The cell membrane, and prokaryotic and eukaryotic cells

In an experiment like Gorter and Grendel's, the lipid from a sample of red blood cells covered $0.94{\mathrm{m}}^{2}0.94\backslash ,\backslash mathrm\{m^2\}$ as a single layer on water; the total surface area of the cells was $0.47{\mathrm{m}}^{2}0.47\backslash ,\backslash mathrm\{m^2\}$ (illustrative values). (a) Calculate the ratio. (b) Explain what it shows. (c) Why were red blood cells a good choice?

1. (a) $\frac{0.94}{0.47}=2.0\backslash frac\{0.94\}\{0.47\}\; =\; 2.0$.
2. (b) There is exactly enough lipid to cover the cells twice, so the membrane is two lipid molecules thick: a bilayer, with the hydrophobic tails facing each other inside.
3. (c) Mature mammalian red blood cells have no nucleus or other membrane-bound organelles, so all the lipid extracted comes from the cell surface membrane.

In 1970 L. D. Frye and M. Edidin fused a mouse cell with a human cell. They labelled the mouse membrane proteins with a green fluorescent dye and the human proteins with a red one. Just after fusion, the colours were on separate halves of the hybrid cell; less than an hour later at 37 °C they were completely mixed; at low temperature mixing was much slower. Explain these results.

1. The proteins were not fixed in place: they moved sideways (diffused) within the membrane, so the membrane is fluid.
2. Mixing was slower at low temperature because molecules have less kinetic energy and the phospholipids become less fluid, more like a gel.
3. The results fit the fluid mosaic model and contradict older models in which proteins formed a fixed, continuous layer over the lipid.

Treat a bacterium as a cube of side 1 µm and an animal cell as a cube of side 10 µm. Compare their surface area to volume ratios, and explain why prokaryotes can survive without internal membranes.

1. Bacterium: surface area $=6\times 1^2=6\mu {\mathrm{m}}^2=\; 6\; \backslash times\; 1^2\; =\; 6\backslash ,\backslash mu\backslash mathrm\{m^2\}$; volume $=1^3=1\mu {\mathrm{m}}^3=\; 1^3\; =\; 1\backslash ,\backslash mu\backslash mathrm\{m^3\}$; ratio $=\frac{6}{1}=6=\; \backslash frac\{6\}\{1\}\; =\; 6$.
2. Animal cell: surface area $=6\times {10}^2=600\mu {\mathrm{m}}^2=\; 6\; \backslash times\; 10^2\; =\; 600\backslash ,\backslash mu\backslash mathrm\{m^2\}$; volume $={10}^3=1000\mu {\mathrm{m}}^3=\; 10^3\; =\; 1000\backslash ,\backslash mu\backslash mathrm\{m^3\}$; ratio $=\frac{600}{1000}=0.6=\; \backslash frac\{600\}\{1000\}\; =\; 0.6$.
3. The bacterium has ten times more surface per unit volume. Its cell surface membrane is large enough to carry all the enzymes of respiration and to exchange materials quickly by diffusion. A large eukaryotic cell needs internal membranes (mitochondria, ER) to provide enough membrane area and to divide its volume into compartments.