I think you could answer this by performing the following thought experiment:
1. Refine the structure to convergence using strict NCS constraints. 2. Switch to using the equivalent 'infinite-in-the-limit weight' restraints, keeping everything else as is & continue refinement of the output from step 1 (assume limitations of finite precision in the code have been overcome by re-programming using whatever precision arithmetic is necessary). 3. Does there exist some finite value of the weight such that the structure changes by less than the experimental error (say by < 0.2 Ang RMSD) at step 2 (and if not then why not?). If the answer to (3) is yes, then there's no significant difference in effect between constraints & 'infinite weight' restraints. Cheers -- Ian On Thu, Sep 23, 2010 at 5:06 PM, MARTYN SYMMONS <[email protected]> wrote: > Dear All > one thing I remembered from what Gerard pointed out was the difference > in the XPLOR/CNS formalism between strict and restrained which is not a > continuum. Restrained was obviously when you had multiple copies and they > were restrained with a weight (which was like a force constant) to be similar > when superimposed. So if you increase the force constant then they can move > during refinement but they all try to move together when they move. > > And the other extreme is strict where there was no force applied at all but > only a single copy of the chain and the ASU is built by applying the NCS > symmetry. The atoms are free to move but, unlike the case with restrained > where there is superimposition on the fly, in the strict case there is no > automatic update of the superimposition matrices. So every move gets > religiously copied to all the chains when the ASU is made. At this point I > guess the copies can bump and so apply a force on each other but that is a > local, and likely to be perturbing, force. > > best wishes > Martyn > > Martyn Symmons > Cambridge > > > > --- On Thu, 23/9/10, Ian Tickle <[email protected]> wrote: > >> From: Ian Tickle <[email protected]> >> Subject: Re: [ccp4bb] Effect of NCS on estimate of data:parameter ratio >> To: [email protected] >> Date: Thursday, 23 September, 2010, 11:21 >> Hi Gerard & Pavel >> >> Isn't this the proviso I was referring to, that one cannot >> in practice >> use an infinite weight because of rounding errors in the >> target >> function. The weight just has to be 'big enough' such >> that the >> restraint residual becomes sufficiently small that it's no >> longer >> significant. >> >> In numerical constrained optimisation the method of >> increasing the >> constraint weights (a.k.a. 'penalty coefficients') until >> the >> constraint violations are sufficiently small is called the >> 'penalty >> method', see http://en.wikipedia.org/wiki/Penalty_method . The >> method >> where you substitute some of the parameters using the >> constraint >> equations is called (you guessed it!) the 'substitution >> method', see >> http://people.ucsc.edu/~rgil/Optimization.pdf . >> There are several >> other methods, e.g. the 'augmented Lagrangian method' is >> very popular, >> see >> http://www.ualberta.ca/CNS/RESEARCH/NAG/FastfloDoc/Tutorial/html/node112.html >> . As in the penalty method, the AL method adds >> additional parameters >> to be determined (the Lagrange multipliers, one per >> constraint) >> instead of eliminating some parameters using the constraint >> equations; >> however the advantage is that it removes the requirement >> that the >> penalty coefficient be very big. >> >> The point about all these methods of constrained >> optimisation is that >> they are in principle only different ways of achieving the >> same >> result, at least that's what the textbooks say! >> >> And now after the penalties and substitutions it's time to >> blow the whistle ... >> >> Cheers >> >> -- Ian >> >> On Wed, Sep 22, 2010 at 10:00 PM, Pavel Afonine <[email protected]> >> wrote: >> > I agree with Gerard. Example: it's unlikely to >> achieve a result of >> > rigid-body refinement (when you refine six >> rotation/translation parameters) >> > by replacing it with refining individual coordinates >> using infinitely large >> > weights for restraints. >> > Pavel. >> > >> > >> > On 9/22/10 1:46 PM, Gerard DVD Kleywegt wrote: >> >> >> >> Hi Ian, >> >> >> >>> First, constraints are just a special case of >> restraints in the limit >> >>> of infinite weights, in fact one way of >> getting constraints is simply >> >>> to use restraints with very large weights >> (though not too large that >> >>> you get rounding problems). These >> 'pseudo-constraints' will be >> >>> indistinguishable in effect from the 'real >> thing'. So why treat >> >>> restraints and constraints differently as far >> as the statistics are >> >>> concerned: the difference is purely one of >> implementation. >> >> >> >> In practice this is not true, of course. If you >> impose "infinitely strong" >> >> NCS restraints, any change to a thusly restrained >> parameter by the >> >> refinement program will make the target function >> infinite, so effectively >> >> your model will never change. This is very >> different from the behaviour >> >> under NCS constraints and the resulting models in >> these two cases will in >> >> fact be very easily distinguishable. >> >> >> >> --Gerard >> >> >> >> >> ****************************************************************** >> >> Gerard J. >> Kleywegt >> >> Dept. of Cell & Molecular Biology >> University of Uppsala >> >> Biomedical Centre Box >> 596 >> >> SE-751 24 Uppsala >> SWEDEN >> >> >> >> http://xray.bmc.uu.se/gerard/ mailto:[email protected] >> >> >> ****************************************************************** >> >> The opinions in this message are fictional. >> Any similarity >> >> to actual opinions, living or dead, is purely >> coincidental. >> >> >> ****************************************************************** >> > >> > > >
