Question

HW #11-14

Erythrocytes (red blood cells) swell or shrink rapidly in response to changes in the osmolarity of the blood by the movement of water molecules through plasma membrane channels called aquaporins (AQP). AQP1 is a tetramer that consists of four identical monomers, each of which has a transmembrane pore. A human erythrocyte has approximately 2.0 × 10 5 AQP1 monomers and a total volume of 9.4 × 10 − 11 mL. Water molecules flow through the plasma membrane at a rate of 5.0 × 10 8 molecules per AQP1 tetramer per second.

1. Calculate the number of water molecules in an erythrocyte. Assume that the erythrocyte consists entirely of water.

number of water molecules: water molecules

2. Calculate how rapidly an erythrocyte could halve its volume when it encounters the high osmolarity ( 1.0 M ) in the interstitial fluid of the renal medulla.

time: seconds

Answer 1

1. Density of water= 1 g / ml

Molar mass of water=33.008 g

No of molecules in one mole=6.02×1023

  or

No of molecules in one mmole=6.02×1020

Volume of water= 9.4 × 10 − 11 mL/cell

The water in H2O is (55mM H2O /mL)

Total molecule of water in the erythrocyte= No of Molecules in total mmole × volume of cell

55 mM H2O /mL× 6.02×1020 molecules/mmol × 9.4 × 10 − 11 mL/cell

= 3.1 × 10 12 molecules

2. Half of these molecule must leave to

half the volume of the erythrocyte i.e.= 3.1 × 10 12    molecules/ 2

1.55 ×1012 Molecules

Total number of AQP1 monomers in cell= 2.0 × 10 5

Total number of AQP1 tetramers in cell= 5.0 × 10 4

5.0 × 10 8 molecules of Water flow through the plasma membrane per AQP1 per tetramer= 1 second

1.55 ×1011 Molecules of Water flow through the plasma membrane 5.0 × 10 4 =

(5.0 × 10 8 H 2 O molecules/s/aquaporin tetramer) × (5 × 104 aquaporin tetramers/cell) =2.5 × 10 13molecule/ sec

Removal of half the volume of water would take (1.55 ×1012

H 2 O molecules)/(2.5 × 1013 H 2 O molecules/s) = 6.2×10 – 2 sec