# Luria-delbruck experiment question

• daniel6874
In summary, the discussion is about the classic study by Luria and Delbrück (1943) that explores mutations in bacteria from virus sensitivity to virus resistance. The authors use the "average division time" of bacteria divided by ln(2) as the time unit in their equations for exponential growth. This is because the doubling time divided by ln(2) gives the appropriate time constant for an exponential growth. This concept is important in understanding exponential growth and decay in various systems.
daniel6874
My question is about the classic study cited below (*) and available as a free pdf download from

http://www.genetics.org/content/28/6/491.full.pdf+html

At page 495 the authors use the "average division time" of bacteria dt, divided by ln(2), as the time unit in the equations

(1) dN_t /dt = N_t , (2) N_t = N_o e^t.

Can anyone tell me why this division by ln(2) was done? N_o is the original number of bacteria present. N_t is the number at time t.

Obviously it has something to do with integration/differentiation, but I am missing the point. Thanks.

*Luria, S. E.; Delbrück, M. (1943). "Mutations of Bacteria from Virus Sensitivity to Virus Resistance". Genetics 28 (6): 491–511.

The doubling time divided by ln(2) gives the appropriate time constant for an exponential growth. Writing the equation for exponential growth in terms of the doubling time (td) gives:

N(t) = No 2^(t/td)

Equivalently, this can be written as:

N(t) = No e^(t ln(2) / td) = No e^(t/tc)

Where tc = td/ln(2). This makes use of the fact that e^ln(2) = 2.

Bacteria double exponentially; 2 become 4, 4 become 8, etc. This describes Log in base 2 (22, 23, etc).

The application then is used to describe things that grow or decay exponentially. A more detailed explanation can be found http://logbase2.blogspot.com/2007/12/log-base-2.html"

Last edited by a moderator:
Ygggdrasil said:
...
N(t) = No 2^(t/td)

Equivalently, this can be written as:

N(t) = No e^(t ln(2) / td) ...

This is crystal clear. I forgot he was starting with 2^t/td as a growth law. Thanks!

Thank you for your question about the Luria-Delbruck experiment.

The division by ln(2) in the equations is related to the concept of exponential growth. In the experiment, the researchers were studying the spontaneous mutation rate in bacteria. They observed that the number of resistant bacteria increased exponentially over time, following the equation N_t = N_o e^t, where N_t is the number of resistant bacteria at time t, N_o is the original number of bacteria, and e is the base of the natural logarithm.

To understand why ln(2) was used, we need to look at the concept of doubling time. Doubling time is the amount of time it takes for a population to double in size. In the case of bacteria, this is the time it takes for one bacterium to divide into two. The doubling time can be calculated by dividing the average division time (dt) by ln(2), which is approximately 0.693. This is because ln(2) represents the natural log of 2, which is the number of times a population must double to reach a certain size.

In the Luria-Delbruck experiment, the researchers were interested in studying the mutation rate per generation, not per unit of time. By dividing by ln(2), they were able to account for the fact that each generation of bacteria would have a different number of individuals due to the exponential growth. This allowed them to compare the mutation rate among different generations of bacteria.

I hope this helps to clarify the reasoning behind using ln(2) in the equations. If you have any further questions, please let me know.

## 1. What was the purpose of the Luria-Delbruck experiment?

The Luria-Delbruck experiment aimed to test the validity of two competing theories on the origin of genetic mutations: the spontaneous mutation theory and the directed mutation theory.

## 2. How was the Luria-Delbruck experiment conducted?

The experiment involved growing several cultures of bacteria and then exposing them to different environments. The number of mutations in each culture was then counted and compared to determine if they occurred randomly or were directed by the environment.

## 3. What were the results of the Luria-Delbruck experiment?

The results showed that the mutations occurred randomly, in support of the spontaneous mutation theory. This disproved the directed mutation theory, which suggested that mutations were directed by the environment.

## 4. What was the significance of the Luria-Delbruck experiment?

The Luria-Delbruck experiment provided evidence for the existence of spontaneous mutations, which are random changes in genetic material. This has important implications for understanding the mechanisms of evolution and the development of drug resistance in bacteria.

## 5. How has the Luria-Delbruck experiment influenced scientific research?

The Luria-Delbruck experiment has had a significant impact on the field of genetics and continues to be cited in scientific literature. It has also influenced the development of new techniques for studying mutations and has contributed to our understanding of the role of randomness in biological processes.

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