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Re: [ccp4bb] Program to fill unitcell randomly |
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CCP4bb navigationCCP4bb <-- 1999 <-- November 1999 <-- 30 November 1999Subject: Re: Program to fill unitcell randomly From: Daniel Anderson dha {- at -} MBI {- dot -} UCLA {- dot -} EDU Date: 2008-12-01 (I don't remember the motivation for the original question.) Shake-and-Bake used to generate random atoms in an asymmetric unit, and the program kept the atoms spaced by at least a bond length. Since PDB entry 2erl, I am not up to date on Shake-and-Bake's current set of tricks. The crystal for 2erl was so densely packed that random atoms spaced by 1.5A produced very good starting phase sets. (but I still don't know what's the motivation underlying the current discussion.) Did that help?, Dan On Mon, 1 Dec 2008, Ethan Merritt wrote: > On Monday 01 December 2008 10:28:34 Edward A. Berry wrote: >> Ethan A Merritt wrote: >>> On Friday 28 November 2008, Mueller, Juergen-Joachim wrote: >>>> Dear all, >>>> does anybody know a program to >>>> fill an unit cell a,b,c randomly by an arbitrary number >>>> of spheres (atoms)? >>> >>> First you would need to define "random". >>> Uniform density throughout the lattice? >>> Uniform distribution of neighbor-neighbor distances? >>> Uniform fractional coodinates? >>> Must the placement conform to space group symmetry? >>> >> Although I am sure it was not intended, this might suggest >> to some that uniform is equivalent to random- >> actually they are the opposite: a random distribution would >> have large areas with nothing and other places where two or >> three spheres are almost on top of each other. >> A uniform distribution is, well, uniform. > > I fear you are muddying the waters rather than clarifying. > What you refer to as "random distribution" is better described > as random sampling from a uniform distribution. > >> Most programming languages have a function to generate a random >> number evenly distributed between 0 and 1. > > My point was that simple random sampling is not correct in the > context of crystallographic symmetry. If you use this procedure to > "fill the unit cell", as originally requested, you will violate > the crystal symmetry. If you use it to fill the asymmetric unit, > then the distribution that describes placement within the full > unit cell is no longer the same distribution as you sampled from, > since it is now perturbed by the additional placements generated > by crystallographic symmetric rather than by random sampling. > That may be acceptable, or it may not, depending on the > intended application. > >> Decide how many atoms >> you want, get three random numbers for each atom, and those are >> your fractional coordinates of your random spheres. Coordconv will >> convert to orthogonal angstroms given your cell parameters. > > That was the "uniform fractional coordinates" case that I listed. > It is unlikely to be the correct choice (although as always it depends > on the question). This problem is that since it is based on fractional > coordinates rather than the true cartesian coordinates, the resulting > density of atomic centers will be strongly anisotropic. The density > along each axis will be inversely proportional to the cell edge. > You would do better to define a cartesian coordinate grid that fills > the region of interest, and then assign an atom to each grid point with > probability 1/N. This produces artifacts of its own, of course, since > the distribution of interatomic distances is now discrete rather than > continuous. > > The question "what is random?" is very deep, and the answer > depends strongly on the intended application. > > -- *********************************************** Daniel Anderson, Ph.D. Email: dha@mbi.ucla.edu Phone: 310-206-3642 Fax: 310-206-3914 Howard Hughes Medical Institute at University of California Los Angeles Lab: Paul Boyer Hall Room 219 For US Postal Service and 2-dimensional, use: Box 951662 MRL5-748 Los Angeles, CA 90095-1662 For UPS, FedEx, DHL, or 2.5-3-dimensional, use: Boyer 219 611 Charles Young Drive East Los Angeles, CA 90095-1570 USA CCP4bb navigationCCP4bb <-- 1999 <-- November 1999 <-- 30 November 1999 |
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