Question #124821

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? (3 marks)

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.

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.

Expert's answer

**a.** First, the surface area of a female egg must be calculated. The following equation can be used:

S = 4 π r^{2}

where S - surface area, π = 3.14, r - a female egg radius (r = diameter / 2 = 100 μm / 2 = 50 μm)

From here:

S(egg) = 4 × 3.14 × (50 μm)^{2} = 31400 μm^{2} = 31400 × 10^{-8} cm^{2} = 3.14 × 10^{-4} cm^{2}

As 25% of the surface of the egg is protein, then 75% of the surface is lipid. As a result, the surface area of the egg covered with lipids equals:

S(lipids) = 3.14 × 10^{-4} cm^{2} × 75% / 100% = 2.355 10^{-4} cm^{2}

The number of lipids can be calculated as following:

n(lipids) = S(lipids) / S(lipid) = 3.14 × 10^{-4} cm^{2} / 10^{-14} cm^{2} = 3.14 × 10^{10}

*Answer: 3.14 × 10*^{10}*.*

**b.** If each cell divides into two cells and there are 30 cell divisions, a single female cell will produce 2^{30 }cells. As lipids present in the egg plasma membrane are separated equally, after thirty divisions, each cell will contain:

n = 3.14 × 10^{10} / 2^{30} = 29 lipid molecules.

As a result, if a grandmother's cell contained 3.14 × 10^{10 }lipids, each mother's cell (including egg) contains 29 lipid molecules. Therefore, 29 lipid molecules were inherited from a grandmother.

*Answer: 29 lpid molecules.*

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