Fluid mosaic membranes — practice questions

The selective permeability of the fluid mosaic membrane arises from the combined actions of its components:

1. Phospholipid Bilayer: The hydrophobic fatty acid tails form a non-polar, lipid-soluble interior, which acts as the primary barrier. This restricts the passage of large molecules, charged ions, and highly polar substances, allowing only small, non-polar molecules (e.g., oxygen, carbon dioxide) and some small polar molecules (e.g., water via osmosis) to pass directly through.
2. Intrinsic Proteins (Channels and Carriers): For substances that cannot cross the lipid bilayer (e.g., ions, glucose, amino acids), specific intrinsic proteins provide pathways. Channel proteins form hydrophilic pores allowing specific ions to pass, while carrier proteins bind to specific molecules and change shape to facilitate their transport across the membrane. This ensures only specific substances are transported.
3. Overall Fluidity: The dynamic nature of the membrane, due to the movement of phospholipids and proteins, allows for processes like endocytosis and exocytosis. These bulk transport mechanisms enable the uptake or release of larger particles or entire substances that would otherwise be unable to cross the membrane, but this is still a controlled and selective process by the cell.

This problem requires calculating the surface area of the red blood cell and then finding the density of the protein channels.

Step 1: Find the radius of the red blood cell. The diameter (d) is given as 7.5 µm. The radius (r) is half of the diameter. $r = d / 2 = 7.5 \mu\text{m} / 2 = 3.75 \mu\text{m}$

Step 2: Calculate the surface area of the cell. The formula for the surface area (A) of a sphere is $A = 4 \pi r^2$. $A = 4 \times \pi \times (3.75 \mu\text{m})^2$ $A = 4 \times \pi \times 14.0625 \mu\text{m}^2$ $A \approx 176.7146 \mu\text{m}^2$

Step 3: Calculate the density of the aquaporin channels. Density is the number of channels per unit area. Density = Total number of proteins / Surface Area Density = $(1.2 \times 10^6) / 176.7146 \mu\text{m}^2$ Density $\approx 6790.5$ channels/µm²

Step 4: Give the answer to 3 significant figures. Rounding the result to 3 significant figures gives 6790.

Final Answer: The density of aquaporin channels is 6790 channels/µm².