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), 13 January 2015]


Max Delbruck (1906 -1981) &  Salvador Luria (1912 -1991)
    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 manifestations of 106s 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 Tons ("T-one sensitive")
     [phage]  ~  [bacteria] some bacterial colonies grow: bacteria are Tonr ("T-one resistant")
      Tonr phenotype is stable, heritable
            all descendant bacteria are Tonr
            phenotype persists in the absence of 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 ( ~ 1 / 107);
        Survivors have altered metabolic phenotypetransmitted to offspring:
             change to phenotype persists in genotype
        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  ( ~ 1 / 107) are already Tonr
             have undergone genetic mutation to a stable genotype
             change to genotype persists in phenotype
        a Darwinian hypothesis: Tonr bacteria are selected

Materials & Methods
    Hypotheses make different predictions as to
         numerical distribution of Tonr phenotypes among bacterial cultures.

Induction 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?
    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 # Tonr
   Suppose 10 Tonr colonies observed: what distribution ("fluctuation") expected?

Induction Hypothesis:
    Tonr induction occurs only in last generation upon exposure to T1
    probability of induction (a) is uniform / bacterium
      a = 10 inductions / 64 cells = 15%
       observe = 3, 1, 5, & 1 Tonr colonies
       mean = 10 / 4 = 2.5 Tonr  per culture
       variance         = 2.75
       Follows a Poisson Distribution for rare, random events: variance = mean
Evaluate Prussian Horse experiment by Chi-Square

Mutation Hypothesis
    Tonr mutation already 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 Tonr as before
        After 4 generations, early mutations leave more offspring (as in Culture 3)
             variance 10.75
       after 5 generations, when the number of Tonr 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 ~ 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





Experiment ##

Bulk culture (e.g., Experiment 10a):
  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 either induced or spontaneous
         [essentially a control experiment]

Individual cultures (e.g., Experiment 16):
    mean ~ mean in bulk
    variance >> variance in bulk:
        Experiment supports Mutation Hypothesis !

 Calculation of Mutation rate (a)
        mean # mutations / culture = aN
        Poisson predicts null class p0  = e(- 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 = 0.2 ml x 108 bacteria / ml
        Then a = -ln 0.55 / (0.2 x 108) = 3 x 10-8 mutations / cell / generation


"On a postcard dated January 24, Delbruck replied:

                    Stamps 1989
January 24, 1943

"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 statistical calculations for Experiments 3 & 21a

All text material ©2015 by Steven M. Carr