GIL .. BIOSCI/Bionet News .. Biosequences .. Software .. FTP

# void volume

Michel PETITJEAN ptitjean at ccr.jussieu.fr
Thu Mar 21 04:26:27 EST 1996

```To: wstzou at GATE.SINICA.EDU.TW
Subject: Re: Void volume
Newsgroups: bionet.molec-model
Organization: CCR Jussieu
Cc:
Bcc:

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 !
>
>regards,
>
>	Wen-Shyong Tzou
>
>   ____________________________________________________________________
>  |                                                                    |
>  |    Wen-Shyong Tzou                 Email:wstzou at gate.sinica.edu.tw |
>  |    Computer Simulation Laboratory        http://www.sinica.edu.tw/ |
>  |    Institute of Biomedical Science       Phone:(886)-2-789-9033    |
>  |    Academia Sinica                       Fax:  (886)-2-785-3569    |
>  |    Taipei, Taiwan, R.O.C.                                          |
>  |                                                                    |
>  |    Address:P.O.Box 1-99, Nankang, Taipei, Taiwan                   |
>  |____________________________________________________________________|
>

Reply to article 744 of bionet.molec-model (void volume):

To: Wen-Shyong Tzou
Email: wstzou at gate.sinica.edu.tw

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.

Michel Petitjean,                     Email: petitjean at itodys.jussieu.fr
ITODYS (CNRS, URA34),                        ptitjean at ccr.jussieu.fr
1 rue Guy de la Brosse,               Phone: +33 (1) 44 27 48 57
75005 Paris, France.                  FAX  : +33 (1) 45 84 98 25

```