Another much simpler (too simple?) way to approach this is that the
number of parameters is:
Ntorsions + Nbvalues + Nplacement*Nmonomers
Nmonomers is the number of monomers in the asymmetric unit and
Nplacement is the number of parameters needed to place each monomer, so
6 for the general case (or the Nth molecule relative to the first), 5
for polar space groups and 3 for triclinic.
NBvalues depends on the B-value refinement model but for individual
isotropic B-values it would be one "free" B-value parameter for each atom
Ntorsion represents the number of "free" torsion angles
For non-covalently bound atoms, like waters, we need to add another term
of "4 * Nfree_atom" to represent the unrestraint coordinate and B-value
parameters for these atoms.
Of course now we can start arguing about what "free" means ...
Bart
Ian Tickle wrote:
> To try and answer Peter & Bernhard's questions in one go: one way of
> looking at counting restraints is to think of it in terms of the
> reduction in the effective number of parameters that it's equivalent to.
> So a bond length restraint is equivalent to reducing the 8 parameters
> for 2 bonded atoms by 1 (if the bond is rotated to be along the z axis
> then you are effectively removing 1 of the 2 z co-ordinates as a
> parameter, the remaining z co-ordinate allows the pair of atoms to move
> together freely along the z axis). So a restraint on say a CB-OG bond
> reduces the effective parameter count by 1 for each occurrence of the
> CB-OG bond in the structure. A restraint is equivalent to an
> 'observation' of the bond length in *your* structure, not the
> observation of the bond length in the amino-acid/peptide structure that
> the restraint was derived from.
>
> On the question of restraint independence it's clear that in general all
> bond length restraints are independent of each other, and similarly all
> angle restraints are independent of each other and of the bond length
> restraints. I say 'in general' because for rings it's not quite true:
> there must be a geometrical relationship between the bond lengths &
> angles in a ring, but fortunately the number of rings in the average
> structure is small relative to the total number of restraints and the
> error resulting from this assumption is at most 1 or 2 restraints per
> ring. As you say torsion restraints are independent except when there's
> a VDW contact, but usually the number of VDW contacts is small, except
> perhaps at low resolution (so maybe count active VDW restraints as 1/2
> each). Planar restraints are more tricky: they are clearly not
> independent of the bond angle restraints because if you say restrain a
> trigonal atom or an aromatic ring to be planar this imposes restrictions
> on the sum of bond angles (360, 540 & 720 for a trigonal atom, 5-ring &
> 6-ring resp). But the planar restraint obviously has an effect so I
> would say count 1 planar restraint per plane (not N-3 as I suggested
> earlier).
>
> It starts to get tricky with NCS because although NCS restraints between
> say 2 molecules apparently halves the number of effective parameters,
> much of this reduction in parameter count will already have been counted
> because of the other types of restraint, so maybe the effective number
> of NCS restraints is 4 * #atoms per monomer minus the number of other
> restraints in 1 monomer (that may not be quite right, I probably need to
> think more carefully about this!).
>
> Finally as you say it gets really murky with B-factor difference
> restraints because differences between bonded atoms and those related by
> a bond angle are clearly not independent, but they are not completely
> correlated either. In my view, B-factors are over-restrained anyway
> (B-factor differences are larger than people like to believe because of
> libration effects): for this reason I now always turn off B-factor
> restraints related by a bond angle and keep only those related by a bond
> (in Refmac you can now do this by making the corresponding SIGBi
> parameter on the BFAC record negative). This has the advantage that
> there are then fewer B-factor restraint parameters to be determined by
> cross-validation.
>
> HTH!
>
> -- Ian
>
>
>>-----Original Message-----
>>From: Meyer, Peter [mailto:[log in to unmask]]
>>Sent: 14 February 2008 23:04
>>To: Ian Tickle
>>Subject: RE: counting constraints?
>>
>>Ian,
>>
>>Thanks for the quick answers.
>>
>><snip>
>>
>>different question from the one I answered. Of course you count the
>>restraints in your structure, not the ones in the dictionary,
>>so in the
>>
>><end snip>
>>
>>I guess my original question is why is this of course? Or,
>>why isn't this counting an observation (expected value of a
>>bond length/angle/etc) multiple times?
>>
>>And yeah, I did mean restraints when I said constraints.
>>
>>Thanks again,
>>
>>Pete
>>
>>
>>
>
>
>
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--
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University of Alberta
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