How many ribosomes are actively synthesizing proteins at any

How many ribosomes are actively synthesizing proteins at any instant in an E. coli cell growing with a doubling time of 45-minutes? Use the following assumptions in your calculations the birth size of E. coli is 1 micron in diameter and 2 microns in length. Water content of the cell is 80% and 50% of the dry cell mass is protein/enzymes. Also, the density of cell material is approximately 1 gram per mL. Rate of amino acid addition per ribosome is 20 amino acids per second, and the average molecular weight of a free amino acid is 126.

Solution

Assume E.coli is a cylinder :

1 x 10³ kg. wet cells / m³ X 0.5 x 10-6 kg.protein / kg. dry material x 0.25 kg.dry material / kg. wet cells x 6.023 x 10 23 amino acids mol / 20 amino acids ribosome . sec = 2.08 x 10⁴ ribosomes.