What_is_life_(生命是什么)_by_薛定谔

WHAT IS LIFE?

ERWIN SCHRODINGER

First published 1944

What is life? The Physical Aspect of the Living

Cell.

Based on lectures delivered under the auspices of

the Dublin Institute for Advanced Studies at

Trinity College, Dublin, in February 1943.

To the memory of My Parents

Preface

A scientist is supposed to have a complete and

thorough I of knowledge, at first hand, of some

subjects and, therefore, is usually expected not to

write on any topic of which he is not a life,

master. This is regarded as a matter of noblesse

oblige. For the present purpose I beg to renounce

the noblesse, if any, and to be the freed of the

ensuing obligation. My excuse is as follows: We

have inherited from our forefathers the keen

longing for unified, all-embracing knowledge.

The very name given to the highest institutions

of learning reminds us, that from antiquity to and

throughout many centuries the universal aspect

has been the only one to be given full credit. But

the spread, both in and width and depth, of the

multifarious branches of knowledge by during

the last hundred odd years has confronted us

with a queer dilemma. We feel clearly that we

are only now beginning to acquire reliable

material for welding together the sum total of all

that is known into a whole; but, on the other

hand, it has become next to impossible for a

single mind fully to command more than a small

specialized portion of it. I can see no other

escape from this dilemma (lest our true who aim

be lost for ever) than that some of us should

venture to embark on a synthesis of facts and

theories, albeit with second-hand and incomplete

knowledge of some of them -and at the risk of

making fools of ourselves. So much for my

apology. The difficulties of language are not

negligible. One's native speech is a closely fitting

garment, and one never feels quite at ease when

it is not immediately available and has to be

replaced by another. My thanks are due to Dr

Inkster (Trinity College, Dublin), to Dr Padraig

Browne (St Patrick's College, Maynooth) and,

last but not least, to Mr S. C. Roberts. They were

put to great trouble to fit the new garment on me

and to even greater trouble by my occasional

reluctance to give up some 'original' fashion of

my own. Should some of it have survived the

mitigating tendency of my friends, it is to be put

at my door, not at theirs. The head-lines of the

numerous sections were originally intended to be

marginal summaries, and the text of every

chapter should be read in continuo. E.S.

Dublin September 1944

Homo liber nulla de re minus quam de morte

cogitat; et ejus sapientia non mortis sed vitae

meditatio est. SPINOZA'S Ethics, Pt IV, Prop.

67

(There is nothing over which a free man ponders

less than death; his wisdom is, to meditate not on

death but on life.)

CHAPTER 1

The Classical Physicist's Approach to the Subject

This little book arose from a course of public

lectures, delivered by a theoretical physicist to an

audience of about four hundred which did not

substantially dwindle, though warned at the

outset that the subject-matter was a difficult one

and that the lectures could not be termed popular,

even though the physicist’s most dreaded

weapon, mathematical deduction, would hardly

be utilized. The reason for this was not that the

subject was simple enough to be explained

without mathematics, but rather that it was much

too involved to be fully accessible to

mathematics. Another feature which at least

1

induced a semblance of popularity was the

lecturer's intention to make clear the fundamental

idea, which hovers between biology and physics,

to both the physicist and the biologist. For

actually, in spite of the variety of topics involved,

the whole enterprise is intended to convey one

idea only -one small comment on a large and

important question. In order not to lose our way,

it may be useful to outline the plan very briefly

in advance. The large and important and very

much discussed question is: How can the events

in space and time which take place within the

spatial boundary of a living organism be

accounted for by physics and chemistry? The

preliminary answer which this little book will

endeavor to expound and establish can be

summarized as follows: The obvious inability of

present-day physics and chemistry to account for

such events is no reason at all for doubting that

they can be accounted for by those sciences.

STA

TISTICAL PHYSICS. THE

FUNDAMENTAL W DIFFERENCE IN

STRUCTURE

That would be a very trivial remark if it were

meant

only

to

stimulate

the

hope

of

achieving

in

the

future what has not been achieved in the past.

But the meaning is very much more positive, viz.

that the inability, up to the present moment, is

amply accounted for. Today, thanks to the

ingenious work of biologists, mainly of

geneticists, during the last thirty or forty years,

enough is known about the actual material

structure of organisms and about their

functioning to state that, and to tell precisely

why present-day physics and chemistry could not

possibly account for what happens in space and

time within a living organism. The arrangements

of the atoms in the most vital parts of an

organism and the interplay of these arrangements

differ in a fundamental way from all those

arrangements of atoms which physicists and

chemists have hitherto made the object of their

experimental and theoretical research. Yet the

difference which I have just termed fundamental

is of such a kind that it might easily appear slight

to anyone except a physicist who is thoroughly

imbued with the knowledge that the laws of

physics and chemistry are statistical throughout.

For it is in relation to the statistical point of view

that the structure of the vital parts of living

organisms differs so entirely from that of any

piece of matter that we physicists and chemists

have ever handled physically in our laboratories

or mentally at our writing desks. It is well-nigh

unthinkable that the laws and regularities thus

discovered should happen to apply immediately

to the behaviour of systems which do not exhibit

the structure on which those laws and regularities

are based. The non-physicist cannot be expected

even to grasp let alone to appreciate the

relevance of the difference in ‘statistical

struc

ture’ stated in terms so abstract as I have

just used. To give the statement life and colour,

let me anticipate what will be explained in much

more detail later, namely, that the most essential

part of a living cell-the chromosome fibre may

suitably be called an aperiodic crystal. In physics

we have dealt hitherto only with periodic crystals.

To a humble physicist's mind, these are very

interesting and complicated objects; they

constitute one of the most fascinating

and complex material structures by which

inanimate nature puzzles his wits. Yet, compared

with the aperiodic crystal, they are rather plain

and dull. The difference in structure is of the

same kind as that between an ordinary wallpaper

in which the same pattern is repeated again and

again in regular periodicity and a masterpiece of

embroidery, say a Raphael tapestry, which shows

no dull repetition, but an elaborate, coherent,

meaningful design traced by the great master. In

calling the periodic crystal one of the most

complex objects of his research, I had in mind

the physicist proper. Organic chemistry, indeed,

in investigating more and more complicated

2

molecules, has come very much nearer to that

'aperiodic crystal' which, in my opinion, is the

material carrier of life. And therefore it is small

wonder that the organic chemist has already

made large and important contributions to the

problem of life, whereas the physicist has made

next to none.

THE NAIVE PHYSICIST'S APPROACH TO

THE SUBJECT

After having thus indicated very briefly the

general idea -or rather the ultimate scope -of our

investigation, let me describe the line of attack. I

propose to develop first what you might call 'a

naive physicist's ideas about organisms', that is,

the ideas which might arise in the mind of a

physicist who, after having learnt his physics and,

more especially, the statistical foundation of his

science, begins to think about organisms and

about the way they behave and function and who

comes to ask himself conscientiously whether he,

from what he has learnt, from the point of view

of his comparatively simple and clear and

humble science, can make any relevant

contributions to the question. It will turn out that

he can. The next step must be to f compare his

theoretical anticipations with the biological facts.

It will then turn out that -though on the whole his

ideas seem quite sensible -they need to be

appreciably amended. In this way we shall

gradually approach the correct view -or, to put it

more modestly, the one that I propose as the

correct one. Even if I should be right in this, I do

not know whether my way of approach is really

the best and simplest. But, in short, it was mine.

The 'naive physicist' was myself. And I could not

find any better or clearer way towards the goal

than my own crooked one.

WHY ARE THE ATOMS SO SMALL?

A good method of developing 'the naive

physicist's ideas' is to start from the odd, almost

ludicrous, question: Why are atoms so small? To

begin with, they are very small indeed. Every

little piece of matter handled in everyday life

contains an enormous number of them. Many

examples have been devised to bring this fact

home to an audience, none of them more

impressive than the one used by Lord Kelvin:

Suppose that you could mark the molecules in a

glass of water; then pour the contents of the glass

into

the

ocean

and

stir

the

latter

thoroughly

so

as

to

distribute the marked molecules uniformly

throughout the seven seas; if then you took a

glass of water anywhere out of the ocean, you

would find in it about a hundred of your marked

molecules. The actual sizes of atoms lie between

about 1/5000 and 1/2000 the wave-length of

yellow light. The comparison is significant,

because the wave-length roughly indicates the

dimensions of the smallest grain still

recognizable in the microscope. Thus it will be

seen that such a grain still contains thousands of

millions of atoms. Now, why are atoms so

small? Clearly, the question is an evasion. For it

is not really aimed at the size of the atoms. It is

concerned with the size of organisms, more

particularly with the size of our own corporeal

selves. Indeed, the atom is small, when referred

to our civic unit of length, say the yard or the

metre. In atomic physics one is accustomed to

use the so-called Angstrom (abbr. A), which is

the 10lOth part of a metre, or in decimal notation

0. metre. Atomic diameters range

between 1 and 2A. Now those civic units (in

relation to which the atoms are so small) are

closely related to the size of our bodies. There is

a story tracing the yard back to the humour of an

English king whom his councillors asked what

unit to adopt -and he stretched out his arm

sideways and said: 'Take the distance from the

middle of my chest to my fingertips, that will do

all right.' True or not, the story is significant for

our purpose. The king would naturally I indicate

a length comparable with that of his own body,

knowing that anything else would be very

3

inconvenient. With all his predilection for the

Angstrom unit, the physicist prefers to be told

that his new suit will require six and a half yards

of tweed -rather than sixty-five thousand

millions of Angstroms of tweed. It thus being

settled that our question really aims at the ratio

of two lengths -that of our body and that of the

atom - with an incontestable priority of

independent existence on the side of the atom,

the question truly reads: Why must our bodies be

so large compared with the atom? I can imagine

that many a keen student of physics or chemistry

may have deplored the fact that everyone of our

sense organs, forming a more or less substantial

part of our body and hence (in view of the

magnitude of the said ratio) being itself

composed of innumerable atoms, is much too

coarse to be affected by the impact of a single

atom. We cannot see or feel or hear the single

atoms. Our hypotheses with regard to them differ

widely from the immediate findings of our gross

sense organs and cannot be put to the test of

direct inspection. Must that be so? Is there an

intrinsic reason for it? Can we trace back this

state of affairs to some kind of first principle, in

order to ascertain and to understand why nothing

else is compatible with the very laws of

Nature? Now this, for once, is a problem which

the physicist is able to clear up completely. The

answer to all the queries is in the affirmative.

THE WORKING OF AN ORGANISM

REQUIRES EXACT PHYSICAL LAWS

If it were not so, if we were organisms so

sensitive that a single atom, or even a few atoms,

could make a perceptible impression on our

senses -Heavens, what would life be like! To

stress one point: an organism of that kind would

most certainly not be capable of developing the

kind of orderly thought which, after passing

through a long sequence of earlier stages,

ultimately results in forming, among many other

ideas, the idea of an atom. Even though we select

this one point, the following considerations

would essentially apply also to the functioning of

organs other than the brain and the sensorial

system. Nevertheless, the one and only thing of

paramount interest to us in ourselves is, that we

feel and think and perceive. To the physiological

process which is responsible for thought and

sense all the others play an auxiliary part, at least

from the human point of view, if not from that of

purely objective biology. Moreover, it will

greatly facilitate our task to choose for

investigation the process which is closely

accompanied by subjective events, even though

we are ignorant of the true nature of this close

parallelism. Indeed, in my view, it lies outside

the range of natural science and very probably of

human understanding altogether. We are thus

faced with the following question: Why should

an organ like our brain, with the sensorial system

attached to it, of necessity consist of an

enormous number of atoms, in order that its

physically changing state should be in close and

intimate correspondence with a highly developed

thought? On what grounds is the latter task of the

said organ incompatible with being, as a whole

or in some of its peripheral parts which interact

directly with the environment, a mechanism

sufficiently refined and sensitive to respond to

and register the impact of a single atom from

outside? The reason for this is, that what we call

thought (1) is itself an orderly thing, and (2) can

only be applied to material, i.e. to perceptions or

experiences, which have a certain degree of

orderliness. This has two consequences. First, a

physical

organization,

to

be

in

close

correspondence

with thought (as my brain is

with my thought) must be a very well-ordered

organization, and that means that the events that

happen within it must obey strict physical laws,

at least to a very high degree of accuracy.

Secondly, the physical impressions made upon

that physically well-organized system by other

bodies from outside, obviously correspond to the

4

perception and experience of the corresponding

thought, forming its material, as I have called it.

Therefore, the physical interactions between our

system and others must, as a rule, themselves

possess a certain degree of physical orderliness,

that is to say, they too must obey strict physical

laws to a certain degree of accuracy.

PHYSICAL LAWS REST ON ATOMIC

STA

TISTICS AND ARE THEREFORE ONL

Y

APPROXIMATE

And why could all this not be fulfilled in the case

of an organism composed of a moderate number

of atoms only and sensitive already to the impact

of one or a few atoms only? Because we know

all atoms to perform all the time a completely

disorderly heat motion, which, so to speak,

opposes itself to their orderly behaviour and does

not allow the events that happen between a small

number of atoms to enrol themselves according

to any recognizable laws. Only in the co-

operation of an enormously large number of

atoms do statistical laws begin to operate and

control the behaviour of these assemblies with an

accuracy increasing as the number of atoms

involved increases. It is in that way that the

events acquire truly orderly features. All the

physical and chemical laws that are known to

play an important part in the life of organisms

are of this statistical kind; any other kind of

lawfulness and orderliness that one might think

of is being perpetually disturbed and made

inoperative by the unceasing heat motion of the

atoms.

THEIR PRECISION IS BASED ON THE

LARGE OF NUMBER OF ATOMS

INTERVENING

FIRST EXAMPLE (PARAMAGNETISM)

Let me try to illustrate this by a few examples,

picked somewhat at random out of thousands,

and possibly not just the best ones to appeal to a

reader who is learning for the first time about

this condition of things -a condition which in

modern physics and chemistry is as fundamental

as, say, the fact that organisms are composed of

cells is in biology, or as Newton's Law in

astronomy, or even as the series of integers, 1, 2,

3, 4, 5, ...in mathematics. An entire newcomer

should not expect to obtain from the following

few pages a full understanding and appreciation

of the subject, which is associated with the

illustrious names of Ludwig Boltzmann and

Willard Gibbs and treated in textbooks under the

name of 'statistical thermodynamics'. If you fill

an oblong quartz tube with oxygen gas and put it

into a magnetic field, you find that the gas is

magnetized. The magnetization is due to the fact

that the oxygen molecules are little magnets and

tend to orientate themselves parallel to the field,

like a compass needle. But you must not think

that they actually all turn parallel. For if you

double the field, you get double the

magnetization in your oxygen body, and that

proportionality goes on to extremely high field

strengths, the magnetization increasing at the rate

of the field you apply. This is a particularly clear

example of a purely statistical law. The

orientation the field tends to produce is

continually counteracted by the heat motion,

which works for random orientation. The effect

of this striving is, actually, only a small

preference for acute over obtuse angles between

the dipole axes and the field. Though the single

atoms change their orientation incessantly, they

produce on the average (owing to their enormous

number) a constant small preponderance of

orientation in the direction of the field and

proportional to it. This ingenious explanation is

due to the French physicist P. Langevin. It can

be checked in the following way. If the observed

weak magnetization is really the outcome of rival

tendencies, namely, the magnetic field, which

aims at combing all the molecules parallel, and

the heat motion, which makes for random

orientation, then it ought to be possible to

5

increase the magnetization by weakening the

heat motion, that is to say, by lowering the

temperature, instead of reinforcing the field. That

impact of one single molecule of those which

hammer their surface in perpetual impacts. They

are thus knocked about and can only on the

is confirmed by experiment, which gives the

magnetization inversely proportional to the

absolute temperature, in quantitative agreement

with theory (Curie's law). Modern equipment

even enables us, by lowering the temperature, to

reduce the heat motion to such insignificance

that the orientating tendency of the magnetic

field can assert itself, if not completely, at least

sufficiently to produce a substantial fraction of

'complete magnetization'. In this case we no

longer expect that double the field strength will

double the magnetization, but that the latter will

increase less and less with increasing field,

approaching what is called 'saturation'. This

expectation

too

is

quantitatively

confirmed

experiment. Notice that this behaviour entirely

depends on the large numbers of molecules

which co-operate in producing the observable

magnetization. Otherwise, the latter would not be

an constant at all, but would, by fluctuating quite

irregularly of from one second to the next, bear

witness to the vicissitudes of pe the contest

between heat motion and field.

SECOND EXAMPLE (BROWNIAN

MOVEMENT, DIFFUSION)

If you fill the lower part of a closed glass vessel

with fog, pt consisting of minute droplets, you

will find that the upper or boundary of the fog

gradually sinks, with a well-defined velocity,

determined by the viscosity of the air and the

size and the specific gravity of the droplets. But

if you look at one of the droplets under the

microscope you find that it does not permanently

sink with constant velocity, but performs a very

irregular movement, the so-called Brownian

movement, which corresponds to a regular

sinking only on the average. Now these droplets

are not atoms, but they are sufficiently small and

light to be not entirely insusceptible to the

average follow the influence of gravity. This

example shows what funny and disorderly

experience we should have if our senses were

susceptible to the impact of a few molecules only.

There are bacteria and other organisms so small

that they are strongly affected by this

phenomenon. Their movements are determined

by the thermic whims of the surrounding

medium; they have no choice. If they had some

locomotion of their own they might nevertheless

succeed in on getting from one place to another -

but with some difficulty, since the heat motion

tosses them like a small boat in a rough sea. A

phenomenon very much akin to Brownian

by

movement is that of diffusion. Imagine a vessel

filled with a fluid, say water, with a small

amount of some coloured substance dissolved in

it, say potassium permanganate, not in uniform

concentration, but rather as in Fig. 4, where the

dots indicate the molecules of the dissolved

substance (permanganate) and the concentration

diminishes from left to right. If you leave this

system alone a very slow process of 'diffusion'

sets in, the at permanganate spreading in the

direction from left to right, that is, from the

places of higher concentration towards the places

of lower concentration, until it is equally

distributed of through the water. The remarkable

thing about this rather simple and apparently not

particularly interesting process is that it is in no

way due, as one might think, to any tendency or

force driving the permanganate molecules away

from the crowded region to the less crowded one,

like the population of a country spreading to

those parts where there is more elbow-room.

Nothing of the sort happens with our

permanganate molecules. Every one of them

behaves quite independently of all the others,

which it very seldom meets. Everyone of them,

whether in a crowded region or in an empty one,

6

suffers the same fate of being continually

knocked about by the impacts of the water

molecules and thereby gradually moving on in

an unpredictable direction -sometimes towards

the higher, sometimes towards the lower,

concentrations, sometimes obliquely. The kind

of motion it performs has often been compared

with that of a blindfolded person on a large

surface imbued with a certain desire of 'walking',

but without any preference for any particular

direction, and so changing his line

continuously. That this random walk of the

permanganate molecules, the same for all of

them, should yet produce a regular flow towards

the smaller concentration and ultimately make

for uniformity of distribution, is at first sight

perplexing -but only at first sight. If you

contemplate in Fig. 4 thin slices of

approximately constant concentration, the

permanganate molecules which in a given

moment are contained in a particular slice will,

by their random walk, it is true, be carried with

equal probability to the right or to the left. But

precisely in consequence of this, a plane

separating two neighbouring slices will be

crossed by more molecules coming from the left

than in the opposite direction, simply because to

the left there are more molecules engaged in

random walk than there are to the right. And as

long as that is so the balance will show up as a

regular flow from left to right, until a uniform

distribution is reached. When these

considerations are translated into mathematical

language the exact law of diffusion is reached in

the form of a partial differential equation

§

p/§

t= DV2

P

which I shall not trouble the reader by explaining,

though its meaning in ordinary language is again

simple enough. The reason for mentioning the

stern 'mathematically exact' law here, is to

emphasize that its physical exactitude must

nevertheless

be

challenged

in

every

particular

application. Being based on pure chance, its

validity is only approximate. If it is, as a rule, a

very good approximation, that is only due to the

enormous number of molecules that co- operate

in the phenomenon. The smaller their number,

the larger the quite haphazard deviations we

must expect and they can be observed under

favourable circumstances.

THIRD EXAMPLE (LIMITS OF ACCURACY

OF MEASURING)

The last example we shall give is closely akin to

the second c one, but has a particular interest. A

light body, suspended by a long thin fibre in

equilibrium orientation, is often used by

physicists to measure weak forces which deflect

it from that position of equilibrium, electric,

magnetic or gravitational forces being applied so

as to twist it around the vertical axis. (The light

body must, of course, be chosen appropriately

for ! the particular purpose.) The continued effort

to improve the accuracy of this very commonly

used device of a 'torsional balance', has

encountered a curious limit, most interesting in

itself. In choosing lighter and lighter bodies and

thinner and longer fibres -to make the balance

susceptible to weaker and weaker forces -the

limit was reached when the suspended body

became noticeably susceptible to the impacts of

the heat motion of the surrounding molecules

and began to perform an incessant, irregular

'dance' about its equilibrium position, much like

the trembling of the droplet in the second

example. Though this behaviour sets no absolute

limit to the accuracy of measurements obtained

with the balance, it sets a practical one. The

uncontrollable effect of the heat motion

competes with the effect of the force to be

measured and makes the t' law single deflection

observed insignificant. You have to multiply

never- observations, in order to eliminate the

7

effect of the Brownian Being movement of your

instrument. This example is, I think, particularly

illuminating in our present investigation. For our

to the organs of sense, after all, are a kind of

instrument. We can see in the how useless they

would be if they became too sensitive.

THE

/n RULE

So much for examples, for the present. I will

merely add that there is not one law of physics or

chemistry, of those that are relevant within an

organism or in its interactions with its

environment, that I might not choose as an

example. The second detailed explanation might

be more complicated, but the salient point would

always be the same and thus the description

would become monotonous. But I should like to

add one very important quantitative statement

concerning the degree of inaccuracy to be

expected in any physical law, the so-called /n

law. I will first illustrate it by a simple example

and then generalize it. If I tell you that a certain

gas under certain conditions of pressure and

temperature has a certain density, and if I

expressed this by saying that within a certain

volume (of a size relevant for some experiment)

there are under these conditions just n molecules

of the gas, then you might be sure that if you

could test my statement in a particular moment

of time, you would find it inaccurate, the

departure being of the order of

/n. Hence if the

number n = 100, you would find a departure of

about 10, thus relative error = 10%. But n = 1

million, you would be likely to find a departure

of about 1,000, thus relative error = 110%. Now,

roughly speaking, this statistical law is quite

general. The laws of physics and physical

chemistry are inaccurate within a probable

relative error of the order of 1/ /Vn, where n is

the number of molecules that co-operate to bring

about that law -to produce its validity within

such regions of space or time (or both) that

matter, for some considerations or for some

particular experiment. You see from this again

that an organism must have a comparatively

gross structure in order to enjoy the benefit of

fairly accurate laws, both for its internal life and

for its , interplay with the external world. For

otherwise the number of co-operating particles

would be too small, the 'law' too inaccurate. The

particularly exigent demand is the square root.

For though n is a reasonably large

number, an accuracy of Just 1in 1,000 is not

overwhelmingly good, If a thing claims the

dignity of being a 'Law of Nature.

CHAPTER 2

The Hereditary Mechanism

THE CLASSICAL PHYSICIST'S

EXPECTATION, FAR FROM BEING

TRIVIAL, IS WRONG

Thus we have come to the conclusion that an

organism and all the biologically relevant

processes that it experiences must have an

extremely 'many-atomic' structure and must be

safeguarded against haphazard, 'single- atomic'

events attaining too great importance. That, the

'naive physicist' tells us, is essential, so that the

organism may, so to speak, have sufficiently

accurate physical laws on which to draw for setting up

its marvellously regular and well-

ordered working. How do these conclusions,

reached, biologically speaking, a priori (that is,

from the purely physical point of view), fit

in with actual biological facts? At first sight one

is inclined to think that the conclusions are little

more than trivial. A biologist of, say, thirty years

ago might have said that, although it was quite

suitable for a popular lecturer to emphasize the

importance, in the organism as elsewhere, of

statistical physics, the point was, in fact, rather a

familiar truism. For, naturally, not only the body

of an adult individual of any higher species, but

every single cell composing it contains a

'cosmical' number of single atoms of every kind.

8

And every particular physiological process that

we observe, either within the cell or in its

interaction with the cell environment, appears -or

appeared thirty years ago -to involve such

enormous numbers of single atoms and single

atomic processes that all the relevant laws of

physics and physical chemistry would be

safeguarded even under the very exacting

demands of statistical physics in respect of large

numbers; this demand illustrated just now by the

/n rule. Today, we know that this opinion would

have been a mistake. As we shall presently see,

incredibly small groups of atoms, much too

small to display exact statistical laws, do play a

dominating role in the very orderly and lawful

events within a living organism. They have

control of the observable large-scale features

which the organism acquires in the course of its

development, they determine important

characteristics of its functioning; and in all this

very sharp and very strict me biological laws are

displayed. I must begin with giving a brief

summary of the situation in biology, more

especially in genetics -in other words, I have to

summarize the present state of knowledge in a

subject of which I am not a master. This cannot

be helped and I apologize, particularly to any

biologist, for the dilettante character of my

summary. On the other hand, I beg leave to put

the prevailing ideas before you more or less

dogmatically. A poor theoretical physicist could

not be expected to produce anything like a

competent survey of the experimental evidence,

which consists of a large number of long and

beautifully interwoven series of breeding

experiments of truly unprecedented ingenuity on

the one hand and of direct observations of the

living cell, conducted with all the refinement of

modern microscopy, on the other.

THE HEREDITARY CODE-SCRIPT

(CHROMOSOMES)

Let me use the word 'pattern' of an organism in

the sense in be which the biologist calls it 'the

four-dimensional pattern', meaning not only the

structure and functioning of that organism in the

adult, or in any other particular stage, but the

whole of its ontogenetic development from the

fertilized egg the cell to the stage of maturity,

when the organism begins to reproduce itself.

Now, this whole four-dimensional pattern is

known to be determined by the structure of that

one cell, the fertilized egg. Moreover, we know

that it is essentially determined by the structure

of only a small part of that cell, its large nucleus.

This nucleus, in the ordinary 'resting state' of the

cell, usually appears as a network of chromatine,

distributed over the cell. But in the vitally

important processes of cell division (mitosis and

meiosis, see below) it is seen to consist of a set

of particles, usually fibre-shaped or rod-like,

called the chromosomes, which number 8 or 12

or, in man, 48. But I ought really to have written

these illustrative numbers as 2 X 4, 2 X 6, ..., 2 X

24, ..., and I ought to have spoken of two sets, in

order to use the expression in the customary

strict meaning of the biologist. For though the

single chromosomes are sometimes clearly

distinguished and individualized by shape and

size, the two sets are almost entirely alike. As we

have shall see in a moment, one set comes from

the mother (egg cell), one from the father

(fertilizing spermatozoon). It is these

chromosomes, or probably only an axial skeleton

fibre of what we actually see under the

microscope as the chromosome, that contain in

some kind of code-script the entire pattern of the

individual's future development and of its

functioning in the mature state. Every complete

set of chromosomes contains the full code; so

there are, as a rule, two copies of the latter in the

fertilized egg cell, which forms the earliest stage

of the future individual. In calling the structure

of the chromosome fibres a code-script we mean

that the all-penetrating mind, once conceived by

Laplace, to which every causal connection lay

9

immediately open, could tell from their structure

whether the egg would develop, under suitable

conditions, into a black cock or into a speckled

hen, into a fly or a maize plant, a rhododendron,

a beetle, a mouse or a woman. To which we may

add, that the appearances of the egg cells are

very often remarkably similar; and even when

they are not, as in the case of the comparatively

gigantic eggs of birds and reptiles, the difference

is

not

been

so

much

the

relevant

structures

as

in

the

nutritive material which in these cases is

added for obvious reasons. But the term

code-script is, of course, too narrow. The

chromosome structures are at the same time

instrumental in bringing about the development

they foreshadow. They are law-code and

executive power -or, to use another simile, they

are architect's plan and builder's craft -in one.

GROWTH OF THE BODY BY CELL

DIVISION (MITOSIS)

How do the chromosomes behave in ontogenesis?

The growth of an organism is effected by

consecutive cell met divisions. Such a cell

division is called mitosis. It is, in the life of a cell,

not such a very frequent event as one might

expect, considering the enormous number of

cells of which our body is composed. In the

beginning the growth is rapid. The egg divides

into two 'daughter cells' which, at the next step,

will produce a generation of four, then of 8, 16,

32, 64, ..., etc. The frequency of division will not

remain exactly the same in all parts of the

growing body, and that will break the regularity

of these numbers. But from their rapid increase

we infer by an easy computation that on the

average as few as 50 or 60 successive divisions

suffice to produce the number of cells in a grown

man -or, say, ten times the number, taking into

account the exchange of cells during lifetime.

Thus, a body cell of mine is, on the average, only

the 50th or 60th 'descendant' of the egg that was I.

IN MITOSIS EVERY CHROMOSOME IS

DUPLICATED

How do the chromosomes behave on mitosis?

They duplicate -both sets, both copies of the

code, duplicate. The process has been intensively

studied under the microscope and is of

paramount interest, but much too involved to

describe here in detail. The salient point is that

each of the two 'daughter cells' gets a dowry of

two further complete sets of chromosomes

exactly similar to those of the parent cell. So all

the body cells are exactly alike as regards their

chromosome treasure. However little we

understand the device we cannot but think that it

must be in some way very relevant to the

functioning of the organism, that every single

cell, even a less important one, should be in

possession of a complete (double) copy of the

code-script. Some time ago we were told in the

newspapers that in his African campaign General

Montgomery made a point of having every

single soldier of his army meticulously informed

of all his designs. If that is true (as it conceivably

might be, considering the high intelligence and

reliability of his troops) it provides an excellent

analogy to our case, in which the corresponding

fact certainly is literally true. The most

surprising fact is the doubleness of the

chromosome set, maintained throughout the

mitotic divisions. That it is the outstanding

feature of the genetic mechanism is most

strikingly revealed by the one and only departure

from the rule, which we have now to discuss.

REDUCTIVE DIVISION (MEIOSIS) AND

FERTILIZATION (SYNGAMY)

Very soon after the development of the

individual has set in, a group of cells is reserved

for producing at a later stage the so-called

gametes, the sperm cells or egg cells, as the case

may be, needed for the reproduction of the

individual in maturity. 'Reserved' means that

they do not serve other purposes in the meantime

10

and suffer many fewer mitotic divisions. The

exceptional or reductive division (called meiosis)

is the one by which eventually, on maturity, the

gametes posed to are produced from these

reserved cells, as a rule only a short time before

syngamy is to take place. In meiosis the double

chromosome set of the parent cell simply

separates into two single sets, one of which goes

to each of the two daughter cells, the gametes. In

other words, the mitotic doubling of the number

of chromosomes does not take place in meiosis,

the number remains constant and thus every

gamete receives only half -that is, only one

complete copy of the code, not two, e.g. in man

only 24:, not 2 X 24: = 4:8. Cells with only one

chromosome set are called haploid (from Greek

α

π

< br>λ

ο

?

χ, single). Thus the gametes are

haploid,

the ordinary body cells diploid (from Greek

Ο

π

λ

?

χ, double). Individuals with three,

four, ...or generally speaking with many

chromosome sets in all their body cells occur

occasionally; the latter are then called triploid,

tetraploid, ..., polyploid. In the act of syngamy

the male gamete (spermatozoon) and the female

gamete (egg), both haploid cells, coalesce to

form the fertilized egg cell, which is thus diploid.

One of its chromosome sets comes from the

mother, one from the father.

HAPLOID INDIVIDUALS

One other point needs rectification. Though not

indispensable for our purpose it is of real interest,

since it shows that actually a fairly complete

code-script of the 'pattern' is contained in every

single set of chromosomes. There are instances

of

meiosis

not

being

followed

shortly

after

by

fertilization, the haploid cell (the 'gamete')

under- going meanwhile numerous mitotic cell

divisions, which result in building up a complete

haploid individual. This is the case in the male

bee, the drone, which is produced

parthenogenetically, that is, from non- fertilized

and therefore haploid eggs of the queen. The

drone has no father! All its body cells are haploid.

If you please, you may call it a grossly

exaggerated spermatozoon; and actually, as

everybody knows, to function as such happens to

be its one and only task in life. However, that is

perhaps a ludicrous point of view. For the case is

not two quite unique. There are families of plants

in which the haploid gamete which is produced

by meiosis and is called a spore in the such cases

falls to the ground and, like a seed, develops into

a the true haploid plant comparable in size with

the diploid.

Fig. 5 is a rough sketch of a moss,

well known in our forests. The leafy lower part is

the haploid plant, called the gametophyte,

because at its upper end it develops sex organs

and gametes, which by mutual fertilization

produce in the ordinary way the diploid plant,

the bare stem with the capsule at the top. This is

called the sporophyte, because it produces, by

meiosis, the spores in the capsule at the top.

When the capsule opens, the spores fall to the

ground and develop into a leafy stem, etc. The

course of events is appropriately called

alternation of generations. You may, if you

choose, look upon the ordinary case, man and the

animals, in the same way. But the 'gametophyte'

is then as a rule a very short-lived, unicellular

generation, spermatozoon or egg cell as the case

may be. Our body corresponds to the sporophyte.

Our 'spores' are the reserved cells from which, by

meiosis, the unicellular generation springs.

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 owes just half of his

inheritance to his mother, half of it to his father.

11

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 every one of my

maternal chromosomes. Moreover, all the 48

issues are fi entirely independent. Even if it were

known that my paternal it 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. LOCA

TION 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

tacitly assumed, or even explicitly stated, that a

particular chromosome as a whole was either

from the grandfather or back to from the

grandmother; in other words that the single

chromosomes are passed on undivided. In actual

fact they are not, or on one of not always. Before

being separated in the reductive division, No.5

my say the one in the father's body, any two

'homologous' chromosomes come into close

contact with each other, during chance in which

they sometimes exchange entire portions in the

way illustrated in Fig. 6. By this process, called

'crossing-over', days later two properties situated

in the respective parts of that chromosome 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 issues are frequent, has

provided us with invaluable information

regarding the location of properties in the

chromosomes. For a full account we should have

to draw on conceptions not introduced 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 in

mixing together, no descendant receiving one of

them without receiving the other as well; but two

properties, due to different it has been

chromosomes,

would

either

stand

a

50:50

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 off-spring in

extended breeding experiments, suitably laid out

for at 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

12

'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 h 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 it between any two of

that group, so that there is little doubt h 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 understand 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'. Now, 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 by property,

to my view, is really the fundamental concept

rather than property itself, notwithstanding the

apparent linguistic out for and logical

contradiction of this statement. The differences

of Its the 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 each

colour.

MAXIMUM SIZE OF A GENE

We have just introduced the term gene for the

hypothetical same material carrier of a definite

hereditary feature. We must now the stress two

points which will be highly relevant to our every

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 chromosome 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

in this 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,

13

measured in a normal-sized cell by their number

(2,000) he finds the volume of a gene equal to a

cube of edge 300 A. Considering the roughness of the

that what is passed on by the parent to the child

is not just this or that peculiarity, a hooked nose,

short fingers, a tendency to rheumatism,

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 /v 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.

It is probably a large protein molecule, in which

every atom, every radical, every heterocyclic

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

Let us now turn to the second highly relevant

question: 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

of the almost absolute. For we must not forget

haemophilia, 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 all

the visible and manifest nature of the individual,

which is reproduced without appreciable change

for generations, permanent within centuries -

though not within tens of thousands of years -and

borne at each transmission by the material in a

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 if all possess the

power of acquiring considerable knowledge

about it. I think it possible that this knowledge

may advance to little just a short of a complete

understanding -of the first marvel. The second

may well be beyond human understanding.

CHAPTER 3

Mutations

'JUMP-LIKE'

MUTATIONS -THE

WORKING- GROUND OF NATURAL

SELECTION

The general facts which we have just put forward

in evidence of the durability claimed for the gene

structure, are perhaps too familiar to us to be

striking or to be regarded as convincing. Here,

for once, the common saying that exceptions

prove the rule is actually true. If there were no

exceptions to the likeness between children and

parents, we should have been deprived not only

of all those beautiful experiments which have

revealed to us the detailed mechanism of

heredity,

but also of that grand, million-fold

experiment of Nature, which forges the species

14

by natural selection and survival of the fittest.

Let me take this last important subject as the

starting-point for presenting the relevant facts -

again with an apology and a reminder that I am

not a biologist. We know definitely, today, that

Darwin was mistaken in regarding the small,

continuous, accidental variations, that are bound

to occur even in the most homogeneous

population, as the material on which natural

selection works. For it has been proved that they

are not inherited. The fact is important enough to

be illustrated briefly. If you take a crop of

pure-strain barley, and measure, ear by ear, the

length of its awns and plot the result of your

statistics, you will get a bell-shaped curve as

shown in Fig. 7, where the number of ears with a

definite length of awn is plotted against the

length. In other words: a definite medium length

prevails, and deviations in either direction occur

with certain frequencies. Now pick out a group

of ears (as indicated by blackening) with awns

noticeably beyond the average, but sufficient in

number to be sown in a field by themselves and

give a new crop. In making the same statistics

for this, Darwin would have expected to find the

corresponding curve shifted to the right. In other

words, he would have expected to produce by

selection an increase of the average length of the

awns. That is not the case, if a truly pure-bred strain of

barley has been used. The new

statistical curve, obtained from the selected crop,

is identical with the first one, and the same

would be the case if ears with particularly short

awns had been selected for seed. Selection has

no effect -because the small, continuous

variations are not inherited. They are obviously

not based on the structure of the hereditary

substance, they are accidental. But about forty

years ago the Dutchman de Vries discovered that

in the offspring even of thoroughly pure-bred

stocks, a very small number of individuals, say

two or three in tens of thousands, turn up with

small but 'jump- like' changes, the expression

‘

jump-like' not meaning that the change is so

very considerable, but that there is a

discontinuity inasmuch as there are no

intermediate forms between the unchanged and

the few changed. De Vries called that a mutation.

The significant fact is the discontinuity. It

reminds a physicist of quantum theory -no

intermediate energies occurring between two

neighbouring energy levels. He would be

inclined to call de Vries's mutation theory,

figuratively, the quantum theory of biology. We

shall see later that this is much more

than figurative. The mutations are actually due to

quantum jumps in the gene molecule. But

quantum theory was but two years old when de

Vries first published his discovery, in 1902.

Small wonder that it took another generation to

discover the intimate connection!

THEY BREED TRUE, THAT IS, THEY ARE

PERFECTL

Y INHERITIED

Mutations are inherited as perfectly as the

original, correctly unchanged characters were.

To give an example, in the first crop of barley

considered above a few ears might turn up

with awns considerably outside the range of

variability shown in Fig. 7, say with no awns at

all. They might represent a de Vries mutation

and would then breed perfectly true, that is to

We must say, all their descendants would be

equally awnless. Hence a mutation is definitely a

change in the hereditary without treasure and has

to be accounted for by some change in the

hereditary substance. Actually most of the

important breeding experiments, which have

revealed to us the mechanism of by a heredity,

consisted in a careful analysis of the

offspring obtained by crossing, according to a

preconceived plan, mutated (or, in many cases,

multiply mutated) with non-mutated or with

differently mutated individuals. On the other

hand, by virtue of their breeding true, mutations

are a suitable material on which natural selection

15

may work and produce the species as described

by Darwin, by eliminating the unfit and letting

the fittest survive. In Darwin's theory, you

just have to substitute 'mutations' for his 'slight

accidental variations' (just as quantum theory

substitutes 'quantum jump' for 'continuous

transfer of energy'). In all other respects little

change was necessary in Darwin's theory, that is,

if I am correctly interpreting the view held by the

majority of biol ogists.

LOCALIZATION, RECESSIVITY AND

DOMINANCE

We must now review some other fundamental

facts and notions about mutations, again in a

slightly dogmatic manner, without showing

directly how they spring, one by one, from the

experimental evidence. We should expect a

definite observed mutation to be caused by a

change in a definite region in one of the

chromosomes. And so it is. It is important to

state that we know definitely, that it is a change

in one chromosome only, but not in the

corresponding 'locus' of the homologous

chromosome. Fig. 8 indicates this schematically,

the cross denoting the mutated a locus. The fact

that only one chromosome is affected is revealed

when the mutated individual (often called

'mutant') is crossed with a non-mutated one. For

exactly half of the offspring exhibit the mutant

character and half the normal one. That is what is

to be expected as a consequence of the

separation of the two chromosomes on meiosis

in the mutant as shown, very schematically, in

Fig. 9. This is a 'pedigree', representing every

individual (of three consecutive generations)

simply by the pair of chromosomes in question.

Please realize that if the mutant had both its

chromosomes affected, all the children would

receive the same (mixed) inheritance, different

from that of either parent. But experimenting in

this domain is not as simple as would appear

from what has just been said. It is complicated

by the second important fact, viz. that mutations

are very often latent. What does that mean? In

the mutant the two copies of the code-script are

no longer identical; they present two different

'readings' or 'versions', at any rate in that one

place. Perhaps it is well to point out at once that,

while it might be tempting, it would nevertheless

be entirely wrong to regard the original version

as 'orthodox', and the mutant version as 'heretic'.

We have to is regard them, in principle, as being

of equal right -for the normal characters have

also

arisen

from

mutations.

What

actually

happens

is

that the 'pattern' of the individual, as a

general rule, follows either the one or the other

rte version, which may be the normal or the

mutant one. The -version which is followed is

called dominant, the other, recessive; in other

words, the mutation is called dominant or

recessive, according to whether it is immediately

effective in changing the pattern or not.

Recessive mutations are even more frequent than

dominant ones and are very important, though at

first they do not show up at all. To affect the

pattern, they have to be present in both

chromosomes (see Fig. 10). Such individuals can

be produced when two equal recessive mutants

happen to be crossed with each other or when a

mutant is crossed with itself; this is possible in

hermaphroditic plants and even happens

spontaneously. An easy reflection shows that in

these cases about one-quarter of the offspring

will be of this type and thus visibly exhibit the

mutated pattern.

INTRODUCING SOME TECHNICAL

LANGUAGE

I think it will make for clarity to explain here a

few technical terms. For what I called 'version of

the code-script' -be it the original one or a mutant

one -the term 'allele' has been; adopted. When

the versions are different, as indicated in Fig. 8,

the individual is called heterozygous, with

respect to that locus. When they are equal, as in

16

the non-mutated individual or in the case of Fig.

10, they are called homozygous. Thus a recessive

allele influences the pattern only when

homozygous, whereas a dominant allele

produces the same pattern, whether homozygous

or only heterozygous. Colour is very often

dominant over lack of colour (or white). Thus,

for example, a pea will flower white only when it

has the 'recessive allele responsible for white' in

both chromosomes in question, when it is

'homozygous for white'; it will then breed true,

and all its descendants will be white. But one 'red

allele' (the other being white; 'heterozygous') will

make it flower red, and so will two red alleles

('homozygous'). The difference of the latter two

cases will only show up in the offspring,

when the heterozygous red will produce some

white descendants, and the homozygous red will

breed true. The fact that two individuals may be

exactly alike in their outward appearance, yet

differ in their inheritance, is so important that an

exact differentiation is desirable. The geneticist

says they have the same phenotype, but different

genotype. The contents of the preceding

paragraphs could thus be summarized in the brief,

but highly technical statement: 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 that 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 reed 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 of 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')

grand- children of mine who are first cousins.

These do not seem to be but 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 l 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

17

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, were 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 survive.

GENERAL AND HISTORICAL REMARKS

The fact that the recessive allele, when

heterozygous, is completely overpowered by the

dominant and produces no visible effects at all,

is amazing. It ought at least to mentioned that

there are exceptions to this behaviour. When

a 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

our 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 Augustininan Abbot

Gregor Mendel (1822-84). Mendel knew nothing

about mutations and chromosomes. In his

cloister gardens in Brunn (Brno) he made

experiments on the garden pea, of first 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

Brunn. 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

may (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 n, as 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

18

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.

MUTA

TIONS 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 ‘natural’ mutation can also

be induced by X-rays. In Drosophila many

special mutations recur spontaneously again and

to

you

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 say, on

'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 one '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. Timofeeff, in Biological Reviews, vol.

IX, 1934. To a considerable extent it refers to

that author's own beautiful work. The first law is

(I) 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 every

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

19

r-units, that is to say, provided you measure the

dosage by the total amount 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 processes

(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 1/1000 of

1/50000 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. Delbruck, in a

paper by Delbruck, N.W. Timofeeffand K.G

.

Zimmer, 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

Timofeeff 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 marriage between first cousins

might very this 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.

CHAPTER 4

The Quantum-Mechanical Evidence

Thus, aided by the marvellously subtle

instrument of X-rays (which, as the physicist

remembers, revealed thirty years ago really 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

20

possibly much less), and that value 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 In

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 limited 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 (l901-3). 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 each 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.

QUANTUM THEORY -DISCRETE STATES

–

QUANTUM JUMPS

21