Lecture #4
Enzymes Basic Concepts and Kinetics
Slide 1. Today we’ll look the basic character and kinetic function of
enzymes. We will consider how enzymes are constructed and how the
actually function to promote the rates of biochemical reactions.
Slide 2. Enzymes are protein (or nucleic acid) catalysts which speed the
rate of biochemical reactions. Enzyme molecules are highly specific
toward reactants and products. They exhibit high sensitivity to changes in
temperature, pH, substrate concentration, cofactor availability and
ionic environment
Slide 3. Enzyme catalysis occurs after the substrate S binds to the active
site of the enzyme E to form an enzyme-substrate complex ES. This ES
complex then undergoes catalytic alteration to form the product P and
reform the (uncomplexed) enzyme E. The enzyme E is unchanged in the
process and is free to participate in another round of catalysis
Slide 4. The active site of an enzyme occupies a small niche on the surface
of the protein, which is comprised of amino acid side chains from various
parts of the primary sequence. There are two features to enzyme
activity—binding and catalysis.
The substrate is bound to the active site by weak interactions with
various side chains of the enzyme. The specificity of substrate binding
depends on geometric and chemical complementarily between substrate and
the active site amino acid residues. The interactions between enzyme and
substrate include ionic bonds, hydrogen bonds, hydrophobic interactions,
and van der Waals forces.
The key to enzyme catalysis is that the reaction pathway and the energy
level of the transition state are altered by interactions between the
substrate and some of the active site amino acid side chains. Interactions
with these amino acids include such things as acid-base catalysis,
nucleophilic and electrophylic interactions, hydrophobic effects, ionic
stabilization of charged intermediates and in some cases the formation of a
covalent bond between substrate and the enzyme.
Slide 5. There are two hypothesis that are used to explain substrate binding.
The lock and key hypothesis states that the enzyme active site is an exact
complement to the substrate at all times. The substrate fits immediately in
the active site like a key in a lock. Taken to its extreme this hypothesis
would suggest that the shape of the active site remains absolutely the same
before and after the substrate is bound.
Slide 6. The induced fit hypothesis states that the shape of the active site
changes in the presence of the substrate to yield a precise fit. According to
this model, interactions between the substrate and active site amino acids
induce conformational changes in the shape of the active site. In actual fact
both of these hypotheses have some validity. All enzymes undergo some
changes in active site topography when the substrate is bound, but the
enzymes vary considerably in the degree of change that occurs upon
substrate binding.
Slide 7. The enzyme, hexokinase provides a dramatic example of
induced fit. The active site of hexokinase undergoes a significant alteration
in its conformation when its substrate, glucose is bound. In the absence of
glucose the active site exists as an open cleft. In the presence of glucose the
site undergoes a dramatic transformation in which the cleft closes around
and envelopes the substrate.
Slide 8. The temperature has a significant effect on enzyme activity. In
general enzyme reactions are more sensitive than equivalent chemical
reactions to changes in temperature. At lower temperatures the rates of
enzyme reactions increase markedly as the temperature is raised. This
sensitivity to temperature is sometimes measured as a Q10—the increase in
activity for a ten degree rise in temperature. The Q10 for enzyme reactions is
generally higher than it is for chemical reactions. Enzymes are subject to
inhibition at higher temperatures. Enzyme activity increases with
temperature up to some optimal temperature range, but then decreases as the
temperature is raised even higher. Above a certain critical temperature
enzymes completely lose activity because they are irreversibly denatured
.
Slide 9. Most enzymes are highly sensitive to changes in pH. There is
generally a pH range in which optimal activity is observed. At pH values
below or above this optimal range enzyme activity decreases, and at pH
extremes most enzymes are denatured. As with temperature, the effects of
pH on enzyme reactions are more pronounced than on most chemical
reactions. That is because in addition to effects on the substrate, the pH
influences the shape and charge of the active site, which in turn changes the
functionality of the enzyme in catalysis.
Slide 10. The catalytic activity of an enzyme relates to the ability to
convert substrate (S) to product (P). Catalytic activity is generally
measured as mole of product/minute (Enzyme Units). Specific activity
describes the ratio of enzyme activity to the amount of protein present
and is measured as Enzyme Units/mg of protein. The specific activity of
an enzyme is generally relative low in a crude biological extract and
increases as the enzyme is purified. One indication that an enzyme
preparation has reached homogeneity is that the specific activity does not
increase when further purification procedures are attempted.
Slide 11. The enhancement in reaction rate for enzyme catalysis is
generally enormous. The data in our figure, which compares the rates of
enzyme catalyzed and uncatalyzed reactions, show rate enhancements that
range from about 106 to 1017. In the case of OMP decarboxylase, the
uncatalyzed reaction would take 78 million years, whereas the catalyzed
reaction occurs in seconds. One of the fastest enzymes, carbonic anhydrase
catalyzes the breakdown of one million substrate molecules per second.
Slide 12. Many enzyme reactions require small molecules called
cofactors in addition to the protein structure itself. In this case catalysis
depends on three factors interacting to form an active complex—Enzyme,
Substrate and Cofactor all participate in the catalytic reaction. Cofactors can
be inorganic ions or organic molecules. An enzyme that lacks an essential
cofactor is called an apoenzyme. The enzyme with the cofactor bound is
called a holoenzyme.
Organic cofactors commonly participate in oxidation-reduction reactions
and in the transfer of various organic functional groups. The organic
cofactors often are vitamins or contain vitamin components. By definition
these vitamin components must be provided in the diet, because humans lack
the necessary metabolic pathways for their synthesis.
Inorganic cofactors participate in oxidation-reduction reactions, in
substrate binding, and may also be needed to facilitate the correct active
conformation of a protein. The inorganic cofactors must be obtained from
dietary sources, and thus constitute part of the minimal nutritional
requirements for human survival.
Slide 13. The initial rates (speed of product formation) of enzyme
reactions are often very rapid, but these rates decrease relatively soon, as
the substrate level decreases and the reaction approaches equilibrium. In
contrast uncatalyzed reactions are generally very slow and can take days or
years to approach equilibrium. Eventually both types of reaction approach
the same equilibrium value.
Slide 14. The equilibrium constant for a reaction corresponds to the
ratio of product to substrate when a reaction is allowed to achieve
equilibrium. At equilibrium the rates of the forward and reverse reactions
are exactly equal and there is no net change in substrate or product
concentration. NOTE: ENZYMES INFLUENCE THE RATE OF
CHEMICAL REACTIONS, BUT THEY DO NOT CHANGE THE
EQULIBRIUM OF THE REACTION. THE RATES OF THE
FORWARD AND REVERSE REACTIONS ARE ENHANSED TO
THE SAME DEGREE. THUS, THE EQULIBRIUM CONSTANT IS
THE SAME FOR A CATALYZED OR UNCATALYZED REACTION.
Slide 15. The turnover number (Kcat) of a reaction is given by the formula
Kcat = Vmax/[Et]. The turnover number gives the number of molecules of
substrate that can be converted per second per molecule of enzyme (or per
enzyme active site for a multi-subunit enzyme).
Turnover numbers range from a ripping 40,000,000 per second to a snaillike 0.5 per second.
Turnover numbers relate to the molecules of a specific enzyme (not the
total protein in a preparation), and thus unlike the specific activity which
increases as an enzyme is purified, the turnover number of an enzyme is a
intrinsic property which does not change with purification.
(NB. Keep in mind that although turnover numbers do not change, the
number of turnovers in a bakery can change from a high number first thing
in the morning to low or none at the close of the business day. If this fact
seems trivial to you, keep in mind that it could appear on your next exam.)
Slide 16. The free energy of a reaction (G) is the amount of energy
released or consumed by a reaction. The standard free energy (Go)
measures the energy released or consumed by a reaction when all substrates
are present at 1 M concentrations under standard conditions of temperature
and pressure.
-The energy diagram shows an thermodynamically favorable reaction (a
reaction with a negative G).
-The difference in energy levels between A (substrate) and B (product)
equals the free energy of the reaction.
-The free energy of a reaction (G) is a thermodynamic factor that is
dependent upon the energy levels of the reaction substrate and product. The
intervention of an enzyme does not change these values and thus does not
change the overall free energy of a reaction.
-The free energy of activation is the difference between the energy level of
a substrate and the activated intermediate or "transition state" of the reaction.
An enzyme can provide an alternate transition state for a reaction and thus
can change the free energy of activation of a reaction.
Slide 17. The three energy diagrams show reactions in which the substrates
and products are at various energy levels.
-when product B is at a lower energy level than substrate A it denotes
an energy releasing reaction with a negative G. At equilibrium there will
be more product than substrate.
-When substrate C and product D are at the same level there is no
energy released and the G is zero. At equilibrium there is no difference
in relative concentrations of substrate and product.
-When the product F is at a higher energy level that the substrate E the
transformation of E to F is an energy requiring reaction with a positive
G. At equilibrium there will be more substrate than product.
Slide 18. The third energy diagram shows that an enzyme can lower the
activation energy of a reaction. This is how an enzyme can increase the
rate of reaction. A lower energy barrier means substrate is converted into
product at a faster rate. Note: an enzyme changes the energy of activation
but does not change the free energy of the reaction and does not change
the equilibrium.
Very important, so I will say it again! Enzymes do not, not, not change the
thermodynamics of a reaction. That is enzymes do not change G, the
equilibrium constant Keq, the amount free energy released or required, or
the net balance of substrate and product at equlibrium.
Slide 19. The next series of figures explore the relationship between
standard free energy and equilibrium constant. These two factors are
inextricably related to each other by a mathematical relationship which we
will define.
Slide 20. The standard free energy (Go) measures the energy released or
consumed by a reaction when all substrates are present at 1 M
concentrations under standard conditions of temperature and pressure. This
(Go) is a useful value for chemists and physicists, it becomes a problem for
biochemists when hydrogen ions constitute part of a reaction. A hydrogen
ion level of 1M is equivalent to pH 0 and biochemical reactions generally
take place at or around pH 7.0.
Slide 21. Because most biological reactions take place at or around pH 7.0,
biologists use a modification of standard free energy (Go'). The prime (')
denotes the fact that the [H+] concentration is set at pH 7 (10-7 M) instead of
at 1 M.
Slide 22. At equilibrium G equals zero and Go' = -RTlnK'eq where K'eq
is the equilibrium constant for the reaction. Note that ln is a "natural log"
that can be converted to a log to the base 10 by multiplying by 2.3. That is
lnX = 2.3log10X. (These days everyone wants to be natural, so I know that
you all really wanted to know all about natural logs. I am not going to tell
you anything about unnatural, logs because this is not that kind of course.)
The point here is really that the equlibrium constant of a reaction is related
to the standard free energy. Neither of these factors can be changed in the
presence of an enzyme. They are both determined by the energy levels of
substrate and product.
On other point—because there is a negative logarithmic relationship
between Go' and K'eq the following relationships exist:
If Go' is negative the K'eq will be a positive number greater than one.
If Go' is zero the K'eq will be equal to one.
If Go' is positve the K'eq will be a positive number less than one.
Slide 23. We are now going to segue subtly from thermodynamics to
enzyme kinetics. We have seen this slide previously. It gives the simplest
kinetic approximation for describing the kinetics of an enzyme catalyzed
reaction. If this were a real enzyme reaction, there would also be one or
more transition states and an enzyme product complex between E + S and E
+ P. This simplified mechanism is useful in deriving the most basic
equation for describing the kinetics of an enzymatic reaction.
Slide 24. The figure shows the rates of product formation in an enzyme
reaction conducted at a series of increasing initial substrate concentrations:
[S]1, [S]2, [S]3, [S]4. You can see that the initial reaction rate, V0 of an
enzyme reaction (taken by measuring enzyme rates as close to time zero as
possible) increases with increasing substrate levels.
Slide 25. When those initial rates of the enzyme reaction [V0] are plotted
against the substrate concentration a hyperbolic plot is obtained. This type
of hyperbolic enzymatic response is described by the the Michaelis-Menten
equation.
Slide 26. The basic form of the Michaelis-Menten equation is:
V = Vmax x [S]/ [S] + Km.
This equation describes a rectangular hyperbola. V equals the observed
reaction velocity; Vmax equals the maximum reaction rate, [S] is the
substrate concentration; Km is (some mathematical VooDoo) called the
Michaelis constant.
Slide 27. The Michaelis-Menten equation is derived for an enzyme
reaction under steady state conditions. This means that the concentration of
ES is assumed to remain relatively constant during the course of the reaction.
The other assumption use in the derivation is that there is essentially no
product around. This latter condition allows one to ignore the reverse
reaction in which P +E revert to ES.
Slide 28. The Michaelis constant, Km is equal to k2 + k-1/k1. The term k1 is
the rate constant for the formation of the ES complex, k -1 is the rate constant
for the reversion of ES to E + S and k2 is the rate constants for the
conversion of ES to E + P. (The k -2 term is not used in the equation because
enzyme kinetics are generally measured at time zero when there is little or
no product present, so the back reaction is negligible. For anyone who
enjoys kinetics it is possible to see how Km is obtained by studying the
derivation of the M-M equation. It is also possible to conclude that if K2 is
rate limiting, then the Km is equal to the dissociation constant for the ES
complex into E + S. This means that when K2 is rate limiting the Km is an
approximate measure of the affinity of E for S.)
.
Slide 29. At low [S] the M-M equation reduces to a straight line
equation:
V = K[S].
At slightly higher [S] the reaction rate curves off. At this substrate level the
response to substrate levels cannot be approximated by a linear equation and
the whole M-M equation must be used.
Slide 30. At very high [S] the equation reduces to V = Vmax. When the
substrate concentrations are high the reaction rate approaches Vmax as a limit.
At that point the rate is not significantly increased by raising the [S] to even
higher levels.
Slide 31. When [S] = Km, V = 1/2 x Vmax. The term Km thus gives an
indication of how efficient an enzyme is at low [S]. A low Km tells us that
the enzyme is efficient at low [S]. A high Km tells us that the enzyme is not
efficient at low [S].
Slide 32. Enzymes are very diverse when it comes to their kinetic efficiency.
For example turnover numbers vary hugely from one enzyme to
another. The range in turnover numbers varies from a ripping 40,000,000
per second to a snail-like 0.5 per second.
Slide 33. Michaelis constants generally vary considerably. Most enzymes
exhibit Km values between 1 mM and 1 M, but some Km’s are as high a
1M. (This latter value is for the enzyme catalase. Generally that would
indicate a very inefficient enzyme. However, catalase has a turnover number
of 40,000,000, so it can still function efficiently with a poor Km.)
Slide 34. The Lineweaver-Burk plot is an alternative method of plotting
kinetic data. The L-B equation can be derived by inverting the M-M
equation.
That inversion gives the equation: 1/V = 1/Vmax + Km/Vmax[S]
(When you use the L-B equation instead of plotting V vs.S, you would plot
1/V vs. 1/S.)
Slide 35. The advantage of the L-B plot is that it gives a straight line, which
aids in extrapolation from experimental data and allows an accurate
determination of Vmax and Km. The intercept of this plot on the ordinate
is equal to 1/Vmax, and the intercept on the abscissa is equal to 1/Km. The
slope of the line is Km/Vmax.
Slide 36. Because enzymes are relatively fragile proteins with a variety of
functional groups, they are subject to many kinds of inhibitors. These
chemical inhibitors slow or sometimes totally prevent enzyme activity.
Such inhibitors include biochemical reagents, toxins, venoms, antibiotics or
drugs.
Slide 37. There is a geometric and chemical complimentarity between
an enzyme and its substrate.
Slide 38. Competitive inhibitors often look like an enzyme’s substrate
(or one of its transition state intermediates) and they inhibit the enzyme
by competing for occupancy of the active site.
Slide 39. Methotrexate is a competitive inhibitor that resembles
dihydrofolate, and it inhibits enzymes that use dihydrofolate as a cofactor.
Methotrexate is used in chemotherapy treatment of a number of types of
cancer.
Slide 40. Competitive inhibitors bind reversibly to the active site of an
enzyme, and they can be displaced by the substrate. Thus, competitive
inhibition can be completely overcome by increasing the substrate
concentration to high levels.
Slide 41. Competitive inhibitiors raise the apparent Km but do not effect
the Vmax. This is demonstrated when Lineweaver-Burk plots are determined
in the absence and presence of a competitive inhibitor. The 1/V intercept
remains the same in the absence or presence of the inhibitor, indicating that
the Vmax does not change. The 1/[S] intercept (which gives -1/Km)
becomes less negative, indicating that the apparent Km increases in the
presence of a competitive inhibitor. (NB. Remember that this is a double
reciprocal plot so that the inhibited reaction plot is higher than the
uninhibited reaction plot. You might have to know that on an exam.)
Slide 42. Uncompetative inhibitors bind reversibly only to the ES
complex. The prior binding of S to E is a prerequisite for the binding of I to
ES.
Slide 43. When uncompetitive inhibition takes place, a portion of the
ES complex is diverted to form a non-productive ESI complex. The ESI
complex is totally unreactive in the formation of product. Because of this,
Vmax cannot be achieved even at high substrate concentrations. In addition
for reasons that I cannot explain, the apparent Km value is lowered
becoming progressively smaller as more inhibitor is added.
Slide 44. A Lineweaver-Burk plot of uncompetitive inhibition shows
that the slope of the double-reciprocal plot does not change in the presence
of inhibitor. Both the Vmax and the Km are reduced by equivalent
amounts. The maximal rate is reduced but it is approached at lower
substrate concentration. Again, because this is a double reciprocal plot the
inhibited reaction line is higher than the uninhibited line.
Slide 45. Noncompetitive inhibitors generally bind reversibly away
from the active site to reduce or prevent catalytic activity.
Slide 46. With noncompetitive inhibition the substrate can still bind,
but the ESI complex does not proceed to form product. Noncompetitive
inhibition cannot be overcome by raising the substrate level, because the
substrate does not displace the inhibitor.
Slide 47. A Noncompetitive inhibitor lowers the Vmax but does not effect
the Km. A Lineweaver-Burk plot of noncompetitive inhibition shows that
the 1/[S] intercept is not changed. Thus, the Km value is not altered. The 1/V
intercept is raised showing that the Vmax is decreased. Keep in mind yet
again that the inhibited line is the higher one.
Slide 48. Irreversible inhibitors generally stick to an enzyme covalently
and cannot be easily removed from the enzyme by mild techniques such
as dialysis. The irreversible inhibitor, TPCK is an analog of the natural
substrates for the enzyme, chymotrypsin.
Slide 49. TPCK is an example of an irreversible inhibitor that is also an
affinity label (reactive substrate analog). It binds at the active site of
chymotrypsin and then reacts irreversibly with a histidine residue in the
active site of the enzyme.
Slide 50. DIFP is a group specific irreversible inhibitor. It specifically
modifies unusually active serine residues in the active sites of serine
proteases such as chymotrypsin, and it also modifies the active site serine
residue of acetylcholinesterase.
Slide 51. The irreversible inhibitor, iodoacetamide exhibits similar
ability to react with activated cysteine residues in the active sites of various
enzymes. The acetamide portion of the inhibitor molecule forms a covalent
bond with the sulfur atom in the active site of these enzymes.
Slide 52. Although there are 1000's of different enzyme reactions in nature,
there are only six basic types of enzyme reactions. These are
oxidoreductases, transferases, hydrolases, lyases, isomerases, and ligases.
Almost all biochemical reactions fall into one of these six categories.