Table of Contents
Fundamentals of Biochemistry
Biochem 380 - Fall 2006
Lecture 014
Outline
- Quiz
- Announcements
- Questions from previous lecture
- Section 5.4: Catalytic Proficiency
- Section 5.5: Measurement of Km and Vmax
- Section 5.6: Multisubstrate Kinetics
- Section 5.7: Reversible Inhibition
Announcements
- Lecture 13 notes are online, with a small correction
- Assigned homework problems for Chapter 5:
Questions
- Any questions on the material from the previous lecture?
The Meaning of Km
- In the previous lecture, we introduced the Michaelis-Menten equation and briefly discussed the
meaning of Km, the Michaelis constant
- As shown above, it represents a ratio between the rate constants for the dissociation and
formation of the enzyme-substrate complex
- If k2 is much smaller than k-1 (as is often the case), then the Michaelis
constant is equivalent to
k-1 / k1, which is just the equilibrium constant
for the dissociation of ES to E + S
- This represents the affinity that the enzyme has for the substrate.
- However, for many enzymes, Km may be a more complex function of multiple rate constants
One Last Kinetics Analogy
- One last time, let's consider Mick Jagger as our highly effective money-generating enzyme. Consider
two potential substrates that can associate with Mick. One is a Rolling Stones fan, the other
prefers AC-DC:
- Which association would have the larger Km value?
- A larger Km value indicates a reduced affinity, so it would be the one between Mick
and the AC-DC fan
The Catalytic Constant kcat
- When an enzyme is saturated with substrate, the velocity of a catalyzed reaction will be at a maximum,
Vmax. The rate constant under these conditions is referred to as the catalytic constant,
kcat, and is defined as follows:
- kcat is also called the turnover number, because it refers to the maximum amount of
substrate molecules that can be converted to product by an enzyme in a given amount of time
- For a simple single-substrate reaction, the catalytic constant is simply equal to k2,
the rate constant in the second reaction step:
Some Example kcat Values
Section 5.4: Catalytic Proficiency
- At this point, you should have some familiarity with the two kinetic parameters Km and kcat
- Since Vmax is equal to kcat times the total amount of enzyme, then in conditions where
the substrate concentration is very small, we can substitute this for Vmax in the
Michaelis-Menten equation:
- This gives a second-order rate constant equal to kcat / Km.
- This can then be compared to a non-enzymatic rate constant in order to assess
the catalytic proficiency of an enzyme, which is the ratio of the enzymatic rate to the non-enzymatic rate
of a reaction
Catalytic Proficiencies of Some Enzymes
Section 5.4: Measurement of Km and Vmax
- The determination of the Km and Vmax values of an enzyme can be determined
from a plot of the initial velocity of the reaction for a range of substrate concentrations
- However, because the velocity curve is hyperbolic, it can be difficult to determine the
asymptote that defines Vmax and the halfway point that determines Km
- These days, a computer program can extrapolate the curve from a smaller number of data points,
but in the old days, a different method was used. This method involves plotting the reciprocal of
the velocity against the reciprocal of the substrate concentration, which gives a linear curve
instead of a hyperbolic one:
Lineweaver-Burk Plot
- This double-reciprocal plot is also called the Lineweaver-Burk plot. Because it is a straight
line, the curve is represented by the general formula y = mx + b, where m is the slope and b is the y intercept
- Here, we see from the equation that the y intercept is 1 / Vmax. If we set y = 0 and solve
for x, we find that the x intercept is equal to -1/Km
- Although computers have made the experimental use of Lineweaver-Burk plots unnecessary, they are still
useful for representing changes in Vmax and Km, as we will see in the subsequent sections on
enzyme inhibition
Section 5.6: Multisubstrate Kinetics
- Many enzyme reactions are more complicated than the single-substrate, single-product example that
we have been using
- Enzymes often catalyze reactions with multiple substrates and products. There can also be multiple
kinds of sequences, where the order in which substrates enter and products leave can vary
- The kinetics of such multisubstrate reactions is considerably more complex as well, and we won't
be covering them in this course. But it's important to be aware of the kinds of additional steps and interactions
that can occur
- We'll take a quick look at some of the diagrams and notation used in multisubstrate reactions
Sequential and Ping-Pong Reactions
- Shown above are diagrams for two types of multisubstrate reactions: sequential and ping-pong
reactions
- In sequential reactions, all substrates enter before product is produced. The sequence can be either
ordered or random
- In a ping-pong reaction, one substrate is converted and released as a product, leaving the enzyme in
a modified state. A second substrate then binds and is converted to complete the reaction
Section 5.7: Reversible Inhibition
- The activity of enzymes can be affected by the binding of molecules other than the substrate. When
the activity is reduced, such molecules are called inhibitors. There are two main types of inhibition,
reversible and irreversible
- Reversible inhibition generally consists of non-covalent interactions between the inhibitor and the enzyme.
By contrast, irreversible inhibition usually involves a covalent interaction that permanently destroys the
activity of the enzyme
- Most biological types of inhibition are reversible, and are used to regulate the activity of enzymes
- There are different kinds of reversible inhibition, but we will focus only on the classical examples of
the two main types:
competitive and noncompetitive inhibition
Classical Competitive Inhibition
- In classical competitive inhibition, either the substrate or the inhibitor can bind to the
enzyme, but not both
- The effect of a competetive inhibitor is to reduce the effective concentration of the substrate,
so that more will be required to produce the same amount of ES complex. This effect is shown in the LB plot
by a smaller inverse Km value, which means that the apparent Km value is increased.
However, once ES is formed, the catalytic rate is the same, so Vmax is not affected
Classical Noncompetitive Inhibition
- In classical noncompetitive inhibition, the substrate and the inhibitor can both be bound to the enzyme at
the same time, but the bound inhibitor renders the enzyme inactive
- This reduces the effective Vmax, but since substrate binding is not affected by the inhibitor,
the Km value remains the same
- In general, the effect of inhibitors can be more complex, with both Km and Vmax being affected.
Such cases are referred to as mixed inhibition
Questions
- Questions about the material covered today?
Next Lecture: Sections 5.8 - 5.11