Scientific Teaching
ANALOGIES

| Electrophoresis | Chromatography | Molecular Sieves | Ion Exchange | Gas Laws |
|Energetics of Respiration and Photosynthesis |Utilization Cascade of Body Energy Sources |
| The Chemical Bond |
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Qualitative Analytical Separation Techniques

A great deal of confusion arises in the initial stages of learning when the subjects of electrophoresis, affinity and ion exchange chromatography are first introduced to students of almost any age. Two reasons for this confusion seem to be (a) that the students link the technique as a procedure unique to the isolation problem at hand (DNA fragment electrophoresis, or pigment chromatography) and fail to realize that it is a general procedure that can be applied to a wide variety of analytical situations, and (b) the students become unwittingly dazzled by the "neatness" of the technique and fail to actually internalize the basic principles by which the process works. Both of these pitfalls are the likely reason, for example, for the low scores on the Molecular Biology section of the College Board Exams in the United States. The students cannot separate the 'big-picture' notion of wanting to separate DNA-fragments according to size, from the method for doing it.

While teaching time is short, it is of overriding importance that the essence of a particular topic be taught. If the essence is missed; the experience was mostly a waste of time. Thus, to overcome the aforementioned problems, some teachers have been trying a "preliminary" approach to the molecular biology and photosynthetic pigments sections in their courses. They use the techniques for an entirely different, and very simplied analysis of, for example, ink analysis, which can utilize BOTH electrophoresis and affinity chromatography. After that simple lab experience, the students are then led into the needs to separate DNA fragments, iso-enzymes, cytochromes and photosynthetic and floral pigments. These teachers find the students quickly decide upon which separation technique holds the greatest promise of success - and usually their choice is correct.

But how to enter the subject! Parables and analogies are often the most effective teaching vehicles, and so let us look at several that pertain to electrophoresis and chromatography, along with molecular sieves and ion exchange chromatography!

ELECTROPHORESIS

ANALOGY ONE:One the first floor, a huge hulk of an American football player gets onto an empty elevator with his little son. After they push the destination button for the third floor. It goes up one floor to the second, and when the door opens a horde of other people get on and push the first two occupants back against the rear wall. Finally, at the third floor the door opens for the large man and his son. Which gets off the elevator first - the huge man or the little boy? Answer: the little boy who can squeeze more easily through the cracks in the crowd than can his monstrous father. (This analogy is attributed to Emily Devine of Fotodyne, Inc. in 2001)

ANALOGY TWO: (For those of you not living in southern California, let it be said that the only part that is not true is the part about the shopping mall.)

Imagine that you are travelling with a six-year old child from Los Angeles to Las Vegas on I-15. The trip is mostly through volcanic mountains in the desolate Mojave Desert. At one point, you have just driven up several thousand feet to the crest of a pass between mountains to where one of the most unusual intersections exist in North America. Yes, there it is: "Zyzzx Road"! But just then your engine quits and you pull off the highway ('freeway' to Californians!). It is terribly hot outside, and you cannot stay in your car. In the distance, and fortunately downhill, you see the town of Baker at the bottom in a desert basin that is a sister to Death Valley. So you and the child start walking towards town five miles distant. Wow, is it hot! You walk and walk, and nobody stops to help you. Finally you reach a sign that says "Baker One Mile". Just then another car sputters to a halt, and another adult joins you on the trek into town. By this time you see can read that it is 118 degrees F on the world's largest thermometer atop Bun Boy, a hamburger place. Finally, the three of you reach town and enter the regional shopping mall. How nice the coolness feels, but you three have developed quite a thirst. Where's the water? Over the heads of the throngs of milling people in the mall, you see a distant sign "Drinking Fountain". Which of the three of you get to the water first, and then second?

Solution: Consider that you and the child are VERY thirsty - more so than the other adult. Also consider that the child is much smaller than the two of you adults. So the very thirsty, small child rushes ahead and easily threads a path between legs and bodies of the milling crowd and reaches the water first. You, who are much more thirsty than the other adult rush ahead with greater fervor and get there second. Thus 'thirst' is analogous to 'charge' and 'size' is 'size' So in electrophoresis, speed of movement is dependent on net charge AND size.

Now applying this to the DNA-fragment analysis: the sizes are different, but the charge per mass or length of DNA-fragment is constant (2 negative charges per base pair; the interior amino groups don't enter into the discussion as they are not charged in a double helix). Hence, in this experiment, only size matters. But in the "preliminary" experience with inks or enzymes, charges might very well vary.

For those of you dealing with vertical electrophoretic systems (e.g.: SDS-PAGE), which employ a minor low-density "stacking" gel atop the main gel, there is an analogy especially for you! Imagine a 100 meter long column of troops all marching neatly in rank and file. Each rank is one arm's length behind the rank in front of it as they begin marching on concrete pavement. The going is easy on this smooth surface. When the column reaches the edge of the pavement, the front rank steps into short grass. Marching is not quite as easy there, and so the front rank marches only half as fast as on the pavement. This allows the second rank to get a little closer to it before the second rank finds itself in the grass and marching slower, which, in turn allows the third rank to move up a little closer, and so on and on. By the time all the troops are marching forward in the grass, the total column length has shrunk to 50 meters long. After a short while the column enters a meadow of waist-high uncut grass, and the same bunching phenomenon happens all over again, such that by the time all the troops are marching in the tall grass, the column is only 20 meters long with everyone stepping on the heels of the ones in front. Eventually, the column might approach a thicket of brambles or cactus, and no forward penetration can be made. In this event, all the troops would squash together in a big crush with the theoretical column length of zero!

In your vertical setup, you have loaded your sample as a liquid in a well. The solution, usually colored with a "tracking dye" may be half a centimeter deep (the troops' original column length). The solute molecules find it very easy to move here (concrete pavement). Then the solute molecules move into the "top gel" (short grass). The molecules are bunched more tightly together to perhaps only 2 mm in thickness. Finally they enter the "running" or "resolving" gel (tall grass). Here they bunch together even more tightly to maybe 0.5 mm which will be the aesthetically pleasing very fine line produced by this type of electrophoresis. (Of course your resolving gel might be what is called a gradient gel, which gets denser and denser the further the molecules move. Eventually each class will reach a density or thickness in which the holes in the gel are too small for the molecules to fit through (brambles), and then migration stops.)

For a quick way to make "linear" gradients, CLICK HERE, and look for "Making equipment/alternative supplies."

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PAPER CHROMATOGRAPHY

Paper chromatography is only one type of affinity chromatography. Certain types of column chromatography as also of the affinity type.

Imagine that it is the Grand Opening of a new department store for children's clothes, accessories and toys. On this opening day, the clothes are an especially good buy, and that is what adults have in mind. So hundreds of people are milling around at the front door waiting for it to be unlocked. Many are adults shopping alone, but there are also many who are parents and have one or more kids in tow. Unbeknownst to them beforehand is that the large toy department is the first thing they will encounter. Suddenly the doors open, and this horde stampedes inside.

What happens as the adults try to move quickly to the clothing department? Those adults without children rush right through to the clothing department. However those adults with kids almost instantly find themselves being held back by their children wishing to see all the new toys. Of course, the more kids, the harder it is for the parent to move the group along.

So you see that lone adults have little propensity to stop to look at the toys before moving to the clothing section. 'Little propensity' means little affinity. Kids, on the other hand, have lots of affinity for new toys, and therefore have to stop and look at every one of them and so delay the movement towards the rear of the store, where the parent wants to look at clothes. Thus lone adults are easily swept along with the crowd and reach the clothing section far ahead of those adults shepherding children.

In the department store scenario, the mobile phase is the crowd of moving people, and the fixed or immobile phase are the attractive shelves full of toys. In the laboratory, the mobile phase is the solvent, and the immobile or fixed phase is the paper that is made up of cellulose molecules, with all their hydrophilic hydroxyl groups for which other hydrophilic solutes have more affinity than to the mostly hydrophobic solvent. Mobility of the solutes is proportional to the "partition coefficient," which is the ratio of the amounts of solute in the hydrophilic versus the hydrophobic phases. "Rf" is the classical way to express how far the solute moved: it is expressed as how far it moved relative to how far the solvent front moved.

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GAS LAWS

One of the more perplexing gas-law questions students ask teachers goes something like this: "How can you say that there are just as many molecules of hydrogen in a given volume as there are heavy molecules of carbon dioxide? I would think that there would be a lot more of the tiny hydrogen molecules able to fit in." In a way the student has right thinking - for liquids and solids, but not for gases. How to get right thinking about gases into the student's head is the problem. (In all of the following, assume the conditions of standard temperature and pressure, STP.)

Let's start off with an analogy of sorts. You are going to throw two parties - one is for 36 adults and the other is for 36 five-year olds. The question is, how much space do you need for each party? At first you might think that since the average adult weighs 3 or 4-times as much as the average five-year old, you would need more space for the adults. But when you get to picturing the parties in your mind you see that the adults tend to move around slowly, and often are standing close together in bunches as they chat. On the other had, the children are running about in a frenzy of excitement. Were you to take a snapshot of both parties, the room with the adults would seem much more crowded than the one with the children. However, were you to take a motion picture of the two parties, you would see the big people moving slowly about, while the little ones would be in constant motion - each little body filling up lots of jostling space. Were you to open a side room to allow the party-goers to have more room, you might see two or three adults wander into the side room, but six to nine little ones would go streaming into there. So you see it is all a matter of the amount of jostling room each individual needs.

This analogy can even be extended to the "law of partial pressures." Suppose you have a party for families and you have 18 adults and 18 little children. How much room do you need? It is not that the children will fit between the large adults and thus take up no added room. As the children dilute into the mass of adults, there will be lots of childish jostling that spreads the adults apart.

In sum, you see that size doesn't matter how much space is needed! Space is only affected when the people are "crystallized" and told to sit in seats that are in rows and columns. The little kids will have small chairs bunched closely together, while the large adults will have more widely spaced big chairs. A further interesting extension is that the adults will be sitting nearly motionless, while the kids will be squirming. This is just like the atomic nucleic in crystals!

Returning to the two parties before they were told to sit down in orderly fashion, we had milling crowds (a gas) with each individual requiring a certain amount of elbow room. And it turned out that the amount of elbow room needed by a five-year old was the same as that needed by an adult. There thus must be some relationship between the amount of elbow room needed and the mass of the individual plus how much that individual jostles around.

Scientists have, of course, come up with an equation for this: F = mv², in which your thoughts about the two parties are confirmed: the amount of jostling is more important to how much elbow room is needed (force) than is the mass of each individual.

ENERGETICS: Respiration and Photosynthesis

These are two of the most important topics in biology: how to harness energy from the environment. But students are often overwhelmed by the complexity of all the intermediary biochemical structures, and the many unfamiliar terms for both structures and functions. This is fertile ground for a simple analogy - one that was told to this author by a near-Nobel laureate!

Speaking of energetics, why not talk Power Companies? Normally the power companies must be able to satisfy peak demand. While this might last for only a few minutes each day, sufficient numbers of large and expensive generators must be built just to satisfy that brief period - UNLESS the company can think of a way to use medium sized generators around the clock and store any excess energy that can later be released to augment the generators' output at those peak times. This is the strategy many companies use, and here is the form of energy storage they employ. It is called "PUMP STORAGE."

High above the city, in hills or mountains, an artificial lake is made. During off-peak times, excess electrical energy is used to pump water up into the lake. During times when customers are using more electricity than the generators can make, water is allowed to flow out of the lake and down through turbines that provide the needed power. (This is like a temporary form of hydroelectric power plant in river dams such as Hoover Dam that spans the Colorado River.)

In both "electron transport/phosphorylation" and in the light reaction of photosynthesis, electrons are stripped off molecules and protons (H⁺) are pumped across membranes into separate spaces, where the proton concentration (essence of acidity!) increases. Once the proton concentration passes a critical concentration, and a very steep pH differential is formed by the membrane, the protons are allowed to slip through transmembrane/enzyme channels (chemiosmosis) to power the phosphorylation of ADP to make ATP.

Utilization Cascade of Body Energy Sources
ATP is used first, and then what and then what?

When a person sets out on a long distance run at a speed that is too fast, energy reserves are used in a fixed order. But before we get into the biochemistry, let us look at an analogy of a steam engine on an old railroad.*

At first the engine is standing still and slowly hissing steam at the station. As it sits there, you know that there are several sources of energy at various states of readiness. Most readily available for instant use is the pressurized steam in the boiler, then under the steam is a lot of superheated water some of which would become steam if the pressure dropped, and below that are some slowly burning coals, and behind the engine is the tender full of coal (or oil).

Let's get the train going.

1. The first movement is made possible by the existing pressurized steam in the boiler. It is directed into the cylinders and the pistons are alternating pushed on one side and then the other to move the arms that are connected to the engine's drive wheels.
2. Removing some of the steam causes the boiler pressure to drop, which, in turn, causes more water to boil to make more steam for pushing the pistons.
3. But the boiling of the water causes its temperature to drop resulting in steam of less and less pressure, and hence less and less powerful pushing on the pistons.
4. To keep the temperature up, the fireman starts shovelling more and more coal into the furnace beneath the boiler. But it takes time for the cold coal to ignite and begin burning evenly at its hottest.
5. But once the coal is burning at its hottest, the heating of the water keeps up with the use of the steam, and thus the boiler pressure remains constant.
6. Of course, in the real world, the fireman starts shovelling coal minutes before the train is expected to depart - so as to "get up a full head of steam." He's putting the engine through 'warm up' exercises!

Now let's look at our runner.

1. The pre-existing steam in the engine is like the pre-existing supply of ATP within the cells. It is there for the first "chug" or two of muscle flexing, and then it is exhausted. But creatine-phosphate is also around and it reacts with ADP to make ATP (and creatine, of course). (Since ATP has a very short halflife in aqueous environments (cytoplasm, for example), it behooves the cell to stash the high-energy phosphates in a more stable form - as creatine-phosphate.)
2. Quickly the working cell depletes its ATP and creatine-phosphate. So it draws upon its next soluble reserve - glycogen, and begins the rapid catabolism of glycolysis. But the heat content of anaerobic glycolysis is not very efficient, but it is very fast and generally is enough to allow the sprinter to escape the wild ox or other threat. This is like the pre-existing hot water in the engine's boiler.
3. Finally, the runner starts breathing in gulps of air and aerobic breakdown of glycogen and glucose occur with lots and lots of ATP being produced. Here the fireman is shovelling in coal, and the furnace also gulps in air for combustion. Thus you see that warm up exercises gets your body ready for highly efficient aerobic work, and is an attempt at circumventing the anaerobic pathways.

The steam engine analogy finally breaks down when you want the runner to go too fast for too long - when the runner's breathing cannot keep up with ATP needs. Then anaerobic metabolism starts in. The analogy breakdown occurs because anaerobic metabolism gives rise to toxic byproducts that cause the muscles to cramp and fail to do anything at all except hurt. With the steam engine, asking it to go too fast, will cause it to speed up for a short time, but then as the coal can't get shovelled in fast enough, the speed slows to match the rate of shovelling. Total breakdown doesn't occur as it did in muscles.

* This analogy was paraphrased from: Stephen Budiansky. 1997. "The Nature of Horses: Their Evolution, Intelligence and Behavior." Butler and Tanner Ltd., London. p. 218. (ISBN 0-75380-531-6)

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