S. E. Luria and M. Delbruck (1943). Mutations of bacteria from vrius sensitivity to virus resistance. Genetics 28:491

[Presented by: Steve Carr (scarr@mun.ca), 07 January 2012]

Background & Introduction

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
    No nuclei, do they have "genes"?
    Bacterial "phenotypes": manifestations of 106s of bacteria simultaneously
    No 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 Tons ("T-one sensitive")
     [phage]  ~  [bacteria] some bacterial colonies grow: bacteria are Tonr ("T-one resistant")
      Tonr phenotype stable
            all descendant bacteria Tonr
            phenotype persists absent T1

Two Hypotheses (d'Herelle 1926 vs Brunet 1929)
    1. Tonr phenotype induced by exposure of bacteria to phage
        Each bacterium has (small, finite) chance of survival (say  ~ 1 / 107);
        Survivors have altered metabolic phenotype, transmitted to offspring
             [distinction between phenotype & genotype not clear]
        Bacteria adapt to their environment :
            a Lamarckian hypothesis: inheritance of acquired characteristic

    2. Tonr phenotype occurs spontaneously, prior to exposure of bacteria to phage
        Some rare bacteria (say ~ 1 / 107) already Tonr
        genetic mutation to a stable genotype
              [phenotype persists absent phage]
        a Darwinian hypothesis: Tonr bacteria selected

Theory:
    Hypotheses make different predictions as to
         statistical distribution of Tonr phenotypes among bacterial cultures.

Induction (Adaptation) Hypothesis predicts: n / N = a
    where n = number of Tonr bacteria observed out of
               N = number of Tons bacteria plated, and
                a = probability of conversion from Tons to Tonr
   Then, n should be a constant fraction of N

Mutation Hypothesis predicts: n / N = ga2g / 2g = ga
    where a = mutation rate (# mutations / cell / generation)
               g = # generations to go from 1 N bacteria, so that
               N = 2g doublings occur, of which
               n = ga2g produce mutant Tonr  bacteria
                      [because a mutation in the i th generation contributes a2i2g-i = a2g 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 Tons mutant each
    after g generations there are N = 2g  bacteria in each culture
                 mean number of Tonr bacteria is  = (xi) / c
                 variance is 2 =  [ - xi]2 / c

Thought experiment:
    Consider four cultures 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 # Tonr
   10 Tonr colonies observed: what  distribution ("fluctuation") expected?

Induction Hypothesis:
    Tonr induction occurred only in fourth generation upon exposure to T1
    probability of induction (a) is uniform / bacterium
      a = 10 inductions / 64 cells = 15%
       mean occurrence = 10 / 4 = 2.5 Tonr  per culture
       variance = [(2.5 - 3)2 + (2.5 - 1)2 + (2.5 - 5)2 + (2.5 - 1)2] / 4 = 2.75   [alternative calculation]
       Follows a Poisson Distribution: variance = mean

Mutation Hypothesis
    Tonr mutation has occurred spontaneously, prior to exposure to T1
     mutation rate (a) = 2 events / 60 cell divisions = 0.033 mutations / cell / generation
        mean rate of occurrence = (2 + 0 + 8 + 0) / 4 = 2.5 Tonr as before
        earlier Tonr mutations leave more offspring (as in Culture 3)
       variance =  [(2.5 - 2)2 + (2.5 - 0)2 + (2.5 - 8)2 + (2.5 - 0)2] / 4 = 10.75
       after  5 generations, when the number of Tonr cells has doubled in each culture:
            variance =  [(5.0 - 4)2 + (5.0 - 0)2 + (5.0 - 16)2 + (5.0 - 0)2] / 4 = 48.00

        Mutation Hypothesis predicts variance >> mean, as g increases
Methods:

"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 ~ 103 bacteria @
    Grow for g = 17 generations
           ~108 bacteria / ml
         Plate entire "individual cultures"
                  & 200 ul aliquots of "bulk culture" on petri dish w/ T1


Results
 

Bulk
Cultures
 Individual
Cultures
Experiment ##
1, 10, 11, 15
 16, 17, 21a
Mean
 16.7
11.3
Variance
 15
694

In bulk cultures,
  a = n / N = (16.7 / (0.2 ml x 108 bacteria / ml) = 8 x 10-7  variants / cell
    variance ~ mean random distribution
    Expected result if changes are induced (also compatible with mutation)
         [essentially a control experiment]

In individual cultures,
    mean ~ mean in bulk
    variance >> variance in bulk:
        Experiment supports prediction of Mutation Hypothesis !

    Mutation rate (a) can be calculated
        mean # mutations / culture = aN
        Poisson distribution predicts p0  = exp (- a / N)
           where p0 = fraction of cultures with no Tonr mutants
           Rewrite as    a = - ln p0 / N
                   p0  = 11 / 20 = 0.55 from data in Experiment 16
                   N = 0.200 ul x 108 bacteria / ml
        Then a = -ln 0.55 / (0.2 x 108) = 3 x 10-8 mutations / cell / generation

Conclusions
"On a postcard dated January 24, Delbruck replied:

Nobel Stamps 1989
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

All text material ©2012 by Steven M. Carr