Subject: SAS summary

From: Nathaniel (noj) Malcolm <[email-masked]>
Date: Mon, 3 Apr 95 14:00:39 BST

Here is the summary of replies that i recieved 
 concerning the location of a number of points
 (solvation sights) on the accessable molecular
 surface (AMS as defined by Richards) 

my original question was:
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>Does anyone have a program that will generate a
>set of equally spaced  points (in xyz coordinates)
>on a surface of over-lapping spheres?
>
>   If so i would be very interested,and will summarise
>any replies that i get for respondants.
>
>        thank-you
>        Noj Malcolm
>
>        [email-masked]
>
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Thanks to all who replied, i had tried implementing a triangulation
method for generating the points around the spheres, this is of course the
easy bit.  Removing points that are too close (on adjacent spheres etc.) , 
and setting up  points to replace is as has benn pointed out the "tricky"
bit. This is probably a larger problem than i first imagined and 
involves more work than i have time for at the moment.

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I would be particularly interested in your summary.  I have written a
program (GERM) to generate a receptor site model by placing a shell of
atoms around one or more active ligands.  I first tried a rectangular grid
of points for generating the shell.  Currently I am generating a shell by
(1) centering the ligand(s) in the coordinate system; (2) placing points on
a sphere much larger than the ligands; (3) bringing each point in radially
toward the origin until it contacts the ligands.  It's better than the
rectangular grid, but I suspect it is still not ideal.  Please let me know
what you find.

Best regards,

Eric Walters

  D. Eric Walters, Ph.D., Associate Professor, Biological Chemistry
  Finch University of Health Sciences/The Chicago Medical School
  3333 Green Bay Road, North Chicago, IL  60064
  ph 708-578-3000, x-498;fax 708-578-3240; email: [email-masked]

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It depends what you mean by "equally-spaced":  this is not as simple
mathematically as you may think.

I think that the "gnomonic projection" should interest you - see the 
papers from P. M. Dean's group  (J. Molec. Graph.  5, 97, (1987) and later
papers).

In addition about 1 year ago there was a similar posting (I think from the
group at U. Montreal) on CCL about methods to disperse points on the
surface of a sphere.  There were quite a number of replies - you should
definitely check the archives.

Yours, 

Richard Bone

__________________________________________________________

Richard G. A. Bone, PhD.
Computational Chemist
Terrapin Technologies, Inc.
South San Francisco
USA

E-mail  [email-masked]

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It's not quite clear to me what type of point distribution you're 
interested in but you should have a look at GEOPOL from QCPE, e-mail 
[email-masked].  This "vanilla" f77 program generates an regular 
array of points on the surface of intersecting spheres (polyhedra) such 
that each point then represents an equal fraction of the spheres surface 
area.  Points within neighboring spheres are eliminated.  The equilateral 
triangles, tesserae, formed by neighboring points give the appearance of a 
geodesic dome if visualized - a more pleasing appearance than simple dots. 
GEOPOL is very fast and you, as I have, could easily compute higher dot 
densities by computing the centers of the tesserae and extrapolating to the 
sphere's surface.

You might also want to check an article by Truhlar, Cramer, et. al., in the 
most recent J. Comp. Chem. on improved solvation models for AMSOLV, also 
available from QCPE.  They discuss their new/improved method analytical 
computation of solvent-accessible surface areas.
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I was impressed with the optimal distribution of
points on the surface of a sphere given by
Scott leGrand and Ken Merz in J Comp. Chem. 14, 349-352
(1993) in their paper titled, "Rapid Approximation to
molecular surface area via the use of boolean logic
and look-up tables". 

Their implementation minimizes the function:

U(x,y) = SUM((180 - B)**2)

where B is the arc length on the sphere in degrees
between points x and y.

-----> richard

***********************************************************
Richard D. Macdonald, Ph.D.  voice: (619) 546-5527
Lead Scientist                 fax: (619) 458-0136
Biosym Technologies     internet: [email-masked]
9685 Scranton Road
San Diego, CA 92121-2777
***********************************************************

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The following article proposes an improved 'marching-cube' method
for molecular surface triangulation.
-Dongchul Lim, Dept. of Chemistry, Yale Univ.

X. Zhexin, S. Yunyu, and X. Yingwu, "Calculating the Electric
Potential of Macromolecules: A Simple Method for Molecular
Surface Triangulation", J. Comp. Chem. 1995, 16, 512-6.

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> 
> The following article proposes an improved 'marching-cube' method
> for molecular surface triangulation.
> -Dongchul Lim, Dept. of Chemistry, Yale Univ.
> 
> X. Zhexin, S. Yunyu, and X. Yingwu, "Calculating the Electric
> Potential of Macromolecules: A Simple Method for Molecular
> Surface Triangulation", J. Comp. Chem. 1995, 16, 512-6.

I belive that the marching cubes algorithm is already implemented in the
program GRASP available from Anthony Nicholls (Barry Honig's group).  He
can be reached at [email-masked].

Cheers
-raman
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