Showing Quantitative Enzyme Inhibition on a Shoe String

CORRESPONDING AUTHOR:
Carl W. Vermeulen, Ph.D (Microbiology), MS (Biochemistry)
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Showing Quantitative Enzyme Inhibition on a Shoe String
(Editors dictate that the style use active tense and be conversational.)
While a number of enzymes are qualitatively inspected in teaching laboratories, studies of inhibition of those enzymes are fraught with the problems that the inhibitors are usually highly toxic (e.g.: cyanide, heavy metals) and do not lend themselves to neat presentation due to their insoluble properties (e.g.: the use of phenyl-thiourea to inhibit catechol oxidase, tyrosinase). In the course of pursuing an A-levels project, one of us (MC) postulated that feed-back inhibition should be readily exhibited with lactase, which is one of the classic enzyme systems of choice used in courses. In subsequent collaboration we streamlined the experiment so that, at 30 minutes, it would fit easily into the time frame of the teaching laboratory. Several aspects of the experiment were especially exciting to us - the speed of the demonstration, its absolute safety as no appreciable amounts of toxic materials were involved, the near-zero expense, and the fact that the system easily avails itself to further quantitative study of the type of inhibition (competitive vs allosteric or other types).
While almost all previous attention paid to lactase and &beta-galactosidase has been on the genetic or lac-operon expression level, one of us (MC) initially reasoned that the digestive enzyme lactase would itslef be subject to "product inhibition." After reporting this was indeed true in her A-levels research thesis, we then streamlined the protocol so that it would fit within the limited teaching parameters of time and resources.
Lactase is a digestive enzyme that hydrolyzes the disaccharide lactose to two monosaccharides, glucose and galactose. Normally, the galactose is itself converted to its epimer glucose using another enzyme classed as an epimerase, which upon its discovery was humorously named "Waldenase" because it caused a Walden Inversion. NAD⁺ is a cofactor of that reaction because the mechanism is that the #4-carbon of galactose is oxidized and then reduced back in the inverted orientation yielding glucose. The two glucoses, of course, proceed through glycolysis and onwards (Fig. 1).

Figure 1: The Basic Hydrolysis of the Sugar Lactose by the Enzyme Lactase.
To avail the general principle of substrate inhibition to the teaching laboratory, we substituted ONPG (o-nitrophenyl-&beta-D-galactopyranoside) for the enzyme's normal substrate lactose(___). This exchange allowed continuous colorimetric assay as the ONPG is split and one part becomes yellow (Fig. 2). This makes use of the Nobel work by Jacob, Monod, Cuzin and Brenner in their study of the lac-operon (___). We feel this use of ONPG also holds an important benefit as it allows the discussion of chemical analogs, which are so important to understand today in chemotherapeutic treatments.

Figure 2: "ONPG" Is a Chemical Analog of the Sugar Lactose and Is Hydrolyzed by the Enzyme Lactase.
MATERIALS
Specifically we used lactase as purchased from the supermarket or chemist shop (pharmacist over here), galactose, ONPG (Sigma Chem Co., cat. no. N-1127), glucose, sucrose, and lactose. If a more quantitative exercise is desired, add a clock, and a spectrophotometer (420 μm) or simple colorimeter with a green filter.
Were quantitative methods used, you should expect obtaining a graph such as shown in Fig. 3. However, for demonstrating product inhibition, we found that the purely qualitative protocol was more than sufficient to show galactose inhibition because with galactose present, the ONPG reaction barely occurred.

Figure 3: The Effect of Increasing Galactose (the inhibitor) on Enzymatic Activity of Lactase.
PROCEDURE
One of the main tricks in enzymology is to keep the enzyme and the substrates apart until you are ready to begin the reaction. In this exercise you wish to test various candidate inhibitors, and so you will make two batteries of tubes, and then mix them both when you want to start timing the reactions. When you dump the one set into the other, it is like opening the starting gate at a horse race.
In this particular experiment, it is very important that you recognize the difference between lactase and lactose. (What do the suffixes -ase and -ose mean?)

Figure 4: The Set-Up for The Qualitative Experiment. The circled numbers in the diagram indicate the order of adding components.
1. Making Battery 1 (ONPG):
  1. Label 5 tubes as follows (use the capital letters): W (water), S (sucrose), L (lactose), G (galactose, and D (dextrose = glucose)
  2. Add 10 drops of ONPG into each tube.
    .
2. Making Battery 2 (lactase and diluents):
  1. In front of Battery 1 place five more similarly labelled tubes.
  2. Into each tube add 1 ml of lactase solution
  3. Into the appropriate tube, add 4 ml of the respective diluent (W, S, L, G or D).
    .
3. Prepare to observe and record results!.
  .
4. To START the reactions simultaneously, dump Battery 2 tubes into their respective Battery 1 tubes..
  .
5. Observe and record the order (1 to 5) in which the tubes turn yellow (some may not)..
  .
6. Discuss within your group three possible molecular mechanisms for the result in each tube, particularly why ones are slower (if any)..
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7. Record your data and conclusions.
We have seen how the incorporation of ONPG allows rapid visual analysis of lactase's activity, and this affords the opportunity to discuss the concept of analogs (analogues), which are so important in the treatment of cancers, for example.
In addition, comparisons of adding other sugars to the reaction solutions gives the opportunity of discussing how inhibitors work. Your students will rapidly see how galactose, and the ultimate competitive inhibitor on ONPG's hydrolysis, lactose, markedly slows the production of yellow color. Since none of the other sugars slow down the reaction, they must not fit into the reactive site of the enzyme - another important concept in the study of enzymology.
Turning to safety precautions, we see that, while the only toxic reagent in this whole experiment is ONPG, it is used in such trace quantities as to be harmless. Thus this is one of the very few enzymatic reactions that involves essentially no dangerous toxins. Indeed, all the other components are nutrients for humans. With regard to disposal problems, there is nothing that cannot be put down the drain.
The two most problematic aspects of doing this experiment are the cross-contamination of reagents and the proper simultaneous mixing of a small battery of reaction tubes. For this reason we suggest that you isolate the preparations of the two batteries of tubes by having half the members of each group make one battery and the remaining students make the other series. For further isolation of the preparations, the batteries could be prepared on opposite sides of the room. One of the most common problems results from students' using a lactase dropper for distributing ONPG. Not only is the ONPG battery ruined, but also the stock solution of ONPG becomes contaminated and rapidly degraded. This isolation cannot be stressed too strongly to the students! Then, you must also advise the students that just prior to dumping the one battery of tubes into the other, if they see ANY yellow in any of the tubes, they have committed a "start-all-over" error of cross-contamination.
Only then, at a predetermined clock time, the battery of tubes of larger volume are dumped (with consequent rapid mixing) into the other battery. If each set of tubes is in a separate test-tube rack, one can carefully pick up one rack and tilt the rack such that all tubes can be poured simultaneously. (Students should try this beforehand with water until they can do it with confidence and skill. Next the receiving tubes can be mixed by shaking their whole rack. The sequence of which tubes turn yellow is then noted. As mentioned previously, the galactose and lactose are a strong inhibitors, while the control, glucose, and sucrose tubes become rapidly yellow - all this forming a very conspicuous demonstration of inhibition.
So far the above is only a qualitative reaction. Of course, timed spectrophotometic quantitative readings could have been taken, but we recommend against jumping immediately into doing that because learning the operation of spectrophotometric assay is itself a time consuming experience for the novice students. Pedagogically, we also advise against it because there are too many examples of students' becoming confused with the differences and boundaries between science and technology. Thus, allow the students to gain a good grasp of the science qualitatively before having them jump into the intricacies of technology.
QUANTITATIVE ASSAYS
LEADING TO THE DETERMINATION OF THE TYPE OF INHIBITION.
Once, however, the students do have a good grasp of enzyme activity, and how the use of the ONPG analog is valuable, then allow those students who would like to do an advanced project to determine the type of inhibition according to Michaelis-Menton principles using the graphing techniques of Lineweaver and Birk. They will become fluent in spectrophotometry.
You must, of course, teach the students about the two major types of inhibition. Some unknown students of the past came up with the Pacman models for competitive and allosteric inhibitions. A competitive inhibitor is one that fits into Pacman's mouth (active site) just as well as the real substrate. Thus Pacman wastes time trying Uselessly to "bite" the inhibitor before spitting it out and trying the next "bite." The inhibitor competes for the same location as does the substrate.
On the other hand, an allosteric inhibitor might be of several types. Just imagine Pacman with blinders on and unable to find the substrate on its plate, or wearing a necktie that is tied so tightly he cannot swallow. Note that the inhibitor does not affect the active site, but some "other site," which is literally what allosteric means. We know that these are crude analogies, but they are, hopefully, the initial keys to understanding as we pedagogically move from the familiar to the unfamiliar ideas of the nature of enzymes.
There are two stages for identifying the type of inhibition: determining the velocities of the reaction under various substrate and inhibitor concentrations, and knowing how to graph the results. You will thus be required to run the lactase reaction over various ONPG concentrations (let's say six different concentrations, both lower and higher than those used in the qualitative exercise, above). For each concentration, the students must determine the initial rate of the reaction, which is abbreviated V_o. For each galactose concentration, points are graphed thusly:

Figure 5: How to Determine the Initial Velocity (V_o) of a Reaction.
What the units are, is up to the students. The important thing is that once a units system is chosen, it must be used consistantly throughout the remaining series of data points. We suggest the units be the number of OD_units per minute (how much yellow forms per minute). Note: each such V_o requires the construction of its own graph, so have a quantity of graph paper on hand.
Next, all those V_o points are themselves plotted on a graph that was devised by Michaelis and Menton (Fig. 6). From the graph, some important values can be ascertained: V_max, and K_m. V_max is the fastest that this enzyme can ever work. From the graph you see that it is the line reached when [gal] reaches infinity. It can be pictured as a Pacman, who, no matter which way he turns, there is another lactose or ONPG molecule to be bitten in half. It doesn't matter if more substrate molecules were added, Pacman can only bite just so fast.

Figure 6: The Michaelis-Menton Plot of the Control Reaction of the effect of varying ONPG concentration on the rate of its hydrolysis.
The value K_m is a more esoteric number that deals with the affinity that the enzyme has for its substrate. We will not discuss this college level function further although it will remain parts of several of the following graphs.
Let's turn from the graphs of the uninhibited "control" over to the inhibited experimentals in which galactose has been added. This requires that the whole series be done over again, but this time with a judiciously chosen constant amount of galactose added. This data collecting is time-consuming, but the students will obtain perhaps another six different values of reaction velocity, that are to be graphed on the Michaelis-Menton graph above to yield Fig 7. (And as stated, the students will become fluent in the operation of the spectrophotometer.)

Figure 7: The Effect of Inhibitor on the Michaelis-Menton Plot of Lactase.
Unfortunately humans are not too perceptive of potential insights lying behind curved lines. Two other scientists became partners and came up with what is called the Lineweaver-Burk Plot, which is a reciprocal graphing of the Michaelis-Menton style plot. Fig. 8 shows what results: a pleasing straight line that can be easily interpolated and extrapolated. One neat thing they found was that you could calculate the V_max with considerable precision at infinite substrate concentration, because this type of graph has a place for infinity on it: the vertical axis, which represents 1/0, which equals infinity. Hence, any line of data points that extrapolates and crosses the vertical axis means that the substrate concentration is at a theoretical infinite concentration.

Figure 8: The Reciprocal of the Michaelis-Menton Plot.

Finally, if you were to add in you data collected from an inhibited reaction, you would get one of two types of graphs. In Fig. 9A, you will not that the V_max has changed, while in Fig. 9C it has not as both data curves intersect at the vertical axis.

Figure 9: The Lineweaver-Burk Reciprocal Plots of Possible Acquired Data. Plot "A" is what you would expect for an allosterically inhibited enzymatic system, while Plot "C" depicts a competitively inhibited enzyme.

So let us now try to understand why these two graphs are this way. First we have to remember that the inhibitor concentration has been held constant in both cases. Therefore, when the substrate (ONPG in our case) is at infinite concentration, the ratio of galactose to ONPG is zero. Therefore as our enzymatic Pacman is snapping away left and right as fast as he can, the only molecules ever encountered are ONPG's (the chance of biting a galactose is zero). Therefore, if the only action of the inhibitor is to get in the way of the "mouth" (active site) and compete with the normal substrate (ONPG in our case), then at infinite ONPG concentration, the effect of the galactose is nil and V_max doesn't change. But a blinded Pacman still cannot snap left and right as efficiently (lower V_max, or higher 1/V_max) as one without a blindfold even if the ONPG concentration is infinite. Hence, it is an allosteric inhibitor.
1. Pardee, A. B., F. Jacob, and J. Monod. 1959. The Genetic Control and Cytoplasimic Expression of "Inducibility" in the Synthesis of β-Galactosidase by E. coli. J. Mol. Biol.ف:𧆥.
2. Miller, J. H. 1972. Experiments in Molecular Genetics. pp: 352-355. Cold Spring Harbor Lab.