|Chiral Restraints in gelly
Appendix E: CHIRAL Restraints in gelly
Copyright © 2007 Global Phasing Ltd.
All rights reserved.
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 autoBUSTER and gelly_refine but can be zero weighted
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
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
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:
GEOMETRY ALA CHIRAL 1 1 CA N CB C
|Vchiral = || 0.0
||if Ωmodel < Ωcutin |
| ||(Wchiral/σchiral2)*( Ωmodel-Ωcutin)2
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)
- Here Ωmodel is the improper torsion angle as defined in
the TNT GEOMETRY *** CHIRAL term. For example the ALA Calpha term quote above
will mean that the Ωmodel is the improper torsion
angle CA-N-CB-C. For an ideal geometry this angle is around -34 degrees. The angle increases
to zero degrees as the chiral center becomes planar. Positive angles mean that the alanine has
flipped to a D enantiomer - most undesirable.
- Ωcutin is the angle above which the restraint becomes active.
In practice an angle of -25 degrees is found to be optimal - this is the hardcoded default. It is possible
to override this by using a NOTE BUSTER_CHIRAL_ANGLECUT card,
although in practice it is unlikely to be necessary.
- The weight Wchiral and "sigma"
σchiral control how step the penalty preventing inversion is.
Conveniently autoBUSTER already sets the WEIGHT for the TNT CHIRAL term (despite
this term originally only producing a report). The default WEIGHT is set to 5.0 and
this should normally be left unaltered. With this weight and
it was found that a "sigma" σchiral=3
degrees produced a penalty that could in practice flip incorrect chiral centres.
If it is desired to turn off the new penalty this can be done by setting
the weight of the term to zero. To do this within autoBUSTER by setting the
command line option wchiral="0.0" - see
For gelly_refine use a card:.
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.
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
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 autoBUSTER 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 autoBUSTER 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.
GEOMETRY DAL CHIRAL 1 1 CA CB N C ! D-amino acid Calpha
Page Author: Oliver S. Smart
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Last modification: 10.07.08