FLAT s [0.2] four or more atomsIf precisely four atoms are named, they are restrained to be coplanar (within the effective standard deviation s) by restraining the volume of the tetrahedron with the four atoms as corners to zero. The edges of this tetrahedron do NOT have to appear as bonds in the connectivity list. The algebra involved is the same as for CHIV (!), and so the units of s are Angstroms3. If more than four atoms are specified, the fourth and all remaining atoms are used in turn as the fourth corner of a tetrahedron involving the first three atoms, for which the volume is again restrained to be zero. The first three atoms should be chosen so that they define a triangle for which the area is as large as possible; for example alternate atoms could be used for a six-membered ring.
Although it might be objected that this method could cause the first three atoms to be 'more coplanar' than the others, in practice FLAT is a very simple and effective way of restraining a group of atoms to be approximately coplanar. Alternative methods involve either (a) biasing the plane towards the existing least-squares plane, (b) extra least-squares variables (which cost computer time), or (c) complicated calculations and problems with numerical precision. An alternative objection to this (and to some other) algorithms is that it will tend to cause the atoms to be 'attracted' towards one another (since this also reduces the volume of the tetrahedron). However this error becomes negligible as the atoms become nearly coplanar; tests with typical phenylalanine residues in a polypeptide showed that the bias introduced was of the order of 0.0001 Angstroms. The default value of s for CHIV and FLAT may be changed by a preceding DEFS instruction.
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