void volume

Gerard Kleywegt gerard at xray.bmc.uu.se
Fri Mar 22 17:06:03 EST 1996

In article <4ir7c3$4csc at moka.ccr.jussieu.fr>, ptitjean at ccr.jussieu.fr
(Michel PETITJEAN) wrote:

?> In article <Pine.SOL.3.91.960318143527.10824C at gate> you write:
?> >Dear Netters:
?> >       I had a protein in crystal environviroment. I know its coordinate 
?> >and the space group ( P 21 21 21 ). I had visulized the packing pattern 
?> >in cell display. I want to calculated the void volume the protein had not 
?> >occupied. Does anybody know any program can calculate this void volume in 
?> >a unit cell ? Any help will be appreciated !
?> >
?> May I suggest the following Monte-Carlo algorithm to evaluate the
?> void volume of a molecule in its cell:
?> 1) Compute the volume of the cell,i.e. Vc=Det/6, Det being the determinant
?> of the direct trihedron bounding the cell.
?> 2) Insert the cell in a parallelepipedic window (the smallest is the better)
?> 3) Generate N random points in the window, i.e. each coordinate is uniformly
?> distributed
?> 4) Let Nv be the number of points falling both inside the cell and outside
?> all of the atomic spheres. Let be: p=Nv/N and q=1-p.
?> The void volume is estimated as Vv=Vc*p, and its standard deviation is
?> estimated as s=Vc*sqrt(p*q/N).
?> A similar algorithm is in J.Comput.Chem.1994,15[5],507-523 (appendix 3).
?> Using N=1000 or 10000 is generally sufficient, but remember that you get
?> different results if you use different sets of atomic radii.

and all the poor bugger wanted to know was the solvent content ;-)

calculate the volume of one molecule
multiply by the number of molecules in the unit cell
subtract from the unit cell volume

Gerard J. Kleywegt
Department of Molecular Biology, Biomedical Centre
Uppsala University, Uppsala, SWEDEN

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