# Biological Calculations

(a) At the moment of fertilization a female egg is about 100μm in diameter. Assuming that each lipid molecule in the plasma membrane has a surface area of 10-14 cm2 , how many lipid molecules are there in the egg plasma membrane if 25% of the surface is protein?

(b) Each fertilized egg cell (zygote) divides 30 times to produce all the eggs that a female child will need in her lifetime. One of these eggs will be fertilized giving rise to a new generation. If lipid molecules are never degraded, how many lipid molecules have you inherited that were synthesized in your grandmother? Assume for calculation purposes that the lipid molecules synthesized by your grandmother is equally divided between the daughter cells at each cell division.

My answer: (a) Given, a female egg is about 100μm in diameter. Radius = 50μm Each lipid molecule in the plasma membrane has a surface area of 10-14 cm2. 25% of the egg surface is protein and 75% of the surface is lipids. Therefore, Surface area of egg is = 4π(radius)2 = 4*3.14*2500*10-12 = 3.14*10-8 m2 Area for the presence of lipid molecules = 3.14*10-8 *3 / 4 = 2.355*10-8 m2 = 2.355*10-8 * 104 cm2 Number of lipid molecules in egg plasma membrane = 2.355*10-4/10-14 = 2.355*1010 molecules

(b) Each fertilized egg cell divides 30 times into 2,4,8……230 cells. Assuming that the lipid molecules synthesized by our grandmother is equally divided between daughter cells at each cell division. • After 30 divisions we have 230 cells synthesized in grandmother Initially the zygote has 2.355*1010 lipid molecules from above calculations. Therefore, each cell has 2.355*1010/230 = 21.93 molecules. • After mother takes birth, she inherits lipid molecules present in zygote, that is a single cell

Number of lipid molecules that is inherited from grandmother by mother is 21.93 molecules.

This zygote undergoes division for 30 times. Thus, each cell inherits = 21.93/230 = 2.0424*10-8 lipid molecules from zygote

• Finally, a single cell in mother undergoes the zygote formation that leads to our birth.

Hence, we have 2.0424*10-8 lipid molecules inherited from our grandmother.

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• For (a) are you taking into account the fact that the lipid membrane is a bilayer? (I haven't checked the calculation) – user1136 Jul 5 at 21:17