How fast to replicate?

Algebra Level 2

A bacterial cell with adequate food can replicate in under an hour. In this time, everything in the cell must be copied, including its genome (i.e. the DNA). A copy of the DNA is made by molecular machines called DNA polymerase, which can copy 600 base pairs per second. If the genome of the strain B. acterium is $4.5\times10^6$ base pairs long, and there are 6 molecules of DNA polymerase in the cell, how long (in seconds) would it take to copy the entire genome?

The answer is 1250.

1 solution

Abhishek Sharma
Apr 21, 2015

1 DNA polymerase can copy $600$ base pairs per second.

Therefore 6 DNA polymerase can copy $3600$ base pairs per second.

Let the time required to copy all the base pairs be $t$ . Therefore,

$3600t=4.5\times10^6$

$\boxed{t=1250s}$

But a bacterial genome has only one origin of replication! So how can more than two polymerases operate in parallel? (In practice, more than two polymerases can be active because replication can begin on a chromosome before the chromosome is fully replicated itself, but this doesn't help us duplicate a single genome as specified in the statement of problem.)

Helen Bergstrom - 5 years, 10 months ago

Technically, DNA polymerase copies one strand of DNA at a time. If a polymerase can produce 600 bases per second, then yes 6 DNA polymerase molecules could, in theory, copy one strand of the genome in 1250 seconds. Therefore, the entire genome would take 2500 seconds.

If the intent was to keep the problem simpler by expressing the rate of the DNA polymerase in base pairs, my apologies for over complicating it.

Melanie McCarter - 2 years, 4 months ago

How fast to replicate?

The answer is 1250.

1 solution

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