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ASV: Analytical calculation of van der Waals surfaces and volumes


M. Petitjean, On the Analytical Calculation of van der
Waals Surfaces and Volumes: Some Numerical Aspects,
J. Comput. Chem. 1994,15[5],507-523

Author email:

ASV reads the cartesian coordinates of the molecule and the van der
Waals radii of the atoms, then performs both Monte-Carlo and analytical
calculation of the van der Waals surface and volume.

Input data and parameters:

  CAS : Reserved for internal purposes
  HIN : Hyperchem-type files
  MDL : Cambridge Crystallographic Model files
  ML2 : SYBYL Mol2 files
  PDB : Protein Data Bank or Nucleic Acid Data Bank files
        (only HEADER, ATOM, ENDMDL and END records are recognized)
  BIO : Biosym (MSI) files
  ISU : Reserved for internal purposes

INPUT  MOLEC FILE NAME: name of the input file containing the molecule

IMOL: Sequential position number of the molecule in the input file

van der Waals radii: SYMBOL=RADIUS , SYMBOL=RADIUS ...
  When SYMBOL is a valid chemical symbol, all atoms bearing this symbol
  type get a van der Waals radius equal to RADIUS.
  When SYMBOL is an number pertaining to [1..N], N being the number of atoms
  of the molecule, the pointed atom get the assigned RADIUS, dicsarding the
  rest of the SYMBOL=RADIUS list.
  Exemple: "H=1.17 , 34=1.5 , C=1.75 , Cl=1.77" means that the atom number
  34 in the molecule file get the radius 1.5, discarding if it is a carbon,
  an hydrogen or anything else.
  Atoms cited neither by symbol nor by number get a null radius.

  Enter an integer number n. The n first atomic radii and coordinates are
  printed. Nothing is printed if n is not positive.

  Number of random points for the Monte-Carlo estimation of surface and volume.
  No Monte-Carlo is done when a negative or null value is entered.

  Number of additional analytical calculations performed with random
  rotated and renumbered copies of the molecule.
  No analytical calculation is done when a negative value is entered.
  The analytical calculation is done when NPERM=0 is entered.
  When NPERM>0, NPERM additional analytical calculations are done with
  random copies. Among the NPERM+1 analytical calculations, the first
  one is done on the original non rotated non renumbered molecule.

  Generate randomly perturbated cartesian coordinates.
  Independant random 3-tuples (x,y,z) are added to the spatial atomic
  positions. Each random 3-tuple is uniformly distributed in a sphere
  with radius equal to EPSTAB and centered on the atomic position.
  The coordinates are not modified when EPSTAB is negative or null.
  The EPSTAB parameter applies even when NPERM=0.

  Any positive value indicates than the surface and volume of all
  sphere overlaps are printed.
  No overlap list is printed when ILIST is negative or null.

  CAUTION : activating the ILIST parameter may cause considerable
            amounts of output for medium or large molecule.

Output results:

When NOBST positive:
  The estimated surface and volume of the union of the van der Waals
  spheres, the associated standard deviations and the ratio of the 
  standard deviation to the Monte-Carlo estimate.

When NPERM is not negative, NPERM+1 analytical calculations are done.
For each analytical calculation, the number of overlaps, the surface and
volume, and the sphericity index are printed.


The number of atoms is currently limited to 15000 for each molecule.
The source has to be recompiled to read larger molecules.

ASV computes the surface and volume of any union or intersection of
spheres, discarding whether it is a molecular model or not.

The sphericity index is computed as follows: the squared volume is divided
by the cube of the surface, and the ratio is multiplied by 36*pi to get the
sphericity index pertaining to ]0;1].

The analytical surfaces and volumes are printed with six decimals.
The NPERM parameter is useful to detect if some numerical instability
appears. When this situation is detected, the EPSTAB parameter can be
used to remove them (e.g. try EPSTAB=1.E-6).
Using small values of EPSTAB may be also useful to evaluate the numerical
impact of the precision of the coordinates upon the surfaces and volumes.

The ILIST parameter is useful to compute the surface and volume of the
intersections of any number of spheres, rather than their union.

The number of random observations (NOBST) should be multiplied by 100
to get a standard deviation of the Monte-Carlo estimate divided by 10.

The computing time of the analytical calculation is mainly related to
the number of overlaps. This latter can be very high for large molecules,
such as proteins.
Thus, for QSAR and other poor precision applications involving large
molecules, Monte-Carlo estimates should be preferred to analytical
calculations. These latter are rather used when a high precision is
required, such as computing finite difference approximations of gradients.

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