index
Announcements
Questions
Chapter 5: Enzymes
Section 5.1: Classes of Enzymes
Oxidoreductase Reaction
Transferase Reaction
Hydrolase Reaction
Lyase Reaction
Isomerase Reaction
Ligase Reaction
Section 5.2: Kinetics
Reaction Velocity
Initial Velocity of a Reaction
A Macroscopic Analogy
A Macroscopic Analogy (2)
Enzyme Kinetics
Rate Constants of a Catalyzed Reaction
Another Macroscopic Analogy
Another Macroscopic Analogy (2)
Velocity of a Catalyzed Reaction
Enzyme Saturation
Non-Saturation Kinetics
Section 5.3: The Michaelis-Menten Equation
The Michaelis-Menten Equation
Michaelis-Menten Kinetics
Questions
Next Lecture: Sections 5.4 - 5.8

Fundamentals of Biochemistry

Biochem 380 - Fall 2006

Lecture 013

Outline

Announcements
Questions from previous lecture
Section 5.1: Classes of Enzymes
Section 5.2: Kinetics
Section 5.3: The Michaelis-Menten Equation

Announcements

Lecture 12 notes are online
Quiz on Friday will be on Chapter 4, except for sections 6, 7, 8, 11 and 14

Questions

Any questions on the material from the previous lecture?
What does 'allosteric' mean?
What allosteric molecule interacts with hemoglobin? What does the interaction do?
What is the 'Bohr effect'?

Chapter 5: Enzymes

In this chapter, we are introduced to a very important group of biomolecules known as enzymes. Enzymes are highly specific catalysts of biochemical reactions
Enzymes cannot change the overall equlibrium of a particular reaction, they only affect the rate at which the reaction can come to equilibrium
However, enzymes can couple two reactions. Here, the energy from one reaction can be used to affect the equilibrium of the other reaction, making it more favorable
Another important feature of enzymes is that they can be regulated. This is often done through the binding of a molecule at an allosteric site, changing the effectiveness of enzyme catalysis at the active site

Section 5.1: Classes of Enzymes

To better manage the large number of enzymes, they have been organized by the IUBMB into 6 main categories, based upon the general kinds of reactions that they catalyze:
1. Oxidoreductases (oxidation-reduction reactions)
2. Transferases (transfer of a group from one molecule to another)
3. Hydrolases (cleavage of a bond by water)
4. Lyases (addition/removal of a double bond)
5. Isomerases (intramolecular rearrangement)
6. Ligases (joining of substrates using ATP)

Oxidoreductase Reaction

An oxidoreductase is an enzyme that catalyzes oxidation-reduction reactions.
Shown above is lactate dehydrogenase, which catalyzes the oxidation of lactate and the corresponding reduction of NAD⁺
Many enzymes have both a common name and a formal name. The formal name of lactate dehydrogenase is lactate:NAD oxidoreductase

Transferase Reaction

Transferases catalyze group-transfer reactions, where a functional group is transferred from one substrate to another
Above is the reaction catalyzed by alanine transaminase, in which an amine group is transferred from glutamate to pyruvate, producing alanine (reverse reaction)
We'll see this reaction again in the section on amino acid synthesis

Hydrolase Reaction

Hydrolases catalyze the breaking of bonds, where a water molecule reacts with one of the groups
We've seen this reaction before with peptide bonds cleaved by proteases
Above, a pyrophosphate bond is broken by pyrophosphatase to produce two molecules of phosphate

Lyase Reaction

A lyase is an enzyme that breaks apart a substrate, resulting in the production of double-bonds
Above is a decarboxylation reaction, catalyzed by pyruvate decarboxylase, that produces CO₂ and acetaldehyde from pyruvate
A Lyase is also sometimes referred to as a synthase

Isomerase Reaction

An isomerase catalyzes an intramolecular rearrangement of groups
Above, alanine racemase catalyzes the interconversion of L-alanine and D-alanine
Because only one substrate and product are involved, these are among the simpler catalyzed reactions

Ligase Reaction

The final type of enzyme is a ligase, which joins two substrates together using an energy molecule such as ATP
Above, glutamine synthetase adds an amino group onto glutamate to produce glutamine
Ligase are often referred to as synthetases

Section 5.2: Kinetics

Kinetics is the study of the rates of chemical reactions
We'll begin with a look at the kinetic properties of uncatalyzed reactions
Next, we'll look at a model of a simple enzyme-catalyzed reaction
The goal of a kinetic analysis is concerned with determining the rate constants and rate equations that can describe the velocity of catalyzed and uncatalyzed reactions

Reaction Velocity

What is the velocity of a reaction? The velocity, v, (also called the rate) is defined as the amount of product produced per time:

The rate of a reaction is determined by two things: the concentration of the reactants and the intrinsic speed (rate constant k) of an individual reaction. For the simple reaction S → P, with just one reactant, the velocity is given by the following rate equation:

Each kind of reaction has its own particular rate constant. For a simple reaction such as the one shown above, the units of the rate constant are s^-1

Initial Velocity of a Reaction

Because the velocity of a reaction is dependent upon the substrate concentration [S], then if [S] changes, the velocity will change too. For reactions with a fixed initial amount of substrate, the result will be that the velocity will decrease over time as the substrate is converted to product
Because of this, the maximum velocity of the reaction will be the initial velocity of the reaction, v₀
The initial velocity can measured from the slope at the beginning of a reaction progress curve:

Note how the slope approaches zero over time. This can mean that no more product is produced because all the substrate has been converted, or it can simply mean that the reverse reaction rate equals the forward reaction rate, with no net creation of product (equilibrium)

A Macroscopic Analogy

Sometimes it helps to understand kinetics in the context of more familiar objects. Consider a slumlord near the university with lots of houses for rent
In such a situation, we have the following reactant S that can be converted into product P:

A Macroscopic Analogy

The progress of this reaction, and the resulting velocity, can be quantified as follows:

Month	[S]	[P]	velocity (Δ[P] / Δt)
0	1000	0
1	100	900	900
2	10	990	90
3	1	999	9

At the start of the school year, assume that 1000 students show up. In the first month, the slumlord converts 900 students into money
In the next month, there are only 100 homeless students left, so the slumlord can only convert 90 of them into money
Finally, in the third month, there are only 10 students left, resulting in a very small velocity of $9 produced for the poor slumlord

From the table, we see that the initial measured velocity is 900. This is the velocity v₀ that is used for analyzing the kinetics of a reaction

Enzyme Kinetics

So far we have been considering uncatalyzed reactions. When an enzyme catalyzes the reaction, an intermediate step is introduced in which an enzyme-substrate complex (ES) is formed
In the case of a single substrate and product, the following sequence occurs for the enzyme-catalyzed reaction:

E + S → ES → E + P

This equation represents a two-step process where the substrate first associates with the enzyme by binding to it, followed by the second step, where the enzyme accelerates the conversion of substrate into product:

Rate Constants of a Catalyzed Reaction

In the two-step catalyzed reaction, there are additional rate constants needed to describe the progress of the reaction:

k₁, is a forward rate constant that describes the rate at which the free substrate associates with the enzyme
k_-1, is the reverse rate constant for the first step, which describes how quickly the substrate dissociates from the enzyme, without a reaction taking place
k₂, describes the rate at which the enzyme converts bound substrate to product
In general, the association and dissociation rates are very rapid because only noncovalent interactions occur. Bond breaking and formation typically occur for k₂, so the conversion rate is usually much slower, and thus is the rate-limiting one for the overall reaction

Another Macroscopic Analogy

Let us return to our friend the slumlord. Because of a recent housing inspection, he realizes that he must do all of his business in a single day (as opposed to months) if he is to survive
Being a good entrepreneur, he finds a way to accelerate his student-to-money reaction by employing a catalyst:

In this reaction Mick Jagger stands next to a housing unit. When a student runs into him, Mick sings a song about how great it is to live there, very rapidly converting the student into money

Another Macroscopic Analogy

Let's suppose again that it's the beginning of school, with 1000 students wandering around town
Assume that when a student wanders by and sees Mick, it takes only 30 seconds for the student to come over and stand next to him This would be the forward rate constant k₁ (association)
Let's also assume that the rate at which a student walks away from Mick is around 5 minutes. This is the reverse rate constant k_-1 (dissociation)
Finally, assume that Mick has to sing to a student for about an hour before the student is converted to money. This would be the forward rate constant k₂ (conversion)

Velocity of a Catalyzed Reaction

In considering the progress and velocity of a catalyzed reaction, we have some additional things to think about. In the uncatalyzed reaction, we have seen how the substrate concentration affects the velocity
In a catalyzed reaction, the concentration of the enzyme [E] also affects the velocity:

In a reaction with a very high substrate concentration, the enzyme will be saturated
In this situation, doubling the amount of enzyme will double the initial velocity of the reaction
Conversely, if substrate concentration is very low, doubling the enzyme concentration will not double the velocity
Why not?

Enzyme Saturation

At high concentrations of substrate we have a condition called saturation where almost all of the enzyme will be bound to substrate, in the ES state:

When there are lots of students are around, if the slumlord triples the amount of Mick Jagger (using a cloning machine), he will triple his production of money!
In this situation, there is a simple, linear relationship between the velocity and the enzyme concentration. The velocity is essentially equal to the enzyme concentration times the conversion rate:

Non-Saturation Kinetics

The alternative situation is when the substrate concentration is low enough, so that the enzyme is not saturated:

Here, we have some cloned Micks just standing around not making money, because there are not enough students to keep all of the Micks fully occupied
How do we describe the velocity of the reaction in this situation?

Section 5.3: The Michaelis-Menten Equation

In the early 1900's, Michaelis and Menten developed an equation that describes the kinetics of enzyme-catalyzed reactions
The equation describes how the initial velocity of the reaction, v₀, changes with varying concentrations of substrate, [S]
Although the equation is strictly correct only for very simple types of reactions, the general behavior that it describes is also useful for understanding more complex reactions and reaction rates

The Michaelis-Menten Equation

The Michaelis-Menten (MM) equation is defined as:

In this equation, there are two new terms, V_max and K_m
V_max is the maximum velocity of the reaction. This occurs under saturation conditions and is equal to the total amount of enzyme times the conversion rate constant k₂
The other term, K_m, is called the Michaelis constant. It is defined in terms of the rate constants of the two-step reaction:

Michaelis-Menten Kinetics

The velocity of a reaction with Michaelis-Menten kinetics depends on the substrate concentration as follows:

At low substrate concentrations, the curve is a steep line, indicating that the rate is strongly dependent on substrate concentration
At high substrate concentrations, the enzyme becomes saturated, so that increasing the concentration of the substrate has little effect on the velocity
In between, when the substration concentration [S] is equal to K_m, then the velocity is exactly equal to one-half of V_max

Questions

Questions about the material covered today?

Next Lecture: Sections 5.4 - 5.8

Read Sections 5.4 - 5.8

Table of Contents

Fundamentals of Biochemistry

Biochem 380 - Fall 2006

Lecture 013

Outline

Announcements

Questions

Chapter 5: Enzymes

Section 5.1: Classes of Enzymes

Oxidoreductase Reaction

Transferase Reaction

Hydrolase Reaction

Lyase Reaction

Isomerase Reaction

Ligase Reaction

Section 5.2: Kinetics

Reaction Velocity

Initial Velocity of a Reaction

A Macroscopic Analogy

A Macroscopic Analogy

Enzyme Kinetics

Rate Constants of a Catalyzed Reaction

Another Macroscopic Analogy

Another Macroscopic Analogy

Velocity of a Catalyzed Reaction

Enzyme Saturation

Non-Saturation Kinetics

Section 5.3: The Michaelis-Menten Equation

The Michaelis-Menten Equation

Michaelis-Menten Kinetics

Questions

Next Lecture: Sections 5.4 - 5.8