3.3. Excursion: A lesson from heredity[[Student version, December 8, 2002]] 91
Figure 3.16: (Schematic.) Max Delbr ̈uck’s simplified model for X-ray induced mutagenesis. Incoming X-rays
(diagonal arrows)occasionally interact with tissue to create free radicals(stars)with number densityc∗depending
on the X-ray intensity, thewavelength of the X-rays, and the duration of exposure. The chance that the gene of
interest lies within a box of volumevcentered on one of the radicals, and so has a chance of being altered, is the
fraction of all space occupied by the boxes, orc∗v.
When X-rays pass through any sort of matter, living or not, they knock electrons out of a few of
the molecules they pass. These electrons in turn rip apart other molecules, breaking chemical bonds
and creating highly reactive fragments. Some of these fragments are charged; they are ions. Others
are highly unstable; these are generically called “free radicals.” The densitycionof ions created per
volume is a convenient, and physically measurable, index of total radiation dose.
The reactive molecular fragments generated by the radiation can in turn encounter and damage
other nearby molecules. We assume that the densityc∗of these damage-inducing fragments is
some constant times the measured ionization:c∗=Kcion.The hypothesis that the gene is a single
molecule implies that the breakage of a single chemical bond in it could induce a permanent change
in its structure, and so cause a heritable mutation. Since free radicals are themselves unstable
molecular fragments, a single encounter with one of them can induce a mutation. Suppose that a
free radical can wander through a volumevbefore reacting with something, and that a particular
gene (for example, the one for eye color) has a chanceP 1 of suffering a particular mutation if it is
located in this volume (and zero chance otherwise). Then the total chance that a particular egg or
sperm cell will undergo the chosen mutation is (see Figure 3.16):
probability of mutation =P 1 c∗v=(P 1 Kv)×cion. (3.28)Delbr ̈uck did not know the actual numerical values of any of the constantsP 1 ,K,andvappearing
in this formula. Nevertheless, the argument showed that:
The hypothesis that the gene is a single molecule suggests that a single molecular
encounter can break it, and hence that the probability of mutation equals a
constant times the dose measured in ionizations per volume,(3.29)
as found in Timof ́eeff’s experiments.
Equation 3.28 tells a remarkable story. On the left-hand side we have abiologicalquantity, which
wemeasure by irradiating a lot of flies and seeing how many have offspring with, for example, white
eyes. On the right side we have a purelyphysicalquantitycion.The formula says that the biological
and the physical quantities are linked in a simple way by the hypothesis that the gene is a molecule.
Data like those in Figure 3.15 confirmed this prediction.