# 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.1994,15,507-523 (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
--------------------------------------------------------------------
Gerard J. Kleywegt
Department of Molecular Biology, Biomedical Centre
Uppsala University, Uppsala, SWEDEN

```