S. E. Luria and M. Delbruck (1943). Mutations of
bacteria from vrius sensitivity to virus resistance. Genetics
28:491
Background
Max Delbruck
(1906 1981) & Salvador Luria
(1912 1991)
Shared 1969
Nobel Prize in Physiology or Medicine
Bacteriology
in 1940s not heavily influenced by genetic thinking
Bacteria
have
no
nuclei:
do
they
have "genes"?
Bacterial
"phenotypes"
are
the
manifestations
of 10^{6}s of bacteria simultaneously
Bacteria
don't
have
sex:
crosses
not possible
[Discovery
of
bacterial
sex
led to 1958
Nobel
Prize]
bacteriophages ("phages") 
"subcellular parasites that infect,
multiply within, & kill bacteria."
T1 phages are
active on E. coli
[phage] >> [bacteria] no bacterial colonies grow: bacteria
are Ton^{s} ("Tone
sensitive")
[phage] ~ [bacteria] some bacterial colonies grow:
bacteria are Ton^{r }("Tone
resistant")
Ton^{r} phenotype is stable
all descendant bacteria are Ton^{r}
phenotype persists in
the absence of T1
Two Hypotheses (d'Herelle 1926 vs Brunet 1929)
1. Ton^{r }phenotype is induced by exposure of
bacteria to phage
Each
bacterium
has
a
(small, finite) chance of survival (~ 1 / 10^{7});
Survivors have altered metabolic phenotype, which is transmitted
to offspring:
change to phenotype persists
in genotype
Bacteria adapt to their environment :
a Lamarckian
hypothesis: inheritance of
acquired characteristic
2. Ton^{r }phenotype occurs spontaneously, prior to exposure of bacteria to
phage
Some
rare
bacteria
(say
~ 1 / 10^{7}) are already Ton^{r}
These
bacteria
have
undergone
genetic mutation to a stable genotype
change to genotype persists in phenotype
a Darwinian hypothesis: Ton^{r}
bacteria are selected
Materials &
Methods
Hypotheses make different predictions as to
numerical distribution of Ton^{r}
phenotypes among bacterial cultures.
Induction
(Adaptation)
Hypothesis predicts:
n / N = a
where n = number of Ton^{r} bacteria
observed out of
N = number of Ton^{s} bacteria plated, and
a = probability of conversion
from Ton^{s} to Ton^{r}
Then,
n should be a constant fraction of N
Mutation
Hypothesis predicts: n / N = ga2^{g}
/ 2^{g} = ga
where a = mutation rate
(# mutations / cell / generation)
g = # generations to go from 1 N bacteria, so
that
N = 2^{g} doublings occur, of which
n = ga2^{g} produce mutant Ton^{r} bacteria
[because
a
mutation
in
the i th generation contributes a2^{i}2^{gi} = a2^{g}
mutants]
Then, n should increase
wrt N , as g increases
How can differences in n be
evaluated?
Suppose c cultures are started from a single Ton^{s}
mutant each
after g generations there are N
= 2^{g} bacteria in each culture
Statistical
foundations
of Luria  Delbruck experiment
Thought experiment:
Consider four cultures
each started from a single bacterium
after g = 4 generations, expect 16 cells
from 15 divisions @,
total 64 cells from 60 divisions
plate
each
culture
separately
w/ T1, count total # Ton^{r}
Suppose 10 Ton^{r }colonies
observed: what
distribution ("fluctuation") expected?
Induction Hypothesis:
Ton^{r }induction
occurred only in fourth generation upon exposure to T1
probability of induction (a) is uniform /
bacterium
a = 10 inductions / 64 cells = 15%
observe = 3, 1, 5, & 1 Ton^{r}
colonies
mean = 10 / 4 = 2.5
Ton^{r} per culture
variance = 2.75
Follows a Poisson Distribution for
rare, random events: variance = mean
Homework: Evaluate Prussian Horse experiment
by ChiSquare
Mutation Hypothesis
Ton^{r }mutation
has occurred spontaneously, prior to exposure to T1
mutation rate (a) = 2 events / 60 cell
divisions = 0.033
mutations / cell / generation
mean = (2 + 0 + 8 + 0) / 4 = 2.5 Ton^{r}
as before
After
4 generation, earlier Ton^{r} mutations leave
more offspring (as in Culture 3)
variance = 10.75
after
5
generations,
when
the
number of Ton^{r} cells has doubled in each culture:
variance = 48.00
Mutation Hypothesis predicts variance >> mean, as g
increases
Experimental procedure:
"The first experiment was done on
the following Sunday morning.
(In a letter dated January 21 [1943], Delbruck exhorted me to
go to church"
Twenty
x 200 ul "individual cultures"
One x 10 ml "bulk culture"
Inoculate with ~ 10^{3} bacteria
@
Grow for g = 17 generations
~10^{8}
bacteria / ml
Plate entire
"individual cultures"
&
200
ul
aliquots
of "bulk culture" on petri dish w/ T1
Results
Bulk culture (e.g., Experiment
10a):
a
= n / N = (16.7 / (0.2 ml x 10^{8} bacteria / ml) = 8 x 10^{7} variants
/ cell
variance ~ mean
random distribution
Expected result if changes are either induced or
spontaneous
[essentially a control
experiment]
Individual cultures (e.g.,
Experiment 16):
mean ~ mean in bulk
variance
>> variance in bulk:
Experiment
supports
prediction
of
Mutation Hypothesis !
Calculation of Mutation rate (a)
mean # mutations /
culture = aN
Poisson predicts
null class = p_{0} = e^{(
a / N)}
where
p_{0} = fraction of cultures with no Ton^{r}
mutants
Rewrite as a =  ln (p_{0} /
N )
p_{0} = 11 / 20 = 0.55 from data in Experiment 16
N = 0.2 ml x 10^{8} bacteria / ml
Then a = ln 0.55 / (0.2 x 10^{8})
= 3 x 10^{8} mutations / cell / generation
Conclusions
"On a postcard dated January 24, Delbruck replied:
January 24, 1943
From: Max
To: Salvador
"You are right about the difference in fluctuations
of resistants, when plating samples from one or from
several cultures. In the latter case, the number of
clones has a Poisson distribution. I think
what this problem needs is a worked out and written down
theory, and I have begun doing so."

The MS of the theory arrived on
February 3rd ...."
Luria on the significance of
these experiments:
(1) "Adequate evidence" of spontaneous
mutation as source of genetic variation
(2) Provided method for
measuring mutation rates,
and therefore is
(3)"The
Birth of Bacterial Genetics"
bacteria
can be used to measure extremely low mutation rates
Homework:
repeat all calculations for Experiments 3 & 21a
All text material ©2014 by Steven M.
Carr