An approximately spherical eukaryotic cell has a radius of 20 pm. A rod-shaped p

Question

An approximately spherical eukaryotic cell has a radius of 20 pm. A rod-shaped prokaryotic cell has a diameter of 0.35 pm and length of 0.9 pm. The total mass of protein in the cell is 2 Times 10^-12 g (2 picograms). The average molecular weight of proteins in the cell is 50 kDa (50,000 g/mole). Calculate the volume of each cell type in mL. Calculate the molar concentration of protein in each cell type. On average there are approximately 10,000 different types of protein molecules present in the prokaryotic cell. Compute the average number protein molecules of a single type present in the prokaryotic cell.

Explanation / Answer

A) Volume of spherical eukaryotic cell= 4/3 * 22/7* (20*10^-6)^3 =3.3523* 10^-18 m3.    Volume of rod-shaped prokaryotic cell = 22/7*( 0.175* 10^ -6 m) ^2 * (0.9* 10^-6m) = 0.0866* 10^ -18 m3. B) no.of moles of protein = 2* 10^-12 g/ 50000 gmol-1 = 0.0004* 10^ -12 mol.    So, molar concentration of protein in spherical eukaryotic cell = 0.0004* 10^-12 mol/ 3.3523* 10^-18 m3 =0.011 mol/ litre.    Molar concentration of eukaryotic cell= 0.0004* 10^-6/ 0.0866*10^-18 = 0.46 mol/ litre. C)   

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