Hi Gunnar, A couple of comments, to clarify a few of the similarities and dissimilarities between DEN and analogous technologies:
According to your very nice paper from 2010, DEN refinement with gamma=0 gives a higher weight to external information, whilst gamma=1 ignores external information in favour of self-restraints. Thus, unless I am mistaken, isn't it gamma=1 that would be more analogous to jelly-body refinement? Both jelly-body and DEN with gamma=1 are similar in that they are both independent of explicit externally-derived information. Indeed, DEN with gamma in [0,1] is analogous, but not equivalent, to a combination of jelly-body (or self-restraints) and external reference structure restraints as implemented in REFMAC5. In fact, jelly-body is actually quite different to DEN with gamma=1. Since jelly-body "restraints" are not applied to the target function (or 1st derivative), the "restrained" atoms are allowed to move easily if there is evidence to suggested that they should, e.g. from the electron density, or from other (external) restraints. The principal purpose of jelly-body restraints is simply to act as a regulariser thus stabilise refinement, not to inhibit deformation of interatomic distances where appropriate. Jelly-body is only applied to the 2nd derivative simply due to the form of the function: X=(d-d_current)^2. Note that d_current is updated at each step, thus we always have d=d_current. Thus, X=0, X'=0, but X''!=0. This formulation makes sense - in the absence of any external prior knowledge, we shouldn't change the likelihood function or the gradient, as we want the minima to remain in the same place. However, we can reasonably change the 2nd derivative, and we would like to benefit from the decreased effective parameter-to-observation ratio from this regulariser. Hopefully, that explains why jelly-body is actually quite different to DEN with gamma=1. Importantly, note that with jelly-body d_current is updated/reset at each step, which means that the structure is indeed very deformable. The structure is allowed to move away from the start values - in fact, d_current at cycle n is not dependent on d_current at cycle 0. I believe this contrasts with DEN, unless kappa=1. In contrast with jelly-body, external restraints and local NCS restraints are applied to the target function. In order to allow the inter-atomic distances to exhibit large deviations from the prior information, the Geman-McClure robust estimator function is used instead of assuming least squares residuals (i.e. parameters are estimated using generalised M-estimators instead of the traditional maximum likelihood method). Consequently, when using jelly-body and external restraints, regions of structure that need to move far should be able to do so, whilst the regions that are happy should remain where they are (ideally with more stable refinement and less overfitting) . Hopefully that helps to clarify a few of the similarities and dissimilarities between DEN and the analogous technologies implemented in REFMAC5 to anyone who may find it useful! Regards Rob On 28 Aug 2012, at 20:23, Gunnar Schroeder wrote: > Just a quick comment on low resolution refinement: > > The concept of Deformable Elastic Network (DEN) refinement > is quite similar to jelly-body refinement in the special case of > gamma=0, for which the network is not deformable. > In contrast to jelly-body refinement, the DEN restraints are > however actually applied to the target function (and the first > derivative). > > For gamma>0 the minimum of the elastic network potential > is allowed to move and, thus, to deform the restraints (which > changes their equilibrium distances). Some individual distances > can deform more than others depending on the force they feel > from the target function. > > This automatically discriminates between those regions in the > structure that need to move far (and are allowed to do so) and > those regions that are happy where they are (and remain > restrained). > > DEN refinement is implemented in CNS (1.3) and > now also in Phenix (>=1.7.3). > > Cheers, > Gunnar
