## Report on Molecular Motors

The report on the molecular motors consists of answers to the following questions. The answers should be complete and written in such
a way that the Chemist (who doesn’t know anything about the project
other than the structure of the molecules) can understand them. Keep
it self-contained, short but clear. The structure of the report should
follow the questions below. The report is due March 11. Send it by
email to [email protected]
I) (10) Describe the problem the chemist presented to us. In particular, describe the shape of the molecular motor and the main questions
II) (10) Describe the model, a Markov process, for the flipper motion
of a single molecule.
III) (10) Explain how the model can be used to predict the concentrations of molecules in the different states. Explain how this can be
used to validate the model.
IV) (10) Explain the dynamical situation at equilibrium.
V) (10) Describe a simulation of the flipper motion of a single molecule. Explain how the output of a simulation, given by the second
program, of a single molecule relates to the actual motion of the flipper. Include several examples.
VI) (10) What is the problem with the simulations and how can we
solve it? Explain why we have to use statistical methods. Explain with
data/examples: Present the results of the simulations. Explain what
is the time scale to get reasonable results. (The results are tables with
estimated rotational speed for different values of T).
VII) (10) Give the final table of rotational speeds dependent on the
light intensity. Use groups of molecules and simulations of long enough
time. Explain that the size of the groups and the time you use are
suffciently large. What is the influence of the simulation time?
VIII) (10) Give a formula for the speed in terms of the probability
matrix and the equilibrium concentrations. Compare with the results
of the table of question VII).
IX) (10) Discuss the qualitative behavior of the rotation speed in
terms of the light intensity. When is the speed optimal? Hint: give two
1
2
differences between low light freuency (k=0) and high light freuency
(k=15). Explain qualitatatively the observed velocity for k=0 and
k=15.
X) (10) Give a summary for the chemist of the results. Suppose
the motor is build into a nanocar. Make a manual for the chemist
describing how to drive the car.
The numbers between parenthesis are the points you can get for the
question. Grade=total number of points/ 10, something between 0 and
10.
Often math majors use these reports to satisfy their writting requirements (MAT487). At the end of the semester let me know whether you
want to use your reports for this purpose.

Sample Solution