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Chiral Restraints in gelly

Appendix E: CHIRAL Restraints in gelly

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CHIRAL Restraints: Summary

A restraint has been added to the TNT geometry function that restrains the improper torsions of chiral centres. The restraint only becomes active when atoms start to approach planarity. The restraint should "flip" the chirality of any incorrect centres. It will be turned on by default in BUSTER and gelly_refine but can be zero weighted if wished.

The gelly CHIRAL Restraint term

The TNT geometry program includes analysis that the chirality of atoms, such as the α carbon in amino acids is correct. For example, our standard dictionary for proteins csdx_protgeo.dat includes the term, for the CA atom from alanine
GEOMETRY ALA CHIRAL 1 1 CA N CB C
This in the TNT geometry program will result in a report of bad chirality if an alanine CA atom flips into a D rather than the L enantiomer. But no actual restraint penalty is produced to prevent such a flip. The TNT geometry program does provide an harmonic IMPROPER torsion term but this must be weighted very highly to force incorrect chiral centres to flip to correct values.

To remedy this deficiency, in the release of Feb 2007, we introduced a new restraint to prevent chiral atoms approaching planarity and flipping to the incorrect enantiomer. This restraint takes a half-harmonic form:
Vchiral = 0.0 if Ωmodel < Ωcutin
(Wchiral/σchiral2)*( Ωmodel-Ωcutin)2 otherwise
To restrain the chirality of a D amino acid it is simply necessary to change the order of the atoms in the TNT GEOMETRY restraint term. For instance D-alanine (residue type DAL) has a chiral term for its CA atom (from csdx_protgeo.dat)
GEOMETRY DAL CHIRAL 1 1 CA CB N C ! D-amino acid Calpha
Compared to normal ALA the 2nd and 3rd atoms in the improper torsion are swapped. The improper torsion angle consequently has an opposite sign. The restraint will therefore favour the D-form and prevent flipping to the L.

Background work for the chiral restraint term

The main purpose of the term would be to restrain the chirality of chiral centres in amino acids (and other molecules) to correct enantiomeric form. The restraint should flip incorrect centres but should not interfere with other restraints for good geometry. For the α carbon of normal L-amino acids, the restraint would apply on the improper torsion CA-N-CB-C. It was decided initially to make a survey of the value found for this improper torsion in 5 well refined very high resolution (< 0.81 Å) structures, from the pdb (1ucs 1us0 1yk4 1fn8 1gci). Results are shown in the histogram with blue bars:
The average improper torsion was found to be -33.9 degrees with a std deviation of 1.7 degree - shown by the red dotted lines.

If a normal L-amino acid is distorted so that its chirality is pushed first towards planar and then inverted the bond angles around the CA are strained (the angles are CB-CA-N, CB-CA-C and C-CA-CB). This means that the TNT geometry function already has restraints that would act to prevent an alpha carbon inverting. To judge whether these restraints produce reasonable behaviour the TNT geometry function value cost of the chiral inversion of a single alanine residue was studied. The method used was adiabatic mapping, otherwise known as co-ordinate driving. The weights used for each term were set to the BUSTER default. A graph of function value found for each improper torsion is shown above (green line). It should be noted that no explicit restraint on the improper torsion (or any other chiral measure) was used.

The minimum in the geometry value accords well with the mean from the distribution (central red dotted line). Furthermore, a function value of 1.0 is reached close to plus/minus sigma from the mean.

It can be concluded that the Engh and Huber parameters for the three bond angles N-CA-CB, C-CA-CB and N-CA-C are very well suited to describe behaviour near the minimum. Introducing a restraint on the improper torsion that was active near the minimum would produce "double counting" and be unwise.

If the atom is distorted to planarity and beyond the angle restraints do not favour the L-form over D-form. This can be shown by plotting the graphs on a larger scale:
The penalty for inversion is just over 120 sigma squared. It was concluded what was required was additional restraint that only operated when the chiral improper torsion was above -25 degrees and was sufficiently large to wipe out the D minimum. The gelly CHIRAL Restraint term does exactly this:
Note the function value now uses a log scale. The new chiral penalty wipes out the second minimum but leaves behavour near the normal L-minimum unaltered.

Trials where undertaken on structures with incorrect flipped chiral centres. Refinement using BUSTER using gelly and the new restraint term invariably resulted in the chiral centre being flipped to the correct chirality. In some cases where the model was very poorly placed into density occasionally the centre would remain with a near planar improper torsion (-15 degrees). Even if this was the case the new restraint ensures that centre has the correct chirality.
Page Author: Oliver S. Smart
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Last modification: 24.11.2016