31. It takes 40 minutes for a typical E. coli cell to completely replicate its chromosome. Simultaneous to the ongoing replication, 20 minutes of a fresh round of replication is

completed before the cell divides. What would be the generation time of E. coli growing at 37^oC in complex medium?

(1) 20 minutes

(2) 40 minutes

(3) 60 minutes

(4) 30 minutes

Introduction

Escherichia coli (E. coli) is a model bacterium known for its rapid growth under optimal conditions. A typical E. coli cell takes about 40 minutes to replicate its chromosome completely. However, under fast growth conditions, E. coli initiates new rounds of replication before the previous round finishes, a phenomenon known as overlapping replication cycles. This strategy allows the bacterium to divide faster than the time required to replicate its chromosome.

Given Data and Problem Context

• Time for complete replication of the chromosome (C period): 40 minutes

• A fresh round of replication is completed 20 minutes before cell division (D period): 20 minutes

• The question: What is the generation time (doubling time) of E. coli under these conditions?

Understanding the C and D Periods

• C period: The time required to replicate the entire chromosome (40 minutes).

• D period: The time from the end of replication to cell division (20 minutes).

• Generation time (τ): The time interval between two successive cell divisions.

Relationship Between C, D, and Generation Time

In fast-growing E. coli, replication initiation occurs before the previous replication cycle completes, allowing overlapping rounds. The generation time (τ) can be calculated using the formula:

$$\tau =C+D-t$$

where $t$ is the time before cell division when a new round of replication is initiated.

Given that a fresh round of replication is completed 20 minutes before cell division, this implies:

• The initiation of the fresh round occurs $t=\tau -(C+D)$ minutes before division.

• Since the fresh round finishes 20 minutes before division, the generation time is:

$$\tau =C+D-20$$

But this is contradictory because we know C and D, and the fresh round completes 20 minutes before division, meaning:

$$\tau =C+D-\text{(time before division when replication finishes)}=40+20-20=40\text{ minutes}$$

However, the overlapping rounds imply that the generation time is less than the sum of C and D.

Standard Formula for Generation Time with Overlapping Replication

The generation time can also be expressed as:

$$\tau =C+D-\text{overlap time}$$

Given that the new round finishes 20 minutes before division, the overlap time is 20 minutes.

Thus:

$$\tau =40+20-20=40\text{ minutes}$$

But the problem states that 20 minutes of a fresh round of replication is completed before division, meaning the new round started 20 minutes before division.

Therefore, the generation time is 20 minutes.

Explanation

• The cell initiates replication every 20 minutes (generation time).

• It takes 40 minutes to replicate the chromosome (C period).

• Since replication takes longer than the generation time, the cell starts a new round before the previous one finishes (overlapping replication).

• The D period (time from replication completion to division) is 20 minutes.

• This matches the observed data where a fresh round is completed 20 minutes before division.

Supporting Evidence from Literature

• Under optimal growth conditions (37°C, rich medium), E. coli has a doubling time of approximately 20 minutes.

• Overlapping rounds of replication enable this rapid growth despite the 40-minute chromosome replication time.

Summary Table

Final Answer

The generation time of E. coli under these conditions is 20 minutes.

Conclusion

E. coli can divide every 20 minutes in rich medium at 37°C by initiating new rounds of DNA replication before the previous round finishes. This overlapping replication strategy allows the bacterium to grow faster than the time required for a single replication cycle, ensuring rapid population expansion.

Correct answer:
(1) 20 minutes