a. Calculate the approximate length of time for a molecule of oxygen to diffuse

Question

a. Calculate the approximate length of time for a molecule of oxygen to diffuse from your lungs to your calf muscles. Assume that D02 = 1.78 x 10-5 cm2 s-1 , the value of the O2 diffusion coefficient in water.

b. Compare the time of oxygen diffusion to the time required to move blood from the heart to the muscles. Estimate this from the velocity of blood as it leaves the heart (as calculated in Problem #1) and the distance from the heart to the calf muscle.

3. The concentration of TnC in heart muscle cells is estimated at about 70 nmol/g wet weight of tissue. O2 consumption is estimated to be about 0.09mL O2 per min per g wet weight of tissue. Assume the TnC is 60% saturated during normal, resting contractions. Assume that 85% of the activating Ca2+ originates from SR stores. Assume a heart rate of 70/min. Assume free energy of ATP hydrolysis is 57 kJ/mol of O2 consumed and that metabolism obtains 20.3 kJ/L of O2 consumed. (7 points, one point per section)

a. How much Ca2+ is released and taken back up per heart beat, per g of tissue?

b. How much energy is consumed to take the Ca2+ back up into the SR, per heart beat?

c. What fraction of the cell’s energy consumption is used for this purpose?

Explanation / Answer

We calculate the approximate length of time for a molecule of oxygen to diffuse from lung to calf muscles as time = (distance in cm)2/(2×Do2) i.e (100cm)2/(2×1.78×10-5cm2s-1) =2808 ×10 to power 5 sec = 2.81 × 10 to power 8 sec...then now we divide it by 60 sec min -1 × 60 min hr -1 , which is equal to 78027 hours; this is equal to 3251days and this is equal to 8.91 yrs . b) velocity is calculated by a simple formula distance / time taken . Velocity of blood in aorta from above is 0.6m/s since distance to calf muscle is approximately 2m and time taken is 3 sec i.e 2÷3 =0.6m/s.

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