[ccp4bb]: estimating errors of refined parameters

["Ulrich K. Genick" <genick@brandeis.edu>]

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Hi,

this issue seems to come up frequently
in slightly different diguises.

Here is a general strategy to calculate the
estimated error for any parameter you are refining.

The procedure is a little tedious and not recommended
if you want to get errors for a large number of parameters.

No fancy crystallography specific tricks just
good old plain error analysis.

The approach outlined below includes a refinement at each
parameter value. So the error estimate includes both
contributions from the variance of the parameter itself and
contributions from the covariances with all the other
refined parameters.

If one skips the refinement step, and just calculates
the minimized function (energy function or R-factor)
while varying the parameter one obtains something similar
to the variance alone.

The strategy works as follows:

- fix the parameter for which you are trying to
   obtain the error, turn of all stereochemical restraints
   which might influence this parameter. Run a refinement of all
   other parameters in X-PLOR or CNS until you get convergence
   (i.e. your R-factor does not change anymore)

- do this for multiple different values of the parameter
   under question.

- plot the value of the function the program is minimizing
   versus the parameter. If I remember correctly, for X-PLOR and
   CNS the minimized fuction is called the total energy.

- the plot will have a minimum for the optimal value of your
   parameter. If the uncertainty is low, you should have one clean,
   symmetrical, narrow, downward spike in your plot. If the
   uncertainty is high the plot will have the shape of a rough,
   broad depression.

- to get your standard deviation fit the resulting plot to a function
   that consists of a baseline minus a gaussian normal distribution.

- gnuplot or a similar fittig program will perform such a fit for you.
   You will have to fit four parameters:
                the constant (i.e. baseline value)
                the mean of the gaussian
                the amplitude of the gaussian
                the sigma of the gaussian
   The sigma is the error you are looking for.

- since you are fitting 4 parameter to this function,
   make sure that you do your refinement for at least,
   15 to 20 different parameter values and choose the parameters
   so that the values you get are in the area where the plot is
   varying most quickly.



-- 
Ulrich K. Genick
Assistant Professor
Department of Biochemistry
Brandeis University, MS009
Waltham, MA, 02454

Room   Kosow 108
Phone  781-736 2304
Fax    781-736 2349
Email  genick@brandeis.edu