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PCI: Computation of pocket or cavity descriptors (named PCI, PSI, and DISC).


References:

N. Cerisier, L. Regad, D. Triki, A.-C. Camproux, M. Petitjean,
Cavity versus ligand shape descriptors: Application to urokinase binding pockets.
J. Comput. Biol., 2017, 24[11], 1134-1137. DOI 10.1089/cmb.2017.0061

A. Borrel, L. Regad, H. Xhaard, M. Petitjean, A.-C. Camproux,
PockDrug: A Model for Predicting Pocket Druggability That Overcomes Pocket Estimation Uncertainties.
J. Chem. Inf. Model., 2015, 55[4], 882-895 (see Table 1). DOI 10.1021/ci5006004


Author email: petitjean.chiral@gmail.com


PCI reads the cartesian coordinates of the atoms bounding the pocket.
    This set of atoms must be read as a molecule. Bonds are ignored during the calculus.
    Several atomic sets can be concatenated within one input file.
    PCI computes the Pocket Convexity Index, the Pocket Sphericity Index,
        the best fit sphere, and the Distributional Sphericity Coefficient (DISC).


Input data and parameters:
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INPUT  FORMAT:
  BIO : Biosym (MSI) files
  CAS : Reserved for internal purposes
  HIN : Hyperchem-type files
  ISU : Reserved for internal purposes
  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)
  SDF : Symyx Mol/SDF files
        (data between 'M  END' and '$$$$' are treated as comments)
  XYZ : n+2 lines. Line 1: n; line 2: free comment,
        Next n lines: label or atomic symbol, x, y, z
        (separator: spaces; no tabulation allowed).

INPUT  MOLEC FILE NAME: name of the input file containing the molecule or set of atoms.

EPSTAB:
  Generate randomly perturbated cartesian coordinates.
  The coordinates are not modified when EPSTAB is negative or null.
  Independant random 3-tuples (x,y,z) are added to the spatial atomic positions.
  Each random 3-tuple follow an isotropic normal law of std.dev equal to EPSTAB.
  with radius equal to EPSTAB and centered on the atomic position.
  *** WE DO RECOMMEND TO USE THIS OPTION IN ORDER ***
  *** TO AVOID POTENTIAL NUMERICAL INSTABILITIES ***
  Most of the time, EPSTAB=1.D-7 is effective.


Output results:
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3D CONVEX HULL: the K atoms of the hull, i.e. the K vertices of the
                smallest convex polyhedron containing the set of the
                N atomic positions, and the corresponding list of
                the oriented triangular faces (such that the
                direct normal is the exterior one)

DIAMETER: the distance D of the longest atom-pair of the molecule
          The two D-extremal nodes are exhibited.


RADIUS: the radius R of the smallest sphere containing the N atoms
        (smallest circumscribed sphere).
        The center and the R-extremal nodes are exhibited.
        The ratio DIAMETER / RADIUS may be smaller than 2.

MIN SPHERE CENTER: the center of this minimal circumscribed sphere.


BARYCENTER: Geometric center of the N atoms.


CAVITY CENTER: center of the pocket, assumed to be spherical (best fit sphere).

DISTANCE BETWEEN CENTERS:
  Distance between the barycenter and the pocket center.

CAVITY RADIUS:
  Radius of the pocket: the pocket is modelized by a best fit sphere.
  This sphere should neither be confused with the smallest circumscribed one,
  nor with the largest inscribed one (see further).

SQRT(STD. DEV):
     STD. DEV is the square root of the minimized variance of the
              squared distances between the N atoms and the pocket center.

NORMALIZED VARIANCE:
  Ratio of the minimized variance to the fourth power of the cavity radius.
  This ratio can take arbitray large values.

DISTRIBUTIONAL SPHERICITY COEFFICIENT (DISC, takes values in [0..1[):
  Ratio of the minimized variance to the sum of
      the fourth power of the cavity radius plus the minimized variance.
  DISC is also equal to the ratio : (normalized variance) / (1 + normalized variance)
  DISC=0 when all pocket atoms lie on the surface of a common sphere.
  DISC values close to 1 indicate that the pocket sphericity assumption is the very bad.
       This upper bound cannot be reached.


QUADRATIC MEAN DISTANCE TO HULL:
  Quadratic mean distance of the N atoms to the boundary of their convex hull.

INRADIUS: the radius of the largest sphere inscribed in the pocket convex hull.

INCENTER: the center of this largest sphere.


POCKET CONVEXITY INDEX (PCI, takes values in [0..1]):
  Ratio of the squared quadratic mean distance to the square of the inradius,
  followed by the square root of this ratio.
  PCI=0 when all pocket atoms are on the boundary of their convex hull.
  PCI=1 indicates that the pocket convexity assumption is very bad.

POCKET SPHERICITY INDEX (PSI, takes values in [0..1[):
  Ratio inradius/R.
  PSI=0 indicates a flat pocket.
  PSI=1 indicates that the pocket hull is spherical.
        This upper bound cannot be reached by a finite set of points.

Remarks:
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The following spheres are distinct:
    - the smallest enclosing sphere (min circumscribed sphere).
    - the sphere modeling the pocket (even if it is not spherical).
    - the largest inscribed sphere.

The number of atoms is currently limited to 15000 for each set of atoms.
The source has to be recompiled to read larger atomic sets.

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