Question 7 1 pts Human erythrocytes have about 1.9 x 105 aquaporin (AQP-1) monom

Question

Question 7 1 pts Human erythrocytes have about 1.9 x 105 aquaporin (AQP-1) monomers. If water molecules flow through the plasma membrane at a rate of 4.8 x 108 per AQP-1 tetramer per second, and the volume of an erythrocyte is 5 x 1011 mL, how rapidly (in seconds) could an erythrocyte halve its volume as it encounters the high osmolarity (1 M) in the interstitial fluid of the renal medulla? Assume that the interior of the erythrocyte consists entirely of water. Also, the rate of diffusion of water across the membrane can be ignored in this problem. Report your answer to two significant figures.

Explanation / Answer

Ans. Given,

Number of aquaporin (AQP) monomers= 1.9x 105

So, Number of AQP tetramers = (1.9 x 105)/ 4 = 4.75 x 104

# Step 1: Calculate flowrate in terms of mL/s:

Given, Flow rate per AQP-tetramer = 4.8 x 108 water molecules per second.

= 4.8 x 108 molecules s-1 / (6.022 x 1023 molecules / mol)

= 7.9708 x 10-16 mol s-1

= 7.9708 x 10-16 mol s-1 x (18.0 mL / mol)

= 1.4347 x 10-14 mL s-1

Note: 1 mol H2O = 18.0 g = 18.0 mL. That is, the volume of 1 mol H2O at RTP can be considered to 18.0 mL. Or, molar volume of H2O at RTP = 18.0 mL/ mol

Step 2: Calculate required time:

Given, Volume of erythrocyte = 5.1 x 10-11 mL

Volume of H2O to be removed = ½ x Erythrocyte volume

= ½ x (5.1 x 10-11 mL)

= 2.550 x 10-11 mL

Now,

Required time = Volume of water to be removed / Flowrate

= (2.55 x 10-11 mL) / (1.4347 x 10-14 mL s-1)

= 1.7773 x 103 seconds

= 1.8 x 103 s

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