The Outstanding Relevance Of The Reductive Division

The important, the really fateful event in the process of reproduction of the individual is not fertilization but meiosis.

One set of chromosomes is from the father, one from the mother. Neither chance nor destiny can interfere with that.

Every man lowes just half of his inheritance to his mother, halfofit to his father. That one or the other strain seems often to prevail is due to other reasons which we shall come to later.

(Sex itself is, of course, the simplest instance of such prevalence. )

But when you trace the origin of your inheritance back to your grandparents, the case is different. Let me fix attention on my paternal set of chromosomes, in particular on one of them, say NO.5. It is a faithful replica either of the NO.5 my father received from his father or of the NO.5 he had received from his mother.

The issue was decided by a 50:50 chance in the meiosis taking place in my father’s body in November 1886 and producing the spermatozoon which a few days later was to be effective in begetting me.

Exactly the same story could be repeated about chromosomes Nos. 1,2,3, … , 24 of my paternal set, and mutatis mutandis about everyone of my maternal chromosomes.

Moreover, all the 48 issues are entirely independent. Even if it were known that my paternal chromosome No. 5 came from my grandfather Josef Schrodinger, the NO.7 still stands an equal chance of being either also from him, or from his wife Marie, nee Bogner.

CROSSING-OVER. LOCATION OF PROPERTIES

But pure chance has been given even a wider range in mixing the grandparental inheritance in the offspring than would appear from the preceding description, in which it has been ‘At any rate, every woman.

To avoid prolixity, I have excluded from this summary the highly interesting sphere of sex determination and sex-linked properties (as, for example, so-called colour blindness).

Fig. 6. Crossing-over. Left: the two homologous chromosomes in contact.

Right: after exchange and separation.

tacitly assumed, or even explicitly stated, that a particular chromosome as a whole was either from the grandfather or from the grandmother; in other words that the single chromo- somes are passed on undivided.

In actual fact they are not, or not always. Before being separated in the reductive division, say the one in the father’s body, any two ‘homologous’ chromosomes come into close contact with each other, during which they sometimes exchange entire portions in the way illustrated in Fig. 6. By this process, called ‘crossing-over’, two properties situated in the respective parts of that chromo- some will be separated in the grandchild, who will follow the grandfather in one of them, the grandmother in the other one.

The act of crossing-over, being neither very rare nor very frequent, has provided us with invaluable information regard- ing the location of properties in the chromosomes. For a full account we should have to draw on conceptions not intro- duced before the next chapter (e.g. heterozygosy, dominance, etc.); but as that would take us beyond the range of this little book, let me indicate the salient point right away.

If there were no crossing-over, two properties for which the same chromosome is responsible would always be passed on together, no descendant receiving one of them without receiv- ing the other as well; but two properties, due to different chromosomes, would either stand a 50:5° chance of being separated or they would invariably be separated - the latter when they were situated in homologous chromosomes of the same ancestor, which could never go together.

These rules and chances are interfered with by crossing- over. Hence the probability of this event can be ascertained by registering carefully the percentage composition of the offspring in extended breeding experiments, suitably laid out for the purpose. In analysing the statistics, one accepts the suggestive working hypothesis that the ’linkage’ between two properties situated in the same chromosome, is the less frequently broken by crossing-over, the nearer they lie to each other.

For then there is less chance of the point of exchange lying between them, whereas properties located near the opposite ends of the chromosomes are separated by every crossing-over. (Much the same applies to the recombination of properties located in homologous chromosomes of the same ancestor.) In this way one may expect to get from the ‘statistics of linkage’ a sort of ‘map of properties’ within every chromosome.

These anticipations have been fully confirmed. In the cases to which tests have been thoroughly applied (mainly, but not only, Drosophila) the tested properties actually divide into as many separate groups, with no linkage from group to group, as there are different chromosomes (four in Drosophila).

Within every group a linear map of properties can be drawn up which accounts quantitatively for the degree of linkage between any two out of that group, so that there is little doubt that they actually are located, and located along a line, as the rod-like shape of the chromosome suggests.

Of course, the scheme of the hereditary mechanism, as drawn up here, is still rather empty and colourless, even slightly naIve. For we have not said what exactly we under- stand by a property. It seems neither adequate nor possible to dissect into discrete ‘properties’ the pattern of an organism which is essentially a unity, a ‘whole’.

What we actually state in any particular case is, that a pair of ancestors were different in a certain well-defined respect (say, one had blue eyes, the other brown), and that the offspring follows in this respect either one or the other. What we locate in the chromosome is the seat of this difference.

(We call it, in technical language, a ’locus’, or, if we think of the hypothetical material structure underlying it, a ‘gene’.) Difference of property, to my view, is really the fundamental concept rather than property itself, notwithstanding the apparent linguistic and logical contradiction of this statement. The differences of properties actually are discrete, as will emerge in the next chapter when we have to speak of mutations and the dry scheme hitherto presented will, as I hope, acquire more life and colour.

MAXIMUM SIZE OF A GENE

We have just introduced the term gene for the hypothetical material carrier of a definite hereditary feature. We must now stress two points which will be highly relevant to our investigation. The first is the size - or, better, the maximum size - of such a carrier; in other words, to how small a volume can we trace the location? The second point will be the permanence of a gene, to be inferred from the durability of the hereditary pattern.

As regards the size, there are two entirely independent estimates, one resting on genetic evidence (breeding experiments), the other on cytological evidence (direct microscopic inspection).

The first is, in principle, simple enough. After having, in the way described above, located in the chromo- some a considerable number of different (large-scale) features (say of the Drosophila fly) within a particular one of its chromosomes, to get the required estimate we need only divide the measured length of that chromosome by the number of features and multiply by the cross-section.

For, of course, we count as different only such features as are occasionally separated by crossing-over, so that they cannot be due to the same (microscopic or molecular) structure.

On the other hand, it is clear that our estimate can only give a maximum size, because the number of features isolated by genetic analysis is continually increasing as work goes on. The other estimate, though based on microscopic inspection, is really far less direct.

Certain cells of Drosophila (namely, those of its salivary glands) are, for some reason, enormously enlarged, and so are their chromosomes.

In them you distinguish a crowded pattern of transverse dark bands across the fibre. C. D. Darlington has remarked that the number of these bands (2,000 in the case he uses) is, though considerably larger, yet roughly of the same order of magnitude as the number of genes located in that chromosome by breeding experiments. He inclines to regard these bands as indicating the actual genes (or separations of genes).

Dividing the length of the chromosome, measured in a normal-sized cell by their number (2,000), he finds the volulne of a gene equal to a cube of edge 300 A. Considering the roughness of the estimates, we may regard this to be also the size obtained by the first method.

SMALL NUMBERS

A full discussion of the bearing of statistical physics on all the facts I am recalling - or perhaps, I ought to say, of the bearing of these facts on the use of statistical physics in the living cell- will follow later. But let me draw attention at this point to the fact that 300 A is only about 100 or 150 atomic distances in a liquid or in a solid, so that a gene contains certainly not more than about a million or a few million atoms.

That number is much too small (from the Yn point of view) to entail an orderly and lawful behaviour according to statistical physics - and that means according to physics.

It is too small, even if all these atoms played the same role, as they do in a gas or in a drop of liquid. And the gene is most certainly not just a homogeneous drop of liquid. I t is probably a large protein molecule, in which every atom, every radical, every heterocy- clic ring plays an individual role, more or less different from that played by any of the other similar atoms, radicals, or rings. This, at any rate, is the opinion of leading geneticists such as Haldane and Darlington, and we shall soon have to refer to genetic experiments which come very near to proving it.

PERMANENCE

What degree of permanence do we encounter in hereditary properties and what must we therefore attribute to the material structures which carry them?

The answer to this can really be given without any special investigation. The mere fact that we speak of hereditary properties indicates that we recognize the permanence to be almost absolute. For we must not forget that what is passed on by the parent to the child is not jus t this or that peculiarity, a hooked nose, short fingers, a tendency to rheumatism, haemo- philia, dichromasy, etc. Such features we may conveniently select for studying the laws of heredity.

But actually it is the whole (four-dimensional) pattern of the ‘phenotype’, the visible and manifest nature of the individual, which is repro- duced without appreciable change for generations, permanent within centuries - though not within tens of thousands of years - and borne at each transmission by the material structure of the nuclei of the two cells which unite to form the fertilized egg cell.

That is a marvel - than which only one is greater; one that, if intimately connected with it, yet lies on a different plane. I mean the fact that we, whose total being is entirely based on a marvellous interplay of this very kind, yet possess the power of acquiring considerable knowledge about it. I think it possible that this knowledge may advance to little short of a complete understanding - of the first marvel. The second may well be beyond human understanding.