Dear Edward, Thank you for clarification and giving a comprehensive reply to my query. It all makes sense now. In my logic, I had assumed that the same models are selected for the internal dynamics when swapping to a different diffusion tensor (obviously not the case).
I had read your paper some time ago. It's time for a refresher! Regards, Romel PS : Also thanks for sending me the link with the figure. On 22 July 2013 18:23, Edward d'Auvergne <edw...@nmr-relax.com> wrote: > Hi Romel, > > From the logic that the prolate axially symmetric tensor and full > ellipsoid are nested models, it would normally be the case that > chi-squared value for the ellipsoid be smaller than the prolate model, > or at least close to the same. This logic is only broken if > optimisation is incomplete for the ellipsoidal model. However the > model-free problem is much more complicated than just one diffusion > model verses another. The reason is because of two interlinked > problems - that of finding the diffusion tensor and that of finding > the internal dynamics. The prolate tensor has 4 parameters and the > ellipsoid 6. Therefore it is clear from the difference of 1 in the > parameter number k that it is not just the diffusion models that are > different. > > If you have a close look at the level of the spin, you will see that > the model-free models selected for each diffusion tensor will > different. This is normal, as in the model-free analysis you have a > chicken and egg problem of finding the diffusion tensor and finding > the internal motions. The result of one influences the optimisation - > and model selection - of the other. The model-free problem is quite > complex, as I tried to parametrise in > http://dx.doi.org/10.1039/b702202f. If the diffusion tensor is too > simplified, you have artificial internal motions appearing (both ns > motions and Rex). Hence the models will be different. This is > described in detail in that paper. The artificial motions also occurs > if the XH bond vector orientation is poorly or incorrectly defined in > the structure - and this is also linked to the diffusion tensor > optimisation. > > You do however have a very clean example however of the perfect > nesting of two models. This is quite rare. The oblate and ellipsoid > models have almost identical chi-squared values and a parameter > difference of 2 - this indicates, though not definitively, that the > model-free models selected are the same for both diffusion models. > Anyway, I hope this description helped. If you need more details on > the model-free problem and space, the above link will help explain how > this is not just a simple single-universe optimisation problem, but a > multi-universe optimisation problem with interlinked model selection > and optimisation. You just have your prolate and ellipsoid results in > parallel, but slightly different universes. > > Regards, > > Edward > > > P. S. Note that a chi-squared difference of 15 is not too significant > if you consider how many relaxation data points for all spin systems > you have used. If you divide one by the other, you have the reduced > chi-squared difference which you will see is quite small. > > > > On 22 July 2013 17:48, Romel Bobby <rbob...@aucklanduni.ac.nz> wrote: > > Dear users, > > > > I recently ran a model-free analysis on a ~5kDa protein with relaxation > data > > measured at three fields (600, 800 & 900 MHz). For the analysis, I used > the > > fully automated analysis (dauvergne_protocol.py). > > > > At the end of the diffusion tensor optimisation step, a prolate spheroid > > tensor seemed to be the best description for diffusion, as assessed by > AIC. > > See below the AIC scores for the individual models: > > > > Data pipe k n Chi2 > > Criterion > > sphere 102 204 2479.48833 2683.48833 > > prolate 89 204 2391.34556 > 2569.34556 > > oblate 88 204 2405.33989 > 2581.33989 > > ellipsoid 90 204 2405.90291 > 2585.90291 > > > > My question now concerns the 'large' deviation of ~15 units in > chi-squared > > values between the ellipsoid and prolate models. Shouldn't the value of > the > > ellipsoid be smaller than the axially symmetric models, considering that > two > > additional parameters are used in the ellipsoid? > > Why is the chi-squared value slightly larger for the ellipsoid than the > > prolate? > > > > I looked at the individual models and the log files. The optimisation > > finished after convergence and the analysis didn't report any errors or > the > > like. > > > > Many thanks, > > > > Romel > > > > _______________________________________________ > > relax (http://www.nmr-relax.com) > > > > This is the relax-users mailing list > > relax-users@gna.org > > > > To unsubscribe from this list, get a password > > reminder, or change your subscription options, > > visit the list information page at > > https://mail.gna.org/listinfo/relax-users > > > -- Romel Bobby Biomolecular NMR Research Group School of Chemical Sciences/School of Biological Sciences The University of Auckland +64 (09) 3737599 Ext 83157
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