The distance geometry routines in X-PLOR begin by translating the bond lengths, bond angles, dihedral angles, improper angles, and van der Waals radii in the current molecular structure into a (sparse) matrix of distance bounds between the bonded atoms, atoms that are bonded to a common third atom, or atoms that are connected to each other through three bonds, as appropriate, using the equations in Crippen and Havel (1988). Experimental constraints can be added by the NOE assign statements (Section 18.1) and the restraints dihedral statements (Section 7.2). These lists of restraints are automatically read, translated into distance constraints, and entered into the bounds matrix.

The data translation is subject to the flag statement (Section 4.5); e.g., to include data from the distance restraint database, the following statement should be issued before invoking the mmdg statement :

FLAGsINCLude NOE END

The definition of upper and lower bounds proceeds in the following
order: bond lengths, bond angles, dihedral angles, improper
angles, distance and dihedral angle restraints, van der Waals repulsions,
and rigid group distances.
This order is actually not arbitrary; e.g., the calculation of
1--3 distance bounds from angles requires that distance bounds
among the atoms used to define the parameter (in this case, bond
lengths
between atoms * i* and * j* and atoms * j* and * k*,
as specified by the parameter statement) be defined previously.

For each bond, the accuracy parameter BACC is added to and subtracted from the equilibrium bond length as specified in the parameter statement (Section 3.2.1) or obtained from the reference coordinate set to give, respectively, the upper and lower bound on the particular 1--2 interatom distance.

Bond angle constraints are obtained from the parameter statement if REFErence=PARAmeter is specified or from the 1--3 distance obtained from the reference coordinate set if REFErence=COORdinates is specified. The accuracy parameter TACC is added to and subtracted from the equilibrium bond angle if REFErence=PARAmeter is specified, and BACC is added to and subtracted from the 1--3 distance if REFErence=COORdinates is specified.

Dihedral angle constraints for single-minimum dihedral angles defined by atoms i,j,k,l are obtained from the parameter statement if REFErence=PARAmeter is specified or from the distance between atoms i and l obtained from the reference coordinate set if REFErence=COORdinates is specified. The accuracy parameter PACC is added to and subtracted from the equilibrium bond angle if REFErence=PARAmeter is specified, and BACC is added to and subtracted from the i,l distance if REFErence=COORdinates is specified. For dihedral angles with multiple minima, the upper and lower bounds correspond to the dihedral angle settings of 180 and 0. In addition to reading all dihedral angles from the parameter statement database, a generic list comprising all possible dihedral angles in the current molecular structure is generated. The upper and lower bounds for these generic dihedral angles are set to 180 and 0.

Improper angle constraints defined by atoms i,j,k,l are obtained from the parameter statement if REFErence=PARAmeter is specified or from the distance between atoms i,l obtained from the reference coordinate set if REFErence=COORdinates is specified. The accuracy parameter IACC is added to and subtracted from the equilibrium bond angle if REFErence=PARAmeter is specified, and BACC is added to and subtracted from the i,j distance if REFErence=COORdinates is specified.

For distance restraints
(see NOE statement,
Section 18.1), the current
distance database is read. Upper and lower bounds are
set to
, , where **d**, ,
and are specified through the NOE assign statements
and is specified through the NOE SQOFfset statement
(by default is zero).

For dihedral angle restraints defined by atoms i,j,k,l (Section 7.2), the database is read as specified by the assign statements and interpreted as upper and lower bounds for the corresponding i,l distance.

To handle the repulsive van der Waals interactions , the nonbonded value (see NONBonded statement in Section 3.2.1) is converted into a van der Waals distance (see Eq. 4.10) and then multiplied by the REPEl parameter as part of the NBONd statement in the parameter statement (see Section 3.2.1). All atom-atom repulsions are included except for 1--3 and 1--2 atom interactions, regardless of the NBXMOd parameter.

The group option calculates the distance between each pair of atoms in the group and enters it into the bounds matrix. It is important that the main coordinate set be well defined for the selected atoms. Multiple GROUp statements define multiple groups. The accuracy parameter specifies a value that will be added to and subtracted from the precise distance as obtained from the coordinates.

Sat Mar 11 09:37:37 PST 1995