BMEN E 3500, fall 1999

Problem Set 2.  Note added 9/26/99.  You are responsible for these two problems.  The case of sinusoidal excitation for a linear system will be discussed  in the coming week.

  1. A compartment (I) of 250 ml volume and 300 cm2 surface area has a permeability of 0.12 cm/sec. The compartment lies within another compartment (II) whose concentration is cAs. This concentration is suddenly changed from 0.27 to 0.6 moles/liter.

Graph the change in cA in compartment I over the 30 sec following the change in cAs. The solute A is non-reactive and compartment I experiences no convective flow.

Another way to excite compartment I is to allow cAs to fluctuate sinusoidally.

Calculate the characteristic time for the effect of cAs on cA and based on the value you obtain pick a sinusoidal frequency, in radians per second that you do not expect to allow cA to fluctuate very much. Calculate the amplitude ratio cA/cAs and the phase angle, phi, for this frequency. This is a frequency at which the compartment parameters act as a "filter": the potential disturbance to cA from fluctuations in cAs is filtered, not felt.

Pick another sinusoidal frequency, in radians per second, which you expect will allow cA to follow or "track" fluctuations in cAs. Calculate the amplitude ratio cA/cAs and the phase angle, phi, for this frequency. Convince yourself that the relationship between cA and cAs is "quasistatic". You are responsible for understanding this concept and being able to discuss it.

  1. A cell that is to be treated as a spherical bag of diameter 10 micrometers (10-3 cm) has a plasma membrane whose apparent permeability to tryptophan is about 10-7 cm/sec.

Calculate the characteristic time for transport from the surrounding medium into this cell.

What is the maximum rate at which tryptophan can be incorporated into protein in this cell when the concentration in the surrounding medium is 0.01 M? Give your answer in micromoles per second. Identify cogent reasons, at least two, why this rate would not, in practice, be reached.

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