Hi Martin,
Please see below:
among various substantial improvements over the available old-school mf
modeling packages, relax implements a different set of model-free models
than e.g. Art Palmer's Modelfree4 or Martin Blackledge's TENSOR2. Neither
of the above programs includes the m0 model (as relax does), where no mf
parameters are determined. You described the m0 model as a special case,
where none of the internal motions / model-free parameters are
statistically significant.
This is correct. The key point here is that we are dealing with
applied physics. Hence we don't deal with physical significance, only
statistical significance. These are quite different concepts and
often confused in the field of NMR.
Is this equivalent of a "failed" model-free analysis?
Most definitely not!
Does that also mean, in such a case where relax chooses m0, TENSOR or
Modelfree would choose a nonsignificant model which of course wouldn't be
appropriate?
If relax chooses m0, then TENSOR, Modelfree and Dasha should choose
model m1 (this is assuming that the diffusion tensor and other
parameters are identical in all these programs).
Would relax also choose a model by "chance" if I just left out m0 from the
analysis?
The next level of statical significance if m0 is not present is m1, as
this is the simplest model available with a single S2 parameter. All
other models are more complex. Note that an exception is model m9,
which is also only available in relax, which competes with m1 for
statistical complexity.
I'm not sure what the reason for all parameters being insignificant is and
what the implications are, i.e. what it means in terms of protein mobility.
The key is again that this is applied physics. There is much more
happening in your system than what you can see through your relaxation
data. But you can only see what you can see. Therefore a motion
being statistically insignificant, with respect to your data and
experimental errors, does not mean that it is not present! This is
often the case with nanosecond loop motions which when using the old
model-free protocols are much more often judged to be insignificant,
even though proper statistics (AIC, BIC, ICOMP, etc.) says otherwise.
It cannot mean that the "m0"-residues behave like a static body (S^2 would
be 1).
Statistically, yes. Physically, no. You just can't see it from the
data you have. That is the meaning of this model. A good analogy is
as follows - you could have a picture of an elephant but, if you only
have 4 pixels in that picture, you probably won't be able to tell that
your picture is of an elephant.
Does it simply mean that the supplied data and models are not sufficient
for the type of motion that the protein is exhibiting? I learned that
model-free works best if the motions are in the extreme narrowing limit,
but it is a misconception that it is limited to this time domain. But
aren't there limitations to the kind of motions that can be modeled by mf?
The information that "model-free works best if the motions are in the
extreme narrowing limit" is itself a misconception! This comes from
the original Lipari and Szabo model-free papers themselves. One thing
they did to help them with the optimisation, back when computers were
much slower, was to use the extreme narrowing limit to simplify their
equations for the calculations used in the 1982 papers. Look
specifically at Equation 36 in the original paper.
I don't know if this is completely relevant to your question, but
noise is another issue which affects the reliability of the te
parameters. As te increases, so does the errors. The cause of this
is that you need to look at this upside-down. The real parameter
affecting your relaxation data is the diffusion rate equal to
1/(6*te). On the diffusion rate scale, the errors are relatively
invariant, but if you invert this then you have hyperbolic behaviour
of the te errors. Note that you won't find such information written
anywhere in the literature.
If the motions approach the NMR timescale, I'd first of all expect
broadened peaks (which I have a lot). From my understanding, that precludes
analysis, but would not be a limitation of the mf formalism itself. These
motions could be picked up by the Rex parameter ... So m0 wouldn't occur if
I have amides moving around at a nanosecond timescale.
Here I'm not exactly sure what you mean. Rex broadens peaks whereas
nanosecond timescale motions cause you peaks to be the strongest in
the spectrum.
Maybe this relates to model m9 in relax. Sometimes the very weak
peaks, broadened by chemical exchange, are too noisy to extract
model-free motions from. This is visible in relax as the selection of
model m9. In such a case, model m0 will probably not be picked.
I'm also not sure what would happen if the internal motions approach the
global correlation time ...
As I mentioned above, the errors on te become bigger and bigger.
There is a point where te and tm merge, and this is governed again by
noise and statistics. For example with relax I easily am able to
separate a te value of 8.192 ns from a tm of 10 ns when no noise is
present (see my 2008 paper
http://www.nmr-relax.com/refs.html#dAuvergneGooley08a).
Note you can physically have motions above tm contributing to
relaxation, but that it is very hard to statistically extract this
from the noise (the feasibility of te > tm is talked about in the
original papers). So despite people saying te cannot be slower then
tm, this is another misconception. Physically yes you can, but
statistically we currently cannot.
I don't know if inaccurate or inconsistent data would favor such a
behavior. We now use selective pulses in the R1 and NOE-experiments,
temperature compensatio
Inaccurate/inconsistent data is not noise, but rather bias. Whereas
noise shifts parameter values around randomly and governs which
motions are statistically significant, bias on the other hand shifts
everything in one direction. I describe this is detail in my PhD
thesis (http://www.nmr-relax.com/features.html#primary_refs),
specifically in section 2.1.4 and figure 2.1. The effect on a
model-free analysis is generally the introduction of artificial
motions (either Rex or nanosecond). Bias could probably in some cases
hide motions, but more likely will result in artificial motions. Bias
could also be introduced if the spherical, spheroidal, or ellipsoidal
diffusion is too simplified for the system or if partial dimerisation
is occurring.
I hope some of these explanations help.
Regards,
Edward
Re: m0 models