Hi,
In relaxation data analysis, you can only view the components of the
Brownian rotational diffusion tensor that the XH bond vectors sample.
So if your macromolecule diffuses as a prolate spheroid but the XH
bond vectors are close to perpendicular to the unique axis of the
tensor, the only component of the diffusion tensor that the relaxation
data contains information about is the eigenvalue Dper (the
perpendicular component of the tensor). The result is that the
diffusion will appear to be spherical where Diso has the value of
Dper! In relax the parameters tm (which is essentially Diso) and Da
are optimised. For this case, Da (and hence Dratio) would be
undefined - it can have any geometrically possible value while having
zero effect on the results.
Have you tried starting with the calculated Da value (or Dratio if you
wish)? This is not possible using the 'full_analysis.py' script, but
the other sample scripts can be modified to do this. As these
parameters will be statistically undefined, the final optimised values
should be pretty close to the input values. This assumes tm (or Diso)
is set to be close to the Dper value as the curvature of the space may
cause optimisation to shift Da. The parameter Dr would also be
undefined and this would fully explain the Dr value of 1 reported in
bug #7297 (https://gna.org/bugs/?7297).
The problem of the undefined Da and Dr, and hence the molecule
appearing to diffuse as a sphere, could be resolved by having a few
vectors which deviate from the perpendicular. However this is only
important if you are actually interested in characterising the
Brownian rotational diffusion. In any case, attempting to optimise
these values using relaxation data of perpendicular XH's will only
result in statistically insignificant values - it's not statistically
possible to pull out these parameters. It is almost guaranteed that
AIC model selection will select spherical diffusion. Would the ribose
CH's together with the base XH's adequately sample three-dimensional
space?
I hope this info helps,
Edward
On 10/5/06, Alexandar Hansen <viochemist@xxxxxxxxx> wrote:
Hello all,
In studying RNA you run into a number of limiting factors of your data set.
a) NH data is available only on half of the residues (G's and U's), b) these
G's and U's must be in a helix, or the NH becomes exchanged with solvent,
and c) the NH vectors on the bases in a helix don't sample space randomly
and are oriented ~perpindicular to the diffusion axis (RNA is almost always
prolate shaped). This last scenario, for you protein folks, would be
similar to the situation where you had a single alpha helix and only NH
data, ie. sample only directions paralell to the helix axis.
With this in mind, one can easily imagine that any relaxation analysis would
be happy to fit them to a lower diffusion model, such as spherical, than
what is in reality highly anisotropic. What I'd like to know how to do is
impose additional limits on the minimization step such that, for instance,
the Dratio could be fixed between some values. With the data I've been
analyzing, relax happily fits my NH data to the spherical case and, for the
prolate model, fits the Dratio to 1 -> 1.1. From hydrodynamic simulation,
we know, however, that the Dratio should be between 4-5. Are there any
thoughts on how to do this? On one level, it appears to be forcing the data
into a particular model. But if you can know something about the diffusion
parameters or anything else a priori from a different source than NMR,
shouldn't that be allowed to factor into the analysis?
Thanks,
Alex Hansen
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Re: analysis of limited data sets