Have we achieved anything? Well, now it is only necessary to determine the arrangement of the amino-acids in each of the two varieties of chains. The number of possible arrangements in Chain II is 3 x 1027 and that of Chain I is 6 x 1015. These aren’t exactly small numbers, but in comparison to 10100, they are nothing. Nothing at all. Why 3 x 1027 is only half the size of the number of grams of mass contained in the Earth. As for 6 x 1015, it is only six million billion, which is laughable.

  So Sanger and company have made progress.

  Where next?

  Suppose we take Chain II and subject it to acid treatment. The acid breaks the links between the amino-acids more or less at random, sometimes here, sometimes there, in no particular order. If you let it work to the bitter end, all the links between amino-acids are broken. But what if you stop the action by neutralizing the acid before the job is completed? In that case, you end up with various fragments of the chain that haven’t been completely broken apart. Two amino-acids remain stuck together from one portion of the chain, two from another, three from still another, four from yet another. In short, you get a potpourri of just about every possible combination of two, three, or four amino-acids that the chain can yield.

  This potpourri can be partially separated. Actually, five different groups of chain fragments can be isolated by conventional chemical treatment. Each group is still a complex mixture, of course, yet each group can be separated easily enough into its different components by two-dimensional paper chromatography.

  Once separated, each individual chain fragment can be dissolved out of the paper and placed in a separate test tube. Each fragment can be separately treated with acid and this time the acid is allowed to do the complete job. Each chain fragment is cut up into individual amino-acids and that mixture then takes the filter-paper path to analysis. The individual amino-acids in each separate chain are thus identified.

  In this way, it is found that one chain fragment consists of amino-acids E, H, and R. Another one consists of D, G, R, and M. And so on and so on and so on.

  But what about the order of amino-acids in these fragments? If a fragment contains E, H, and R, is its structure E-H-R, E-R-H, R-E-H, R-H-E, H-E-R, or H-R-E?

  One piece of information can be obtained by treating a particular chain fragment with Sanger’s Reagent before subjecting it to acid and thus identifying the amino-acid at the right-hand end of the fragment.

  If the fragment happens to consist only of two amino-acids, that gives us its structure at once. If it contains A and B and it is B that is on the right, obviously its structure is A-B. Nothing else is possible. In this way, nearly thirty-two amino-acid fragments were identified as coming from the partial break-up of Chain II.

  From that point, a process of reasoning follows that is similar to the type used in solving jigsaw puzzles or cryptograms.

  For instance, Chain II contains only one of amino-acid, D. Two different chains of two amino-acids, each containing D, were isolated. One had the structure G-D and the other D-R. Obviously then, Chain II must contain the combination G-D-R. It is the only combination from which one can obtain both G-D and D-R.

  There is an amino-acid chain of three amino-acids which contains D, R and M, with M at the right-hand end. The chain of three can only be D-R-M or R-D-M. But we know that R follows the only D in the chain. The three combination can only be D-R-M. Furthermore, we know that G precedes the only D in Chain II. So, it is now known that Chain II contains the following sequence of four amino-acids, G-D-R-M.

  Analysis proceeds in this manner. There is only one amino-acid, B, in the chain. Since H-B and B-F are found, the sequence H-B-F is established.

  Again there is only one amino-acid N present. A fragment of structure N-P is found. Also one containing three amino-acids with N at the right end is found. The latter is either L-A-N or A-L-N. No fragment of structure L-A is ever found, however. One of structure A-L is found. The three-amino-acid chain must, therefore, be A-L-N and since there is also the N-P previously mentioned, a four-amino-acid sequence, A-L-N-P, has been established.

  Little by little the chain sequence is put together until finally the only (!!!!) arrangement of thirty amino-acids which will account for all the chain fragments located by paper chromatography is decided upon. One arrangement out of 3 x 1027 possibilities. One arrangement only. It’s like looking for a particular two-gram chunk of matter—1/14th of an ounce—somewhere in Earth’s massive rotundity, and finding it.

  By similar methods, the arrangement of amino-acids in Chain I is also determined. The arrangements for both chains is shown in Figure 14. The manner in which two Chain I’s and two Chain II’s are hooked up to form insulin becomes a mere detail, and it can be stated that Sanger and his group have determined the exact amino-acid structure of insulin.

  It would be pleasant if I could proceed now to say that the determination of insulin’s structure shed an immediate and brilliant light on insulin’s method of working or that it served to present an immediate hope for an improved treatment of diabetes.

  Unfortunately, I can’t. So far, the victory on (filter) paper remains only a victory on paper as far as clinicians are concerned.

  The arrangement of amino-acids in insulin seems to have no significance. We stare at it and it makes no illuminating sense. Minor changes in the insulin molecule destroy its effectiveness completely and no one part of the molecule appears more important than another part.

  Is no further progress possible? Can no chemical even slightly simpler than insulin possibly substitute for it?

  I don’t know. Yet I’m not entirely depressed, either.

  It took Sanger and his men eight years to solve the ‘impossible’ problem of finding one arrangement out of several googols of possible arrangements. We shouldn’t object to giving biochemists a few more years to see what other impossibilities they can knock off.

  NOTE

  Since this article was first written, in March 1955, the various methods for working out the intimate structure of protein molecules have advanced to the point where they have become routine—even automated. There are now a great many protein molecules, most far larger and more complex than insulin, the structures of which have been worked out to the last atom. Hemoglobin is one of them, as I said in the note at the end of the previous chapter. In addition, chemists have been working out the intimately detailed structure of various nucleic acids, the only other group of compounds to compare in complexity and importance to the proteins.

  CHAPTER FIVE—THE ABNORMALITY OF BEING NORMAL

  A common catch-phrase is the one that goes, ‘There is no such thing as a normal person.’

  The question, though, is this: ‘Why is there no such thing as a normal person?’

  We’ll get to that.

  People sometimes say, with a certain smugness: ‘A normal person is like a perfect gas or absolute zero; a useful abstraction that doesn’t exist in actual reality.’

  This has the virtue of placing psychology on a kind of par with the physical sciences, but doesn’t help explain why a normal person doesn’t exist in actual reality.

  We know why a perfect gas doesn’t exist. A perfect gas is one in which the individual molecules are assumed to occupy mathematical points and to have zero volume. It is also one in which the attraction of neighbouring molecules for one another is zero. When these criteria are met, the way a gas behaves can be readily calculated from a few basic assumptions, some geometry and a bit of statistical technique. In this way, certain neat and orderly ‘gas laws’ are evolved.

  Unfortunately, however, the molecules of all actual gases invariably take up a certain volume. Small as they are, they are never mathematical points. Moreover, molecules always have some attraction for one another. Sometimes the attraction is minute, but it is never zero.

  Both facts invalidate the gas laws. In order to account for the behavior of actual gases, physical chemists have learned to make empirical allowance for the manner in which actual molecules fall short of the ‘ideal’.

  Any actual gas can be made to behave so as to approach an ideal gas. If a gas is placed under very low pressure, its molecules move apart. As they move apart, their attraction for one another decreases. The volume of the individual molecule, moreover, becomes so small compared to the space between molecules, that the individual molecule can be considered more and more as a simple point. In this way, the conditions of the perfect gas are approached. (The same is true if the temperature of a gas is raised.)

  An actual gas becomes a perfect gas at zero pressure. Unfortunately, at zero pressure the molecules are at infinite distance from one another and we have no gas at all, only the very best vacuum.

  A perfect gas is therefore a ‘limiting condition’. It can never be actually reached. It can be approached asymptotically (fancy word for: you-can-get-closer-and-closer-and-closer-but-you-can’t-ever-quite-reach-it) but only asymptotically.

  Now for absolute zero.

  Absolute zero is the temperature at which all molecular motion ceases. In actual practice, it is impossible to reach that temperature. Temperatures as low as a few thousandths of a degree above absolute zero have been reached but that is no sign that the goal is within sight. It is hard to get from 4 degrees above absolute zero to 2 degrees above. It is just as hard to travel from 2 to 1; equally as hard to go from 1 to 0.5; again as hard to go from 0.5 to 0.25 and so on.

  Again, we have a limiting condition that can be approached only asymptotically.

  Now we get back to our ‘normal’ person. If the normal person were like a perfect gas or absolute zero, it too might represent a limiting condition of some sort, a limit which could be approached but not reached.

  We can easily imagine one sort of limit of human behavior. We can think of a human being who is incredibly strong, incredibly wise, incredibly virtuous, incredibly all-that-is-praiseworthy, a superman, a godlike creature. But this is no ‘normal person’; this is more like an ‘ideal person’ and we can see quite plainly that a man so incredibly this and that is also incredibly scarce.

  You can see that the adjectives used for these limiting abstractions are very suggestive: ‘perfect’, ‘absolute’, ‘ideal’. Adjectives such as that fit unreachable limits.

  But how then does the word ‘normal’ come to be applied to something which seems to be an abstraction? The word ‘normal’ is synonymized in the dictionary by such words as ‘common’, ‘natural’, ‘ordinary’, ‘regular’, ‘typical’, and ‘usual’. When we say that a normal person doesn’t exist, aren’t we indulging in a contradiction in terms? How can something which is common, natural, ordinary, regular, typical and usual not exist?

  Well, then, what is a normal person to a psychologist? He is the sum of the million and one (or is it a trillion and one?) individual characteristics that go into the making of a human being. And in every one of these characteristics, he is normal. That is, in the case of every component characteristic, our normal human being has whatever attribute is common, natural, ordinary, regular, typical and usual.

  Some of the characteristics are universal. Every living human being breathes, everyone has a heart that beats and so on. In these respects, every living human being is normal.

  There are also factors that are not universal. For instance, a person may have an overwhelming urge to kill strangers who have done him no harm. On the other hand, he may not have. The second alternative is normal in the sense that it is common, natural, etc., but it is not universal. There are a certain number of people who have uncontrollable homicidal drives. To have such a drive is an abnormal characteristic; to not have it is normal. Our ‘normal person’ would therefore not have one.

  In any given individual, any factor in his makeup can be considered either normal or abnormal. The normal is that which occurs in most people; perhaps in nearly all; in some cases, actually in all. (Mind you, the normal characteristic need not be a particularly admirable one, merely a common on. All people are selfish, to an extent; cowardly, to an extent; stubborn, to an extent; stupid, to an extent. Our ‘normal man’ would be selfish, cowardly, stubborn and stupid to the normal extent.)

  Now, then, if most people are normal in any given characteristic, why are there no ‘normal people’ who are normal in all characteristics?

  In other words, if we add common, natural, ordinary, regular, typical and usual characteristics together, why don’t we end up with common, natural, ordinary, regular, typical and usual people?

  Let’s switch, temporarily, from people to atoms, and see if we can find the answer?

  The atoms of most elements consist of two or more different varieties that are similar in chemical properties but different in certain other respects. These varieties are referred to as isotopes of that element.

  Some elements are split up fairly evenly among two or more isotopes. Some, on the other hand, are preponderantly (but often not entirely) one isotope, with other isotopes occurring only rarely. Now it so happens that of the elements that make up the body, the most important ones fall into the second classification.

  At this point, please look at Table XV.

  By ‘fractional occurrence’, I mean, of course, the fraction of the atoms of a certain element (in any random sample) which are a particular isotope. For instance, if we concentrate on hydrogen, then what the table is saying is that out of every 100,000 hydrogen atoms, 99,984 (on the average) are hydrogen-1 and only 16 are hydrogen-2. (Never mind the significance of the numbers that are used to distinguish isotopes from one another. That’s not important for our purpose here.)

  Put it another way. Suppose you are sitting before a sack of hydrogen atoms which have been expanded to the size of marbles and suppose you are dipping in blindly and taking out any hydrogen atom you touched. The chances are 99,984 out of 100,000 that you would pull out a hydrogen-1 atom. The chances are only 16 out of 100,000 that you would pull out a hydrogen-2 atom.

  Under those conditions you would naturally expect to pull out a hydrogen-1 atom at any particular try. If you did pull one out, you would consider the event a ‘normal’ one. Every once in a while, though, you would withdraw your hand and find yourself staring at a hydrogen-2 atom and you could not help but be astonished. It would be an ‘abnormal’ occurrence.

  The same would be true for the other elements listed in the table, though not to the same extent as hydrogen. The other elements are not quite so preponderantly one isotope as is hydrogen. Still, even iron is more than 9/10 one isotope and less than 1/10 the other three put together.

  Therefore, let’s call hydrogen-1, carbon-12, nitrogen-14, oxygen-16, sulfur-32 and iron-56 the ‘normal’ isotopes. The others are ‘abnormal’ isotopes. (Naturally, I’m not implying there is anything morally wrong with hydrogen-2, carbon-13 or any of the others, or anything physically distorted, either. I am simply calling that isotope normal which is the common, natural, ordinary, etc. one.)

  Now let’s proceed. Hydrogen atoms don’t exist by themselves under ordinary conditions. They tie up in pairs to form hydrogen molecules. You can see, then, that three different kinds of combinations of two hydrogen atoms (three different kinds of molecules, that is) can be formed if the combination is formed in a random manner. A hydrogen-1 can tie up with a hydrogen-1. A hydrogen-1 can tie up with a hydrogen-2. A hydrogen-2 can tie up with a hydrogen-2.

  Naturally, most of the combinations are hydrogen-1 with hydrogen-1, simply because there are so few hydrogen-2 atoms present. But exactly what proportion of the hydrogen molecules would be hydrogen-1, hydrogen-1 combinations?

  The probability of any given hydrogen atom being hydrogen-1 is the same as its fractional occurrence, i.e. 0.99984. The probability of a second hydrogen atom being hydrogen-1 is also 0.99984. Now what’s the chance of picking out two hydrogen atoms from that sack of ours and finding them both hydrogen-1?

  The probability of two occurrences both happening is determined by multiplying the probabilities of each occurrence happening individually.

  In other words the probability of any two hydrogen atoms both being hydrogen-1 (as in a hydrogen-1, hydrogen-1 molecule) is 0.99984 multiplied by 0.99984. The answer to that is 0.99968. That means that 99,968 hydrogen molecules out of every 100,000 are hydrogen-1, hydrogen-1 combinations. Only 32 out of every 100,000 are hydrogen-1, hydrogen-2 or hydrogen-2, hydrogen-2 combinations.

  The hydrogen-1, hydrogen-1 molecules are ‘normal’ in the sense that they are the common, natural, ordinary, regular, typical and usual ones. The other types of molecules are abnormal.

  We can stop at this point and make a trial definition which may turn out to be a good one or may not. Let’s say this: Any molecule is normal if it is made up entirely of normal isotopes. (Notice that this is analogous to saying that a ‘normal person’ is one who is made up entirely of normal individual characteristics.)

  Now to proceed. Note that the fractional occurrence of normal hydrogen molecules, 0.99968, is not quite as high as the fractional occurrence of normal hydrogen atoms, 0.99984. This makes sense since a number of the normal hydrogen-1 isotopes are ‘spoiled’ by hooking up with hydrogen-2 isotopes to form part of the abnormal hydrogen-1, hydrogen-2 molecules.

  We can also consider this from the standpoint of simple arithmetic. Whenever two numbers less than 1 are multiplied, the product is smaller than either of the original numbers. The closer the numbers are to 1, the less the shrinkage of the product.

  If the numbers were actually 1, then there would be no shrinkage. The product would be 1, too. If the probability of the occurrence of hydrogen-1 were 1, that would mean that every hydrogen atom would be hydrogen-1, without exception. They would all be normal. In that case, every hydrogen molecule would be the normal hydrogen-1, hydrogen-1 combination since there would be no other kind of hydrogen to interfere. This is analogous to people being made up of universal traits only, such as all having pumping lungs and beating hearts.