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Chapter 28: Problem 4

Refer to a typical Escherichia coli bacterium. This is a cylindrical cell about \(2 \mu\) m long and \(1 \mu\)m in diameter, weighing about \(2 \times 10^{-12}\)g and containing about \(80 \%\) water by volume. A single chromosomal DNA molecule contains about 4.5 million nucleotide units. If this molecule were extended so that the nucleotide units were \(450 \mathrm{pm}\) apart, what would be the length of the molecule? How does this compare with the length of the cell itself? What does this result suggest about the shape of the DNA molecule?

Short Answer

Expert verified
The DNA molecule is approximately 2.025 meters long, which is significantly longer than the bacterium in which it resides, suggesting it must be supercoiled within the cell.

Step by step solution

01

Calculating the length of the DNA molecule

The length of the DNA molecule can be calculated by multiplying the total number of nucleotide units, which is approximately 4.5 million, by the distance between these units, which is given as 450 pm, or picometers. To convert the distance between these units to a more accurate scale for this exercise, let's remember that 1 meter consists of \(10^{12}\) picometers. So, the complete formula will look like this: \(4.5 \times 10^{6}\) nucleotide units \(\times 450 \times 10^{-12}\) meters/nucleotide unit.
02

Calculating and comparing

By performing the multiplications, it is found that the length of the DNA molecule is approximately \(2.025\) meters. Comparing this to the length of the bacterium cell, which is only \(2 \mu\)m, it becomes clear that the DNA molecule is much longer than the physical cell in which it resides. This could not be possible if the DNA molecule were stretched out straight within the cell.
03

Interpreting the result

Given the fact that the DNA molecule is massively longer than the bacterium cell, it's indicative that the DNA molecule isn't stretched out in a straight line, rather it must be in a highly folded, or 'supercoiled' state, in order for such a long molecule to fit inside such a tiny cell.

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