3.3. Excursion: A lesson from heredity[[Student version, December 8, 2002]] 89
T 2 Section 3.3.2′on page 95 mentions the role of double crossing-over.
3.3.3 Schr ̈odinger’s summary: Genetic information is structural
Forsome time, it seemed as though the techniques of classical genetics and cell biology, powerful
though they were, could shed no further light on the nature of the chromosomal charm bracelet.
Even the physical size of a gene remained open for dispute. But by the mid-twentieth century, new
experimental techniques and theoretical ideas from physics were opening new windows on cells.
Schr ̈odinger’s brief summary of the situation in 1944 drew attention to a few of the emerging facts.
To Schr ̈odinger, the biggest question about genes concerned the nearly perfect fidelity of their
information storage in spite of their minute size. To see how serious this problem is, we first need to
know just how small a gene is. One crude way to estimate this size is to guess how many genes there
are, and note that they must all fit into a sperm head. Muller gave a somewhat better estimate
in 1935 by noting that a fruit fly chromosome condenses during mitosis into roughly a cylinder of
length 2μmand diameter 0. 25 μm(see Figure 3.14b). The total volume of the genetic material in a
chromosome is thus no larger than 2μm×π(0. 25 μm/2)^2 .When the same chromosome is stretched
out in the polytene form mentioned above, however, its length is more like 200μm.Suppose that
asingle thread of the genetic charm bracelet, stretched out straight, has a diameterd. Then its
volume equals 200μm×π(d/2)^2 .Equating these two expressions for the volume yields the estimate
d≤ 0. 025 μmfor the diameter of the genetic information carrier. While we now know that a strand
of DNA is really less than a tenth this wide, still Muller’s upper bound ondshowed that the genetic
carrier is an object of molecular scale. Even the tiny pits encoding the information on an audio
compact disk are thousands of times larger than this, just as the disk itself occupies a far larger
volume than a sperm cell.
Tosee what Schr ̈odinger found so shocking about this conclusion, we must again remember that
molecules are in constant, random thermal motion (Section 3.2). The words on this page may be
stable for many years, but if we could write them in letters only a few nanometers high then random
motions of the ink molecules constituting them would quickly obliterate them. Random thermal
motion becomes more and more destructive of order on shorter length scales, a point to which we
will return in Chapter 4. How can genes be so tiny and yet so stable?
Muller and others argued that the only known stable arrangements of just a few atoms are single
molecules. Quantum physics was just beginning to explain this phenomenal stability, as the nature
of the chemical bond became understood. (As one of the architects of quantum theory, Schr ̈odinger
himself had laid the foundations for this understanding.) A molecule derives its enormous stability
from the fact that a large activation barrier must be momentarily overcome in order to break
the bonds between its constituent atoms. More precisely, Section 1.5.3 pointed out that a typical
chemical bond energy isEbond≈ 2. 4 · 10 −^19 J,about sixty times bigger than the typical thermal
energyEthermal.Muller argued that this large activation barrier to conversion was the reason why
spontaneous thermally induced mutations are so rare, following the ideas of Section 3.2.4.^7
The hypothesis that the chromosome is a single molecule may appear satisfying, even obvious,
today. But in order to be convinced that it is really true, we must require that a model generate
some quantitative, falsifiable predictions. Fortunately, Muller had a powerful new tool in hand:
(^7) Today we know that eukaryotes enhance their genome stability still further with special-purpose molecular
machines for the detection and repair of damaged DNA.