Question

The density of the plasma membrane of a cell was found to be 1.04 g/mL. If the density of the lipid component is 0.92 g/mL and the density of the protein component is 1.35 g/mL, what is the percent composition (to the nearest ones) of the lipid component of the membrane, assuming the plasma membrane consists only of the lipid and protein components?

Answer 1

Ans. Given,

            Density of membrane = 1.04 g/ mL

            Density of lipid component = 0.92 g/ mol

            Density of protein component = 1.35 g/ mL

# We proceed with unit volume of plasma membrane. [Proceeding with unit mass of the membrane would yield the same result].

So, volume of plasma membrane = 1.0 mL

Mass of 1.0 mL plasm membrane = Volume x density

                                                = 1.0 mL x (1.04 g/ mL)

                                                = 1.04 g

#. Let mass of protein in 1.0 mL membrane = P grams

Let the mass of lipid in 1.0 mL membrane = F gram

Now,

            Total mass of protein and lipid in 1 mL membrane = 1.04 g

            Or, P g + F g = 1.04 g

            Or, P + F = 1.04       - equation 1

# Volume of P gram protein = Mass / Density

                                    = P g / (1.35 g/ mL)

                                    = 0.740741P mL

# Volume of F gram protein = F g / (0.92 g/ mL) = 1.086957F mL

# Since the volume of membrane taken is 1.0 mL, sum of volume of protein and lipid must be equal to 1.0 mL.

So,

            0.740741P mL + 1.086957F mL = 1.0 mL

            Or, 0.740741P + 1.086957F = 1.0                       - equation

# Comparing (equation 1 x 0.740741) - equation 2-

            0.740741P + 0.740741F = 0.77037064

      (-) 0.740741P + 1.086957 F = 1.0

                        Or, - 0.346216 F = - 0.22962936

                        Or, F = 0.22962936 / 0.346216 = 0.66325

Hence, mass of lipid in 1.04 g (= 1.0 mL) plasma membrane = F gram = 0.66325 g

Now,

            % lipid in membrane = (Mass of lipid / Total mass of membrane) x 100

                                                = (0.66325 g / 1.04 g) x 100

                                                = 63.77 %

                                                = 64 %