A spherical cell of radius takes in oxygen only through its membrane
PHYSICS · Multi-part · Fermi University Physics · Biophysics & Medical Physics · Physical foundations of the living cell · Physical foundations of the living cell
Life at Thermal Energy, Ch The scales of life and the thermal energy
Problem
A spherical cell of radius a takes in oxygen only through its membrane. Suppose each square micrometre of membrane can let in at most 1.0×106 oxygen molecules per second, and each cubic micrometre of the interior uses 1.5×106 oxygen molecules per second, a use close to that of a fast-growing bacterium.
((a)) Write down the condition for the supply through the surface to keep up with the use inside, and show that it holds only while a is no greater than three times the uptake per unit area divided by the use per unit volume.
((b)) Find the largest radius, in μm, that this cell can have.
((c)) A resting person's power density is roughly 103 times smaller than a growing bacterium's. If a cell's use per unit volume were 103 times smaller, with the same uptake per unit area, what would the largest radius become?
((d)) Name two assumptions of this model that a real cell of that size could break.