With these two constants,
they came up with this beautiful equation which can use the velocity of the enzyme, at what rate the enzyme
is able to produce products. That is related to the substrate, and then there is the rate constant Km.
Understanding Km [S21]
CLASS: Fundamentals I 10:00-11:00
Scribe: Caleb Landrum
DATE: 8/20/2010
Proof: Jordan Ridgeway
PROFESSOR: Deivanayagam
Enzyme Kinetics
Page 4 of 6
a. If you want to understand what this Km means, when they say the substrate binds very tightly because the
Km is very small. What it means is the rate constants are much lower, in this case, when the substrate is
binding very tightly.
b. And if the substrate is weak binding, then the Km is higher.
c. Km is a constant, and it is derived from constants, which is something you should remember, as it is a
derivation from all three constants in this equation. Most of the time when using enzymes in the lab, we
always try to figure out what the Km and Vmax are, based upon which we determine if it is a tightly bound
enzyme.
XX. The Km values for some enzymes and their substrates [S22]
a. Here are some values that are listed in your book for Km values for different substrates and enzymes.
b. As I told you earlier, most enzymes are specific, but some enzymes do have different types for substrates for
which they bind to and they all have different Km values.
c. So based upon these values you can say this enzyme is more specific to some particular substrate and less
specific to some particular substrate.
XXI.
Understand Vmax
a. The next thing is Vmax, which I’ve already defined. It is also a constant and it’s a theoretical maximum rate
that is never achieved in reality.
b. To reach Vmax, all the enzyme molecules would have to be tightly bound to the substrate and never release
them, and that will never happen in an enzyme reaction.
c. Vmax is asymptotically approached as substrate is increased as shown here.
XXII. The Dual Nature of the Michaelis-Menten Equation [S24]
a. We have defined these two big constants, now this is something I’ve already talked about regarding the zero
and first order character.
XXIII. The Turnover Number Defines the Activity of One Enzyme Molecule [S25]
a. The next important number that you want to know about is called the turnover number, also called Kcat.
b. The Kcat is nothing but Vmax divided by Et.
c. The value of Kcat ranges from one second to many millions per second, which is shown here in this table.
d. This is a measure of catalytic activity, so this is a constant that tells you how much of the product is being
released.
The Ratio kcat/Km Defines the Catalytic Efficiency of an Enzyme [S26]
a. But there is a better number that defines the catalytic efficiency of the enzyme. You have to remember that
the substrate has to bind in order for it to be released, right? So if we take both of those actions into account,
then that defines the efficiency.
b. The earlier one that we defined (turnover number) only defines the second portion, or how much product is
released. So this ratio defines the complete efficiency of an enzyme.
c. So this is one of the characteristics that we defined when we said “what do enzymes have?” They have
catalytic power - that was the first definition, and that is what we have covered so far. The second one is
specificity which we will come to a little later.
XXV. Linear Plots Can Be Derived from the Michaelis-Menten Equation [S27]
a. Much earlier people were trying to plot these equation by hand, but these days it’s much easier to these
things with the advent of computers and programs like Excel. From the Michaelis-Menten equation, one can
simplify these things and these asymptotic curves into straight lines.
b. How is that done? You simply take the Michaelis-Menten equation v = Vmax[S]/(Km + [S]) and take the
reciprocal of this equation to get a very simple straight line formula. You can say it is equal to Y = mx +b.
c. If you plot 1/v vs. 1/S, you get a slope, and this is called a Lineweaver-Burk plot. It simplifies looking at the
values of Vmax and Km.
d. Usually you start at zero and if you want to extrapolate and then define Km and Vmax, it is very easy to
extrapolate and figure out. I told you that realistically you cannot figure out the Vmax of an enzyme, but
theoretically you can and that’s why you extrapolate what you observe in experiments. These plots are very
useful for you to figure out what the Vmax and Km are.
XXVI. Hanes-Woolf plot [S28]
a. There is another set of improvements that were made, but they are much more detailed and you may never
get to use these things. This is called the Hanes-Woolf plot, in which they began with the Lineweaver-Burk
equation and divided both sides by [S].
b. Usually the other equation has some errors associated with it, because at the beginning of the reaction the
substrate concentration inside the enzyme is very low, giving rise to errors in experiments, but the HanesWoolf plot is able to overcome them.
XXVII. Enzymatic Activity is Strongly Influenced by pH [S29]
XXIV.
CLASS: Fundamentals I 10:00-11:00
Scribe: Caleb Landrum
DATE: 8/20/2010
Proof: Jordan Ridgeway
PROFESSOR: Deivanayagam
Enzyme Kinetics
Page 5 of 6
a. How are enzymatic activities affected by other parameters? In the lab the other parameters would be the pH
and the temperature. How do these two factors affect the activity? Every enzyme has an optimal pH.
b. That is because the active site always contains residues that have to be protonated in order to be reactive. If
you discover a new enzyme in the lab, you take it and dialyze it in different buffers at different pHs and plot
the curves to figure out at what pH the enzyme is active.
c. You’ll usually find that it is a Gaussian-type curve. They are always within a certain range. But there are some
enzymes (like I always say, there is a sub-clause to every clause), that will function over a wide range.
d. Typically, however, enzymes function over a narrow pH range. There are reasons for these enzymes to work
at a particular pH.
XXVIII. The Response of Enzymatic Activity to Temperature is Complex [S30]
a. What happens when temperature is increased?
b. In general, the rule of thumb says that an enzyme activity doubles every ten degrees, but after a certain
temperature the enzyme activity begins decreasing because the enzyme is denatured and is no longer viable.
c. We can measure all of these things in one way or another because these days you have spectrophotometers
that have temperature probe attachments. You place an enzyme in a cuvette, add your substrate, then you
start plotting your graph. Keep raising the temperature and suddenly you’ll find that there is no more activity.
d. So enzyme response to temperature is slightly different. It keeps increasing to certain level, then drops off
very quickly.
XXIX. What Can Be Learned from the Inhibition of Enzyme Activity? [S31]
a. At the beginning of this lecture, I asked “why do we need enzyme kinetics?” It’s because when you have an
enzyme and you want to inhibit it, you want to know how it is being inhibited. There are many ways an
enzyme can be inhibited.
b. One way is reversible inhibition, which can be controlled to some extent.
c. There is also irreversible inhibition.
d. One way of defining these things is looking at the characteristics of these enzymes, and then we can say “this
is an irreversible enzyme” or “this is a reversible enzymes. I just threw these equations in here to show you
how the complexity rises every time you add a new factor. In this case, it is not just the enzyme plus the
substrate, but now we one more actor in the field - the inhibitor. Now there is a third complement that is
coming in.
e. Each type of inhibition can be defined with a rate equation. When you have an inhibitor and you plot the
graph, you are quickly able to see whether it is a competitor or non-competitor, or a mixture, or uncompetitive.
f. We will define these things in a much more detailed manner in the next few slides. This is where enzyme
kinetics plays a major role.
XXX. Competitive Inhibitors Compete With Substrate for the Same Site on the Enzyme [S32]
a. What does competitive inhibition mean? The substrate site is being occupied by the inhibitor. The inhibitor
and the substrate compete for the spot in the enzyme active site.
b. In this case, the inhibitor and substrate will look very similar. In this case, when there is competitive inhibition,
you can increase [I] and you will see that it only changes the Km and not the Vmax. Why is that? If you
imagine the situation, Km is a rate constant, right? When an inhibitor sits in the pocket, it affects the release
of a product, affecting the Km.
c. But then the velocity of the enzyme is unchanged, because the enzyme has not been modified, it just cannot
function. What has been changed is the rate at which the product is being formed.
d. In a competitive inhibition situation, if you raise the amount of substrate to much higher than the amount of
the inhibitor, you can still overcome the inhibition in order to get product.
XXXI. Pure Noncompetitive Inhibition – where S and I bind to different sites on the enzyme [S33]
a. In pure noncompetitive inhibition, the inhibitor binds to some other site of the enzyme, which alters the
conformation of the enzyme in such a way that the substrate cannot bind to the active site.
b. Here, Km is unchanged, but the Vmax is changed because the enzyme is altered.
c. If you plot these graphs and they follow a certain pattern, then you know whether it is a pure competitive or
noncompetitive situation.
XXXII. Mixed Noncompetitive Inhibition: binding of I by E influences binding of S by E [S34]
a. In a mixture situation, it becomes more difficult. The binding of inhibitor influences the binding of substrate to
the enzyme.
b. In this case, both the Vmax and the Km change.
c. This also subject to certain conditions, which I won’t go into. Just look at the plots, the other two situations
are good enough for you to understand. In one case the enzyme is changed, in the other case the enzyme is
unchanged. In each case, one parameter is affected while the other remains unaffected.
XXXIII. Uncompetitive Inhibition, where I combines only with E, but not with ES [S35]
CLASS: Fundamentals I 10:00-11:00
Scribe: Caleb Landrum
DATE: 8/20/2010
Proof: Jordan Ridgeway
PROFESSOR: Deivanayagam
Enzyme Kinetics
Page 6 of 6
a. In uncompetitive inhibition, it is a totally different situation. What happens is your substrate is bound and your
inhibitor is not competing for the site, but it kind of disturbs the area of binding, in which case it also slightly
modifies the enzyme’s characteristics.
b. In this case, the Km and Vmax both change.
c. If you have parallel lines coming out in any situation (graph), you know that you don’t have a very specific
inhibitor, you have a very uncompetitive inhibitor that is trying to stop the reaction, but you don’t know how it
does, so it is a very different situation.
[End 50:12]
Definition of enzyme (catalytic power specificity, regulation), coenzyme, active site, cofactors, holoenzyme,
apoenzyme
How do enzymes affec the thermodynam of reaction?
Michaelis menten, km vmax
Turn over rate
Catalytic efficiency
Single double displacement rxns
Lock and key vs induced fit specificity