Bacterial
Physiology

Edited by
Cc. H. Werkman

Department of Bacteriology, Iowa State College, Ames, Iowa

and

P. W. Wilson

Department of Bacteriology. University of Wisconsin,
Madison, Wisconsin

ACADEMIC PRESS INC. - PUBLISHERS
1951 - NEW YORK
r

~ name GR JOSHUA LEDERBERG

in the course of which, presumably, significant properties are unaltered.
That is, we postulate a uniform and conservative transmission of charac-
ters in heredity.

For some early bacteriologists, the limit of bacterial genetics was this
theory of perfect stability, or “monomorphism.” Unfortunately, as
Dubos (1945) points out, ‘‘the blind acceptance by several generations
of bacteriologists of the Cohn-Koch dogma of constancy of cell forms and
immutability of cultural characteristics discouraged for many years the
study of the problems of morphology, inheritance, and variation in
bacteria.’ Monomorphism is no longer acceptable, principally because
variations can no longer be dismissed as poor technique. But an equally
cogent objection to monomorphism is its inability to interpret the
differentiation of microbic species by evolutionary processes which leaves
the incredible alternative of special creation.

We now know that bacteria are liable to a nearly unbounded array of
hereditary variations that are of utmost importance in all areas of
bacteriological research. During the past decade, especially, the integra-
tion of the experimental data of bacterial genetics into a unified theory
that includes all living forms has rapidly approached consummation.

I. The Gene Theory

The existence of material within the cell especially concerned with
genetic functions can be inferred on general grounds from the cyclical
behavior of organisms (Muller, 1947). In higher animals, the life cycle
is outwardly apparent, involving an intricate developmental process from
the outwardly undifferentiated egg to the adult. The series of cycles,
egg-adult-egg-adult, suggests some system or substance which is acyclic
and whose continuity is responsible for the perpetuation of characters.
This substance would also have the property of reduplication, in parallel
with the proliferation of the organism at each cycle. This material is
called, collectively, the ‘‘genes.’’ The individual genetic unit or gene is
recognized, or rather defined, in a number of ways, the most pertinent
for the present being the control of a distinct and unique character. The
definition of an individual gene as an ultimate unit is however one of the
most mooted problems of contemporary genetics.

The cycles of bacteria are so much less obvious that, at first, the entire
cell might be thought genetic. Closer examination shows, however, that
bacteria may also show cyclical behavior analogous to ontogenetic cycles.
For example, typhoid bacteria characteristically produce flagella on
ordinary nutrient medium, but this potentiality is suppressed in the
presence of phenol. When the bacteria are replanted into ordinary
medium, flagella reappear which are serologically identical with those
INHERITANCE, VARIATION, AND ADAPTATION 69

originally formed. The flagellum cannot, therefore, be entirely self-
determined; its potential production must depend at least partly on the
genetic continuity of something outside the visible flagellum, persisting
and reduplicating when the flagellum itself is suppressed. Such per-
sistence in latent form, and subsequent reappearance, fits our definition
of a gene. A similar cycle is seen in the production by cells of an adap-
tive enzyme formed only when they are grown in the presence of its
specific substrate. The inhibition of pigment formation at elevated
temperatures by Serratia marcescens or Staphylococcus aureus and its
renewal at lower temperatures constitute another similar cycle.

Although these experiments justify a conception of the genes as some-
thing more restricted in quality or extent than the cell as a whole, they
tell nothing of genetic variation, 7.e., the crucial exception to the rule of
hereditary constancy.

II. Genetic Variation

A. Spontaneous MuratTIon

Sudden, unpredictable changes in the morphology, serology, or bio-
chemistry of a bacterial culture are familiar to every bacteriologist (for
examples, see Dubos, 1945). On a uniform medium, a “pure culture,”
perhaps even carefully isolated as a single cell, may give rise to a colony
different in color or texture from its siblings, or to one which has lost or
gained certain enzymes or antigens. Characteristically, the new variants
will breed true to their new quality, although they are no more immune
to variation than their parent, and may even on occasion revert to the
original type. Inasmuch as these differences will be maintained between
cultures propagated side by side under identical conditions, they cannot
be temporary physiological modifications like those cited as cycles above,
but must represent changes in the intrinsic hereditary quality of the
cells, z.¢.,in the genes. Genetic variations which are (presumably) based
upon qualitative changes in single genes are called mutations. Probably,
most bacterial variations are mutations (Lederberg, 1949b).

1. Autonomy of Spontaneous Mutation

The most striking characteristic of mutation in higher organisms is
its “blindness,” or “molar indeterminacy” (Muller, 1947). That is, it
occurs without reference to the life conditions of the organism, or to its
benefit or injury to the organism or species. As yet, we have no chemical
or physical agent by means of which we can approach particular genes or
induce their mutation in a predetermined direction.

Mutations which occur independently of consciously designed experi-
e

~ ames FQ) JOSHUA LEDERBERG

mental procedures are called spontaneous. Spontaneous gene mutations
may be thought of as chemical accidents, perhaps errors in reduplication
during growth, or collisions with occasional molecules with sufficient
kinetic energy to activate a chemical change in the gene. The kinetic
activation theory is supported by the temperature dependence of spon-
taneous mutation rates, whereas the reduplication hypothesis finds sup-
port in the apparent correlation of spontaneous mutation with bacterial
growth, as will be subsequently discussed.

The prevalent theory of organic evolution through natural selection
proposes that the environment in general has no directive influence on
mutational events as they occur. Despite this autonomy, the environ-
ment must and does play a decisive role in determining whether a mutant
cell, arising among millions of other offspring, will be so favored in its
growth and survival that its descendants will have a discernible part in
natural history or laboratory experiment. The geneticist finds the
bacteria unique material for his experiments: each culture tube is literally
a microcosm in which he may trace evolutionary processes on a scale
otherwise out of human bounds. Thisadvantage poses a unique dilemma.
In the most cogent processes, mutations can be detected only by applica-
tion of the selective environment. How can the role (or lack of it) of
such an environment in the initial event of mutation be tested when it is
an indispensable element of the experiment?

Since d’Herelle’s classic observations, it has been common knowledge
that most bacterial cultures which have been lysed by bacteriophage
later give rise to a secondary growth which is resistant to the phage.
Since the resistant form can be freed from phage and propagated side by
side with the original sensitive form without alteration of its properties,
the resistants clearly represent genetic variants or mutants. Usually,
they can be distinguished from the original sensitives only by their
reaction to the phage. In addition, the mutation is so infrequent that
the only dependable method of isolating resistant mutants from a sensi-
tive culture is selective removal of the sensitives by phage lysis.” Since,
by all appearances, untreated bacteria remain sensitive, whereas bacteria
exposed to phage become immune, it might be speculated that the phage
evoked the immunity (direct induction hypothesis). Alternatively,
resistance mutations might be occurring sporadically but constantly at a
low rate, and the phage might merely remove the preponderant, sensitive,
non-mutants and allow the resistant mutants to overgrow the population
(spontaneous mutation hypothesis). The second hypothesis implies
that the resistance mutations occur during the growth of the culture
prior to the application of the phage; according to the first, they would
occur during the brief interval between the application of the phage and

¢
M
INHERITANCE, VARIATION, AND ADAPTATION 71

the destruction of the sensitive bacteria. The discrimination between
these hypotheses is complicated, however, because phage must be added
to detect the mutants.

A simple experiment to settle this issue has been provided by New-
combe (1949), using the phage T, on F. coli strain B. A relatively small
number of bacteria (among which no mutants were already present) was
spread on the surface of a series of nutrient agar plates. After the plates
had been incubated several hours, and a thin film of bacterial growth had
formed, phage was applied as a spray so as not to dislocate the bacteria.

8 8

7 Unspread ~

~~ Spread ~

20 8

Fic. 3.1. Diagram of Newcombe’s spreading experiment. The upper portion of
each plate represents the number of phage resistant colonies found on unspread
plates, on either the spontaneous mutation or the direct induction hypothesis of phage
resistance. However, on the spontaneous mutation hypothesis, as shown on the left,
the colonies originate from clones of different size, since the mutations had occurred
prior to the application of the phage. On the direct induction hypothesis, it should
make no difference whether the culture is respread prior to the application of the
phage. The experimental result shows an increase of phage-resistant colonies after
spreading, comparable to the left-hand figure, and therefore supports the spontaneous
mutation hypothesis.

A series of duplicate plates was treated in the same way, except that the
cells were redistributed on the plate with a glass spreading rod imme-
diately before the phage was sprayed. The number of resistant colonies
which appeared was much higher on the plates which had been respread
before exposure to phage. This difference is expected if the mutations
had occurred during the growth of the bacteria because mutations taking
place prior to the last bacterial division would be represented by a clone
of two or more resistant cells. On the undisturbed plates, each clone
would be intact, and would count as a single resistant colony, whereas
after redistribution of the cells, each member of the clone would be
counted as a separate resistant colony. This result cannot be accounted
for by the direct induction hypothesis without resort to highly implausible
explanations. It may be concluded, therefore that the phage acts to
select for those mutants which have occurred spontaneously prior to its
application. The experiment is diagrammed in Fig. 3.1.
ee eel

72 JOSHUA LEDERBERG

The conclusion had been verified less directly by Luria and Delbriick
(1943) with the same bacterium-phage system. These authors at first
looked for an increasing proportion of resistant cells during the growth
of a culture from a sensitive inoculum as would be expected if spontaneous
mutations occurred during growth. However, this experiment was
hindered by an unusually large variance in the numbers of resistant cells
from one replicate culture to another. Delbriick’s theoretical analysis
showed, however, that a large variance is expected if mutations occur
throughout the preliminary growth of cultures from small inocula.
The experimental variance between cultures was found, in agreement
with Delbriick’s theory, to be some thousand times as large as the mean,
while the sampling variance, which should characterize consistent treat-
ments of comparable cells, would be only as large as the mean itself.
The null hypothesis, contradicted by the inordinately large variances, is
that the cells in identical physiological condition have been exposed to
identical treatments, that induce mutations conferring resistance.
Therefore some variable factor not under experimental control influences
the different cultures prior to their exposure to the bacteriophage. The
spontaneous mutation hypothesis is a restatement of this conclusion.
However, the argument is not as direct as that applied later by New-
combe, as has been described. In addition, it is couched in mathematical
terms not readily followed by all students. Methods developed by
Luria and Delbriick and others for the quantitative measurement of
mutation rates are given in the Appendix. Newcombe (1949) has sum-
marized the adaptive mutations whose spontaneous origin is suggested
by variance analysis. They include mutations for resistance to strepto-
mycin and to penicillin, for phage resistance, and for a variety of nutri-
tional changes.

More recently, the accumulation of spontaneous mutants during pro-
longed cultivation has been verified (Novick and Szilard, 1950; Stocker,
1949; Atwood, Schneider, and Ryan, 1951).

Innumerable claims have been made of induced hereditary variations
in bacteria directed by chemical and physical agents. None of these
claims, however, has yet been supported by the detailed analysis, of the
kind just discussed, which is desirable to disqualify spontaneous muta-
tions and natural selection. It is important to emphasize that the direc-
tions of natural selection must be verified by carefully designed recon-
struction experiments, rather than by a priori reasoning (Braun, 1947b;
Lederberg, 1948, 1949b). This is not to say that bacteria, or any other
organisms, are incapable of adaptive responses to their environment.
However, direct adaptation, such as adaptive enzyme formation, is
nonheritable, a distinction which should be clearly formulated.

 
 

 

INHERITANCE, VARIATION, AND ADAPTATION 73

2. Independent Occurrence of Spontaneous Mutations

Mutations of different genes are generally assumed to occur inde-
pendently of one another. This concept is somewhat circular, however,
because one of the most often used criteria for distinguishing two genes
is independent mutation. In bacteria, where this may often be the
sole criterion, it is impossible to test the universal applicability of this
assumption. There are, however, any number of verified examples.
For instance, mutation to resistance to different antibacterials, such as
sulfonamides, penicillin, and streptomycin, occurs independently, so that
a mutant resistant to one agent is generally unaltered in its sensitivity
to any of the others. Similarly, Audureau has described independent
mutations leading to the ability to utilize succinic, glutamic, or glutaric
acid by Morazella lwoffi, the type form of which is unable to utilize any
of these compounds. References for these and similar examples are
given by Luria (1947) and Lederberg (1948).

The apparent exceptions to this generalization are more difficult to
interpret. For example, Luria (1946) has described certain so-called
“‘complex-resistance mutations’? which make E. coli resistant to phages
from more than one cross-resistance group. The complex mutations
occur less frequently than do the simpler mutations of which they seem
to be superimpositions, but still much too frequently to be coincidences
of mutation of two independently mutating genes. However, in the
E. coli strain (B) used by Luria, there is no independent way of determin-
ing whether the complex mutants represent two interdependent muta-
tions, or merely a change of an altogether distinct gene with complex
physiological effects. Physiologically distinct characters are usually
controlled by independently mutating genes. To date, the independent
mutation of distinct genes is uncontradicted. However, more complex
genetic phenomena are known (viz., segregation, vide infra) which may
simulate non-independent mutations.

3. Phenotypic Lag

The estimation methods summarized in the Appendix postulate that
each mutation is reflected immediately in the appearance of the organism.
A priori, a mutation would be unlikely to revise the cell phenotype
instantaneously, and experiments with protozoa prove that several cell
divisions may be needed for genotypic changes to become phenotypically
effective. This delay is referred to as phenotypic lag.

At present, the evidence for phenotypic lag in bacteria is indirect.
Newcombe (1948, Newcombe and Scott, 1949) has shown that discrep-
ancies in the evaluation of the mutation rate of EZ. coli B to phage resist-
teen! + te

74 JOSHUA LEDERBERG

ance, using different methods (see Appendix), can be accounted for by
phenotypic lag. If mutations became phenotypically expressed only
after a few divisions, the average number of apparent resistants for each
clone containing one or more resistants will be exaggerated. From
Newcombe’s (1949) spreading experiment (see Fig. 3.1), it could be
inferred that the resistant clones were about ten times larger than
expected, which speaks for a phenotypic lag of three generations or so.
Luria and Delbriick had rejected the possibility of phenotypic lag in
setting up their model of spontaneous mutation because they found
cultures with a single cell in about the expected proportion of their
experiments. To account for this, Newcombe suggests that one clonal
descendent of a recently mutated bactertum may sometimes become
phenotypically resistant before the others. Other inadequacies of the
hypothetical model of spontaneous mutation may also contribute to
discrepancies. The postulates have been discussed in some detail by
Luria and Delbriick (1943), Newcombe and Scott (1949), and Lea and
Coulson (1949).

Under certain conditions, where growth is contingent upon a muta-
tion, phenotypic lag may be prolonged indefinitely. Davis (1950) has
reported that certain spontaneous or radiation-induced mutations in
E. coli, which will permit growth on a synthetic medium, may fail to
come to phenotypic expression at all unless a small amount of the required
growth factor is added, to allow a minimal amount of growth of the
parent cells. This ‘‘phenomic barrier’ is presumably the result of a
vicious cycle in which phenotypic lag must be overcome to effectuate a
mutation, while the mutation’s effect is needed for growth to start. The
phenomena of phenotypic lag are, so far, imperfectly understood, but
must be allowed for in all experiments on bacterial mutation.

4. Pseudo-Mutational Processes

The genetic model of the bacterial cell that we have been using
implicitly with certain reservations throughout this discussion is a uni-
nucleate cell, carrying one set of genes, so that changes of individual genes
will be reflected in phenotypic alterations and vice versa. This model is
probably inaccurate for vegetative cells. If the current cytological
evidence is interpreted correctly, even the small spherical cells of cocci
may contain two nuclei, while the rods and filaments of other bacteria
may be more complex. It is also by no means certain that the individual
nuclei of all bacteria are haploid (7.e., carry just one set of genes). Di- or
polyploidy in bacteria leaves the door open to complex genetic processes
that simulate mutation, but do not consist of immediate changes of
individual genes.
 

 

 

oe Rigen

 

INHERITANCE, VARIATION, AND ADAPTATION 75

The most prominent of these pseudo-mutational processes is segrega~
tion, the separation from a cell containing two gene forms of a nucleus in
which only one form is represented. That is, a cell whose genetic con-
stitution were A.A Aaaa might segregate a cell whose constitution is a or
aa... . Such a segregation will be reflected in a phenotypic change if
the gene form, or allel, A is dominant over a in cells where both are
represented. That is, the segregation will simulate a “mutation” from
A to a.

It must be emphasized that segregation does not take the place of
mutation as a source of genetic variability. In our example, a mutation
of the ‘‘A”’ gene must have occurred at some previous time to allow two
forms. The immediate observation of a genetic change may represent
the unmasking, by segregation, of a mutation which had occurred long
before.

Very likely, segregation does not play the important role in bacterial
variation that it does in the filamentous fungi (Luria, 1947). However,
one verified instance of segregation, found in EZ. coli, will be discussed
later (page 91).

B. InpucED Mutation

In previous paragraphs, the gene was regarded as a chemical sub-
stance which was not internally modified by its commerce with the imme-
diate environment through which it carries on its functions. This model,
of course, cannot be strictly accurate, because the gene is a material sub-
stance, not immune to change. As implied earlier, the insularity of the
gene means merely that at present no reagent is known which can dis-
criminate chemically between any one gene and its neighbors. That is,
even under treatments which induce mutations, the particular genes
affected appear to be indeterminate, but merely because of our ignorance
of the molecular differences between genes.

1. Radiations

The lack of knowledge in this field is pointed up by the fact that, until
recently, the only agents for inducing mutations have been radiations—
X-rays, gamma rays, neutrons, ultraviolet light (UV)—that have, at
best, topographical specificity. That is, the locus of action of such radia-
tions is determined preeminently by a topographically random quantum
event, the absorption of the radiation. UV may show a higher order of
specificity of absorption, but none of these agents could conceivably
distinguish one gene from another, and the probability of a successful
quantum hit will depend initially on whether a quantum happens to be
absorbed in proximity to a gene, so that its energy can be transferred to
 

eee 76 JOSHUA LEDERBERG

it. In a sense, then, we might better refer to radiations as random
accelerators of the ‘‘spontaneous” mutation process.

Soon after Muller’s proof of the mutagenicity of X-rays for Drosophila
in 1928, reports began to appear of the comparable effects of X-rays and
radium emanations in stimulating variations in yeasts and bacteria.
However, the characters used in the earlier studies were often vague, and
the results difficult to interpret. We owe our most precise information
on the mutagenic effects of radiations on bacteria to the comparatively
recent work of Demerec and Latarjet (1946). These authors used the
same phage resistance system that has been already discussed as the test
material for their work. After irradiation, they spread the bacterial
suspensions on the surface of agar plates, and assayed the bacterial films
for mutations by spraying phage on them. This technique has the
advantage of counting each new mutation, rather than each mutant, as a
single colony. Aliquots were taken from the irradiated and unirradiated
samples to determine the extent of killing by the radiation, and to esti-
mate how many mutant cells, if any, were already present before the
treatment. This number, corrected for the extent of sterilization by the
radiation, must be subtracted from the number of resistant colonies which
are counted, to give the number of mutations induced by the radiation.

The most striking common effect of all known mutagens is that they
kill cells, roughly in proportion to their mutafacient efficiency. It is
usually assumed that the mutants under study are no more resistant to
radiation than are the non-mutant cells, but this should be (as it was
here) verified by direct experiment. Because of this pronounced killing
action (see Chapter V), it may turn out that the preexistent spontaneous
mutants killed by a given dose of radiation exceed the new viable mutants
induced. For this reason, and assuming that the radiation does not affect
the mutants differentially, the results of induced mutation experiments
are usually expressed in terms of increased proportion of mutants among
the surviving cells, rather than as the absolute number. Under excep-
tional circumstances—if the spontaneous mutants in the original culture
are infrequent compared to the mutation rate, and if the proportion of
cells killed has not exceeded two-thirds—increases in the absolute num-
bers of the mutants can be demonstrated. This type of experiment may
be useful to prove conclusively that an apparent mutagen is inducing,
rather than selecting, mutations (Witkin, 1950).

Demerec and Latarjet found that both X-rays and ultraviolet light
acted on £. coli to induce mutations for phage resistance. However, the
effects of these agents cannot be detected as an immediate increase in the
output of phenotypically resistant cells. Although a few new mutations
were detected among the bacteria sprayed with phage immediately after
 

 

 

 

INHERITANCE, VARIATION, AND ADAPTATION 77

irradiation, most of the induced mutants were not detectable for some
time afterwards. The growth from an irradiated inoculum continued to
produce additional mutations for a period equivalent to thirteen bacterial
generations, although the peak rate of appearance was noticed after
one or two divisions.

The delayed effect after irradiation may come from a number of
causes. Firstly, as we shall see, it is possible that some of the effects of
ultraviolet light may depend on the accumulation of a mediating chemical
substance, so that, perhaps, the mutational chemical change may be
itself delayed. Then, phenotypic lag would be expected to advance the
time at which a genetically resistant cell would be scored as a mutant.
The effects of phenotypic lag are probably exaggerated, in absolute
time units, by the long and variable periods during which still viable
cells may fail to proliferate after ultraviolet irradiation (Newcombe and
Scott, 1949). Finally, since many bacterial cells contain several nuclei
(Robinow, 1945), “dominance” effects become possible. That is, if
only one of the several nuclei of the cell should contain a mutated “resist-
ance gene,” it might have no effect on the phenotype owing to the domi-
nating action of unmutated “‘sensitive genes” in the sister nuclei (see
Lederberg, 1949a, b). In this event, it would not be until resistant
nuclei had been sorted out during subsequent divisions that a cell would
be produced that possessed a genotype that would lead to resistance.
The existence of such segregation phenomena, after irradiation, is sug-
gested by the finding that fermentation mutants of E. cold are frequently
found as sectors in colonies grown out from irradiated cells.

Some idea of the relative mutagenicity of X-rays and ultraviolet can
be conveyed by comparing them at doses for which the killing effect is
thesame. In the experiments of Demerec and Latarjet 100,000 roentgens
of X-rays left 10-® of the original population as survivors, and induced
200 endpoint mutations per million survivors. Ultraviolet light,
incident at 3550 ergs/mm.*, caused the same killing, but induced 3300
endpoint mutations per million survivors. Thus, from the point of view
of mutations induced per cell killed, ultraviolet light is more effective
than X-rays. Demerec and Latarjet point out, however, that at these
doses, each bacterial cell will have absorbed more than 200 times as much
energy from ultraviolet as from X-rays. On an energetic basis, therefore,
X-rays are more effective both in killing and in mutating bacteria. For
most purposes, however, it is more important to conserve the biological
material than radiant energy.

A quantitative comparison of X-rays and ultraviolet light is, however,
hindered by differences in the shape of the response curves. The steriliz-
ing effects of X-rays are, over a considerable range, in accord with a
 

“y

wean 7B JOSHUA LEDERBERG

“‘single-hit’”’? mechanism: 7.e., each increment of dose kills a constant
fraction of the surviving bacteria. Thus, there appears to be no cumula-
tive effect, and if a first absorption of an X-ray quantum fails to kill a cell,
the cell is not made more or less sensitive to subsequent doses. However,
the quantum efficiency for X-ray sterilization is not accurately known,
primarily because we do not certainly know the site of action. The
kinetics of ‘“‘single-hit”’ killing is expressed graphically by a linear plot
of log S (survival ratio) against dose (usually in roentgens).

When log S is plotted against dose of ultraviolet light (in energy, or in
energy /surface), however, a sigmoid rather than a linear relationship is
usually observed. The initial doses of ultraviolet have a smaller effect
than subsequent dose increments. This suggests that the quantum
events which underly killing by ultraviolet light may be cumulative.
However, the kinetic data do not tell whether the cumulative effect 1s
due to the presence of a number of different target sites (nuclei?) each of
which must be altered, or to the accumulation of some toxic material,
and both may be involved.

The same comparative picture is obtained when the mutagenic effects
of these two radiations are compared. Because the fraction of mutants
is always small, it is more convenient to plot the number of mutations
obtained (rather than its logarithum) against the dose. Whereas X-ray
induced zero-point mutations show no evidence of a threshold, the ultra-
violet response is again sigmoid, and there is in fact an optimum dose
beyond which the fraction of mutants increases erratically if at all.

Although the kinetics of X-ray effects is simpler, it does not neces-
sarily imply a mechanism entirely different from ultraviolet. The
quantum of X-rays is much more energetic than that of ultraviolet, and
it is possible that any absorption of a single X-ray quantum at a suitable
site will be effective, while several ultraviolet quantum hits would be
needed either to accumulate enough of a chemical, or to ‘‘destroy” a
wide enough area, to have the same influence.

Research on radiation mechanisms is progressing very rapidly, partly
under the impetus of the development of atomic energy. That X-rays,
no less than UV, may have chemical intermediation of their biological
effect is suggested by experiments carried out in air, oxygen, and other
atmospheres, which were found to have profound effects on the extent of
X-ray damage. A more detailed account of radiobiological advances
cannot be given here, but their pertinence to bacteriology is matched only
by the usefulness of bacteria as material for radiobiological investigation.

2. Photorecovery

The concept of a chemical intermediate for the effects of UV has been
greatly strengthened by the recent discovery of the phenomenon of
wee cent

 

INHERITANCE, VARIATION, AND ADAPTATION 79

photorecovery (Kelner, 1949; Novick and Szilard 1949). This consists
of the apparent reversal of the lethal and mutagenic effects of ultraviolet
light by a subsequent exposure of the irradiated organisms to longer
visible wavelengths. The quantitative effect of the treatment with
visible light can be regarded as a ‘“‘dose-reduction”’ of the UV effects, for
the combined responses are, under optimal conditions equivalent to those
of a dose of UV alone, but reduced to 40%. Although the extent of
photorecovery, expressed in these terms, is not impressive, the sigmoid
response (either lethal or mutagenic) to UV exaggerates the effect when

Log SURVIVORS

 

 

 

—— UV dose——>

Fic. 3.2. Photorecovery of UV-inactivated cells. Adapted from Novick and
Szilard (1949). £. coli B/r was exposed to various UV doses, and aliquots plated to
determine the viable count with (light) and without (dark) exposure to an optimum
of visible light. The light treatment is equivalent to a UV dose reduction by the
factor 0.4, but at certain doses, e.g., where the dark survival is only 103, this may
result in a photorecovery ratio of 10°, owing to the non-linearity of the survival curves.

expressed in terms of microbial survivors. For example, a suspension of
bacteria exposed to a dose of UV that would leave only one survivor per
million if left in the dark, can be photoreactivated so that 10% of the
treated cells will recover in the light.

Photorecovery appears to be widespread among microorganisms, and
has already been reported for actinomycetes, bacteria, fungus spores,
yeast, paramecia, and bacteriophage. Bacteriophage, however, can be
photoreactivated only while adsorbed on sensitive bacteria. This sug-
gests that the chemical (?) which has altered under the influence of UV
is not itself decomposed by visible light, but that the latter activates
other reactive systems which in turn reverse the UV effects. A chemi-
cally distinct intermediate is hypothesized to explain UV killing and pho-
torecovery because UV-treated cells can be photoreactivated even several
hours after irradiation. Any energetically excited molecule would not
be expected to remain in such a metastable state for any appreciable time
unless it were somehow isolated from energy transfers associated with
thermal, molecular collisions. Preliminary experiments indicate that
 

eet eee BO JOSHUA LEDERBERG

the mutagenic effects of UV-visible light combinations are comparable
to the lethal responses. That is, the proportion of mutants in a photo-
reactivated population will be less than among the distinctly fewer dark
survivors. The absolute number of viable mutants might be the same
or more, however, owing to the much greater overall survival (Newcombe
and Whitehead, 1951).

These observations raise the question whether the lethal effects of
radiations may be ascribed entirely to the induction of mutations which
cause irreparable damage. This problem cannot be discussed fully here,
but its current status seems to be that only a small part of the lethal
effect of radiations can be accounted for by simple lethal mutations.
Various aspects of this problem have been discussed by Demerec and
Latarjet (1946); Latarjet (1946); Lea (1947); Witkin (1947); and Leder-
berg et al. (1951).

3. Chemical Mutagens

Although radiations of various kinds have been known to be muta-
genic in numerous organisms for many years, convincing evidence of
chemical influences on mutation rates dates only to the time of World
War II, with the work of Auerbach and collaborators on war ‘‘gases.”’
The potency of 8-chloroalkyl sulfides and amines (mustard gases and
nitrogen mustards) as extremely effective mutagenic agents has been
proved beyond doubt in a variety of organisms, including bacteria
(reviewed by Auerbach, 1949). In general the effects of the mustard
compounds are similar to those of radiations. These substances are
extremely toxic, they mimic the histopathological effects of radiations
and like radiations, they have little if any specificity in their mutafacient
effects. These compounds will combine chemically with a great variety
of functional groups found in proteins and nucleic acids—amino, carboxyl,
hydroxyl, phenolic—indeed with very nearly any group carrying a
reactive hydrogen atom. It would be surprising if this reactivity were
not the chemical basis of mutagenicity, but this would imply that other
group reagents might also be mutagenic. This notion, however, may
help to understand the mutagenic activity demonstrated in Drosophila
for allyl isothiocyanate and for formaldehyde.

In addition to the mustards, many other chemicals have been reported
to have mutagenic effects for bacteria, including carcinogenic hydro-
carbons, some alkaloids, dyestuffs and bile acids. The reader is referred
to Auerbach’s review for a detailed discussion of the present significance
of this work (Auerbach, 1949). Among these newer reports, however,
the finding that organic peroxides may be potent mutagens (Dickey et al.,
1949) is of special interest, as it may also give a clue to the mechanism of

 
 

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INHERITANCE, VARIATION, AND ADAPTATION 81

action of ultraviolet light. Wyss eé al. (1948) found that nutrient broth
exposed to heavy doses of UV becomes mutagenic. The effects of UV
could be duplicated by treating the broth with hydrogen peroxide, so
that the indirect mutagenic effect of UV can be fully accounted for by the
hydrogen peroxide which is liberated in UV irradiated water. The
supposition that part of the ‘‘direct”’ effects of UV on living cells may be
mediated by the same mechanism is not unreasonable. The work of
Dickey et al. (1949) provides a tangible clue to the type of mutagenic
products produced when broth is treated with hydrogen peroxide, as well
as a basis for speculation concerning the intermediate involved in the
photoreactivation of UV-treated bacteria.

IlI. Characteristics of Bacterial Mutants

Searcely any limit can be placed on the range of physiological effects
mediated by genetic changes in bacteria. Presumably, all bacterial
forms, and for that matter all living things, differ from one another
entirely on the basis of a finite number of differences of gene content,
quality, and organization. The scope of effects of single gene changes
may appear to be restricted or broad depending on the specific instance,
and on the investigator’s point of view. However, the presumption that
even the most diverse effects of single gene changes can usually be traced
back to an ultimate simple direct biochemical effect has had considerable
empirical success (see Beadle, 1945). Contemporary genetic research on
bacteria is concerned primarily with two types of mutants—mutations
for resistance to growth inhibitors, phages, and the like, or mutations
affecting the biochemistry of the organism in a direct, obvious manner,
detectable as nutritional, fermentative, or similar enzymatic changes.
Other mutations amenable to genetic analysis include effects on pigment
formation, colonial appearance, antigenic structure, virulence, motility,
antibiotic production, and vitamin excretion.

Nutritional mutants have proven to be especially useful, both for
physiological and for more strictly genetic research. Many bacteria,
such as E. coli are auxoautotrophic, z.e., they have no special nutritional
needs beyond a medium containing minerals, inorganic nitrogen, and an
organic carbon and energy source. Such a simple nutritional pattern
actually reflects an exceedingly complex biochemical apparatus, for the
organism must synthesize all of the amino acids, vitamins, and other
constituents of its protoplasmic and metabolic machinery. Auxoauto-
trophy does not mean, in general, that an organism has dispensed with
growth factors, but contrariwise that it manufactures them for itself.
A mutation that blocks the synthesis of an essential metabolite imposes
on the cell a requirement for the substance it can longer manufacture.
a tee eee

82 JOSHUA LEDERBERG

The nutritional mutant is, therefore, unable to grow on the unsupple-
mented minimal medium.

Nutritional mutants, chiefly in the fungus Neurospora, but also in
bacteria (Tatum, 1949; Davis, 1950), have been particularly useful in
tracing the steps in the biosynthesis of various growth factors. Two
types of experiment are in general application. When an amino acid, for
example, is synthesized by a sequence of reactions, the response of a
nutritional mutant to the intermediary compounds depends on the par-
ticular step of the reaction sequence that is blocked in the mutant. If
an early step is blocked, then the mutant can utilize any added inter-
mediate that comes later in the sequence. If a late step is blocked,
however, then the mutant will be unable to use an added intermediate
which has an earlier place in the sequence. Insight into a biosynthetic
sequence can thus be obtained by comparing the availability of a group
of postulated intermediates for a group of mutants blocked at different
stages in the synthesis of a given metabolite. Many mutants, in which
the further transformation of a biosynthetic intermediate is blocked by
genetic change, may accumulate the compound and excrete it into the
medium in far larger amounts than the original auxoautotroph. Such
intermediates can then be isolated by standard chemical procedures,
providing more direct evidence for their probable role in the synthesis of
the growth factor required by the mutant. This supposition is strength-
ened if an intermediate accumulated by one mutant permits the growth
of another mutant, blocked at an earlier step.

The excretion of such intermediates is the basis for syntrophism, or
nutritional symbiosis, whereby mutants blocked at different steps may be
able to feed each other, so that mixed cultures of two mutants will grow
far better in a minimal medium than will the isolated mutants. Con-
versely, syntrophic growth may be a useful test to differentiate two
mutants which have similar nutritional requirements, but which may be
blocked at different steps in the synthesis of the growth factors (Davis,
1950; Lederberg, 1950).

IV. Interclonal Variation

Up to this point, the discussion has been concerned exclusively with
genetic variations which occur within clones, and which do not involve
the interaction of different bacterial strains. In recent years, increasing
attention has been devoted to the ways in which different bacteria may
interact genetically in mixed culture. It is likely that the classical
emphasis on pure culture technique has caused many interesting aspects
of interclonal variation to be neglected. On the other hand the complete
control of intraclonal variations in pure cultures is a necessary preliminary
 

ws eee gpa

 

 

INHERITANCE, VARIATION, AND ADAPTATION 83

to any study of interclonal variation. The mechanisms of genetic
interaction between clones may be classified: (a) ‘infective transmis-
sions,’’ in which the interaction is mediated by extracts or filtrates which
can be separated from the bacterial cells; and (b) sexual phenomena
which appear to require the integrity of both of the interacting clones.

A. INFECTIVE TRANSMISSION

1. Transformation

The first example of infective hereditary transmission to be widely
accepted was the transformation of pneumococcal types, discovered by
Griffith (1928). Pneumococci are recognized in two phases, S and R
(also called M and S, respectively) depending on the presence or absence
of a polysaccharide capsule. R Bacteria are not readily distinguished by
serological methods, but the many S types are characterized by the
serologically specific reactions of the capsular material. The S types are
designated with a roman numeral, for example, S-IIJ is one of the more
prevalent types. KR Mutants can be obtained from any of the S types,
particularly with the help of selection with anti-S serums. Such R
mutants are generally avirulent for mice, but many are unstable, and will
occasionally revert to S, though only to the same S type from which they
arose. Other R mutants are stated to be completely stable, as corrobo-
rated by their avirulence in large doses. Griffith found that certain R
cultures, by themselves avirulent, killed mice when inoculated with heat-
killed .S cells of various types. Viable S cells of the same type as the
heat-killed vaccine were recovered from the blood of the infected mice.
Although Griffith was unable to duplicate this interaction in vitro, he
concluded that material from the killed S cells had transformed the
living F cells into the same S type as used for the source of the vaccine,
a type that might be different from the original S type from which the R
culture had been isolated.

Griffith’s work was promptly confirmed and subsequently the con-
ditions necessary for transformations in vitro were discovered. These
researches culminated with the extraction and partial purification of the
transforming principle by Avery et al. (1944). This and subsequent
work (McCarty, 1946) demonstrated that the active principle consists
principally of a highly polymerized desoxyribonucleic acid, which, con-
trary to earlier speculations, does not require serologically detectable
amounts of the capsular polysaccharide for its transforming action.
Studies with specific desoxyribonucleases established that the polymeric
desoxyribonucleic acid is a necessary constituent of the transforming
principle. Avery and his collaborators have claimed also that the
y

 

cones BA JOSHUA LEDERBERG

nucleic acid is sufficient, and that protein is not responsible for the
specificity of the transforming agents. This claim has been disputed,
however, chiefly on the grounds that even the most purified preparations
(which still consist mostly of inert material) of the transforming prin-
ciples are not entirely free from detectable protein (Mirsky and Pollister,

1946). This controversy has attracted wide interest because of the

frequently stated analogy between transforming agents and genes.
Although it is undisputed that nucleic acids play an important role in
gene function, many workers had speculated that, by analogy with
enzymes, gene specificities were ultimately determined by protein
configurations.

The demonstration of type transformations in vitro requires a rather
complex experimental system, provided by some serums, which has been
analyzed as follows. In the transformation of F to S, the R cells must
firstly be made to grow in aggregates. This 1s usually accomplished by
the R agglutinins present in many normal sera. However, it is possible
to replace such agglutinins with semisolid agar. Secondly, the F cells
must be sensitized by exposure for several hours to a duplex system,
consisting of a non-dialyzable component (possibly an enzyme) that
occurs in serum albumin and of a dialyzable component replaceable by
pyrophosphate plus neopeptone. Sensitization is apparently necessary
for the fixation of the transforming principle on the cells. Presensitized
cells require only a few minutes exposure to the transforming agent to
produce S transformed cells. No estimate is yet available of the frac-
tion of the R cell population which is transformed to S, but it is probably
less than one per thousand.

Not all R strains are competent to be transformed under these condi-
tions, and some attention must be given to the isolation of transformable
R strains which are not spontaneously unstable. On the other hand, R
strains have been found (McCarty eé al., 1946) which have less rigorous
requirements for transformation than those just described. So far, the
only characters of the pneumococcal cell which have been transformed
are those which can be correlated with serological specificity: colony
morphology, virulence, and the like. The polysaccharide capsular
transformations have received the most emphasis, but the recently dis-
covered M protein antigen can also be transformed, independently of the
capsule substance (Austrian and MacLeod, 1949). T ransformations
have been described in a variety of other bacteria, but none of these
other examples (reviewed by Luria, 1947; Lederberg, 1948, 1949b; and
McCarty, 1946) has been so well documented as has the pneumococcal
transformation.

At present, no definitive interpretation of this phenomenon can be

acer enn: abe PMR Sues ett om mate
INHERITANCE, VARIATION, AND ADAPTATION 85

offered. The transforming principle is, in a sense, an infectious heredi-
tary agent, since it can be transferred not only in heredity from parent to
offspring, but also between cells of different descent via the medium.
The newly transformed S cells cannot be distinguished from typical S,
and like the latter, can be used as a source for fresh preparations of the
transforming agent. Thus, in many ways, the transforming agent
behaves like a symbiotic intracellular virus. Indeed, the parallelism
between tranformations and symbiotic or lysogenic bacteriophages was
commented on even in the more or less credible transformation work
antedating Griffith.

Recent morphological and genetic investigations may require a rein-
terpretation of some transformation experiments. Many bacteria have
been reported to produce reduced cells (‘‘L-forms’’) which may pass
ordinary bacterial filters and which are unusually resistant to disinfect-
ants. Such forms may require special conditions to regenerate ordinary
bacteria and may lead to a misconstrual of sterility test controls. An
apparent transformation might be due to the regeneration of the bacteria
from which an apparently sterile filtrate or extract had been prepared.
Whether this concept can be applied to the pneumococcus experiments is
doubtful, but fairly direct support for it has been found in Salmonella
typhimurium (compare Ephrussi-Taylor, 1951 and Lederberg ef al., 1951;
Tulasne, 1949).

The crux of the issue is the morphology of the transforming agent:
is it a single nucleic acid or nucleoprotein molecule (naked gene) or an
organized particle into which all of a cell’s genetic material may be
assimilated?

2. Virus Lysogenicity

Although the properties of actively lytic, parasitic bacterial viruses
or bacteriophages are now widely appreciated, owing especially to a
recent resurgence of interest in the growth and genetics of viruses, the
significance of cryptic or lysogenic viruses has been generally under-
estimated. It has been well established (McKie, 1934; Rountree, 1949)
that many bacterial cultures are infected with cryptic, symbiotic viruses.
Such lysogenic bacteria show no obvious manifestation of the virus under
ordinary conditions of pure culture, and other bacterial strains, suscepti-
ble to the virus must be found and exposed to the lysogenic culture to
reveal the presence of the virus. Thus, it cannot be asserted that any
bacterial culture is certainly uninfected without tests on unlimited num-
bers of potentially sensitive indicator strains for a lytic response. Many
cultures, especially among the salmonellae and the micrococci, carry
latent viruses which can be detected with the help of one or another
male! = ee

 

86 JOSHUA LEDERBERG

indicator strain of the same or a related species. Many latent viruses
have weak lytic powers even on sensitive strains, and these viruses might
easily be regarded as transforming agents, provided only that they
modify the physiology of the cell in some way not obviously related to
phage lysis.

A system studied in detail by Burnet and Lush (1936) may be a possi-
ble half-way station in the gradual transition between transforming
agents and latent viruses. The phage, C, has a poor lytic effect on a
micrococcus strain SF. After exposure to C, a large fraction of SF cells
become resistant to C, as well as to another phage B, which differs from
C in lysing almost all cells of an SF population. The resistance of SF
treated with C was shown to result from the establishment of a symbiosis
between the bacterium and the phage which, in addition to making the
bacteria resistant to C, also appears to exclude the phage B. Thus
filtrates of SF/C (SF bacteria once exposed to C), a culture resistant to
phage B, are capable of “transforming” SF, typically sensitive to B, toa
type resistant to B. In this sense the phage C is a transforming agent,
but it can be recognized as a lytic phage by its action on SF on agar. In
liquid medium, however, no bacteriolysis is evident and the virus nature
of C would not be apparent. Inasmuch as resistance to B can also be
conferred by a spontaneous mutation, it can be suggested that the
“transforming agent’’ C mimics a gene effect.

Observations like these do not answer the question of the ultimate
origin either of phages or of transforming agents, although they do sug-
gest a remote connection between them. Some workers have proposed
that viruses may have originated from cytoplasmic hereditary agents
which have gone wild and escaped from the cells in which they arose,
whereas others have argued that “cytogenes” may have evolved from
parasitic viruses which have evolved a symbiotic relationship with their
host cells, and perhaps have gradually become integrated into the genetic
system of the cell. It may be suggested also, perhaps more reasonably,
that both types of evolutionary change of these particles are taking place
concurrently, so that it will be impossible to generalize concerning the
ultimate origin of all viruses. At any rate, no experimental method nor
even a widely accepted definition of the terms exists, by which we can
distinguish between intracellular viruses, transforming agents, and
cytogenes. The accumulated evidence, especially with higher organisms
but also with microbes, suggests, however, that hereditary changes based
upon differences in these virus-like agents are exceptional, and that
nuclear genes bear most of the burden of heredity.

Cytogenes allow for directed “mutations’’ more readily than do
nuclear factors. ‘‘Mutations” based upon the acquisition of such agents
 

a i a ap

Atm A taibe

INHERITANCE, VARIATION, AND ADAPTATION 87

(phages, transforming principles) have already been cited. The deple-
tion of such agents in the previously infected cell which would give the
converse type of hereditary change, might be accomplished by any
influence on the relative rates of increase, or decrease, of the cytoplasmic
agent and the cell as a whole. For example, the cytoplasmic particles
might be more sensitive to heat, radiations, or other deleterious agents
than is the cell, so that some of the cell survivors of such treatments
would be depleted of the cytoplasmic particle. No well-authenticated
examples of such a depletion or attenuation mechanism have been
reported in bacteria, but effects in yeast exposed to acriflavine (Ephrussi
et al., 1949) and in Euglena and higher plants exposed to streptomycin
(see Provasoli e¢ al., 1948) are best explained in this way. An attenua-
tion mechanism is often difficult to prove; some of the methodological
problems are discussed by the authors cited, and by Preer (1948),
Lederberg (1948, 1949b), and Luria (1947).

B. Genetic EXcHANGE VIA SExuaL Fusion

Traditionally, bacteria have been supposed to multiply exclusively
by fission. This concept has even been incorporated in the class name
Schizomyceies, “‘fission-fungi.”” However, the evidence for the absence
of sexuality among bacteria was entirely negative, namely, that no one
had succeeded in a convincing demonstration that bacteria cells can fuse
with one another with any genetically interesting consequences. Such
examinations have been primarily morphological; in view of the minute-
ness and relatively undifferentiated structure of bacterial cells such
negative results could be attributed as much to the limitations of the
techniques as to the true absence of sexual mechanisms in bacteria.

Among the legacy of unconfirmed or unconvincing reports of cell
fusions, very few still command the attention of contemporary bacteriol-
ogists. Perhaps the most credible of these are the observations of Stapp,
confirmed by Braun and Elrod (1946), on the formation of stellate aggre-
gates of Phytomonas tumefaciens by cell fusion, followed by a centripetal
aggregation of the nuclear bodies. These authors themselves point out,
however, that “cytological studies alone will not suffice to clarify this
question. It will be necessary to bring together in a single star different
strains of the same species or individuals of closely related species and
determine from this cross whether a recombination of characters results.”

, 1. B acterial Recombination

In view of the difficulty of interpreting cytological studies, strictly
genetic methods are better applied to this problem. The first clearcut
experiments in this direction were reported by Sherman and Wing (1937),
Y

 

ween BR JOSHUA LEDERBERG

who mixed various fermentative types of H. coli, and then examined
reisolated clones for new combinations of fermentative characters.
Unfortunately, the ‘parental’ cultures were not stable enough to permit
any definite conclusion as to the origin of the observed “new combina-
tions.” That is, in the terms of the previous discussion, uncontrolled
intraclonal variability obscured whatever interclonal variation there
might have been. Gowen and Lincoln (1942) improved the approach by
using as characters that might be recombined visible differences in color
and texture of colonies of Phytomonas stewartit, so that many more
isolates could be feasibly examined than in the previous study. Some
hundreds of thousands of colonies from mixed cultures were examined,
but no greater variability among the mixed cultures was observed than
could be accounted for by the intraclonal variability of the parents.
However, in a further modification of this genetic approach, whereby any
possible recombinations were automatically sieved even from very large
populations of the mixed parents, Tatum and Lederberg (1947) succeeded
in demonstrating genetic recombinations in strain K-12 of E. colt. These
and subsequent observations of these authors, which have been confirmed
in several laboratories, are the basis for the assertion that may now be
made that a sexual stage intervenes in the life cycles of some bacteria.

The selective isolation of genetic recombinations depends.on the
properties of nutritional mutants already mentioned. A mutant, sym-
bolized by A — B+, is unable to synthesize growth factor “A” but can
manufacture ‘B.” Conversely, a second mutant A + B— will require
“B” for growth. Neither A — B+ nor A + B— by itself is capable of
growth in minimal medium, and if the cells are carefully washed, mixtures
of the two mutants may be inoculated into minimal agar without resulting
in syntrophic proliferation. However, if genetic exchanges occurred
betiveen cells of the two mutants, some of the recombinations would be
of the type symbolized A + B+, 7.e., capable of growth in medium like
the original wild type. In this way, a minimal medium can be used for
the selective isolation of genetic recombinants in mixed cultures. The
term prototroph has been suggested to designate cultures like these
recombinants that are nutritionally like the ancestral wild type, which is
auxoautotrophism for Z. coli, but implies a requirement for biotin for
Neurospora.

Prototrophs appear at the rate of approximately one per million cells
inoculated, in experiments with various mutants of EH. colt K-12. This
shows that recombination must occur at a comparably low rate, and thus
why it has been so difficult heretofore to obtain convincing evidence of
sexuality in similar bacteria. The production of prototrophs from mix-
tures of biochemical mutants is only one of many predicted implications
oo!

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INHERITANCE, VARIATION, AND ADAPTATION 89

of a genetic recombination mechanism. By itself, this experiment would
be merely contributory, not conclusive, evidence for a sexual mechanism.
Further experiments are necessary to eliminate two possible fallacies:
(a) that the prototrophs are engendered by intraclonal variation, ‘.e.,
that spontaneous mutations might occur from A — B+ toA + B+; and
(b) that the observed genetic exchanges are mediated by some other
mechanism of interclonal variation, specifically infective transmission or
transformation.

If only single nutritional mutations are used for parental stocks in
these experiments, intraclonal variation is not completely controlled,
since many mutants will reverse mutate at rates of the order of 10-7 per
division. The small but inevitable syntrophic growth of the parent
inocula exaggerates this effect in mixed cultures, which thus might con-
fuse the result. This source of error can be practically eliminated, how-
ever, by the use of double rather than single mutants for the parents.
That is, the cross would now be symbolized as A-—B-C+D+ x
A+B+C—D-, to yield a variety of progeny, including prototrophs
A+B+C+D+. For a double mutant to yield a prototroph would
require a coincidence of two mutations in the same clone, e.g. that both
A— and B— revert to A+ and B+, respectively, in the same A — B—
clone. The theoretical probability of such a coincidence is vanishingly
small, and has never been observed experimentally with these stocks.
The use of double mutants as parents has the additional advantage that
syntrophie growth, which might obscure the formation of prototroph
colonies in minimal agar, is even further restricted.

The most informative experiments have, however, involved the use
of additional unselected markers, such as mutations affecting sugar
fermentations, phage resistance, and drug resistance (see Fig. 3.3). With
suitable stocks, it is possible to use nutritional differences merely for the
selection of a sample of potential recombinants, and among the latter to
find a representative set of recombinations of the unselected markers
which should be assorted among the prototrophs willy-nilly, or else
reveal the laws of the distribution or genetic segregation. Detailed
studies of the segregation of unselected factors have, in the first place,
provided the most critical evidence disqualifying intraclonal variation,
because the unselected markers reassort in a great many different com-
binations, while the parents show no such variation by themselves. But
more important, they have also given direct indications of a linear
arrangement of the genetic factors, entirely comparable to the chromo-
somes of plants and animals (Lederberg, 1947). Such experiments have
also shown that, unlike transformations, a wide variety of genetic factors
are reassorted simultaneously, and lead to the conclusions: (a) that the
ony

90 JOSHUA LEDERBERG

a mag

genetic factors exchanged between cells encompass the full genic con-
stitution of the parents; and (b) that the ‘“‘gametes’’ do not mix, 7.e., that
no more than two parents contribute to a given prototroph. In this
light, if an infective factor were responsible for recombination in EZ. coli
K-12, in terms of its biological functions it would be indistinguishable
from a gamete of the bacterium. Until the cytological basis of recom-
bination has been verified, we cannot be sure of the morphology of the

|a- B+ @] NS

cae t
A-iB+@
At -4
A+B+
+ recombinants

Fic. 3.3. The selection of genetic recombinants by minimal medium. Whether
plated separately or together, the parent mutants (represented by dots) are unable to
form visible colonies in minimal agar. However, in mixed cultures, A + B+ recom-
binants (prototrophs) are produced, and these are capable of forming colonies. The
circle and triangle, shaded and unshaded, represent two additional pairs of factors
which, being unselected by the minimal medium, are free to reassort among the
prototrophs. The new combinations of unselected factors provide the strongest
support for the validity of this experiment.

 

 

 

 

 

 

 

cells or cell products whose union results ultimately in genetic recom-
binations. However, many attempts (Lederberg, 1947; Davis, 1950a)
to replace intact cells of one parent by extracts or filtrates in crossing
experiments have been completely unsuccessful, and it seems most
reasonable to suppose that, as in the simplest algae, yeasts and molds,
the fusion cell results from the copulation of ordinary vegetative cells.
On the basis of the kinds of experiments just discussed, and of cyto-
logical studies of cell division (Robinow, 1945), the usual life cycle of
EH. colt K-12 would be as follows. The vegetative cell contains one or
more haploid nuclei usually all alike, each containing one set of genes.
The variable number of nuclei, which depends on the culture phase, is

 
NO Ie mene iceman ee

INHERITANCE, VARIATION, AND ADAPTATION 91

merely the result of an incomplete synchronization between nuclear
multiplication and cell division. Occasionally, haploid cells fuse, fol-
lowed by fusion of one pair of nuclei to give a diploid nucleus. Ordi-
narily, the diploid nucleus never multiplies as such, but segregates
immediately possibly to give four segregated haploid nuclei, but this is
uncertain. The nutritional selective method permits the recovery,
however, only of these segregants in which there has been a ‘‘crossing-
over’’ or genetic exchange so as to result in a prototroph. This means
that usually only a single prototroph can be isolated from a given fusion,
and that an unknown number of fusions may remain undetected, if none
of the segregated progeny happen to be prototrophic recombinants.
Calculations on the probable amount of recombination, however, suggest
that about half the fusions do result in detectable prototrophs.

In essence, therefore, #. colt exhibits what is called a “‘haplobiontic”’
life cycle, which is typical of most lower fungi and algae, and is analogous
to the yeast Zygosaccharomyces, or to the chlorophyte Chlamydomonas.
Many of the lower thallophytes, however, have evolved a mating type
mechanism, so that fusion occurs only between clones of distinct origin,
v.e., Which carry different forms of a mating type or, loosely, a “‘sex”’
gene. As yet, no evidence is available for the differentiation of ‘‘sexes’”’
in bacteria. However, it may well be that the rather low frequency of
recombination observed may have been due to the use of bacterial strains
which are not sexually differentiated.

The details of the life cycle in H#.*coli K-12, as in other organisms,
(Winge and Roberts, 1949) are under genetic control, and stocks have
been found which show informative deviations from the typical pattern
(Lederberg, 1949a). Here, instead of undergoing immediate segregation,
the fusion nucleus is capable of indefinite proliferation in the diploid
condition, although the diploid cells show a strong tendency to segregate
at every division, and it is technically difficult to maintain a culture in the
diploid condition. Such a life cycle would be termed ‘‘haplo-diplo-
biontic,’”’ and has a precedent, for example, in Saccharomyces cerevisiae
and in higher cryptogams. The persistent diploids are especially
advantageous for studying the effects of gene combinations in the same
cell. Furthermore, they afford additional proof of the tangible existence
of the intermediate diploid stage, in which the genes of the two parents
are momentarily brought together, later to reassort and separate. This
proof is particularly consolidated by experiments in which the diploid
cells are allowed to proliferate under microscopic observation, and in
which the isolation of the progeny with the micromanipulator leaves no
doubt as to the concurrence of the genetic factors of the parents within
single cells which is the essence of sexuality (Zelle and Lederberg, 1951).
92 JOSHUA LEDERBERG

This aspect of bacterial genetics is still so undeveloped that a great
many important questions remain unanswered. Perhaps the most
important of these is how generally sexual reproduction may occur among
bacteria. The answer to this question must wait upon the application
of genetic techniques to a variety of bacterial species. In Z£. colt, inten-
sive study of perhaps half a dozen distinct strains has revealed two
besides K-12 which recombine among themselves, and with K-12 (Cavalli
and Heslot, 1949). More recent developments are summarized in Leder-
berg ef al. (1951). A considerable number of distinct strains of HE. colz
have been found capable of crossing. Comparable methods have also
been used to demonstrate a recombination mechanism in Salmonella
typhimurium, but an agent capable of passing a filter is implicated here—
see the discussion of reduced forms of bacteria on page 85.

Sexuality is generally regarded as a source of genetic variation via the
many new combinations of characters that are generated. The evolu-
tionary importance of this process depends, in large part, on how widely
recombination can take place, which remains to be seen. For the
moment, then, the principal biological importance of bacterial sexuality
may be as a tool in the investigation of the genetics and the life cycle of
bacteria, rather than as one of the underlying principles of organic evolu-
tion, which sexual reproduction is for higher forms.

2. Virus Recombination

For many years, opinions were divided on the living nature of viruses,
and particularly of bacteriophages. Whatever doubts may yet linger
should be dispelled by the recent discovery that bacteriophages have an
elaborate genetic system, and in particular a mechanism of genetic
recombination. Two converging lines of evidence have been adduced.

Luria and Dulbecco (1949) have followed up in detail an observation
previously mentioned by Delbriick and Bailey that irregular plaque
counts were obtained from ultraviolet inactivated phage, according to
the procedure used in diluting the phage suspensions. They conclude
that suspensions of UV-treated phage may contain particles which are
capable to adsorption on to susceptible bacteria, but incapable of further
growth and regeneration of phage, if the particle is the only one to have
infected a given cell. However, if two or more such particles are adsorbed
onto a single bacterial cell, they will have a chance to grow and regenerate
normal phage. The probability that doubly-infected bacterial cells will
produce ‘‘viable”’ phage is dependent on the UV dose given the phage
particles. The irregular counts noted by Delbriick and Bailey depend on
whether the ratio of phage to bacteria was such that multiple adsorptions
per cell could take place.
INHERITANCE, VARIATION, AND ADAPTATION 93

The quantitative results obtained by Luria and Dulbecco in their
experiments on the “reactivation” of phage by multiple infection agree
with a theory of recombination of genetic units. It is postulated that
each phage particle contains a number of different genetic units, such
that if any of these is inactivated (as by UV), the phage particle will be
unable to grow in the bacterial host. However, if two particles, carrying
between them a full active complement of the different units should
infect the same cell, a normal phage particle can be restituted by recom-
bination of the active units. With increasing doses of UV , More and
more of the units in each particle will have been inactivated, thus lessen-
ing the chance that a random pair of particles will be able to make up a
full set of active units between them. By determining the rate at which
the efficiency of reactivation decreases with UV dose, an estimate of the
number of genetic units involved can be made—about 20-40 for various
phages in the T group, attacking Z. coli B. This multiplicity reactiva-
tion should be carefully distinguished from photoreactivation, which is an
independent phenomenon.

Hershey and Rotman (1949), using the same phages, obtained more
direct evidence of recombination of characters. The number of mutant
characters available in phage is limited, but mutations affecting host
range and plaque morphology have been found. These authors report
that, among the output of particles from a cell infected with two kinds
of mutants, new combinations of the characters of the input phages will
be found. Corresponding complementary types occur with equal fre-
quency, and they have also succeeded in mapping a number of mutations
on linear linkage groups in accordance with the observed frequencies of
recombination. These observations leave no doubt of the exchange of
genetic characteristics between phages within the host cell. However,
the details of the mechanism of exchange have not all been clarified.
Both groups of workers have speculated that the phage particle within
the host cell may break up into its genetic components, which are not
reassembled until the cell is ready to lyse.

A similar enterprise with influenza virus has also provided evidence
supporting genetic recombination in this organism. It would be difficult
to overestimate the potential importance of virus recombination in
medical epidemiology (Burnet and Lind, 1951).

V. Variation and Adaptation : Recapitulation

The capacity to adapt is one of the cardinal attributes of life. Stu-
dents of adaptation are customarily classified either as physiologists, who
deal with the adaptive-responses of the individual organism, or evolu-
tionists who deal with organic adaptation, 7.e., the long range responses
 

v

a ager! 6 eee

94 JOSHUA LEDERBERG

of the population or species. The bacterial physiologist cannot ignore
populational adaptation, however, because he always works with popula-
tions, not single individuals. He must be careful to distinguish whether
an adaptive response is physiological, a directed change within each
bacterial cell, or populational, whereby the genetic composition of the
culture is altered by differential rates of growth, death or mutations.
The impression held by many bacteriologists that bacteria have unusual
adaptive flexibility is doubtless based on the concurrence of these mecha-
nisms in the bacterial economy.

Connected with this distinction is a second: whether the adaptation
is hereditary. As previously emphasized, good evidence for any directed
adaptive mutation in bacteria is completely lacking, from which we con-
clude that physiological adaptations in general are not hereditary. The
converse, that populational adaptations are hereditary, holds, in general,
but is not logically necessary. We can imagine, for example, that
quantitative resistance to an antibiotic might be randomly distributed
among the cells in a population. Populational adaptation would not
result from the interaction of these cells with the antibiotic unless some
correlation exists between parent and offspring in resistance, but this
correlation need not be heritable in the sense that it would persist indefi-
nitely in the absence of the antibiotic. In practice, however, the distinc-
tion between physiological and populational adaptation parallels that
between the non-genetic and the genetic.

Not all workers have accepted the duality of adaptation mechanisms.
Hinshelwood (1946), for example, has disregarded the selection of spon-
taneous mutants as an element of bacterial adaptations, apparently in
order to bolster the applicability of his system of chemical kinetics to
problems of bacterial growth. A more eclectic outlook seems to be
justified by the evidence. In earlier paragraphs, examples of adaptive
mutations have been given. Instances of physiological adaptations will
be found in nearly every chapter of this book. Here, we shall discuss a
case of adaptation involving both mechanisms, so that the distinction
between them was confused for some time.

Perhaps the most remarkable of bacterial adaptations consists of the
flexibility in amount and activity of bacterial enzymes, and of their
adjustment in response to new substrates, pH change, and so forth
(Monod, 1947). A lactose-fermenting strain, so-called, of £. colt should
more strictly be re-defined as a strain that is competent to produce
adaptive enzymes for lactose fermentation when exposed to lactose under
appropriate conditions. Cells grown on glucose-containing substrate
have virtually no capacity to ferment lactose, compared to cells harvested
from a medium with lactose. After prolonged exposure to lactose, how-
 

 

INHERITANCE, VARIATION, AND ADAPTATION 95

ever, unadapted cells will slowly acquire fermentative competence for
this carbohydrate. Since this adaptation occurs in the absence of
growth—rather slowly in the present instance—and disappears very
promptly when the adapted cells are transferred back to glucose sub-
strates, this adaptation is clearly physiological and non-genetic.

Variant types of EZ. colt are known which are incompetent to adapt to
lactose or to various other sugars. The designation E. coli-‘‘mutabile”’
has been applied to lactose-negative strains which occasionally mutate to
lactose-positive. Reasonably good evidence can be cited for the view
that the transition from lactose-negative to lactose-positive which is
observed in lactose broth cultures inoculated with EF. coli-““mutabile” is
due to the selective advantage of spontaneous lactose-positive mutants,
so that they overgrow the population (see Luria, 1947). At first sight,
it may seem paradoxical that the same overall adaptive process may be
populational and physiological at the same time. However, the con-
tradiction is resolved when it is realized that the genetic adaptation
changes the potentialities of the cell, so that it then becomes competent
to undergo physiological enzymatic adaptation.

In view of the potentially unlimited scope of physiological effects of
mutations, one might predict that the course of bacterial evolution would
be unerringly adaptive, and in general in the direction of an unlimited
range of biochemical potentialities. That bacteria as we see them are
peculiarly specialized, and that the range of their biochemical activities
is (fortunately for us) often restricted, we ascribe to the microscopic
character of biological evolution. That is to say, the evolution of a
microculture is adaptive only in terms of the immediate local environ-
ment. The microbe’s evolution is not directed by an intelligent fore-
sight which would enable pre-adaptation to other, anticipated micro-
environments. Natural selection favors those types which, at the
moment, proliferate most rapidly, and pays no heed to potential changes
in the environment which may turn the tables on the once dominant
mutant. This principle enables us to understand experimental results
which might otherwise seem paradoxical, for example, the apparently
anomalous selection in minimal medium against prototrophs in mixed
culture with certain biochemical mutants in Neurospora and in E. coli
(Ryan, 1946; Ryan and Schneider, 1949).

These considerations also lead to a more immediate conclusion, namely
that a priori deductions on the direction of selection in a mixed microbial
population may be unsafe, even when based upon measurements of
growth or killing rates on the isolated pure cultures. A number of
examples are now available showing the disaccord between the simple
expectations and the experimental results of mixed culture experiments.
 

ae et ee

96 JOSHUA LEDERBERG

The detailed analysis of bacterial populations may be exemplified by
studies on Brucella abortus (Braun, 1947b; Goodlow, Mika and Braun,
1950). Cultures from smooth inocula regularly accumulate large pro-
portions of rough variants upon aging, but this displacement is not
reflected in differential growth rates of the smooth and rough types. It
was ultimately shown that the amino acid alanine accumulated in aged
cultures, and that this compound selectively inhibited growth of smooth
cells, thus conferring a selective advantage on spontaneously occurring
rough variants.

Several workers studying the increase in proportion of phage-resistant
or other mutants under the influence of mutation ‘‘pressure”’ have been
impressed by sporadic cycles in the numbers of resistants. Following
a period during which the proportion of resistants increases slowly and
linearly; as mutational events convert individual cells from sensitive to
resistant, the resistants may suddenly disappear, and then re-accumulate
at the same rate as before (Stocker, 1949; Novick and Szilard, 1950;
Atwood, Schneider, and Ryan, 1951). The cycles have been ascribed
to subtle, adaptive mutations which result in cells with an improved
adaptation to the conditions of culture. Descendants of these cells over-
grow the culture and displace the previous population. Because the
proportion of resistants is usually very low, the adaptive mutation and
overgrowth will almost always stem from a sensitive cell, giving rise to a
new sensitive population. It has been suggested that periodic selection
may protect microbial cultures from the accumulation of auxotrophic or
other potentially deleterious mutations. However, the long-term equi-
librium between sensitives and resistants, or other pairs of alternatives,
is not likely to be affected by such non-discriminatory selective processes.

We thus conclude that our ignorance equips us very poorly for our
efforts to interpret physiological evolution of bacteria except in the most
general terms. We should not, however, accept the present differentia-
tion of microbes as a fait accompli, but must ask how they came to be as
they are. Bacterial genetics, if it has not yet solved this problem, may at
least hopefully claim that its development has helped the clearer formula-
tion of this as well as other problems of bacterial physiology.

Mathematical Appendix

THE Poisson DISTRIBUTION

Bacteriologists frequently wish to know the statistical distribution
describing events with a low probability, p, and with a large number, n,
of trials, such that n X p, the expectation is of the order of unity. For
example, random samples containing 10-° ml. might be taken from a
INHERITANCE, VARIATION, AND ADAPTATION 97

population of 10° bacterial/ml., and the experimenter would like to know
how many bacteria to expect in a given sample. The average number
of bacteria per sample, m = n X p, will be 10-® X 10° or 1, but if the
bacteria are scattered randomly throughout the suspension, some samples
may contain no bacteria, while others will contain several. The prob-
ability, P(x), that such a sample will contain just z bacteria, is a function
of x and m (the average per sample) known as the Poisson distribution.
It can be shown that P(x) is closely approximated by the terms of the
series

 

 

om o-™m, e7™m? e~™m 8 e-™m4 a em
> 2" BX? 4X3BxX2 x!
for the probability that’ a sample will have 0, 1, 2,3,4 ... or z bacteria.

(For references and further discussion, see Eisenhart and Wilson, 1943.)

The terms of this series are not difficult to compute, but useful tables
of the Poisson distribution are available (Molina, 1942).

The 0’th term of the distribution is of special interest, 7.e., Po = e-™,
as in the form m = — In Py it permits m to be calculated from a fre-
quently recorded experimental datum, Po, which may represent, for
example, the fraction of replicate tubes which remain sterile. The
‘serial dilution code’? method of enumerating viable bacteria is based
upon this expression (Eisenhart and Wilson, 1943).

THE MEASUREMENT OF SpontaNeous Mutation RATES

Spontaneous mutation rates are usually expressed as some function
of the growth rate of the bacterium, rather than in chronological units.
This convention is justified by the correlation of mutations with growth
(Luria and Delbriick, 1943; Englesberg and Stanier, 1949), although this
relationship needs further study.* It is not clear whether spontaneous
mutations are thus directly related to reproduction (hypothesis of error
in duplication), or whether the growth rate merely expresses the overall
metabolic rate. On the latter basis, Luria and Delbriick (1943) defined

*In a further attack on problems of spontaneous mutation, Novick and Szilard
(1950) made use of a device (the ‘‘chemostat”’) in which bacterial cultures were
maintained in a steady state at a fixed growth rate by means of a continuous flow
system. In agreement with previous work, they found that EF. coli cells did not
accumulate phage-resistance mutations when they were prevented from growth by
deprivation of tryptophane. However, cells which were permitted to grow at different
rates by limiting tryptophan concentration mutated at a constant rate per cell per
unit time, independent of growth rate. The effect of temperature on mutation rate
could be expressed as a Qio = 2. These experiments suggest that spontaneous muta-
tions are a result of metabolic activity rather than accidental errors in the copying
of a gene at the time of reduplication. More decisive evidence is needed, however, to
determine if this conclusion can be generalized, and to establish the particular areas
of metabolic activity associated with spontancous mutation.
 

wo mmmwent YQ JOSHUA LEDERBERG

a time unit equal to the mean generation time divided by In 2. In this
appendix the following symbols will be used:

a = mutation rate (probability of mutation per cell per unit time)

N = number of cells (at time ¢)

m = number of mutational events or mutant clones

r = number of mutant cells

As a consequence of the definition of t, the law of growth may be stated

as:

(3.1) dN/dt = N, or N = Neet.

Mutant cells (r) are augmented either by growth, at rate r, or by new
mutations, at rate aN. Thus we have dr/dt = r+ aN, which admits
the solution,

(8.2) r = atN (for No = 1) orr = aN InN,
Solving for a, we have
(3.3) a =r/(N In N)

Expression 3.3 provides a predicted value of r, mutants per culture,
which represents the average over an indefinitely large number of cul-
tures. However, early generations rarely contribute mutations (since NV
is relatively low at that time) but influence r disproportionately because
of the considerable amount of further multiplication that such mutants
enjoy when they do occur. Consequently, the application of 3.3 would
usually result in a considerable underestimate of a if an early mutation
did not occur, and rarely in a very great overestimate if an early mutation
did occur in one of the cultures assayed.

In an attempt to correct the usual underestimation by 3.3, Luria and
Delbriick (1943) formulated a derivation of what they termed a “likely
average,’ 7, which represents what might be expected as the experimental
mean in a finite number of cultures, C. The fictional assumption is made
that no mutations have occurred prior to an arbitrary time, t = 7; 7 is
chosen so that there will have been a single premature mutation, on the
average, in the entire experiment of C cultures. That is, aCN; = 1, or
+= —InaC. Since t = In N,

(3.4) t—7t=InN +1n aC = InaN.

If in the derivation of 3.2 the limits of integration are taken as (i, 2)
rather than (¢, 0), in accordance with our fiction that no mutations occur
prior to ¢ = 2, we obtain

(3.24) r= (t—iaN = aN InaN.

This equation cannot explicitly be solved algebraically, but is readily
INHERITANCE, VARIATION, AND ADAPTATION 99

solved numerically in the form Cr = aCN In aCN, since Cr is known
(total number of mutants counted in all C cultures of the experiment).

Although relation 3.2a offers certain short-term advantages, it does
not mitigate the very high variance of r, calculated by Luria and Del-
briick to be: raCN/InaCN. As aCN is simply the total number of
mutations in the experiment, it may be hundreds or thousands of times
larger than r. Consequently, it will be difficult to obtain consistent
estimates of r. A second limitation of this method is the assumption
that the mutants grow at the same rate as the non-mutants, which is
implicit in the ‘‘r’’ term of 3.2. Small deviations from equal growth
rates will be reflected in large inaccuracies in the measurement of muta-
tion rates. Although this method uses such detailed information as the
number of mutants per culture, it is, therefore intrinsically inefficient
and liable to error.

Rates of mutation can also be estimated by a method that may seem
at first sight to be inefficient, but that is free from the defects listed
above. If po is defined as the fraction of replicate cultures in which no
mutants are present, 7.e., in which no mutations have occurred, it can be
related to a. Since a@ is defined as the probability of mutation per
bacterium per time unit, aNé will give the number of mutations in a
culture, where NV is the mean value of N over t:

No
t

1 f[' No

t
(3.5) V=- | Ndt= Ne f edt = !
0

t
e! | = 5 (N — No)

*. m (number of mutations) = at N/t = aN

This result can also be expressed in the form ‘‘there are N chances for
mutation, each with probability a.”’ Then the probability that none of
the N trials results in a mutation can be expressed:

(3.6) po = a — a) = (1 _— a)*N/a _ ene
or,
(3.6a) a= — In n/N.

Equation 3.6 is, of course, zero term of the Poisson distribution of muta-
tions, with mi = aN.

The fact that some cultures will contain mutants and others will not,
in accordance with 3.6, has been used fallaciously as an argument that
the mutation is spontaneous. This so called fluctuation, however,
simply indicates that some random variable at the time of selection
ae alg rE 2 a

¥ 100 JOSHUA LEDERBERG

 

influences the result, and is by itself not incompatible with the hypothesis
of induced variation. For example, the same kind of result could be
obtained during bacterial disinfection: with an appropriate treatment,
some cultures would be completely sterilized, while others would contain
viable cells, but we could not conclude that sterilization was spontaneous.
Therefore the use of 3.6a, unlike 3.2a, presupposes the hypothesis of
spontaneous mutation, and is useful only for estimating its rate. Other
methods for measuring mutation rate are reviewed by Newcombe (1948).

The spontaneous mutation rate is, of course, not the same for all
bacterial characters, but depends on the stability of the particular genic
material studied. Rates varying from 6 X 10-? to 1 X 107° have been
described for colonial variation in Salmonella typhimurium (Shapiro,
1946) and streptomycin resistance in LE. coli (Newcombe and Hawirko,
1949), respectively. Many bacterial mutations fall within the range
10-* to 10-8, which is quite comparable with the frequency of spontaneous
mutations in higher plants and animals.

While this chapter was being prepared, a publication appeared in
which the theoretical distribution of mutants is derived using the same
sort of model as above (Lea and Coulson, 1949). These authors point
out that the estimation of the mutation rate, a, from the statistic, 7, is
very inefficient, and that the variance does not decrease with an increasing
number of cultures. That is, for a given number of mutants, 7, a single
larger culture gives as satisfactory an estimate as a series of smaller
cultures of the same aggregate size. With the help of the theoretical
distribution, a rather involved method was developed for the maximum
likelihood estimation of a, which uses all of the statistics most efficiently.
However, Lea and Coulson show that a ean be calculated from the median
number of mutants, ro, with little loss of efficiency, and with very much
less computational effort. They show that

(3.7) ro = m(1.24 + In m), where, as before, a = m/N.

Like 3.2a, this expression can be solved for m numerically, or by inter-
polating in Lea and Coulson’s Table III.

In view of the probable inaccuracies of the postulated model, such
as phenotypic lag and nuclear segregation (see text), equation 3.7 seems
to afford the most feasible and economic way of using data involving
numbers of mutants. Inasmuch as it eliminates the necessity of using
precise counts of cultures with inordinately large numbers of mutants,
it is also more practicable than estimates based on the mean number of
mutants. However, when pp is about 20%, the null fraction method is
almost as efficient as any of the others, and is probably generally the
method of choice.
eae Schl