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  1. Problems
  2. /The chromosome of the bacterium Escherichia coli has about 4.6 × 10⁶ base pairs…
MediumChemistryHigh School (11–12)Organic Compounds with Functional Groups › BiomoleculesNumerical

The chromosome of the bacterium Escherichia coli has about 4.6 × 10⁶ base pairs…

StemPy LabContributed by StemPy Lab

Try it on paper first. A hint, the key idea and the worked solution are here when you need them.

The chromosome of the bacterium Escherichia coli has about 4.6×1064.6 \times 10^64.6×106 base pairs. One set of human chromosomes has about 3.1×1093.1 \times 10^93.1×109 base pairs. Take the distance between base pairs as 0.34 nm0.34\ \text{nm}0.34 nm and the turn as 10.510.510.5 base pairs. Find the length of the bacterial DNA in millimetres, the number of turns in it, and the length of one set of human DNA in metres.

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mm
m
Need a reminder? The key ideaShowHide

In B-DNA the base pairs are 0.34 nm0.34\ \text{nm}0.34 nm apart and there are about 10.510.510.5 base pairs in a turn. A codon is three bases, and a stop codon does not code for an amino acid. The mass fraction of an element in a molecule is n×Melement/Mmoleculen \times M_{\text{element}} / M_{\text{molecule}}n×Melement​/Mmolecule​.

The worked solution

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Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.

Step 1. Bacterial DNA. 4.6×106×0.34 nm=1.564×106 nm=1.56 mm4.6 \times 10^6 \times 0.34\ \text{nm} = 1.564 \times 10^6\ \text{nm} = 1.56\ \text{mm}4.6×106×0.34 nm=1.564×106 nm=1.56 mm.

Step 2. Turns. 4.6×106/10.5=438 0954.6 \times 10^6 / 10.5 = 438\,0954.6×106/10.5=438095 turns.

Step 3. Human DNA. 3.1×109×0.34 nm=1.054×109 nm=1.05 m3.1 \times 10^9 \times 0.34\ \text{nm} = 1.054 \times 10^9\ \text{nm} = 1.05\ \text{m}3.1×109×0.34 nm=1.054×109 nm=1.05 m.

Answer: 1.56 mm1.56\ \text{mm}1.56 mm, 438 095438\,095438095 turns and 1.05 m1.05\ \text{m}1.05 m.

Check. The bacterium is about 2 micrometres long, so its DNA is almost a thousand times longer than the cell. This is possible because the DNA is tightly coiled.

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