Prokaryotic cells and viruses

Typical bacteria are about 1 to 5 μm across, roughly the size of a mitochondrion. 10 to 100 μm is the size range of typical eukaryotic cells (animal cells about 10 to 30 μm, plant cells larger). 20 to 300 nm is the size range of viruses, which are too small to be seen with a light microscope. 0.1 to 0.5 mm (100 to 500 μm) is large enough to see with the naked eye, like some single-celled protoctists.

A prokaryotic cell has no nucleus, so it has no nuclear envelope; its circular DNA lies free in the cytoplasm. Bacteria do have ribosomes (70S, smaller than the 80S ribosomes in eukaryotic cytoplasm). They have a cell surface membrane inside the peptidoglycan wall, which controls what enters and leaves. They also have DNA, as a circular chromosome and often as small plasmids.

X has a peptidoglycan wall, only 70S ribosomes and circular DNA with no nucleus: every feature of a typical prokaryote. W has a cellulose wall, 80S ribosomes in the cytoplasm (with 70S in its mitochondria and chloroplasts) and a nucleus, so it is a plant cell. Y has the same features but no wall, so it is an animal cell. Z has a protein capsid, nucleic acid and no ribosomes, so it is a virus, which is not a cell at all.

Every virus has a nucleic acid core (DNA or RNA) inside a protein capsid, and bacteria contain both DNA and proteins, so this pair is common to both. Viruses have no ribosomes; they use the host cell's ribosomes to make their proteins. Viruses have no cell surface membrane of their own; an envelope, where present, is taken from the host's membrane. Peptidoglycan is found only in bacterial cell walls, never in viruses.

2 μm = 2000 nm, so the bacterium is 2000 ÷ 40 = 50 times longer. 0.05 inverts the division (40 ÷ 2000), which would make the virus the larger of the two. 5 converts μm to nm with a factor of 100 (2 μm = 200 nm). 500 uses a factor of 10 000. Since viruses are typically 20 to 300 nm and bacteria 1 to 5 μm, a ratio of tens is expected.

Penicillin's target is the cross-linking of peptidoglycan in the bacterial cell wall. Human cells have no cell wall at all, so there is nothing for it to act on. The difference in ribosome size is true, and it explains why some other antibiotics that act on 70S ribosomes spare human cytoplasm, but penicillin does not act on ribosomes. The nuclear envelope is also a real difference, but penicillin does not act on DNA. Mitochondria supply ATP but cannot protect a cell from a drug that has no target in it; in any case the reason is the absence of the target, not repair.

Both mitochondria and bacteria contain 70S ribosomes (and small circular DNA), whereas the nucleus contains no complete ribosomes; it only assembles ribosome subunits in the nucleolus, and 80S ribosomes work in the cytoplasm. A double membrane surrounds the mitochondrion and also the nucleus (the nuclear envelope), but a bacterium has only a single cell surface membrane. Peptidoglycan is found only in the bacterial wall, not in mitochondria. Linear DNA with histones is the arrangement in the nucleus, not in mitochondria or bacteria.

300 nm = 0.3 μm and 45 mm = 45 000 μm, so the magnification = 45 000 ÷ 0.3 = ×150 000. Image width = 18 nm × 150 000 = 2 700 000 nm = 2.7 mm. ×150 divides 45 by 0.3 without converting mm to μm, which then gives a width of 2.7 μm. 27 mm has the right magnification but slips a factor of 10 converting nm to mm. ×15 000 treats 300 nm as 3 μm. A check: the rod is about 17 times longer than it is wide, and 45 mm ÷ 2.7 mm also gives about 17.