Crown Tutorial Trajectory Analysis

Comparing backbone torsions between Na+, K+ and Cs+ complexes (vacuum)

  Analyze trajectories (Run.carnal):

    % carnal -O -i carnal_na.in > carnal_na.out
    % carnal -O -i carnal_k.in > carnal_k.out
    % carnal -O -i carnal_cs.in > carnal_cs.out

  We compare the 'stiffness' of the crown in both cases by
  measuring the backbone torsions. The statistics for these
  measurements are printed to the .out files. Since torsions
  can vary over 0..+-360, 'circular statistics'** are used. The
  's' parameter corresponds to the standard deviation, and
  it turns out that 's' is more for Na+ than K+, indicating
  less flexibility with the larger ion.

  **  Batschelet, Edward.  Circular statistics  in  Biology  (1981)
      Academic  Press  Inc.,  New York, NY. This method is used for
      averaging angles that can encompass a full 360  degrees.  For
      motivation, think of what the average of 0 and 359 degrees or
      0 and 180 degrees would be. The 'averages' from  this  method
      are  in  the range [-180..180], so e.g. a single value of 183
      would result in a statistical  'average'  of  -177.   Another
      reference  for  circular  statistics  mentioned on the net as
      being easier to find: Fisher, N. I.  Statistical Analysis  of
      Circular Data (1993) Cambridge University Press, New York.

Ion-oxygen distances for a Na+ <-> K+ perturbation

  Analyze trajectory (Run.carnal2):

    % carnal -O -i carnal_pert.in > carnal_pert.out