Biology 403/504, Sixth Lecture
Thursday 7 February 2008

Enzyme Properties

Outline

Classes of enzymes

The International Union of Biochemistry and Molecular Biology (IUBMB) has developed a classification scheme under which enzymes are classified into six major categories. They are summarized in this table, developed from descriptions in Horton's textbook, ch. 5:




EC # Name Reactions Catalyzed Sample Reaction Comments
1 oxido-
reductases
oxidation-reduction lactate + NAD →
pyruvate + NADH + H+
often involves NAD or FMN
2 transferases transfer a group larger than water alanine + α-ketoglutarate →
pyruvate + glutamine
includes kinases
3 hydrolases hydrolysis (elimination or transfer of H2O) pyrophosphate + H2O →
phosphate + phosphate
4 lyases lysis making a double bond;
(converse: addition across double bond)
pyruvate + H+
acetaldehyde + CO2
often called synthases when reverse reaction is emphasized
5 isomerases unimolecular reactions L-alanine → D-alanine some are mutases
6 ligases joining of 2 substrates glutamate +ATP +NH4+ → glutamine + ADP + Pi generally require high-energy phosphate compounds like ATP


Individual enzymes are numbered in a four-component system known as the "EC" system because the organization that originally developed the systm was called the Enzyme Commission. There are periods separating the levels of organization. Thus pancreatic elastase, a protease (enzyme that cleaves peptide bonds) is a hydrolase (category 3) and its full Enzyme Commission designation is 3.4.21.36:

If it helps you understand the system, think of the EC numbers as being like Internet Protocol (IP) addresses; the same logic applies. If you want to see the details of the EC numbering system, consult http://www.chem.qmw.ac.uk/iubmb/enzyme/.

The remainder of these notes concentrate on the kinetics of enzymatic reactions.

Enzyme kinetics

Kinetics is the study of reaction rates and the ways that they depend on concentrations of substrates, products, inhibitors, catalysts, and other effectors. If we consider the simple situation in which a reactant A is being converted to a product B under the influence of a catalyst C, such that at time t=0, [A] = A0, [B] = 0, then the rate or velocity of the reaction is expressed as d[B]/dt. In most situations more product will be produced per unit time if A0 is large than if it is small, and in fact the rate will be linear with the concentration at any given time:

d[B]/dt = v = k[A]

where v is the velocity of the reaction and k is a constant known as the forward rate constant. In this instance, since [A] has units of concentration and d[B]/dt has units of concentration / time, the units of k will be those of inverse time, e.g. sec-1.

Kinetics can become much more complicated than this if more than one reactant is involved or if a catalyst whose concentration influences the production of species B is present. If more than one reactant is required for production of B, then usually the reaction will be linear in the concentration of the scarcest reactant and nearly independent of the concentration of the more plentiful reactants. If in the reaction
A + D → B
the initial concentrations of [A] and [D] are comparable, then the reaction rate will be linear in both [A] and [D]:
d[B]/dt = v = k[A][D] = k[A]1[D]1

This reaction is said to be first-order (rate directly proportional to concentration) in both [A] and [D]. The sum of all the exponents that appear in this equation is 1+1=2, so the reaction overall is said to be second-order. This time the units of k are L/(sec-1mol-1) if [A], [B], and [D] are expressed in moles/L.

The rate in which the reverse reaction occurs may not be the same as the rate at which the forward reaction occurs. If the forward reaction rate of reaction 1 is designated as k1, the backward rate typically designated as k-1. In complex reactions, we may need to keep track of rates in the forward and reverse directions of multiple reactions. Thus in the conversion
A ↔ B ↔ C
we can write rate constants k1, k-1, k2, and k-2 as the rate constants associated with converting A to B, converting B to A, converting B to C, and converting C to B.

Michaelis-Menten kinetics

A very common situation is one in which for some portion of the time in which a reaction is being monitored, the concentration of the enzyme-substrate complex is nearly constant. Thus in the general reaction
E + S ↔ ES ↔ E + P
where E is the enzyme, S is the substrate, ES is the enzyme-substrate complex (or "enzyme-intermediate complex"), and P is the product, we find that [ES] is nearly constant for a considerable stretch. This means that the rate at which new ES molecules are being produced in the first forward reaction is equal to the rate at which ES molecules are being converted to E and P. This is one of five assumptions we will need to make to complete this derivation of the Michaelis-Menten kinetics. The full list of assumptions is:

  1. That [ES] is constant for some interval;
  2. That the amount of available enzyme at any given time is the total enzyme supplied to the system, minus the amount of enzyme that is already wrapped up in enzyme-substrate complex, i.e.
    [E]avail = [E]tot - [ES];
  3. That the reaction is first-order in both [E]avail and [S];
  4. That the concentration of P remains low, so that the back-formation of ES from P is therefore unimportant; and
  5. That the production of P from ES is the rate-limiting (slowest) step in the overall reaction.

These are all reasonable assumptions, but we should be conscious of them. We'll use all of the assumptions below.

The rate of formation of ES is, by assumption (b),
vf = k1[E]avail[S] = k1([E]tot - [ES])[S]
because of assumption (c), which allows us to write the forward reaction as above, and assumption (d), which allows us to ignore production of [ES] from the right. Meanwhile, the rate of disappearance of ES on the right and left is a function of the [ES] concentration, and it is related to the conversion of ES leftward to E and S, which is k-1[ES], and the conversion rightward to E and P, which is k2[ES]. Thus
vd = k-1[ES] + k2[ES]
= (k-1 + k2)[ES].
Based on assumption (a), vf = vd. Therefore k1[ES] = (k-1 + k2)[ES]
which means if we define Km ≡ (k-1 + k2) / k1,
then [E]tot[S]/(Km + [S]) = [ES]
Now we can employ assumption (e), which tells us that the overall reaction rate, v0 = v2, That is, the overall velocity is equal to the velocity of the last step, the conversion of ES to E and P. But the latter velocity is v2 = k2[ES], so
v0 = k2[E]tot[S] / (Km + [S])

Under what circumstances, given a fixed [E]tot, will the reaction operate at its maximal velocity? It is logical to say that the highest possible rate we can achieve would occur when the substrate concentration is very high, i.e. [S] >> [E]tot. If that is true, then v0 will be as large as it possibly can be for a given [E]tot. In that case, since [S] is very large, it will be much larger than Km, so the denominator Km + [S] ≈[S], so for that case
v0 = k2[E]tot[S] / [S] = k2[E]
We describe the reaction velocity under these saturating conditions as Vmax, so we can write the general equation as
v0 = Vmax [S] / (Km + [S])
This is the form of the Michaelis-Menten equation with which we will ordinarily work.

We often are interested in the basic properties of an enzyme. Km is an actual property of the enzyme; Vmax is not, because it will be much larger if we increase the enzyme concentration. So we normalize it to the enzyme concentration and define
kcatVmax / [E]tot
Now for our simple Michaelis-Menten system you can readily see that, kcat = k2; in more complex system kcat may have a more complex relationship with the underlying kinetic parameters.

Kinetic Constants

The kinetic constants, Km, kcat, and Vmax provide information about the properties of an enzyme with respect to its substrates. The Michaelis constant Km measures how stable the enzyme-substrate complex is; kcat tells us the first-order rate constant for converting the enzyme-substrate complex, ES, to the product and the recovered enzyme; it describes the rate of the reaction when the substrate is not limiting. Vmax shows us the fastest possible rate at which the reaction will proceed given the current set of conditions. More briefly, Kcat characterizes the binding of the substrate to the enzyme; kcat characterizes the effectiveness of the enzyme in turnover, i.e. converting reactant to product or vice versa.

It's typical for the Km of an enzyme for a substrate to be close to the cellular concentration of that metabolite. This enables the enzyme to respond proportionally to changes in the substrate concentration; the enzyme then can act as a kind of buffer of the concentration of that substrate as external influences modify that concentration.

An important parameter is the ratio of kcat to Km. As Horton says, this measures the apparent second-order rate constant for the formation of enzyme and product from enzyme and substrate when the overall reaction is limited by the encounter of S with E. Some particularly effective enzymes deliver a value of kcat / Km in the range of 108 to 109 M-1s-1. Under these conditions the reaction is in fact diffusion-limited; that is, the reaction is proceeding as fast as it can given the ability of the two solutes to approach one another.

This ratio, kcat / Km, can be described as a measure of the specificity of the enzyme. Horton provides the details, but the general point is this: given two different substrates, the one with the higher kcat / Km ratio is the one for which the product can be produced the most rapidly.

Kinetic Mechanisms

If a reaction involves more than one reactant or more than one product, there may be variations in kinetics that occur as a result of the order in which substrates are bound or products are released. Examine figure 5.7 in Horton, which depicts bisubstrate reactions of various sorts. As you can see, the possibilities enumerated include sequential, random, and ping-pong mechanisms. The biochemists of the era between 1935 and 1970 spent a good deal of time examining the effect on reaction rates of changing the concentrations of reactants and enzymes, and deducing the mechanistic realities from the kinetic data. In recent years other tools have become available for deriving the same information, including static and dynamic structural studies that provide us with slide-shows or even movies of reaction sequences. But the mechanistic schemes shown in fig. 5.7 do have specific kinetic implications, and it is impressive how many mechanisms were elucidated in this way.

Induced fit

The conformations of enzymes usually don't change enormously when they bind substrates, but they do change to some extent. An instance where the changes are fairly substantial is the binding of substrates to kinases. Here the danger is that the enzyme will catalyze the unproductive hydrolysis of ATP in the same site where the kinase reaction might occur; that is, the unwanted reaction
ATP + H-O-H ⇒ ADP + Pi
will compete with the desired reaction
ATP + R-O-H ⇒ ADP + R-O-P
where the emboldening P indicates a phosphate group that is covalently attached to the organic moeity R-O-. Kinases minimize the likelihood of this unproductive activity by changing conformation upon binding substrate so that hydrolysis of ATP cannot occur until the binding happens. The conformational change that occurs upon binding the alcoholic substrate R-O-H makes the enzyme capable of catalyzing hydrolysis. This is an illustration of the importance of the order in which things happen in enzyme function.