Question

The inner (plasma) membrane of E. coli is about 77% lipid by weight, with the remaining percentage due to protein (also by weight). How many molecules of membrane lipid are there for each molecule of protein? (Assume that the average protein has a molecular weight of 5.1 x 104 and the average lipid has a molecular weight of 7.8 x 102.) Report your answer to the nearest ones

Answer 1

Since Lipid makes up 77% so Total lipid would be

7.8 X 10^2 X 77 = 600.6 X 10^2 or 6.006 X 10^4

Similarlly Protein would be

assuming total 100 = 100-77 = 23

So Total amount of protein would be

5.1 X 10^4 X 23 = 117.3 X 10^4

Total mass of inner plasma membrane would be 117.3 X 10^4 + 6.006 X 10^4 = 123.306 X 10^4

Now calculate moles for each by formula

Number of Moles = GivenMassofCompound / MolarMassofCompound

For lipid it would be 600.6 X 10^2/7.8 X 10^2 = 77

Same for protein 117.3 X 10^4/5.1 X 10^4 = 23

So there are 77 moles of lipid and 23 moles of protein.

No calculate the number of molecules by formula

Number of Molecules= NumberOfMoles × 6.022×10^23 (Avogadro number)

So number of lipid molecules would be

77 × 6.022×10^23 = 463.54 X 10^23

So number of protein molecules would be

23 × 6.022×10^23 = 138.506×10^23

As per question the ration would be

No. of lipid molecules / No. of protein molecules

So

463.54 X 10^23 / 138.506×10^23 = 3.34

So there are average 3.34 or 3 molecules for each single molecule of protein in internal membrane of E.Coli