Question

You are conducting an experiment to measure the metabolic efficiency of two types of spherical cell lines. To do this, you want to test these cells under quasi-starvation conditions, meaning that you want to make sure that the nutrient availability of each cell line is the same but fairly low.

Cell line A is 1/3 the size (diameter) of cell line B. If you put cell line A in a nutrient bath of concentration C0, what must the concentration be in the nutrient bath of cell line B if you want both cell lines to have equal metabolic rates? (i.e. each cell receives by diffusion the same number of nutrient molecules per second per kg)

all help is appreciated!

Answer 1

By the principal of allometric scaling of metabolism, metabolic rate is inversely related to mass of cell. Since mass is volume of cell multiplied by density

That is mass = volume x density

Therefore for a given cell density will be constant and thus metabolic rate will be inversely related to volume

Thus

Thus if diameter of A is 1/3 of diameter of B then metabolic rate of A will be 27 times more than that of B.

Thus to keep same metabolic rates concentration of B should be 27 time concentration of A.