What Is Life (Canto Classics)

by Erwin Schrodinger

  A recessive allele influences the phenotype only when the genotype is homozygous.

  We shall use these technical expressions occasionally, but shall recall their meaning to the reader where necessary.

  THE HARMFUL EFFECT OF CLOSE-BREEDING

  Recessive mutations, as long as they are only heterozygous, are of course no working-ground for natural selection. If they are detrimental, as mutations very often are, they will nevertheless not be eliminated, because they are latent. Hence quite a host of unfavourable mutations may accumulate and do no immediate damage. But they are, of course, transmitted to half of the offspring, and that has an important application to man, cattle, poultry or any other species, the good physical qualities of which are of immediate concern to us. In Fig. 9 it is assumed that a male individual (say, for concreteness, myself) carries such a recessive detrimental mutation heterozygously, so that it does not show up. Assume that my wife is free of it. Then half of our children (second line) will also carry it – again heterozygously. If all of them are again mated with non-mutated partners (omitted from the diagram, to avoid confusion), a quarter of our grandchildren, on the average, will be affected in the same way.

  No danger of the evil ever becoming manifest arises, unless equally affected individuals are crossed with each other, when, as an easy reflection shows, one-quarter of their children, being homozygous, would manifest the damage. Next to self-fertilization (only possible in hermaphrodite plants) the greatest danger would be a marriage between a son and a daughter of mine. Each of them standing an even chance of being latently affected or not, one-quarter of these incestuous unions would be dangerous inasmuch as one-quarter of its children would manifest the damage. The danger factor for an incestuously bred child is thus 1:16.

  In the same way the danger factor works out to be 1:64 for the offspring of a union between two (‘clean-bred’) grandchildren of mine who are first cousins. These do not seem to be overwhelming odds, and actually the second case is usually tolerated. But do not forget that we have analysed the consequences of only one possible latent injury in one partner of the ancestral couple (‘me and my wife’). Actually both of them are quite likely to harbour more than one latent deficiency of this kind. If you know that you yourself harbour a definite one, you have to reckon with 1 out of 8 of your first cousins sharing it! Experiments with plants and animals seem to indicate that in addition to comparatively rare deficiencies of a serious kind, there seem to be a host of minor ones whose chances combine to deteriorate the offspring of close-breeding as a whole. Since we are no longer inclined to eliminate failures in the harsh way the Lacedemonians used to adopt in the Taygetos mountain, we have to take a particularly serious view about these things in the case of man, where natural selection of the fittest is largely retrenched, nay, turned to the contrary. The anti-selective effect of the modern mass slaughter of the healthy youth of all nations is hardly outweighed by the consideration that in more primitive conditions war may have had a positive value in letting the fittest tribe survive.

  GENERAL AND HISTORICAL REMARKS

  The fact that the recessive allele, when heterozygous, is completely overpowered by the dominant and produces no visible effect at all, is amazing. It ought at least to be mentioned that there are exceptions to this behaviour. When homozygous white snapdragon is crossed with, equally homozygous, crimson snapdragon, all the immediate descendants are intermediate in colour, i.e. they are pink (not crimson, as might be expected). A much more important case of two alleles exhibiting their influence simultaneously occurs in blood-groups – but we cannot enter into that here. I should not be astonished if at long last recessivity should turn out to be capable of degrees and to depend on the sensitivity of the tests we apply to examine the ‘phenotype’.

  This is perhaps the place for a word on the early history of genetics. The backbone of the theory, the law of inheritance, to successive generations, of properties in which the parents differ, and more especially the important distinction recessive-dominant, are due to the now world-famous Augustinian Abbot Gregor Mendel (1822–84). Mendel knew nothing about mutations and chromosomes. In his cloister gardens in Brünn (Brno) he made experiments on the garden pea, of which he reared different varieties, crossing them and watching their offspring in the 1st, 2nd, 3rd, …, generation. You might say, he experimented with mutants which he found ready-made in nature. The results he published as early as 1866 in the Proceedings of the Naturforschender Verein in Brünn. Nobody seems to have been particularly interested in the abbot’s hobby, and nobody, certainly, had the faintest idea that his discovery would in the twentieth century become the lodestar of an entirely new branch of science, easily the most interesting of our days. His paper was forgotten and was only rediscovered in 1900, simultaneously and independently, by Correns (Berlin), de Vries (Amsterdam) and Tschermak (Vienna).

  THE NECESSITY OF MUTATION BEING A RARE

  EVENT

  So far we have tended to fix our attention on harmful mutations, which may be the more numerous; but it must be definitely stated that we do encounter advantageous mutations as well. If a spontaneous mutation is a small step in the development of the species, we get the impression that some change is ‘tried out’ in rather a haphazard fashion at the risk of its being injurious, in which case it is automatically eliminated. This brings out one very important point. In order to be suitable material for the work of natural selection, mutations must be rare events, as they actually are. If they were so frequent that there was a considerable chance of, say, a dozen of different mutations occurring in the same individual, the injurious ones would, as a rule, predominate over the advantageous ones and the species, instead of being improved by selection, would remain unimproved, or would perish. The comparative conservatism which results from the high degree of permanence of the genes is essential. An analogy might be sought in the working of a large manufacturing plant in a factory. For developing better methods, innovations, even if as yet unproved, must be tried out. But in order to ascertain whether the innovations improve or decrease the output, it is essential that they should be introduced one at a time, while all the other parts of the mechanism are kept constant.

  MUTATIONS INDUCED BY X-RAYS

  We now have to review a most ingenious series of genetical research work, which will prove to be the most relevant feature of our analysis.

  The percentage of mutations in the offspring, the so-called mutation rate, can be increased to a high multiple of the small natural mutation rate by irradiating the parents with X-rays or γ-rays. The mutations produced in this way differ in no way (except by being more numerous) from those occurring spontaneously, and one has the impression that every ‘natural5 mutation can also be induced by X-rays. In Drosophila many special mutations recur spontaneously again and again in the vast cultures; they have been located in the chromosome, as described on pp. 26–9, and have been given special names. There have been found even what are called ‘multiple alleles’, that is to say, two or more different versions’ and ‘readings’ – in addition to the normal, non-mutated one – of the same place in the chromosome code; that means not only two, but three or more alternatives in that particular ‘locus’, any two of which are to each other in the relation ‘dominant–recessive’ when they occur simultaneously in their corresponding loci of the two homologous chromosomes.

  The experiments on X-ray-produced mutations give the impression that every particular ‘transition’, say from the normal individual to a particular mutant, or conversely, has its individual ‘X-ray coefficient’, indicating the percentage of the offspring which turns out to have mutated in that particular way, when a unit dosage of X-ray has been applied to the parents, before the offspring was engendered.

  FIRST LAW. MUTATION IS A SINGLE EVENT

  Furthermore, the laws governing the induced mutation rate are extremely simple and extremely illuminating. I follow here the report of N. W. Timoféëff, in Biological Reviews, vol. IX, 1934. To a considerable e
xtent it refers to that author’s own beautiful work. The first law is

  (1) The increase is exactly proportional to the dosage of rays, so that one can actually speak [as I did] of a coefficient of increase.

  We are so used to simple proportionality that we are liable to underrate the far-reaching consequences of this simple law. To grasp them, we may remember that the price of a commodity, for example, is not always proportional to its amount. In ordinary times a shopkeeper may be so much impressed by your having bought six oranges from him, that, on your deciding to take after all a whole dozen, he may give it to you for less than double the price of the six. In times of scarcity the opposite may happen. In the present case, we conclude that the first half-dosage of radiation, while causing, say, one out of a thousand descendants to mutate, has not influenced the rest at all, either in the way of predisposing them for, or of immunizing them against, mutation. For otherwise the second half-dosage would not cause again just one out of a thousand to mutate. Mutation is thus not an accumulated effect, brought about by consecutive small portions of radiation reinforcing each other. It must consist in some single event occurring in one chromosome during irradiation. What kind of event?

  SECOND LAW. LOCALIZATION OF THE EVENT

  This is answered by the second law, viz.

  (2) If you vary the quality of the rays (wave-length) within wide limits, from soft X-rays to fairly hard γ-rays, the coefficient remains constant, provided you give the same dosage in so-called r-units, that is to say, provided you measure the dosage by the total amount of ions produced per unit volume in a suitably chosen standard substance during the time and at the place where the parents are exposed to the rays.

  As standard substance one chooses air not only for convenience, but also for the reason that organic tissues are composed of elements of the same atomic weight as air. A lower limit for the amount of ionizations or allied processes3 (excitations) in the tissue is obtained simply by multiplying the number of ionizations in air by the ratio of the densities. It is thus fairly obvious, and is confirmed by a more critical investigation, that the single event, causing a mutation, is just an ionization (or similar process) occurring within some ‘critical’ volume of the germ cell. What is the size of this critical volume? It can be estimated from the observed mutation rate by a consideration of this kind: if a dosage of 50,000 ions per cm3 produces a chance of only 1:1000 for any particular gamete (that finds itself in the irradiated district) to mutate in that particular way, we conclude that the critical volume, the ‘target’ which has to be ‘hit’ by an ionization for that mutation to occur, is only of of a cm3, that is to say, one fifty-millionth of a cm3. The numbers are not the right ones, but are used only by way of illustration. In the actual estimate we follow M. Delbrück, in a paper by Delbrück, N.W. Timoféëff and K.G. Zimmer,4 which will also be the principal source of the theory to be expounded in the following two chapters. He arrives there at a size of only about ten average atomic distances cubed, containing thus only about 103 = a thousand atoms. The simplest interpretation of this result is that there is a fair chance of producing that mutation when an ionization (or excitation) occurs not more than about ‘10 atoms away’ from some particular spot in the chromosome. We shall discuss this in more detail presently.

  The Timoféëff report contains a practical hint which I cannot refrain from mentioning here, though it has, of course, no bearing on our present investigation. There are plenty of occasions in modern life when a human being has to be exposed to X-rays. The direct dangers involved, as burns, X-ray cancer, sterilization, are well known, and protection by lead screens, lead-loaded aprons, etc., is provided, especially for nurses and doctors who have to handle the rays regularly. The point is, that even when these imminent dangers to the individual are successfully warded off, there appears to be the indirect danger of small detrimental mutations being produced in the germ cells – mutations of the kind envisaged when we spoke of the unfavourable results of close-breeding. To put it drastically, though perhaps a little naively, the injuriousness of a marriage between first cousins might very well be increased by the fact that their grandmother had served for a long period as an X-ray nurse. It is not a point that need worry any individual personally. But any possibility of gradually infecting the human race with unwanted latent mutations ought to be a matter of concern to the community.

  1 And what in fluctuating appearance hovers, Ye shall fix by lasting thoughts.

  2 Ample discussion has been given to the question, whether natural selection be aided (if not superseded) by a marked inclination of mutations to take place in a useful or favourable direction. My personal view about this is of no moment; but it is necessary to state that the eventuality of ‘directed mutations’ has been disregarded in all the following. Moreover, I cannot enter here on the interplay of ‘switch’ genes and ‘polygenes’, however important it be for the actual mechanism of selection and evolution.

  3 A lower limit, because these other processes escape the ionization measurement, but may be efficient in producing mutations.

  4 Nachr. a. d. Biologie d. Ges. d. Wiss. Göttingen, 1(1935), 189.

  CHAPTER 4

  The Quantum-Mechanical Evidence

  Und deines Geistes höchster Feuerflug

  Hat schon am Gleichnis, hat am Bild genug.1

  GOETHE

  PERMANENCE UNEXPLAINABLE BY

  CLASSICAL PHYSICS

  Thus, aided by the marvellously subtle instrument of X-rays (which, as the physicist remembers, revealed thirty years ago the detailed atomic lattice structures of crystals), the united efforts of biologists and physicists have of late succeeded in reducing the upper limit for the size of the microscopic structure, being responsible for a definite large-scale feature of the individual – the ‘size of a gene’ – and reducing it far below the estimates obtained on pp. 29–30. We are now seriously faced with the question: How can we, from the point of view of statistical physics, reconcile the facts that the gene structure seems to involve only a comparatively small number of atoms (of the order of 1,000 and possibly much less), and that nevertheless it displays a most regular and lawful activity – with a durability or permanence that borders upon the miraculous?

  Let me throw the truly amazing situation into relief once again. Several members of the Habsburg dynasty have a peculiar disfigurement of the lower lip (‘Habsburger Lippe’). Its inheritance has been studied carefully and published, complete with historical portraits, by the Imperial Academy of Vienna, under the auspices of the family. The feature proves to be a genuinely Mendelian ‘allele’ to the normal form of the lip. Fixing our attention on the portraits of a member of the family in the sixteenth century and of his descendant, living in the nineteenth, we may safely assume that the material gene structure, responsible for the abnormal feature, has been carried on from generation to generation through the centuries, faithfully reproduced at every one of the not very numerous cell divisions that lie between. Moreover, the number of atoms involved in the responsible gene structure is likely to be of the same order of magnitude as in the cases tested by X-rays. The gene has been kept at a temperature around 98°F during all that time. How are we to understand that it has remained unperturbed by the disordering tendency of the heat motion for centuries?

  A physicist at the end of the last century would have been at a loss to answer this question, if he was prepared to draw only on those laws of Nature which he could explain and which he really understood. Perhaps, indeed, after a short reflection on the statistical situation he would have answered (correctly, as we shall see): These material structures can only be molecules. Of the existence, and sometimes very high stability, of these associations of atoms, chemistry had already acquired a widespread knowledge at the time. But the knowledge was purely empirical. The nature of a molecule was not understood – the strong mutual bond of the atoms which keeps a molecule in shape was a complete conundrum to everybody. Actually, the answer proves to be correct. But it is of limit
ed value as long as the enigmatic biological stability is traced back only to an equally enigmatic chemical stability. The evidence that two features, similar in appearance, are based on the same principle, is always precarious as long as the principle itself is unknown.

  EXPLICABLE BY QUANTUM THEORY

  In this case it is supplied by quantum theory. In the light of present knowledge, the mechanism of heredity is closely related to, nay, founded on, the very basis of quantum theory. This theory was discovered by Max Planck in 1900. Modern genetics can be dated from the rediscovery of Mendel’s paper by de Vries, Correns and Tschermak (1900) and from de Vries’s paper on mutations (1901–3). Thus the births of the two great theories nearly coincide, and it is small wonder that both of them had to reach a certain maturity before the connection could emerge. On the side of quantum theory it took more than a quarter of a century till in 1926–7 the quantum theory of the chemical bond was outlined in its general principles by W. Heitler and F. London. The Heitler–London theory involves the most subtle and intricate conceptions of the latest development of quantum theory (called ‘quantum mechanics’ or ‘wave mechanics’). A presentation without the use of calculus is well-nigh impossible or would at least require another little volume like this. But fortunately, now that all work has been done and has served to clarify our thinking, it seems to be possible to point out in a more direct manner the connection between ‘quantum jumps’ and mutations, to pick out at the moment the most conspicuous item. That is what we attempt here.