Mutations of bacteria
from virus sensitivity
  to virus resistance
  S. E. Luria and M. Delbrück
  Indiana University, Blo...
Table of contents

1. Timeline
2. The big Question
3. Materials
4. Methods
 (i) Laboratory
 (ii) Mathematics
5. Results
6....
Timeline

– 1859: Charles Darwin
    – The Origin of Species
– 1866: Gregor Mendel
    – Inheritence of factors in pea pla...
Timeline cont.

– 1928: Fred Griffith
    – Transformation
– 1944: Avery, MacLeod and McCarty
    – Transformation linked ...
The knowledge at the time

– Known:
  – Species change and evolve under pressure.
  – Inheritance follows certain rules.
 ...
The Question:




Are mutations spontaneous
       or directed?
Materials

– A bacterium

– A virus

– Beaker & Petri dishes

– Pencil & Paper
Methods
Inoculate   Add virus




 Medium     Sensitive    Senstive   Resistant
             bacteria    bacteria    bacte...
Two models




Model 1: Directed mutations (DM).   Model 2: Spontaneous mutations (SM).
Individuals are susceptible to    ...
The idea



– The two different models may result in
  different statistical properties.

– This difference may be signifi...
Implications of the DM model

Number of cells at time t:
             n t =2t
Let p be the probability
                ...
Implications of the SM model

Mutations in generation t:

      X t  ~ B 2t , p
                                     0...
Implications of the SM model cont.
                                                t
Mutations in generation t:      E X ...
Measurable property

– DM model                – SM model
                 T
       E  Z =2 
                 p        ...
Experimental results



                 Figure: Histogram of
                 the number of
                 resistant ba...
The aftermath(s)

– 1952: Hershey & Chase
    – Final proof that DNA is the genetic material.


– 1969: Delbrück, Hershey ...
Discussion

– What do we learn from this?

  – Never underestimate the power and
    awesomeness of maths!

  – Before thr...
Upcoming SlideShare
Loading in …5
×

Luria & Delbrueck 1943, Mutations of bacteria from virus sensitivity to virus resistance

1,562 views

Published on

Paper talk from 04/09/2009

Published in: Technology
0 Comments
0 Likes
Statistics
Notes
  • Be the first to comment

  • Be the first to like this

No Downloads
Views
Total views
1,562
On SlideShare
0
From Embeds
0
Number of Embeds
4
Actions
Shares
0
Downloads
23
Comments
0
Likes
0
Embeds 0
No embeds

No notes for slide

Luria & Delbrueck 1943, Mutations of bacteria from virus sensitivity to virus resistance

  1. 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. 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. 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. 4. Timeline cont. – 1928: Fred Griffith – Transformation – 1944: Avery, MacLeod and McCarty – Transformation linked to DNA
  5. 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. 6. The Question: Are mutations spontaneous or directed?
  7. 7. Materials – A bacterium – A virus – Beaker & Petri dishes – Pencil & Paper
  8. 8. Methods Inoculate Add virus Medium Sensitive Senstive Resistant bacteria bacteria bacteria grow die grow
  9. 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. 10. The idea – The two different models may result in different statistical properties. – This difference may be significant and measurable.
  11. 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. 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. 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. 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. 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. 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. 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.

×