Question

The cytoplasm of cells is packed with proteins. If a spherical bacterial cell( 1.5um diameter) contains equal number of 1200 different proteins, all having an average molecular weight of 80,000, what is the molarity of the proteins? Assume the cytoplasm has a density of 1.20 g/ml and is 18% protein by wieght. Show all work

Answer 1

The bacterial cell is of spherical shape with a diameter of 1.5 um which is equal to 1.5 x 10^-4 cm. The radius of the cell will be 0.75 x 10^-4cm. The density of cytoplasm is given as 1.20 g/ml which is equivalent to 1.20 g/cm³. The cytoplasm density can be assumed to be the density of whole bacterial cell, since bacterial cell lacks nucleus considering it's a prokaryote. Mass of the cell can be calculated by multiplying the volume of the cell with it's density as follows:

Plugging the values of 'r' and in the above equation, we have:

Mass = 2.12 x 10^-12 g

Now, it is given that 18% of the cell by weight is protein, hence mass of total protein in the cell will be:

18% of Mass of cell = 0.18 x 2.12 x 10^-12 = 3.81 x 10^-13 g

The average molecular mass of protein in the cell is given as 80,000 Da which is equal to 80,000 g/mol, hence if 80,000 g = 1 mole, 3.81 x 10^-13 g will be equal to:

Thus, number of moles of protein in the bacterial cell is: 4.76 x 10^-18 M

Molarity of protein can be calculated as follows, since volume of cell is already known (4/3πr³ = 1.77 um³ = 1.77 x 10^-15 L):

Molarity = 2.69 x 10^-3 M = 2.69 mM

Hence, the molar concentration of protein in the bacterial cell is 2.69 mM