MUTATIONS OF BACTERIA FROM VIRUS SENSITIVITY

TO VIRUS RESISTANCE’-’

S. E. LURIAS AND M. DELBROCK

Indiana University, Bloomingion, Indiana, and

va’enderbilt Universily, Nashville, Tennessee

Received May 29, 1943

INTRODUCTION

W HEN a pure bacterial culture is. attacked by a bacterial virus, the cul- ture will clear after a few hours due to destruction of the sensitive ceIls

by the virus. However, after further incubation for a few hours, or sometimes

days, the culture will often become turbid again, due to the growth of a bacterial

variant which is resistant to the action of the virus. This variant can be

isolated and freed from the virus and will in many cases retain its resistance

to the action of the virus even if subcultured through many generations in the

absence of the virus. While the sensitive strain adsorbed the virus readily, the

resistant variant will generally not show any affinity to it.

The resistant bacterial variants appear readily in cultures grown from a

single cell. They were, therefore, certainly not present when the culture was

started. Their resistance is generally rather specific. It does not extend to

viruses that are found to differ by other criteria from the strain in whose presence

the resistant culture developed. The variant may differ from the original

strain in morphological or metabolic characteristics, or in serological type or in

colony type. Most often, however, no such correlated changes are apparent,

and the variant may be distinguished from the original strain only by its resistance

to the inciting strain of virus.

The nature of these variants and the manner in which they originate have

been discussed by many authors, and numerous attempts have been made to

correlate the phenomenon with other instances of bacterial variation.

The net effect of the addition of virus consists of the appearance of a variant

strain, characterized by a new stable character-namely, resistance to the

inciting virus. The situation has often been expressed by saying that bacterial

viruses are powerful “dissociating agents.” While this expression summarizes

adequately the net effect, it must not be taken to imply anything about the

mechanism by which the result is brought about. A moment’s reflection will

show that there are greatly differing mechanisms which might produce the

same end result.

D’HERELLE (1926) and many other investigators believed that the virus

by direct action induced the resistant variants. GRATIA(1 921), BURNET(I 929),

and others, on the other hand, believed that the resistant bacterial variants

are produced by mutation in the culture prior to the addition of virus. The

*Aided by grants from the D A Z IF~OU NDATIOFNOR MEDICALR ESEARCHan d from the

- Fellow of the GUGGENHEIFMO UNDATION.

Theory by M. D., experiments by S. E. L.

ROCKEFELLEFRO UNDATION.

GENETICSa 8: 491 November 1943

492 S. E. LURIA AND M. DELBRUCK

virus merely brings the variants into prominence by eliminating all sensitive

bacteria.

Neither of these views seems to have been rigorously proved in any single

instance. BURNET’S(1 929) work on isolations of colonies, morphologically

distinguishable prior to the addition of virus, which proved resistant to the

virus comes nearest to this goal. His results appear to support the mutation

hypothesis for colony variants. It may seem peculiar that this simple and important

question should not have been settled long ago, but a close analysis of

the problem in hand will show that a decision can only be reached by a more

subtle quantitative study than has hitherto been applied in this field of research.

Let us begin by restating the basic experimental finding.

A bacterial culture is grown from a single cell. At a certain moment, the

culture is plated with virus in excess. Upon incubation, one finds that a very

small fraction of the bacteria survived the attack of the virus, as indicated by

the development of a small number of resistant colonies, consisting of bacteria

which do not even adsorb the virus.

Let us focus our attention on the first generation of the resistant variantthat

is, on those bacteria which survive immediately after the virus has been

added. These survivors we may call the “original variants.” We know that

these bacteria and their offspring are resistant to the virus. We may formulate

three alternative hypotheses regarding them.

a. Hypothesis of mutation to immunity. The original variants were resistant

before the virus was added, and, like their offspring, did not even adsorb it. On

this hypothesis the virus did not interact at all with the original variants,

the origin of which must be ascribed to “mutations” that occur quite independently

of the virus. Naming such hereditary changes “mutations” of course

does not imply a detailed similarity with any of the classes of mutations that

have been analyzed in terms of genes for higher organisms. The similarity

may be merely a formal one.

b. Hypothesis of acquired immunity. The original variants interacted with

the virus, but survived the attack. We may then inquire into the predisposing

cause which effected the survival of these bacteria in contradistinction to the

succumbing ones. The predisposing cause may be hereditary or random. Accordingly

we arrive at two alternative hypotheses-namely,

bl. Hypothesis of acquired immunity of hereditarily predisposed individuals.

The original variants originated by mutations occurring independently of the

presence of virus. When the virus is added, the variants will interact with it,

but they will survive the interaction, just as there may be families which are

hereditarily predisposed to survive an otherwise fatal virus infection. Since we

know that the offspring of the original variants do not adsorb the virus, we

must further assume that the infection caused this additional hereditary

change. .

bz. Hypothesis of acquired immunity-hereditary aj[er infection. The original

variants are predisposed to survival by random physiological variations in

size, age, etc. of the bacteria, or maybe even by random variations in the

MUTATIONS OF BACTERIA 493

point of attack of the virus on the bacterium. After survival of such random

individuals, however, we must assume that their offspring are hereditarily

immune, since they do not even adsorb the virus.

These alternative hypotheses may be grouped by first considering the origin

of the hereditary difference. Do the original variants trace back to mutations

which occur independently of the virus, such that these bacteria belong to a

few clones, or do they represent a random sample of the entire bacterial population?

The first alternative may then be subdivided further, according to

whether the original variants do or do not interact with the virus. Disregarding

for the moment this subdivision, we may formulate two hypotheses:

I. First hypothesis (mutation): There is a finite probability for any bacterium

to mutate during its life time from “sensitive” to “resistant.” Every

offspring of such a mutant will be resistant, unless reverse mutation occurs.

The term “resistant” means here that the bacterium will not be killed if exposed

to virus, and the possibility of its interaction with virus is left open.

2. Second hypothesis (acquired hereditary immunity): There is a small finite

probability for any bacterium to survive an attack by the virus. Survival of

an infection confers immunity not only to the individual but also to its offspring.

The probability of survival in the first instance does not run in clones.

If we find that a bacterium survives an attack, we cannot from this information

infer that close relatives of it, other than descendants, are likely to survive the

attack.

The last statement contains the essential difference between the two hypotheses.

On the mutation hypothesis, the mutation to resistance may occur

any time prior to the addition of virus. The culture therefore will contain

“clones of resistant bacteria” of various sizes, whereas on the hypothesis of

acquired immunity the bacteria which survive an attack by the virus will be

a random sample of the culture.

For the discussion of the experimental possibility of distinction between

these two hypotheses, it is important to keep in mind that the offspring of a

tested bacterium which survives is resistant on either hypothesis. Repeated

tests on a bacterium at different times, or on a bacterium and on its offspring,

could therefore give no information of help in deciding the present issue. Thus,

one has to resort to less direct methods. Two main differences may be derived

from the hypotheses:

First, if the individual cells of a very large number of microcolonies, each

containing only a few bacteria, were examined for resistance, a pronounced

correlation between the types found in a single colony would be expected on

the mutation hypothesis, while a random distribution of resistants would be

expected on the hypothesis of acquired hereditary immunity. This experiment,

however, is not practicable, both on account of the difficulty of manipulation

and on account of the small proportion of resistant bacteria.

Second, on the hypothesis of resistance due to mutation, the proportion of

resistant bacteria should increase with time, in a growing culture, as new

mutants constantly add to their ranks.

494

In contrast to this increase in the proportion of resistants on the mutation

hypothesis, a constant proportion of resistants may be expected on the hypothesis

of acquired hereditary immunity, as long as the physiological conditions

of the culture do not change. To test this point, accurate determinations of

the proportion of resistant bacteria in a growing culture and in successive subcultures

are required. In the attempt to determine accurately the proportion

of resistant bacteria, great variations of the proportions were found, and results

did not seem to be reproducible from day to day.

Eventually, it was realized that these fluctuations were not due to any uncontrolled

conditions of our experiments, but that, on the contrary, large

fluctuations are a necessary consequence of the mutation hypothesis and that

the quantitative study of the fluctuations may serve to test the hypothesis.

The present paper will be concerned with the theoretical analysis of the

probability distribution of the number of resistant bacteria to be expected on

either hypothesis and with experiments from which this distribution may be

inferred.

While the theory is here applied to a very special case, it will be apparent

that the problem is a general one, encountered in any case of mutation in uniparental

populations. It is the belief of the authors that the quantitative study

of bacterial variation, which until now has made such little progress, has been

hampered by the apparent lack of reproducibility of results, which, as we shall

show, lies in the very nature of the problem and is an essential element for its

analysis. It is our hope that this study may encourage the resumption of quantitative

work on other problems of bacterial variation.

S. E. LUFUA AND M. DELBRUCK

THEORY

The aim of the theory is the analysis of the probability distributions of the

number of resistant bacteria to be expected on the hypothesis of acquired

immunity and on the hypothesis of mutation.

The basic assumption of the hypothesis of acquired hereditary immunity

is the assumption of a fixed small chance for each bacterium to survive an attack

by the virus. In this case we may therefore expect a binomial distribution

of the number of resistant bacteria, or, in cases where the chance of survival

is small, a Poisson distribution.

The basic assumption of the mutation hypothesis is the assumption of a

fixed small chance per time unit for each bacterium to undergo a mutation to

resistance. The assumption of a fixed chance per time unit is reasonable only

for bacteria in an identical state. Actually the chance may vary in some manner

during the life cycle of each bacterium and may also vary when the physiological

conditions of the culture vary, particularly when growth slows down on

account of crowding of the culture. With regard to the first of these variations,

the assumed chance represents the average chance per time unit, averaged

over the life cycle of a bacterium. With regard to the second variation, it

seems reasonable to assume that the chance is proportional to the growth rate

of the bacteria. We will then obtain the same results as on the simple assumpMUTATIONS

OF BACTERIA 49s

tion of a fixed chance per time unit, we agree to measure time in units of division

cycles of the bacteria, or any proportional unit.

We shall choose as time unit the average division time of the bacteria, divided

by In 2, so that the number Nt of bacteria in a growing culture as function

of time t follows the equations

(1) dNt/dt = N,, and Nt = Noet.

We may then define the chance of mutation for each bacterium during the

time element dt as

(2) adt,

so that a is the chance of mutation per bacterium per time unit, or the “mutation

rate.”

If a bacterium is capable of different mutations, each of which results in

resistance, the mutation rate here considered will be the sum of the mutation

rates associated with each of the different mutations.

The number dm of mutations which occur in a growing culture during a

time interval dt is then equal to this chance (2) multiplied by the number

of bacteria: or

(3 ) dm = adtN,,

and from this equation the number m of mutations which occur during any

finite time interval may be found by integration to be

(4) m = a(Nt - No)

or, in words, to be equal to the chance of mutation per bacterium per time unit

multiplied by the increase in the number of bacteria.

The bacteria which mutate during any time element dt form a random

sample of the bacteria present at that time. For small mutation rates, their

number will therefore be distributed according to Poisson’s law. Since the

mutations occuring in different time intervals are quite independent from each

other, the distribution of all mutations will also be according to Poisson’s law.

This prediction cannot be verified directly, because what we observe, when

we count the number of resistant bacteria in a culture, is not the number of

mutations which have occurred, but the number of resistant bacteria which

have arisen by multiplication of those which mutated, the amount of multiplication

depending on how far back the mutation occurred.

If, however, the premise of the mutation hypothesis can be proved by other

means, the prediction of a Poisson distribution of the number of mutations

’ We assume that the number of resistant bacteria is at all times small in comparison with the

total number of bacteria. If this condition is not fulfilled, the total number of bacteria in this

equation has to be replaced by the number of sensitive bacteria. The subsequent theoretical developments

will then become a little more complicated. For the case studied in the experimental

part of this paper the condition is fulfilled.

496 S. E. LUNA AND M. DELBRUCK

may be used. to determine the mutation rate. It is only necessary to determine

the fraction of cultures showing no mutation in a large series of similar cultures.

This fraction PO, according to theory, should be:

( 5 ) po = e-m.

From this equation the average number m of mutations may be calculated,

and hence the mutation rate a from equation (4).

Let us now turn to the discussion of the distribution of the number of

resistant bacteria.

The average number of resistant bacteria is easily obtained by noting that

this number increases on two accounts-namely, first on account of new mutations,

second on account of the growth of resistant bacteria from previous

mutations. During a time element dt the increase on the first account will be,

by equation ( 3 ) : adtNt. Nt, the number of bacteria present at time t, is

given by equation (I). The increase on the second account will depend on the

growth rate of the resistant bacteria. In the simple case, which we shall

treat here, this growth rate is the same as that of the sensitive bacteria, and

the increment on this account is p dt, where p is the average number of resistant

bacteria present at time t. We have then as the total rate of increase

of the average number of resistant bacteria dp/dt = aNt+p and upon integration

(6) p = taNt

if we assume that at time zero the culture contained no resistant bacteria.

It will be seen that the average number of resistant bacteria increases more

rapidly than the total number of bacteria. Indeed the fraction of resistant

bacteria in the culture increases proportionally to time. This, as pointed out

in the introduction, is a distinguishing feature of the mutation hypothesis

but unfortunately, as will be seen in the sequel, is not susceptible to experimental

verification due to statistical fluctuations.

The resistant bacteria in any culture may be grouped, for the purpose of

this analysis, into clones, taking together all those which derive from the

same mutation. We may say that the culture contains clones of various age

and size, calling “age” of a clone the time since its parent mutation occurred

and “size” of a clone the number of bacteria in a clone at the time of observation.

It is clear that size and age of a clone determine each other. If, in particular,

we make the simplifying hypothesis that the resistant bacteria grow

as fast as the normal sensitive strain, the relation between size and age will be

expressed by equation (I), with appropriate meaning given to the symbols.

The relation implies that the size of a clone increases exponentially with its

age. On the other hand, the frequency with which clones of different ages may

be encountered in any culture must decrease exponentially with age, according

to equations (3) and (I).

Combining these two results-namely, that clone size increases exponentially

with clone age and that frequency of clones of different age decreases

exponentially with clone age-we see that the two factors cancel when the

MUTATIONS OF BACTERIA 49 7

average number of bacteria belonging to clones of one age group is considered.

In other words, at the time of observation we shall have, on the average, as

many resistant bacteria stemming from mutations which occurred during the

first generation after the culture was started as stemming from mutations

which occurred during the last generation before observation, or during any

other single generation.

On the other hand, for small mutation rates it is very improbable that any

mutation will occur during the early generations of a single or of a limited number

of experimental cultures. It follows that the average number of resistant

bacteria derived from a limited number of experimental cultures will, probably,

be considerably smaller than the theoretical value given by equation (6), and,

improbably, the experimental value will be much larger than the theoretical

value. The situation is similar to the operation of a (fair) slot machine, where

the average return from a limited number of plays is probably considerably

less than the input, and improbably, when the jackpot is hit, the return is

much bigger than the input.

This result characterizes the distribution of the'number of resistant bacteria

as a distribution with a long and significant tail of rare cases of high numbers of

resistant bacteria, and therefore as a distribution with an abnormally high variance.

This variance will be calculated below.

For such distributions the averages derived from limited numbers of samples

yield very poor estimates of the true averages. Somewhat better estimates of

the averages may in such cases be obtained by omitting, in the calculation of

the theoretical averages, the contribution to these averages of those events

which probably will not occur in any of our limited number of samples. We

may do this, in the integration leading to equation (6), by putting the lower

limit of integration not at time zero, when the cultures were started, but at a

certain time t o , prior to which mutations were not likely to occur in any of our

experimental cultures. We then obtain as a likely average r of the number of

resistant bacteria in a limited number of samples, instead of equation (6),

r = (t - to)aNt.

It now remains to choose an appropriate value for the time interval t - to.

For this purpose we return to equation (4, in which it was stated that the

average number of mutations which occur in a culture is equal to the mutation

rate multiplied by the increase of the number of bacteria. Let us then choose

t o such that up to that time just one mutation occurred, on the average, in a

group of C similar cultures, or

I = aC(Nt, - NO).

In this equation we may neglect No, the number of bacteria in each inoculum,

in comparison with Nto, the number of bacteria in each culture at the critical

time to. We may also express Nto in terms of Nt, the number of bacteria at the

time of observation, applying equation (I) :

N = N,e-(t-to). t o

498

We thus obtain

(7) t' - to = ln(NtCa).

Equations (6a) and (7) may be combined to eliminate t-to and to yield

a relation between the observable quantities r and Nt on the one hand and

the mutation rate a on the other hand, to be determined by this equation:

(8) r = aNtln (NtCa).

This simple transcendental equation determining a may be solved by any

standard numerical method. In figure I, the relation between r and aNt is

plotted for several values of C.

S. E. LUIUA AND M. DELBRtfCK

FIGUR1E.- The value of aNt as a function of r for various values of C. The upper left hand part

of the figure gives the curves for low values of aNt and of r on a larger scale. See text.

Estimates of a obtained from equation (8) will be too high if in any of the

experimental cultures a mutation happened to occur prior to time to. From the

definition of t o it will be seen that this can be expected to happen in little more

than half of the cases.

While we have thus obtained a relation permitting an estimate of the mutation

rate from the observation of a limited number of cultures, this relation is

in no way a test of the correctness of the underlying assumptions and, in particular,

is not a test of the mutation hypothesis itself. In order to find such

tests of the correctness of the assumption we must derive further quantitative

relations concerning the distribution of the number of resistant bacteria and

compare them with experimental results.

MUTATIONS OF BACTERIA 499

Since we have seen that the mutation hypothesis, in contrast to the hypothesis

of acquired immunity, predicts a distribution of the number of resistant

bacteria with a long tail of high numbers of resistant bacteria, the determination

of the variance of the distribution should be helpful in differentiating between

the two hypotheses. We may here again determine first the true variance-

that is, the variance of the complete distribution-and second the likely

variance in a limited number of cultures, by omitting those cases which are

not likely to occur in a limited number of cultures.

The variance may be calculated in a simple manner by considering separately

the variances of the partial distributions of resistant bacteria, each

partial distribution comprising the resistant bacteria belonging to clones of

one age group. The distribution of the total number of resistant bacteria is

the resultant of the superposition of these independent partial distributions.

Each partial distribution is due to the mutations which occurred during a

certain time interval d7, extending from (t-.) to (t-T+dr). The average

number of mutations which occurred during this interval is, according to

equation (3),

(9) dm = aN,dT = aNte-rd7.

These mutations will be distributed according to Poisson’s law, so that the

variance of each of these distributions is equal to the mean of the distribution.

We are however not interested in the distribution of the number of mutations

but in the distribution of the number of resistant bacteria which stem from

these mutations at the time of observation-that is, after the time interval r.

Each original mutant has then grown into a clone of size er. The distribution

of the resistant bacteria stemming from mutations occurred in the time interval

d7 has therefore an average value which is er times greater than the average

number of mutations, and a variance which is e2r times greater than the variance

of the number of mutations. Thus we find for the average number of

resistant bacteria:

dp = aNtdr,

and for the variance of this number

vanp = aNterd7.

From this variance of the partial distribution, the variance of the distribution

of all resistant bacteria may be found simply by integrating over the appropriate

time interval-that is, either from time t to time o (7 from o to t), if

the true variance is wanted, or from time t to time t o (7 from o to t- to), if the

likely variance in a limited number of cultures is wanted. In the first case we

obtain :

(10) var, = aNt(et - I).

In the second case we obtain:

(1oa) var, = aNt[e(t-to) - I].

500 S. E. LURIA AND M. DELBRUCK

Substituting here the previously found value of (t-to) and neglecting the

second term in the brackets, we obtain:

(11) varr = Ca2Nt2.

Comparing this value of the likely variance with the value of the likely

average, from equation (8), we see that the ratio of the standard deviation

to the average is:

(12) d\/vBT,/r = &/In (NtCa).

It is seen that this ratio depends on the logarithm of the mutation rate and

will consequently be only a little smaller for mutation rates many thousand

times greater than those considered in the experiments reported in this paper.

In the beginning of this theoretical discussion we pointed out that the

hypothesis of acquired immunity leads to the prediction of a distribution of

the number of resistant bacteria according to Poisson’s law, and therefore to

the prediction of a variance equal to the average. On the other hand, if we compare

the average, equation (8), with the variance, equation (11), (not, as above,

with the square root of the variance), we obtain

( 1 4 varr = rNtCa/ln (NtCa).

Equation (Iza) shows that the likely ratio between variance and average is

much greater than unity on the hypothesis of mutation, if (NtCa), the total

number of mutations which occurred in our cultures, is large compared to

unity!

It is possible to carry the analysis still further and to evaluate the higher

moments of the distribution function of the number of resistant bacteria, or

even the distribution function itself. The moments are comparatively easy to

obtain, while the calculation of the distribution function involves considerable

6 In some of the experiments reported in the present paper we did not determine the total

number of resistant bacteria in each culture, but the number contained in a small sample from

each culture. In these cases the variance of the distribution of the number of resistant bacteria

will be slightly increased by the sampling error. The proper procedure is here first to find the

average number of resistant bacteria per culture by multiplying the average per sample by the

ratio

(‘3)

volume of culture

volume of sample’

second, to evaluate the mutation rate with the help of equation (8); third, to figure the likely

variance for the cultures by equation (11); fourth, to divide this variance by the square of the

ratio (13) to obtain that part of the variance in the samples which is due to the chance distribution

of the mutations. The experimental variance should be greater than this value, on account of

the sampling variance. The sampling variance is in all our cases only a small correction to the

total variance, and it is sufficient to use its upper limit, that of the Poisson distribution, in our

calculations. Consequently, when comparing the experimental with the calculated values, we

first subtract from the experimental value the sampling variance, which we take to be equal to

the average number of resistant bacteria.

MUTATIONS OF BACTERIA 501

mathematical difficulties. An approximation to the beginning of the distribution

function-that is, to its values for small numbers of resistant bacteriamay

be obtained by grouping mutations according to the bacterial generation

during which they occurred. For instance, the probability of obtaining seven

resistant bacteria may be broken down into the sum of the following alternative

events: (a) seven mutations during the last generation; jb) three mutations

during the last generation and two mutations one generation back; (c) three

mutations during the last generation and one mutation two generations back;

(d) one mutation during the last generation and three mutations one generation

back; (e) one mutation during the last generation, one mutation one generation

back and one mutation two generations back.

The probability of each of these events depends only on the mutation rate

and on the final number of bacteria.

The grouping of mutations according to the bacterial generation during

which they occurred, and the assumption that the bacteria increase in simple

geometric progression, simplify the calculation sufficiently to permit numerical

computation. On the other hand, the classes with two, four, eight, etc., mutants

are artificially favored by this procedure, so that a somewhat uneven

distribution results, with too high values for two, four, eight, etc., resistant

bacteria (see fig. 2 ) .

MATERIAL AND METHODS

The material used for our experimental study consisted of a bacterial virus

CY and of its host, Escherichia coli B (DELBRUCK and LURIA 1942). Secondary

cultures after apparently complete lysis of B by virus a show up within a few

hours from the time of clearing. They consist of cells which are resistant to

the action of virus CYb, ut sensitive to a series of other viruses active on B.

The resistant cells breed true and can be established easily as pure cultures.

No trace of virus could be found in any pure culture of the resistant bacteria

studied in this paper. The resistant strains are therefore to be considered as

non-lysogenic.

Tests were made to see whether the resistance to virus a was a stable character

of the resistant strains. In the first place, it was found that virus a is

not appreciably adsorbed by any of the resistant strains. In the second place,

when a certain amount of virus CY is mixed with a growing culture of a resistant

strain, no measurable increase of the titer of virus a occurs over a period of

several hours. This is a very sensitive test for the occurrence of sensitive bacteria,

and its negative result for all resistant strains shows that reversion to

sensitivity must be a very rare event.

Morphologically at least two types of colonies of resistant bacteria may be

distinguished. The first type of colony is similar to the type produced by the

sensitive strain both in size and in the character of the surface and of the

edge. The second type of colony is much smaller and translucent. The difference

in colony type is maintained in subcultures. Microscopically the bacteria

from these two types of colonies are indistinguishable. They also do not differ

502 S. E. LURIA AND M. DELBRUCK

from each other or from the sensitive strain in their fermentation reactions on

common sugars and in the characteristics of their growth curves in nutrient

broth. In particular, the lag periods, the division times during the logarithmic

phase of growth, and the maximum titers attained are identical for the sensitive

strain and for the two variants. Both variants, therefore, fulfill the requirements

for the applicability of the theory developed above.

In the presentation of our experimental results we have lumped the counts

of the two types of colonies together, because: (I) theoretically, this is equivalent

to summing the corresponding mutation rates; (2) experimentally, we

are not certain whether each of these types does not actually comprise a diversity

of variants; (3) experimentally, no correlation appeared to exist between

the occurrence of these variants, which shows the independence of the causes

of their occurrence.

Cultures of B were grown either in nutrient broth (containing .5 percent

NaC1) or in an asparagin-glucose synthetic medium. In the latter, the division

time during the logarithmic phase of growth was 35 minutes, as compared

with rg minutes in broth. In synthetic medium, the acidity increased during

the time of incubation from pH 7 to pH 5.

In cultures of strain B, between IO-^ and 10-6 of the bacteria are found

usually to give colonies resistant to the action of virus a when samples of such

cultures are plated with large amounts of virus. In order to be reasonably certain

that the resistant bacteria found in the test had not been introduced into

the test culture with the initial inoculum, the test cultures were always started

with very small inocula, containing between 50 and 500 bacteria from a growing

culture. Thus any resistant bacterium found at the moment of testing

(when the culture contains between IO* and 5x10b~ac teria/cc) must be an

offspring of one of the sensitive bacteria of the inoculum.

All platings were made on nutrient agar plates. The plating experiments for

counting the number of resistant bacteria in a liquid culture of the sensitive

strain were done by plating either a portion or the entire culture with a. large

amount of virus a. The virus was plated first, and spread over the entire surface

of the agar. A few minutes later the bacterial suspension to be tested was

spread over the central part of the plate, leaving a margin of at least one centimeter.

Thus all bacteria were surrounded by large numbers of virus particles.

Microscopic examination of plates seeded in this manner showed that lysis

takes place very quickly; only bacteria which at the time of plating were in

the process of division may sometimes complete the division. The resistant

colonies which appear after incubation are therefore due to resistant bacterial

cells present at the time of plating.

The total number of bacteria present in the culture to be tested was determined

by colony counts in the usual manner.

The resistant colonies of the large type appear after 12-16 hours of incubation,

the colonies of the small type appear after 18-24 hours, and never reach

half the size of the former ones. Counts were usually made after 24 and 48

hours.

MUTATIONS OF BACTERIA 503

EXPERIMENTAL

A Test of the Reliability of the Plating Method

In our experiments we wanted to study the fluctuations of the numbers of

resistant bacteria found in cultures of sensitive bacteria. It was therefore

necessary to show first that the method of testing did not involve any unrecognized

variables, which caused the number of resistant colonies to vary from

plate to plate or from sample to sample.

Therefore, parallel platings were made using a series of samples from the

same bacterial culture. If our plating method is reliable, fluctuations should

in this arrangement be due to random sampling only, and the variance from a

series of such samples should be equal to the mean.

Table I gives the results of three such experiments. It will be seen that in

TABLEI

The number of resistant bacteria in different samples from the same culture.

EXP. NO. loa EXP. NO. 11a EXP. NO. 3

SAMPLE NO.

~ S I S T A N TC OLONIES RESISTANT COLONIES RESISTANT COLONIES

I

2

3

4

5

6

7

8

9

IO

mean

variance

2

P

I4

I5

I3

I5

I4

26

16

I3

21

20

16.7

I5

9

.4

46

56

52

48

65

44

49

51

56

47

51.4

27

5.3

.8

4

2

2

I

5

4

4

7

2

2

3.3

3.8

I2

.2

all three cases variance and mean agree as well as may be expected. There is

therefore no reason to assume that the method of sampling or plating introduces

any fluctuations into our results besides the sampling error.

Fluctuations of the Number of Resistant Bacteria in Samples from a

Series of Similar Cultures

As pointed out in the introduction and in the theoretical part, the hypothesis

of acquired immunity and the hypothesis of mutation lead to radically

different predictions regarding the distribution of the number of resistant

bacteria in a series of similar cultures. The hypothesis of acquired immunity

predicts a variance equal to the average, as in sampling, while the mutation

hypothesis predicts a much greater variance.

Series of five to IOO cultures were set up in parallel with small equal inocula,

and were grown until maximum titer was reached. Three kinds of cultures

504 S. E. LURIA AND M. DELBRUCK

were used-namely: (I) 10.0 cc aerated broth cultures; (2) .2 cc broth cultures;

(3) .2 cc synthetic medium cultures.

The results of all tests for the number of resistant bacteria are summarized

in table 2 and table 3.

TABLEz

The number of resistan! bacteria in series of similar cultures.

EXPERIMENT NO. I IO I1 15 16 17 zia zIb

Number of cultures 9 8 10 10 2 0 1 2 I9 5

Volume of cultures, cc 10.0 10.0 10.0 10.0 .2* .2' .2 10.0

Volume of samples, cc .OS .OS .OS .OS .08 .08 .OS .OS

Culture No.

I

2

3

4

5

6

7

8

9

10

I1

12

13

14

15

16

17

18

I9

20

10 29 30 6 I I 0 38

18 41 10 5 0 0 0 28

125 I7 40 I O 3 0 0 35

10 2 0 45 8 0 7 0 107

14 31 183 24 0 0 8 13

27 30 I2 13 5 303 I

3 7 173 165 0 0 0

17 17 23 15 5 0 I

17 57 6 0 3 0

51 10 6 48 15

107 I 0

0 4 0

0 19

0 0

I 0

0 17

0 11

64 0

0 0

35

Average per sample 26.8 23.8 62 26.2 11.35 30 3.8 48.2

Variance (corrected for

sampling) 1217 84 3498 2178 694 6620 40.8 I171

Bacteriaperculture 3.4X10'0 4 XIO'Q 4 X1ol0 2.gX1olQ 5.6X108 5 XIO~ I . I X I O ~ 3.2X10'~

Mutation rate 1.8X10-8 1.4X10-8 4.1Xio-8 Z.IXIO-8 1.1x1o-6 3.0X10-8 3.3Xro-* 3.0x10-8

L ~ - Standard deviation exp. 1.3 .39 .g5 1.8 2.3 2.7 1 . 7

Average per culture 5360 4760 12400 5240 28.4 . 75 15.1 8440

Average {calc. .35 .33 .33 .37 .94 ,67 1.04 . 2 6

- Cultures in synthetic medium.

It will be seen that in every experiment the fluctuation of the numbers of

resistant bacteria is tremendously higher than could be accounted for by the

sampling errors, in striking contrast to the results of plating from the same

culture (see table I) and in conflict with the expectations from the hypothesis

of acquired immunity.

We want to see next whether these results fit the expectations fromthe

hypothesis of mutation. We must therefore compare the experimental results

with the relations developed in the theoretical part, keeping in mind that the

theory contains several simplifying assumptions.

First we can compare, according to equation (12), the experimental and the

calculated values of the ratio between the standard deviation and the average

of the numbers of resistant bacteria. These ratios are included in tables 2 and

3. It is seen that the experimental and theoretical values are reasonably close.

MUTATIONS OF BACTERIA 50.5

However, in all but one case the experimental ratio is greater than the value

calculated from the theory-that is, the variability is even greater than predicted.

TABL3E

Distribution of the numbers of resistant bacteria in series of similar cdfures.

EXPERIMENT NO. 22 23

Number of cultures I O 0 87

Volume of cultures, cc .2* .2*

Volume of samples, cc -05 . 2

Resistant

bacteria

0

I

2

3

4

5

6- IO

21- 50

51- IO0

201- 500

501-roo0

11- 20

101- 200

Number o j

cultures

57

5

3

7

20

2

I

2

2

0

0

0

I

Resistant

bacteria

0

I

2

3

4

5

6- IO

21- 50

51- I00

201- 500

501-1000

11- 20

101- 200

Number of

cultures

29

I7

4

3

3

5

6

7

5

4

2

2

0

Average per sample IO. I2

Average per culture 40.48

Variance (corrected for sampling) 6270

Bacteria per culture

Mutation rate

Standard deviation exp.

Average i calc.

2.8X IO*

2.3X IO-*

7.8

1.5

28.6

28.6

6431

2.4 Xro*

2.8

1.5

2.37 x 106

- Cultures in synthetic medium.

A part of this discrepancy may be accounted for by the fact that the

time to, mutations occurring prior to which were disregarded by the theory,

was chosen in such a manner that on the average one mutation would occur

prior to time to. This mutation, if it occurs, will of course tend to increase the

variance, and in some of the experiments the high value of the experimental

variance can be traced directly to one exceptional culture in which a mutation

had evidently occurred several generations prior to time to. Unfortunately,

there is no general criterion by which one might eliminate such cultures from

the statistical analysis, because, in a culture with an exceptionally high count

of resistant bacteria, these do not necessarily stem from one exceptionally

early mutation, but may also be due to an exceptionally large number of

mutations after time to.

There may also be other reasons why the observed variances are higher than

the expected ones. First of all, the simplifying assumption that the mutation

506 S. E. LUNA AND M. DELBRtfCK

rate per bacterial generation is independent of the physiological state of the

bacteria may be too simple. If the mutation rate is higher for actively growing

bacteria than for bacteria near the saturation limit of the cultures, early mutations

and big clone sizes will be favored, and therefore higher variations of the

numbers of resistant bacteria can be expected. Second, the assumption of a

sudden transition from sensitivity to resistance may also be too simple. It is

conceivable that the character “resistance to virus” may not fully develop in

the bacterial cell in which the mutation occurs, but only in its offspring, after

one or more generations. However, if this were the case, cultures with only one

or two resistant bacteria should be relatively rare. The last experiment listed

in table 3, in which the entire cultures were plated, shows a rather high proportion

of cultures with only one resistant bacterium. This seems to show that the

cultures

%

50

40

30

20

IO

FIGURE z.-Experimental (Experiment No. 23) and calculated distributions of the numbers

of resistpt bacteria in a series of similar cultures. Solid columns: experimental. Cross-hatched

columns: calculated.

character “resistance to virus” in general does come to expression in the bacterial

cell in which the corresponding mutation occurred, as assumed by the

theory.

Another way of comparing the experimental results with the theory is to

compare the experimental distribution of resistant bacteria with the approximate

distribution calculated by the method outlined at the end of the theoretical

part. The theoretical distribution has to be calculated from the average

number of mutations per culture given by equation (5). Only experiments

wheqe the whole culture is tested can therefore be used for such a

comparison. This method tests the fitting of the expectations for small numbers

of resistant bacteria, in contrast to the comparison of the standard deviations,

which involves predominantly the cultures with high numbers of resistant

bacteria.

Figure 2 shows the experimental and calculated distributions for Experiment

No. 23; the cultures with more than nine resistant bacteria are lumped

together in one class, since the distribution has not been calculated for values

higher than nine.

It is seen that the fitting for small values is satisfactory. In particular, the

MUTATIONS OF BACTERIA 507

number of cultures with one resistant bacterium very closely fits the expectation.

The classes with two, four, eight, etc., resistant bacteria are bound to

be favored in the theoretical distribution, as explained in the theoretical part.

The results shown in figure 2 also confirm the assumption that the discrepancy

between experimental and calculated standard deviations must be

due to an excess of cultures with large numbers of resistant bacteria.

Summing up the evidence, we may say that the experiments show clearly

that the resistant bacteria appear in similar cultures not as random samples

but in groups of varying sizes, indicating a correlating cause for such grouping,

and that the assumption of genetic relatedness of the bacteria of such groups

offers the simplest explanation for them.

Mutation Rate

As pointed out in the theoretical part of this paper, mutation rates may be

estimated from the experiments by two essentially different methods. The

first method makes use of the fact that the number of mutations in a series of

similar cultures should be distributed in accordance with Poisson’s law; the

average number of mutations per culture is calculated from the proportion

of cultures containing no resistant bacteria at the moment of the test, according

to equation (5).

There are two technical difficulties involved in the application of this

method. In the first place, rather large numbers of cultures have to be handled

and conditions have to be chosen so that the proportion of resistant bacteria

is neither too small nor too large. In the second place, the entire cultures have

to be tested, which means, in our method of testing, that cultures of rather

small volume have to be used and great care must be taken to plate as nearly

as possible the entire culture.

Experiment No. 23 (see table 3) permits an estimate of the mutation rate

by this method. Out of 87 cultures, no resistant bacteria were found in 29

cultures, a proportion of .33. From equation ( 5 ) we calculate therefore that the

average number of mutations per culture in this experiment was 1.10. Since

the total number of bacteria per culture was 2.4X108, we obtain as the mutation

rate, from equation (4),

a = .47 X IO-^ mutations per bacterium per time unit

.32 X IO-* mutations per bacterium per division cycle.

This calculation makes use exclusively of the proportion of cultures containing

no resistant bacteria. It is therefore inefficient in its use of the information

gathered in the experiment.

The second method makes use of the average number of resistant bacteria

per culture. The relation of this average number with the mutation rate was

discussed in the theoretical part of this paper and was found to be expressed

by equation (8). The mutation rates calculated by this method for each experiment

are collected in table 4.

508 S. E. LURIA AND M. DELBRUCK

TABL4E

Values oj mutation rate from different experiments.

EXPEBIhUZNT NO. NUMBER OF CULTURES VOLUME OF CULTURES MUTATION RATE

I

IO

I1

1.5

16

17

21a

21b

23

22

9

8

IO

IO

20

I2

I9

5

87

IO0

CC

10.0

10.0

10.0

10.0

.2*

.2*

.2

10.0

.2*

.2*

Mutations per bacterium

per time unil

I , 8X 10-8

I . 4X IO-^

4.1X10-8

2. I x 10-8

I. I x 10-8

3 .OX 10-8

3. OX 10-8

2.3X IO-^

2.4X 10-8

3.3 x IO-'

Average 2.45 x 1 6 '

~~

- Cultures in synthetic medium.

It will be seen that the values of the mutation rate obtained by the second

method are all higher than the value found by the first method. This discrepancy

may be traced back to the same cause as the discrepancy between

the calculated and observed values of the standard deviation of the numbers

of resistant bacteria. This, we found, was due to an excess of early mutations,

giving rise to big clones of resistant bacteria. These big clones do not affect

the mutation rate calculated by the first method, but they do affect the results

of the second method, which is based on the average number of resistant bacteria.

One sees in table 4 that the mutation rate calculated by the second method

does not vary greatly from experiment to experiment. In particular, it will be

noted that there is no significant difference between the values obtained from

cultures in broth and from cultures in synthetic medium, notwithstanding the

considerable difference of metabolic activity and of growth rate of the bacteria

in these two media. This shows that the simple assumption of a fixed small

chance of mutation per physiological time unit is vindicated by the results.

It may also be noted in table 4 that there is no significant difference between

the mutation rates obtained from IO cc cultures and those obtained from .2 cc

cultures, or between the experiments with many and those with few cultures.

The variability of the value of the mutation rate seems to be solely due to the

peculiar probability distribution of the number of resistant bacteria in series

of similar cultures predicted by the mutation theory.

At this point an experiment may be mentioned by which it was desired to

find out whether or not mutations occur in a culture after the bacteria have

ceased growing. A culture was grown to saturation and was then tested repeatedly

for resistant bacteria and for total number of bacteria over several

MUTATIONS OF BACTERIA 509

days. The proportion of resistant bacteria did not change, even when the

sensitive bacteria began to die, showing that the resistant bacteria have the

same death rate in aging cultures as the sensitive bacteria.

DISCUSSION

We consider the above results as proof that in our case the resistance to

virus is due to a heritable change of the bacterial cell which occurs independently

of the action of the virus. It remains to be seen whether or not this is

the general rule. There is reason to suspect that the mechanism is more complex

in cases where the resistant culture develops only several days after lysis

of the sensitive bacteria.

The proportion of mutant organisms in a culture and the mutation rate are

far smaller in our case than in other studied cases of heritable bacterial variation.

The possibility of investigation of such rare mutations is in our case

merely the result of the method of detecting the mutant organisms. In other

cases, the variants are detected by changes in the colony type which is produced

by the mutant organism, either in the pigmentation or in the character

of the surface or the edge of the colony. Often, colonies of intermediate character

occur, and it is difficult to decide whether they are mixed colonies or stem

from bacteria with intermediate character. This is particularly true of cases

where, the mutation rate is high and where reverse mutation occurs. Fairly

high mutation rates, however, are a prerequisite of any study of colony variants,

since the number of colonies that can be examined is limited by practical

reasons.

The study of mutations causing virus resistance is free of these difficulties.

The segregation of the mutant from the normal organisms occurs in the onecell

stage by elimination of the normal individuals, and the character of the

colony which develops from a mutant organism is of secondary importance.

Owing to the total elimination of the normal individuals, the number of organisms

which may be examined is very much higher than for any other method;

more than 108 bacteria may be tested on a single plate. Since the mutations

to virus resistance are often associated with other significant characters, the

method may well assume importance with regard to the general problems of

bacterial variation.

It must not be supposed that the peculiar statistical difficulties encountered

in our case are restricted to cases of very low mutation rates. The essential

condition for the occurrence of the peculiar distribution studied in the theoretical

part of this paper is the following: the initial number of bacteria in a culture

must be so small that the number oj mutations which occur during thefirst division

cycle o j the bacteria is a small number. This will always be true, however great

the mutation rate, if one studies cultures containing initially a small number of

organisms.

In a series of very interesting studies of the color variants of Serratia marcescens,

BUNTING(1 g4oa, 194ob, 1942; BUNTINGan d INGRAH1A94M2) succeeded

to some extent in obviating the statistical difficulties by always using

S O S. E. LURIA AND M. DELBRUCK

inocula of about IOO,OOO bacteria. In some of her cases this number was sufficiently

high to result in numerous mutations during the first division cycle

of the bacteria. In other cases the number was apparently not high enough,

since the author reports troublesome variations of the fractions of variants in

successive subcultures. In those cases where the size of the inocula was high

enough, the author succeeded in deriving reproducible values for the mutation

rates from the study of single cultures, followed through numerous subcultures.

In these cases it is sufficient to apply the equations of the theory referring to

the average numbers of mutants as a function of time. It is clear, however,

that this method is applicable only in cases of mutation rates of at least IO+

per bacterium per division cycle.

In our case, as in many others, the virus resistant variants do not exhibit

any striking correlated physiological changes. There is therefore little opportunity

for an inquiry into the nature of the physiological changes responsible

for the resistance to virus. Since the offspring of the mutant bacteria, when isolated

after the test, are unable to synthesize the surface elements to which the

virus is specifically adsorbed in the sensitive strain, one might suppose that

this loss is a direct effect of the mutation. However, it is also conceivable that

the loss occurs upon contact with virus, since it is detected only after such

contact (hypothesis bl). In some of the cases studied by BURNET (192g),

where the mutational change to resistance is correlated with a change of phase,

from smooth to rough or vice versa, the change of the surface structure must

be a direct result of the mutation, since the mutant colonies may be picked up

prior to the resistance test and, when tested, exhibit the typical change of

affinity of the surface structure. These findings make it more probable that

the loss of surface affinity to virus is a direct effect of the mutation.

The alteration of specific surface structures due to genetic change is a phenomenon

of the widest occurrence. The genetic factors determining the antigenic

properties of erythrocytes are well known. There is evidence (WEBSTER

1937; HOLME1S9 38; STEVENSONS, CHULTZa, nd CLARK1 939) that resistance

or sensitivity to virus in plants and animals is correlated with, or even dependent

on, genetic changes, possibly affecting the antigenic make-up of the

cellular surface. The proof that resistance to a bacterial virus may be traced

to a specific genetic change may assume importance, therefore, with regard to

thegeneral problems of virus sensitivity and virus resistance.

SUMMARY

The distribution of the numbers of virus resistant bacteria in series of similar

cultures of a virus-sensitive strain has been analyzed theoretically on the basis

of two current hypotheses concerning the origin of the resistant bacteria.

The distribution has been studied experimentally and has been found to

conform with the conclusions drawn from the hypothesis that the resistant

bacteria arise by mutations of sensitive cells independently of the action of

virus.

The mutation rate has been determined experimentally.

MUTATIONS OF BACTERIA 511

LITERATURE CITED .

BUNTINGM, . I., 194oa A description of some color variants produced by Serratia marcescens,

strain 274. J. Bact. 40: 57-68.

1940b The production of stable populations of color variants of Serratia marcescens #274

in rapidly growing cultures. J. Bact. 40: 69-81.

1942 Factors affecting the distribution of color variants in aging broth cultures of Serratia

maicescens #274. J. Bact. 43: 593-606.

BUNTINGM, . I., and L. J. INGRAH1A94M2 , The distribution of color variants in aging broth

cultures of Serratia marcescens #274. J. Bact. 43: 585-591.

BURNET, F. M., 1929 Smooth-rough variation in bacteria in its relation to bacteriophage.

J. Path. Bact. 32: 15-42.

DELBRUCKM,. ,a nd S. E. LURIA1, 942 Interference between bacterial viruses. I. Arch. Biochem.

I: 111-141.

GRATIAA, ., 1921

D’HERELLEF,. , 1926 The Bacteriophage and Its Behavior. Baltimore: Williams and Wilkins.

HOLMES, F. O., 1938 Inheritance of resistance to tobacco-mosaic disease in tobacco. Phyto-

STEVENSOFN. ,J ., E. S. SCHULTaZn, d C. F. CLARK1,9 39 Inheritance of immunity from virus X

WEBSTERL,. T., 1937 Inheritance of resistance of mice to enteric bacterial and neurotropic virus

Studies on the d’Herelle phenomenon. J. Exp. Med. 34: 115-131.

pathology 28: 553-561.

(latent mosaic) in the potato. Phytopathology 29: 362-365.

infections. J. Exp. Med. 65: 261-286.