Because the plasma membrane is selectively permeable, glucose cannot pass through the lipid bilayer without the help of transport proteins like GLUTs. The calculation gives us a hypothetical number of 3000 glucose molecules entering the cell in 10 seconds based on the given permeability and area, although in reality the permeability of glucose without transport proteins would be much lower.
The plasma membrane of a cell is selectively permeable, meaning it allows certain substances to pass through while blocking others. Glucose molecules are polar and too large to pass through the lipid bilayer of the cell membrane without assistance. This assistance usually comes from transport proteins, like glucose transporters (GLUTs), which enable glucose to cross the membrane through a process called facilitated transport.
To calculate the number of glucose molecules that would enter the cell in the absence of these transporters, we need to use the given permeability of the lipid bilayer for glucose (10-8 cm/sec) and the surface area of the plasma membrane (5 μm2). However, we must be aware that the permeability is very low for glucose, so under normal conditions very few molecules would enter the cell.
Let's calculate:
- Convert surface area from μm2 to cm2:
5 μm2 = 5 x 10-8 cm2 - Glucose concentration in the solution: 1 mM (1 millimole/L) is equal to 6.022 x 1017 molecules/cm3 (since 1 mole equals Avogadro's number, 6.022 x 1023 molecules).
- Calculate the number of glucose molecules entering per second:
Flux = Permeability x Area x Concentration (assuming 100% efficiency, which is unrealistically high, but used for estimation here) - Calculate the total number for 10 seconds:
Number of molecules = Flux x Time
Now, apply the above formula with the given values:
Flux = (10-8 cm/sec) x (5 x 10-8 cm2) x (6.022 x 1017 molecules/cm3)
Flux ≈ 3 x 102 molecules/sec
Total number of molecules in 10 seconds:
Total ≈ 3 x 102 molecules/sec x 10 sec = 3 x 103 molecules.
The closest answer to the calculation is (a) 3000, but it is crucial to state that this is a hypothetical calculation provided that the glucose could somehow pass through the lipid bilayer without transporters, which is highly unlikely in practice.