In its metabolic process, an animal cell burns glucose molecules to generate ATP

Question

In its metabolic process, an animal cell burns glucose molecules to generate ATP energy compounds. A cell has a typical initial mass of glucose mi= 66 ng. It also receives this sugar through its membrane at a rate min=24 ng/min, it burns it at a rate mb=28.8 ng/min, and even loses some of it through diffusion leaks to the surroundings at a rate mout=8.4 ng/min. The cell was monitored for a time T.

- (15 pts.) Show the right accounting/conservation equation to use (algebraic, integral, or differential). Explain the choice.

- (15 pts.) Use your equation to calculate the net final mass (in ng) of the cell glucose after T=4.8 min of metabolic process.

Explanation / Answer

Given
Initial Mass, mi = 66 ng
Membrane input, m' = 24ng / min
expenditure rate, b' = 28.8 ng/min
diffusion loss, m-out' = 8.4 ng/min
a) If these rates are constant and do not change with time, one can apply algebraic equations for conservation of mass equation
the integral method has to be used when these rates as mentioned in the question are not constant and change with time

So, rate of increase of mass of cell, M' = m' - b' - m-out' = 24 - 28.8 - 8.4 = -13.2 ng / min

b) Net final mass after T = 4.8 min = 66 ng - 13.2*4.8 = 2.64 ng

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