Using Aldolase Antibody 38C2 to Study Enzyme Kinetics

Introduction

The Aldol Reaction.

The aldol reaction is an important carbon-carbon bond forming reaction that can

be found throughout nature and in organic synthesis. It is catalyzed by both acids and

bases, and by enzymes. The new bond is formed between the carbon of an aldehyde or

ketone donor and the carbonyl carbon of an aldehyde acceptor to form a -hydroxy

carbonyl compound (aldol) (Figure 1a). The donor can approach the acceptor from two

distinct faces. By an extension of the Cahn-Ingold-Prelog system, these faces are named

Re and Si. When R2 = H, one stereocenter is generated by the reaction, and the aldol

products are enantiomers (Figure 1b). When R2 H, two stereocenters are generated, and

four stereoisomers are formed (Figure 1c). These four stereoisomers are divided into two

pairs of enantiomers. One pair, the syn enantiomers, places the newly generated hydroxyl

group on the same side of the plane of the molecule as R2, while the anti enantiomers

have the hydroxyl group and R2 on opposite sides.

One well-characterized aldolase enzyme is Fructose 1,6-bisphosphate aldolase

(FBP aldolase), which catalyzes an aldol reaction between Glyceraldehyde 3-Phosphate

and Dihydroxyacetone Phosphate to form Fructose 1,6-bisphosphate (Figure 1d). This

enzyme’s mechanism (Figure 2) is conserved throughout all Class I aldolases. The side-

chain amine of a lysine residue reacts with the carbonyl of the donor ketone to form an

enamine, which then adds to the aldehyde acceptor. Subsequent hydrolysis of the

iminium ion yields the aldol product.

2

Catalytic Antibodies

Antibodies are part of an animal’s immune response to foreign antigens. Animals

can also be immunized with synthetic molecules, called haptens. When an animal, such

as a mouse, is immunized with a hapten which mimics the transition state of a reaction,

antibodies that bind to this transition state analog are produced. Some antibodies that bind

to the transition state analog will bind to the transition state of the reaction, and lower the

activation energy. These antibodies can be used as enzyme catalysts for any reaction with

a suitable transition state analog. However, like enzymes, catalytic antibodies generated

this way catalyze reactions with a limited number of substrates.

Recently, a novel technique, known as reactive immunization (Figure 3), was

developed to generate catalytic antibodies that mimic the mechanism of natural aldolases,

such as FBP aldolase. A mouse was immunized with the reactive -diketone hapten (1)

conjugated to a carrier molecule. This -diketone will react with an appropriately placed

lysine residue on an antibody to form the stable enaminone (2). Because the antibody

forms a covalent attachment with the hapten, antibody evolution stops early, before the

antibody develops specificity for only the hapten. The resulting antibodies are much more

promiscuous in the reactions they will catalyze.

As Woodward's Rules for UV spectroscopy would predict, the enaminone (2) has

a strong UV absorption ( max = 316 nm). Libraries of antibodies raised to the hapten (1)

were screened for this absorption to indicate the presence of the enaminone, which

suggests that the selected antibody evolved the mechanism of natural aldolases such as

FBP aldolase. Through this technique, the commercially available aldolase antibody

3

38C2 was generated. This catalytic antibody has been shown to be both efficient and

broad in scope for catalyzing both the forward and the retro-aldol reaction (Figure 4). In

this lab, we will study the kinetics of antibody 38C2, and look at its activity with and

without an enzyme inhibitor.

4

Lab #1 – Preparing a standard stock solution of antibody 38C2

In this lab we will prepare a solution of the catalytic antibody 38C2 and determine

its concentration spectroscopically. We will also verify that the enzyme molecule has two

binding sites.

A vial containing 10mg of aldolase antibody 38C2 (Aldrich #47,995-0) is

provided as a powder lyophilized from phosphate buffered saline (PBS). Prepare a stock

solution of this antibody by adding 2 mL of distilled water to this vial. Gently mix by

slowly pipetting the water up and down until the antibody is dissolved. Do not shake the

solution or vortex it. Although some particulate solids may not dissolve, this will have

little effect on the catalysis of this antibody.

Measuring Enzyme Concentration. The concentration of this antibody stock

solution will be approximately 5 mg mL-1, or 33.3 µM. In the following experiment, we

will measure the concentration spectroscopically. Add 700 µL of PBS to a 1 mL cuvette

and scan a blank sample from 200 to 400 nm on a UV spectrometer. Add 100 µL of your

antibody stock solution to the cuvette, cap it, and invert to mix. Scan the sample from 200

to 400 nm. The antibody has a maximum absorbance at 280 nm (A280). Divide the A280 by

the of the antibody (1.35) to give the concentration of the antibody in the cuvette in mg

mL-1. Divide this number by 150,000 (~ molecular weight of the antibody) to give the

molar antibody concentration in the cuvette. Multiply this concentration by 8 (the dilution

that you made) to backcalculate the antibody stock solution concentration [38C2]. Save

the cuvette for the next experiment.

Measuring Enzyme Active Site Concentration. Now we will determine the

concentration of enzyme active sites. Because an enzyme can have more than one active

5

site, the enzyme active site concentration can be a multiple of the enzyme concentration.

In the case of catalytic antibodies, the active site is the antigen binding site. Because

antibody molecules have two antigen binding sites (Figure 5), the active site

concentration should be twice the antibody concentration.

Add another 100 µL of the antibody stock solution to the same cuvette used in the

previous experiment. Add 3 µL of a 10 mM solution of 2,4-pentanedione (1; R = Me) in

acetonitrile. This excess of -diketone will saturate the active sites, resulting in

stoichiometric enaminone formation at every active site (Figure 3). Using the

enaminone’s characteristic absorbance at 316 nm ( =15,000), we will quantitatively

determine the concentration of enzyme active sites by spectroscopically measuring

enaminone concentration.

Cap the cuvette, and invert. Scan the sample. Note the new absorbance peak at

316 nm. Continue to scan the sample every 5 minutes until the A316 does not change.

Using the value for the enaminone, calculate the concentration of active sites in the

cuvette, and in your stock solution. This number should be twice the antibody

concentration, since each antibody molecule has two active sites. Record both the stock

solution antibody concentration and active site concentration. The antibody solution can

be stored at -78˚C for up to one year or at -20˚C for up to one month with no detectable

activity loss.

6

Lab #2 – Enzyme Kinetics

Introduction

The kinetic properties of many enzymes can be described by the following

equation:

The enzyme active site (E) binds substrate (S) to form an enzyme-substrate

complex (E•S). The enzyme converts the substrate into product, forming an enzyme-

product complex (E•P). The product (P) is then released, and the enzyme is free to

undergo another round of catalysis. In the most general description, each of these steps is

reversible, with a forward and backward rate constant, indicated above (note that rate

constants always are indicated by a lowercase k, while equilibrium constants are always

indicated by a capital K).

The kinetic parameters of this reaction are measured by determining the rate of

formation of the product (P), when a known concentration of substrate and enzyme are

mixed. Although equation (1) might look complicated, there are some reasonable

assumptions that can be made to simplify it. By measuring the initial rate of the reaction

when the enzyme and substrate are first mixed, the backward reactions k-2 and k-3 can be

neglected because the concentration of product is initially very low. Furthermore, it is a

reasonable assumption that the dissociation of the enzyme-product complex (E•P) to

enzyme (E) and product (P) is both fast and irreversible during the initial stages of the

reaction (k3 >> k2). Therefore, the reaction can be approximated as proceeding directly

(1)

7

from the enzyme-substrate complex (E•S) to the released product (P) and the regenerated

enzyme (E).

Under these assumptions, equation 1 can be rewritten as:

The rate constant for the reaction of the enzyme-substrate complex (E•S) to form

product is kcat, and is assumed to be the rate-determining step for the reaction. Usually,

equation 2 is used to describe enzyme kinetics, instead of equation 1. However, it is

important to remember that equation 2 is only valid when initial rates are measured.

The following equation gives the rate (v) of the reaction:

v =d P[ ]dt

= kcat[E •S]

We will now invoke an important assumption known as the steady-state

approximation, which says that the concentration of the enzyme-substrate complex (E•S)

is constant. Expressed mathematically:

d[E •S]dt

= k1[E][S] k 1[E •S] kcat [E •S] = 0

It is usually difficult to measure [E] and [E•S]. However, their sum is equal to the

initial concentration of enzyme active sites [E0]:

[E]+ [E •S] = [E0]

(3)

(2)

(5)

(4)

8

Recall that [E0] is the active site concentration, and is equal to (enzyme

concentration) (the number of active sites per enzyme molecule). Solving equation 5

for [E] and substituting into equation 4 gives the following expression:

[E • S] = k1[E0][S]

k 1 + kcat + k1[S]

Substitution of this expression for [E•S] into equation 3 gives the following:

v = kcat[E0 ][S]

k 1 + kcat

k1

+ [S]

We will now simplify equation 7. Equation 3 states that the rate of the reaction (v)

is proportional to [E•S]. Therefore, the rate (v) reaches a maximum value (Vmax) when

[E•S] reaches its maximum value ( [E•S] = [E0] ). Therefore:

Vmax = kcat [E0]

Let us define a constant (Km), by the following equation:

KM =k-1+ kcatk1

Substitution of (8) and (9) into (7) gives the following:

v = Vmax[S]Km + [S]

Rewriting equation 4 gives the significance of KM:

[E][S][E •S]

=k-1+ kcatk1

= KM

We see that KM is the dissociation complex for the enzyme-substrate complex. It

is instructive to note that KM has units of concentration, as a bimolecular dissociation

constant should.

(6)

(7)

(8)

(9)

(10)

(11)

9

We wish to determine the values for Vmax and Km. One way is to take the

reciprocal of both sides of equation 10:

1v=

KMVmax[S]

+1Vmax

Equation 12 says that a plot of (1 / v) vs. (1 / [S]) will have a y-intercept of (1 /

Vmax) and a slope of (Km / Vmax). Such a plot is called a Lineweaver-Burk plot, or a

double-reciprocal plot. We will use this method to measure Vmax and KM for the catalytic

antibody 38C2 in the following way: We will determine the rate (v) of the catalytic

antibody at different substrate concentrations. We will then construct a Lineweaver-Burk

plot and determine Vmax and Km. Once we know Vmax, we will determine kcat by dividing

Vmax by the initial enzyme active site concentration [E0].

The rate (v) of an enzyme is determined by measuring the rate of formation of its

product. It is generally desirable if the product’s concentration is easily measured by

spectroscopically. For example, substrates containing a p-nitrophenyl ester are used to

measure the rate of esterase enzymes. When an esterase cleaves the ester bond, p-

nitrophenol is released, which has a characteristic UV absorbance at 406 nm. These

techniques are useful for measuring hydrolytic reactions, such as ester cleavage, but, until

recently, have found little use in measuring carbon-carbon bond formation or cleavage.

Aldol Sensors. Recently, the synthesis of retro-aldol substrates for the antibody

38C2 has been described. These substrates yield products that exhibit a wide range of

chromophoric or fluorophoric properties. Two of the aldol sensors are shown in Figure 6.

Cynol (3) undergoes a retro-aldol reaction to yield 4-dimethylaminocinnamaldehyde ( max

= 400 nm; = 23,000). Because of the formation of an extended -system with the

carbonyl group of the aldehyde product, the max is shifted from 288 nm to 400 nm.

(12)

10

In addition, molecules have been designed which yield fluorescent products.

Methodol (5) reacts to form 6-methoxy-2-naphthaldehyde (6), which, when exposed to

UV light at 330 nm, emits visible light at 452 nm.

Kinetic Measurements

We will use UV spectrometry to determine the kinetic parameters for the reaction

of Cynol (3) with antibody 38C2 to yield 4-dimethylaminocinnamaldehyde (4). A stock

solution of Cynol (5 mM) in acetonitrile is provided. Dilute 20 µl of this solution to 1 mL

with PBS to make a 100 µM solution. We will now determine the rate (v) of the 38C2-

catalyzed retro-aldol reaction of Cynol to yield 4-dimethylaminocinnamaldehyde.

Procedure

Add 935 µL of PBS to a 1 mL cuvette. Place this cuvette in a UV-Vis spectrometer

with the wavelength range set from 200 to 500 nm, and blank the spectrometer on this

sample. Add 50 µL of the 100 µM Cynol stock solution to the cuvette. Cover the

cuvettte, invert it once, and scan the sample. Notice that the substrate has a maximum

absorbance at 288 nm and almost no absorbance at 400 nm.

The next sequence of events must be done both quickly and carefully. Although it is

not necessary to rush, any unnecessary delays must be avoided. It might be good if a

partner helps at this stage of the lab. Add 15 µL of your antibody stock solution to the

cuvette. Pipet up and down a few times to mix the antibody in the cuvette. Cover the

cuvette, invert it once, and place it in the spectrometer. Scan the sample, and at the same

time, start a stopwatch. Record the absorbance at 400 nm as the zero time point. When

11

the stopwatch reads 20 seconds, scan the sample again, and record the new absorbance.

Repeat this until the absorbance at 200 seconds is recorded for a total of 11 data points.

The absorbance values should increase over time, corresponding to an increase in product

concentration.

Repeat this procedure using the conditions specified for reactions 2-6 in Table 1.

The antibody’s activity is not altered by acetonitrile concentrations 10% (v/v).

Therefore, it is not necessary to compensate for differences in acetonitrile concentration

in reactions 1-6. For each concentration, plot absorbance at 400 nm (A400) vs. time in

seconds. The points should form a straight line. Using an appropriate software program,

such as Microsoft® Excel, determine a linear fit to this data. The slope of the line is the

rate in units of sec-1. Using the extinction coefficient ( ) of the product (23,000 M-1 cm-1),

and the unit conversion factor (60 sec min-1) convert the rate into units of M min-1. See

appendix A for an example. Construct a Lineweaver-Burk plot of your data. Determine

Vmax and Km for this reaction. From the antibody active site concentration in your stock

solution (determined in Lab #1), determine the active site concentration [E0] in the

Reaction 1 2 3 4 5 6 PBS 935 µL 885 µL 735 µL 485 µL 965 µL 935 µL Cynol (5 mM) -- -- -- -- 20 µL 50 µL Cynol (100 µM) 50 µL 100 µL 250 µL 500 µL -- -- 38C2 15 µL 15 µL 15 µL 15 µL 15 µL 15 µL [S]Final 5 µM 10 µM 25 µM 50 µM 100 µM 250 µM

Table 1. Reaction conditions for determining the rate of 38C2.

12

reactions. Using this value for E0, determine kcat for the reaction. See appendix B for an

example.

Questions

1. The published kcat and Km values for this substrate are 5.0 min-1 and 25 µM,

respectively. How do your values compare?

2. Although the kcat and Km values that you have determined are for a racemic

substrate mixture, the antibody strongly prefers to catalyze donor attack on the Si surface

of the acceptor over the Re surface. This means that one enantiomer reacts much faster

than the other enantiomer. In this case, the real Km value for the one enantiomer is lower

than your measured value by a factor of 2, while the kcat value remains unchanged. Why?

13

Lab #3 – Enzyme Inhibition

An enzyme inhibitor is a compound that binds to the enzyme and slows down its

rate. In this lab, you will visually compare a reaction catalyzed by antibody 38C2 in both

the presence and absence of an inhibitor.

Fluorescent Aldol Sensors. The compound Methodol (5) undergoes a retro-aldol

reaction catalyzed by 38C2 (kcat = 1.0 min-1, KM = 14 µM) to yield 6-methoxy-2-

naphthaldehyde (6), which is fluorescent at micromolar concentrations when exposed to

long-wave UV light ( ext = 330 nm; em = 452 nm). Because Methodol (5) is not

fluorescent at these concentrations, the appearance of fluorescence is an indicator of

enzyme activity. The high sensitivity of fluorescence allows Methodol to act as a

“sensor” for detecting aldolase activity in enzyme pools. A commercially available

fluorescence plate-reader can detect activity from antibody concentrations 0.5 nM,

several orders of magnitude lower than the concentration of antibody needed to detect

activity by enaminone formation. In this lab, we will use Methodol (5) as a qualitative,

visual test for catalytic activity of 38C2 in both the presence and absence of a diketone

inhibitor.

Diketone inhibition. The aldolase antibody 38C2 was raised against a -diketone

hapten, which “trapped” the -amino group of a lysine residue in the binding pocket in

the form of a -keto hemiaminal, which dehydrates to give a -keto imine that

tautomerizes into a stable enaminone (Figure 3). This “trapping” is what allowed for the

selection of 38C2 out of a large pool of antibodies. Since this reaction inactivates the

antibody, most -diketones are potent, irreversible inhibitors of this antibody. For this

14

lab, the activity of the antibody will be qualitatively determined in the presence and

absence of the inhibitor 2,4-pentanedione (1; R=Me).

Procedure

In three glass vials, setup three reactions according to the conditions specified in

Table 2. The first reaction will have the enzyme present but no inhibitor, the second

reaction will have both enzyme and inhibitor present, and the third reaction will not have

enzyme or inhibitor present.

Let these reactions sit at room temperature for 10 minutes to allow the diketone

inhibitor to bind to the antibody’s active sites. Afterwards, add 50 µL of Methodol (4 mM

in acetonitrile) to each reaction. Start a timer after the Methodol is added and expose the

vials to long wave UV light ( 330 nm). Most commercially available UV lamps have a

long wave setting around 365 nm and will work well. Each vial will have the following

final concentrations:

Reaction 1 2 3 PBS 790 µL 740 µL 950 µL 38C2 stock solution in PBS 160 µL 160 µL -- 2,4-Pentanedione (10 mM in acetonitrile) -- 50 µL --

Table 2. Reaction conditions for studying inhibition

of 38C2 by the diketone 2,4-pentanedione.

Reaction 1 2 3 2,4-Pentanedione -- 500 µ -- Methodol 200 µ 200 µ 200 µ

Table 3. Final concentrations for the reactions used to study

inhibition of 38C2 by the diketone 2,4-pentanedione

15

After only a few minutes, the first vial should start to emit light when held to the

UV lamp (you may have to dim the lights in the lab to see the fluorescence at first).

Record how long it takes for the fluorescence to become visible. Note that vials 2 and 3

do not emit light. In vial 2, the reaction is inhibited by 2,4-pentanedione. Vial 3 does not

fluoresce because there is no enzyme present, and Methodol (5) is not fluorescent at this

concentration, because its -conjugation is less extended than that of 6.

16

Appendix A: Example of determining an initial rate

The following table of hypothetical data was generated and plotted for the first

reaction at a substrate concentration of 5 µM:

Time (sec) A400 0 0 20 .1 40 .2 60 .3 80 .4 100 .5 120 .6 140 .7 160 .8 180 .9 200 1.0

The slope was determined to be 0.005 sec-1. This number was multiplied by 60 sec

min-1, divided by 23,000 M-1 cm-1, and multiplied by a path length of 1 cm to determine

the rate of the reaction.

0.005sec

60 sec1 min

123,000M 1cm 1

1cm1

= 1.3 10 5M min 1

17

Appendix B: Lineweaver-Burk Plots:

The following data table was constructed, and (1 / v) was plotted against (1 / [S]).

[S] (M) v (M min-1) 1 / [S] (M-1) 1 / v (M-1 min) 5.0 10-6 1.3 10-5 2.0 105 7.7 104 1.0 10-5 2.1 10-5 1.0 105 4.8 104 2.5 10-5 3.3 10-5 4.0 104 3.1 104 5.0 10-5 4.0 10-5 2.0 104 2.5 104 1.0 10-4 4.5 10-5 1.0 104 2.2 104 2.4 10-4 4.9 10-5 4.0 103 2.0 104

Vmax = (y-intercept)-1 = (19119 M-1 min)-1 = 52 µM min-1.

KM = (Vmax) (Slope) = (52 10-6 M min-1) (0.28954 min) = 15 µM.

kcat = (Vmax) / [E0] = (52 10-6 M min-1) / (1.0 10-6 M) = 52 min-1.

Note that your value of E0 will vary depending on your measurement for Lab #1.

18

Figure Captions

Figure 1. (a) The aldol reaction forms a carbon-carbon bond between an aldehyde or

ketone donor and an aldehyde acceptor. (b) The ketone donor can approach the aldehyde

acceptor at either the Re or Si surface to form a stereocenter. (c) Stereochemistry of the

two pairs of enantiomers generated by the aldol reaction (R2 H). (d) The aldol reaction

between Glyceraldehyde 3-Phosphate and Dihydroxyacetone Phosphate to form Fructose

1,6-bisphosphate is catalyzed by the Class I aldolase enzyme FBP aldolase.

Figure 2. The mechanism of Class I aldolases proceeds through formation of an enamine

between the donor ketone and an enzyme lysine residue.

Figure 3. Reactive immunization with the -diketone 1. Antibodies that mimic the

enamine mechanism of Class I aldolases are selected through formation of the stable

enaminone 2.

Figure 4. An illustration of some of the aldol reactions that have been shown to be

catalyzed by antibody 38C2.

Figure 5. Ribbon diagram of an antibody molecule. Two heavy chains (gold) and two

light chains (white) associate to form an antibody. The Fab and Fc subunits are illustrated.

Each antibody molecule has two antigen binding sites (one on each Fab subunit). (Drawn

from 1IGY.pdb).

Figure 6. The aldol sensors Cynol (3) and Methodol (5) react with antibody 38C2 to

yield substrates with characteristic chromophoric (4) or fluorophoric (6) properties.

Further Reading

Aldolase Enzymes

19

(1) Gefflaut, T.; Blonski, C.; Perie, J.; Willson, M. Class I aldolases: Substrate specificity, mechanism, inhibitors and structural aspects. Prog. Biophys Mol. Biol. 1995, 63, 301. Enzyme Kinetics (1) Eisenberg, D.; Crothers, D. Physical Chemistry with Applications to the Life Sciences, Benjamin/Cummings: Menlo Park, CA, 1979; pp 212-267. (2) Stryer, L. Biochemistry, 4th ed.; W.H. Freeman & Company: New York, 1995; pp 181-206. Catalytic Antibodies (1) Lerner, R.A.; Benkovic, S.J.; Schultz, P.G. At the crossroads of chemistry and immunology: Catalytic antibodies. Science 1991, 252, 659. (2) Schultz, P.G.; Lerner, R.A. From molecular diversity to catalysis: Lessons from the immune system. Science 1995, 269, 1835. (3) Wirsching, P.; Ashley, J.A.; Lo, C-H.L.; Janda, K.D.; Lerner, R.A. Reactive immunization. Science 1995, 270, 1775. (4) Wagner, J.; Lerner, R.A.; Barbas III, C.F. Efficient aldolase catalytic antibodies that use the enamine mechanism of natural enzymes. Science 1995, 270, 1797. (5) Barbas III, C.F.; Heine, A.; Zhong, G.; Hoffman, T.; Gramatikova, S.; Björnestedt, R.; List, B.; Anderson, J.; Stura, E.A.; Wilson, I.A.; Lerner, R.A. Immune versus natural selection: Antibody aldolases with enzymic rates but broader scope. Science 1997, 278, 2085. (6) Hoffmann, T.; Zhong, G.; List, B.; Shabat, D.; Anderson, J.; Gramatikova, S.; Lerner, R.A.; Barbas III, C.F. Aldolase Antibodies of Remarkable Scope. J. Am. Chem. Soc. 1998, 120, 2768.

20

Antibody Crystal Structure (1) Harris, L.J.; Skaletsky, E.; McPherson, A. Crystallographic structure of an intact IgG1 monoclonal antibody. J. Mol. Biol. 1998, 275, 861. Woodward's Rules (1) Woodward, R.B. Structure and the absorption spectra of , -unsaturated ketones. J. Amer. Chem. Soc. 1941, 63, 1123. (2) Ostercamp, D.L. Vinylogous imides. II. Ultraviolet spectra and the application of Woodward’s rules. J. Org. Chem. 1970, 35, 1632. Aldol Sensors (1) List, B.; Barbas III, C.F.; Lerner, R.A. Aldol sensors for the rapid generation of tunable fluorescence by antibody catalysis. Proc. Natl. Acad. Sci. USA 1998, 95, 15351. Cahn-Ingold-Prelog System (1) March, J. Advanced Organic Chemistry, 4th ed.; John Wiley & Sons: New York, 1992; pp 134-137.