The major goal in the implementation of this part of the package was to make it as easy as possible for the user to specify `ideal' bond lengths and angles. Stereochemical restraints are usually introduced either as energy terms (e.g. Jack & Levitt, 1978) or by expressing all types of stereochemical restraints as distances (e.g. Ten Eyck, Weaver & Matthews, 1976; Dodson, Isaacs & Rollett, 1976; Konnert & Hendrickson, 1980). There are many drawbacks to both approaches. In the first case it may be difficult to obtain reliable energy parameters, expecially for novel chemical groups. Also the introduction of an inappropriate energy term might mask interesting and unexpected features of the structure. On the other hand, if one attempts to define standard geometry in terms of interatomic distances, then such distances must be determined indirectly from a known example with ideal geometry. There are obvious difficulties if no known structure exists for the chemical group in question. In addition, restraints on interatomic distances as a means of specifying bond angles can lead to very distorted planarity of trigonal atoms and aromatic rings.
The method used in this package is to include stereochemical restraints as `observations' but to specify such restraints in a form that is most convenient for the user, i.e. as bond lengths, bond angles and so on. There are six classes of stereochemical information with which the structural model can be restrained; bond lengths, bond angles, torsion angles, trigonal planarity, general planarity and contacts between non-bonded atoms. (Chirality is monitored but not restrained because the chirality function is discontinuous and has no derivatives.) Because the program deals directly with the stereochemical information, some of the derivatives are difficult to derive, and, for the planarity restraints, certain assumptions were used to simplify the calculation. The derivations of the gradients for the stereochemical term are given in Appendix B.
To apply the stereochemical restrains the contents of the asymmetric unit are broken up into different hierarchical units. Each unit can be broken up into small subgroups of atoms in whatever manner is appropriate for the problem at hand. for example, consider the crystal structure of Cro repressor (Anderson, Ohlendorf, Takeda & Matthews, 1981). The asymmetric unit consists of four chemically identical polypeptides, each with 66 amino acids. The first hierarchical unit is defined by CHAIN cards. In this example we specify that there are four chains, named O, A, B and C, each chain being of type `CRO' (see Table 2 for representative data cards). The makeup of a `CRO' chain is then defined by RESIDUE cards. A series of such cards is used to define the sequence of units in the chain (in this case, amino-acid residues) and the types of linkages between successive units (in this case peptide bonds). In this example, the units of the chain are named GLY, ALA, THR, ...etc., and the linkages PEPTIDE, SS, ...etc. The geometric restraints associated with each unit or linkage type are defined with GEOMETRY cards. Each restraint (bond length, bond angle, torsion angle, plane, ...) is specified in a straightforward manner. There is no particular order in which these cards must be given and they can be arranged into different files in any desired manner.
The enumeration of all the stereochemical restraints in this manner may seem to
be time consuming, but most of the files, once created, can be transferred from
one application to another. Also it is easy to inspect and alter the ideal values
of the restraints since they appear in the program in the same form as in everyday
usage. A table which gives the library of `ideal' stereochemistry that has been
adopted in this laboratory, primarily from Bowen, Donohue, Jenkin, Kennard, Wheatley &
Whiffen (1958) and
Vijayan (1976), has been deposited.
Interactions between non-bonded atoms cannot be defined in the manner described above because one does not know in advance which atoms may approach each other. Close contacts are discovered by generating a list of all pairs of atoms which are closer to each other than specified values and discarding from consideration any pairs which are bonded, or and involved in 1-3 or 1-4 type contacts. The 1-3 and 1-4 contacts are better dealt with as bond angles and torsion angles. The standard value for the closest distance allowed before any action is taken is defined in terms of the elemental types of the two atoms. This method of definition allows a closer approach between atoms which have the potential of forming a hydrogen bond or a salt bridge than the distance allowed for atoms in van der Waals contact. The program will prevent non-bonded atoms from moving too close together but no attractive force is applied to atoms that are beyond the specified approach distance.
One novel feature of the program is the ability to avoid steric clashes between adjacent molecules in the crystal. By specifying the appropriate symmetry operators the list of potential non-bonded contacts can be extended to include molecules that surround the reference structure. This procedure is particularly useful in avoiding `duplicate' or `overlapping' solvent atoms.
The program that implements the stereochemistry module has a number of additional features. It can list the worst discrepancies in the model for each type of geometry restraint and provide overall statistics for each class. Also it can produce a table which compares the `ideal' value of each restraint with the average value in the present model. This table is useful when looking for potential errors in the geometry library.