The document describes an experiment conducted by Luria and Delbrück in 1943 to determine if bacterial mutations from virus sensitivity to resistance were spontaneous or directed. They developed mathematical models predicting different statistical properties under the two hypotheses and found that experimental results matched the spontaneous mutation model, suggesting mutations occur randomly without external factors directing the change. This helped prove that natural selection, rather than external pressures, drives evolution.

1. Mutations of bacteria
from virus sensitivity
to virus resistance
S. E. Luria and M. Delbrück
Indiana University, Bloomington, Indiana, USA and
Vanderbilt University, Nashville, Tennessee, USA
May 20, 1943
Genetics 28(6):491-511.

2. Table of contents
1. Timeline
2. The big Question
3. Materials
4. Methods
(i) Laboratory
(ii) Mathematics
5. Results
6. Aftermath(s)
7. Discussion

3. Timeline
– 1859: Charles Darwin
– The Origin of Species
– 1866: Gregor Mendel
– Inheritence of factors in pea plants
– 1902: Walter Sutton
– Chromosome pairs, Mitosis and Meiosis
– 1910: Thomas Morgan
– The 'gene' theory

4. Timeline cont.
– 1928: Fred Griffith
– Transformation
– 1944: Avery, MacLeod and McCarty
– Transformation linked to DNA

5. The knowledge at the time
– Known:
– Species change and evolve under pressure.
– Inheritance follows certain rules.
– Cells contain substances called Protein and
DNA
– Hypothesized:
– Inheritance is linked to DNA?
– Species change independent of pressure?
– Species change due to pressure?

6. The Question:
Are mutations spontaneous
or directed?

7. Materials
– A bacterium
– A virus
– Beaker & Petri dishes
– Pencil & Paper

8. Methods
Inoculate Add virus
Medium Sensitive Senstive Resistant
bacteria bacteria bacteria
grow die grow

9. Two models
Model 1: Directed mutations (DM). Model 2: Spontaneous mutations (SM).
Individuals are susceptible to Individuals change randomly at
change at times. times.

10. The idea
– The two different models may result in
different statistical properties.
– This difference may be significant and
measurable.

11. Implications of the DM model
Number of cells at time t:
n t =2t
Let p be the probability
 0
that a given cell is
currently susceptible to
change.
The number of susceptible
cells in generation T is
binomially distributed.
T
Z ~ Bn t ,  
p
T
~ B 2 , p 

Thus,
T T
E Z =2 p , V  Z =2 p 1− p 
  

12. Implications of the SM model
Mutations in generation t:
X t  ~ B 2t , p
0
Cells in T that originate
from mutation in t:
Y T t  = 2
T−t
X t  t
Mutated cells in T:
T
T
Z t  = ∑ Y T t 
t=1

13. Implications of the SM model cont.
t
Mutations in generation t: E X  = 2 p
t
V  X  = 2 p 1− p
X t  ~ B 2t , p
Cells in T that originate E Y  = 2T −t E  X  = 2T p
from mutation in t: V Y  = 2 2T −t  V  X 
T−t
Y T t  = 2 X t 
T
Mutated cells in T: E Z  = ∑ E Y 
t=1
T = T 2T p
T
Z = ∑ Y T t V Z  = ∑ V Y 
t=1
t=1
= 22T 1−
 
1
2 T
p1− p

14. Measurable property
– DM model – SM model
T
E  Z =2 
p E  Z  = T 2T p
T
V Z =2  1−  
p p V Z  = 2
2T
 
1−
1
2
T p1− p 
T
V Z  V Z  2 −11− p 
= 1− p ≈ 1
 = ≫ 1
EZ EZ T

15. Experimental results
Figure: Histogram of
the number of
resistant bacteria, as
observed in 87
parallel cultures
(black bars), and
corresponding
distribution expected
under directed
mutation (white bars).

16. The aftermath(s)
– 1952: Hershey & Chase
– Final proof that DNA is the genetic material.
– 1969: Delbrück, Hershey and Luria are
awarded the Nobel prize in Medicine.
– Their method is used until today under
the name 'fluctuation test'

17. Discussion
– What do we learn from this?
– Never underestimate the power and
awesomeness of maths!
– Before throwing money and high-tech toys at
a problem we may consider keeping it simple
and use our brains.