Mutations of bacteriafrom virus sensitivityto virus resistance

S. E. Luria and M. Delbrück

Indiana University, Bloomington, Indiana, USA andVanderbilt University, Nashville, Tennessee, USA

May 20, 1943

Genetics 28(6):491-511.

Table of contents

1. Timeline2. The big Question3. Materials4. Methods(i) Laboratory(ii) Mathematics5. Results6. Aftermath(s)7. Discussion

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

Timeline cont.

– 1928: Fred Griffith– Transformation

– 1944: Avery, MacLeod and McCarty– Transformation linked to DNA

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?

The Question:

Are mutations spontaneousor directed?

Materials

– A bacterium

– A virus

– Beaker & Petri dishes

– Pencil & Paper

Methods

Inoculate Add virus

Medium Sensitivebacteriagrow

Senstivebacteria

die

Resistantbacteriagrow

Two models

Model 1: Directed mutations (DM). Individuals are susceptible to change at times.

Model 2: Spontaneous mutations (SM). Individuals change randomly at times.

The idea

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

– This difference may be significant and measurable.

Implications of the DM model

Number of cells at time t:

Let be the probability that a given cell is currently susceptible to change.

The number of susceptible cells in generation T is binomially distributed.

Thus,

0

T

n t =2t

p

Z ~ B n t , p~ B 2T , p

E Z =2T p , V Z =2T p 1− p

Implications of the SM model

Mutations in generation t:

Cells in T that originate from mutation in t:

Mutated cells in T:

0

T

t

X t ~ B 2t , p

Y T t = 2T− t X t

Z t = ∑t=1

T

Y T t

Implications of the SM model cont.

Mutations in generation t:

Cells in T that originate from mutation in t:

Mutated cells in T:

X t ~ B 2t , p

Y T t = 2T− t X t

Z = ∑t=1

T

Y T t

E X = 2t pV X = 2t p 1− p

E Y = 2T−t E X = 2T pV Y = 22T−t V X

E Z = ∑t=1

T

E Y

= T 2T p

V Z = ∑t=1

T

V Y

= 22T1−12T p 1− p

Measurable property

– DM model – SM model

E Z =2T p

V Z =2T p 1−p

V Z E Z

= 1− p ≈ 1 V Z E Z

= 2T−11− p T

≫ 1

E Z = T 2T p

V Z = 22T1− 12T p 1− p

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).

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'

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.