Problems for
Intermediate Methods in Theoretical Physics

Edward F. Redish

Green jellyfish protein

In biology, cells are continually creating and destroying proteins. Suppose a particular protein is created at a rate a. Since the number of proteins needs to be stable, these proteins are destroyed in the cell at the same rate.

If the cell contains a gene for "green flourescent jellyfish protein," (GFP) a marker will be attached to the protein that will flouresce if the cell is illuminated with a particular wavelength of light. This marker is not immediately effective when the protein is created. The protein has to fold into a particular shape before it will flouresce. The newly created protein "brightens" at a rate b.

The mechanism destroying protein at a fixed rate does not care whether the protein is bright or not.

  1. Write a pair of coupled ordinary differential equations that describes the evolution of the number of "bright", (B), and "dark" (not yet brightened), D, proteins in the cell.
  2. What do your equations imply for the total number of proteins, B+D? Is this physically reasonable?
  3. Solve your equations and write them in a form that allows you to "make sense" of the solution.
  4. If you can only measure the number of brights as a function of time, what can you learn about the parameters of the cell (numbers and rates)?

GFP attached to a protein used in the construction of microtubules by the cell, showing location of tubules.


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This page prepared by

Edward F. Redish
Department of Physics
University of Maryland
College Park, MD 20742
Phone: (301) 405-6120

Last revision 6. September, 2004.