For an order-of-magnitude estimate

PHYSICS · Multi-part · Fermi University Physics · Biophysics & Medical Physics · Physical foundations of the living cell · Macromolecules, membranes and cell architecture

Life at Thermal Energy, Ch The scales of life and the thermal energy

Problem

For an order-of-magnitude estimate, model a human red blood cell as a sphere of diameter 8 μm8\,\mathrm{\mu m}, its measured width. Each lipid molecule in the bilayer occupies about 0.6 nm20.6\,\mathrm{nm^2} of membrane area, and the bilayer has two leaflets. ((a)) List the assumptions this estimate makes. ((b)) Estimate the surface area of the modelled sphere, in μm2\mathrm{\mu m^2}. ((c)) Estimate the number of lipid molecules in the whole membrane, to one significant figure. ((d)) A real red blood cell is a biconcave disc with a measured membrane area of about 140 μm2140\,\mathrm{\mu m^2} and a volume of about 90 fL90\,\mathrm{fL}. Recount the lipids using the measured area, and say by what factor, and in which direction, the sphere model was off. ((e)) A biconcave disc is often said to have more surface than a sphere, yet your sphere has more surface than the real cell. Find the area of a sphere holding 90 fL90\,\mathrm{fL}, and use it to explain how both statements can be true.

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