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:[EMAIL PROTECTED] > 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 > > > Disclaimer This communication is confidential and may contain privileged information intended solely for the named addressee(s). It may not be used or disclosed except for the purpose for which it has been sent. If you are not the intended recipient you must not review, use, disclose, copy, distribute or take any action in reliance upon it. If you have received this communication in error, please notify Astex Therapeutics Ltd by emailing [EMAIL PROTECTED] and destroy all copies of the message and any attached documents. Astex Therapeutics Ltd monitors, controls and protects all its messaging traffic in compliance with its corporate email policy. The Company accepts no liability or responsibility for any onward transmission or use of emails and attachments having left the Astex Therapeutics domain. Unless expressly stated, opinions in this message are those of the individual sender and not of Astex Therapeutics Ltd. The recipient should check this email and any attachments for the presence of computer viruses. Astex Therapeutics Ltd accepts no liability for damage caused by any virus transmitted by this email. E-mail is susceptible to data corruption, interception, unauthorized amendment, and tampering, Astex Therapeutics Ltd only send and receive e-mails on the basis that the Company is not liable for any such alteration or any consequences thereof. Astex Therapeutics Ltd., Registered in England at 436 Cambridge Science Park, Cambridge CB4 0QA under number 3751674
