[phenixbb] lower limits on grid spacing/binning

[Pavel Afonine]

Hi Terry,

there are two separate things:

1) grid step for maps calculation (for example, in Xplor/CNS format). 
Here, smaller the grid step, better the maps appear. The price for this: 
1) big map files, 2) slow manipulations in visualization programs (like 
PyMol, SwissPDB, etc...).

2) grid step used in indirect, FFT based, structure factors and 
gradients calculation for refinement. There are three main parameters 
that affect the accuracy of FFT based structure factors and gradients 
calculation: grid step, atomic radius (the region around atom where the 
density is considered non-zero) and additional smearing b-factor. The 
optimization problem here is: given data and model, find such 
combination of {grid step, atomic radius, smearing b-factor}that 
produces the structure factors of desired accuracy (compared to direct 
calculations) for the minimal time. Different programs use different 
strategies to solve this. The default in phenix.refine is grid_step = 
highest_resolution / 3, MAIN uses grid_step = highest_resolution / 4. In 
some programs the atomic radius is preset constant (I believe something 
like 2.0A in CNS), in phenix.refine it is determined dynamically for 
each atom.
To get feeling about how the grid step affects the runtime and accuracy, 
you can play with it in phenix.refine :

% phenix.refine model.pdb data.mtz 
structure_factors_and_gradients_accuracy.grid_resolution_factor=XXX

where for XXX you can try a few values like 1/2, 1/3, 1/4, 1/5, 1/6,

and  grid_step = highest_resolution * grid_resolution_factor

I would suggest the following reading (of course the list is incomplete):

Acta Cryst. (1977). A33, 486-492
Efficient structure-factor calculation for large molecules by the fast 
Fourier transform
L. F. Ten Eyck

Acta Cryst. (1978). A34, 791-809    
A new least-squares refinement technique based on the fast Fourier 
transform algorithm
R. C. Agarwal

Some review and comprehensive set of references:

Acta Cryst. (2004). A60, 19-32   
On a fast calculation of structure factors at a subatomic resolution
P. V. Afonine and A. Urzhumtsev

Pavel.




On 10/29/2007 6:29 PM, Terry Lang wrote:
> Hey Everyone,
>
>        I have been told by several crystallographers that the general 
> rule of thumb for grid spacing when generating a map  is one third the 
> resolution (eg If your crystal structure has a resolution of 1.2 A, your 
> grid spacing should be 0.4).  Is there a mathematical reason why this 
> ratio should be maintained or is this simply a holdover from slower 
> computers with lower memory?  More importantly for my application, is 
> there a lower limit on how fine the grid spacing can be?  In other 
> words, is there a lower limit at which one is oversampling the data for 
> a particular resolution?  Any information and/or references would be 
> greatly appreciated.
>
> Sincerely,
> Terry
>
>