Erythrocytes swell or shrink rapidly in response to changes in the osmolarity of

Question

Erythrocytes swell or shrink rapidly in response to changes in the osmolarity of the blood by moving water molecules through plasma membrane channels call 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 x 105 AQP1 monomers and a total volume of 5 × 10-11 mL. Water molecules flow through the plasma membrane at a rate of 5x10 molecules per AQP1 tetramer per second. Calculate the number of water molecules in an erythrocyte.Assume that the erythrocyte consists entirely of water. Number water molecules Calculate the amount of time that it takes for the erythrocyte to lose half of its volume of water when it encounters the high osmolarity (1 M) in the interstitial fluid of the renal medulla. Number seconds Previous Give Up & View Solution Check AnswerNext nt

Explanation / Answer

Total volume of erythrocyte cell = 5 X 10-11 mL

we know that density of water = 1g /mL

the mass of water in 1mL of water= 1 g

Moles of water in 1mL of water= mass / molecular weight of water = 1/ 18 = 0.0556 moles

So number of molecules in 0.0556moles of water = Moles X Avagadro's number = 0.0556 X 6.023 X 1023 =

Number of molecules / mL =3.349 X 1022 molecules

So total number of water molecules / mL erythrocyte = Volume of erythrocyte cell X Water molecules / mL

number of water molecules / mL erythrocyte = 5 X 10-11 mL X 3.349 X 1022 molecules = 16.745 X 1011 molecules

b) Time:

The half of number of water molecules = 16.745 X 1011 molecules / 2 = 8.372 X 1011 molecules

AQP1 monomers= 2 X 105

Therefore AQP1 tetramers = 2 X 105 /4 = 5 X 104

water flow through plasma membrane at the rate = 5 X 108 molecules / tetramer per second

So for 5 X 104 tetramers, rate will be= 5 X 108 molecules X 5 X 104

So for 5 X 104 tetramers, rate will be= 2.5 X 1013 molecules / s

time taken to lose half water molecules = 8.372 X 1011 molecules / 2.5 X 1013 molecules / s = 3.3488 X 10-2 seconds

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