Surely it can't be as bad as equation 8.86 in the relax manual
(version 1.2.7)?
My equations for the axially symmetric diffusion aren't too bad, but for the ellipsoidal diffusion and asymmetric CSA, it's not good. I'll look into though and post what I can (hopefully without typos :) )
This could be done by creating the 'csa.init()' function. The user
could simply select one of the tables you suggest and the program does
the rest. I.e. the only difference between 'standard' model-free
analysis and handling the more advanced CS tensor info is to use the
'csa.init()' function to selected the table rather than the
'value.set()' function to set the CSA value. That is unless I have
missed something?
You have it right. That sounds reasonable.
Surely homonuclei aren't a problem? If you're looking at the nitrogen
with a single proton attached, decoupling in the experiment will
remove any spin diffusion problems. If you're looking at a carbon
with a single attached proton, can you not decouple it from the other
carbons and remove the cross-correlated relaxation mechanisms through
the pulse sequence?
Yes, absolutely the C-C cross and cross-correlated relaxation can be supressed through appropriate means in the pulse sequence and we can just assume that the user is taking care of those appropriately. However, C-C auto relaxation can't be suppressed and this should be significant for a number of nuclei in uniformly labeled samples. The relation of the CC auto-relaxtion to CH dipolar relaxation is given in Yamazaki et al (1994) JACS, 116, 8266-8278 (equ 1).
rho(HC)/rho(CC) = 3*(gamma_H^2/gamma_C^2)*(R_CC/R_HC)^6*(omega_c * tau_c)^ -2
I don't know the specifics for proteins, but in pyrimidine bases (uracil and cytodine) and in the ribose rings, the C-C bond length are 134pm and 153pm respectively. At 600 Mhz and as small as a 5 ns correlation time, the CC contributes ~13% to the R1 rate of the base relaxation and ~6% for the ribose. The CC rate is equal to the CH rate at a tau( c ) of ~14 ns for the base and ~20 ns for the ribose.
> I would definitely refrain from optimizing anything more than what is
> already done in relax. The number of variables is already increasing out of
> control. Currently I assume (a very poor assumption in all likelihood) that
> the CSA, XH, and XX relaxation mechanisms feel the same modelfree S2 and tau
> parameters. Perhaps in the future more optimization could be addressed, but
> if we worked on that now I would be submitting MY thesis before we have a
> working version of it.
I understand, there is no part of the CS tensor which is optimised.
Essentially to the user the only difference is the selection of a more
complex chemical shift tensor. That should make the implementation
much easier.
Yes, I agree.
> >5. Misc.
Sorry, I think I didn't state the question as I hoped to. What I
meant to ask is, is J_CSA(w) = J_DD(w)? This is really only the case
if the CS tensor is axially symmetric and the two interactions are
collinear, but is that an approximation you are making?
Then no, i'm not making that assumption. I calculate a different spectral density for the two/three mechanisms ... is that a flaw in the way I'm analyzing things? If so, I'm not sure I understand. It does say in Spiess that "The [c_i] contain the coupling parameters delta_lambda and, therefore, are not spectral densities. ... It should be noted, however, that even in the general case, for the l = 2 terms, the coupling constant delta_lambda enters as a common factor .. and, therefore, reduced g_2,lambda = g_2,lambda / delta_lambda^2 are independent of the strength of the coupling and only depend on the assymetry parameter eta_lambda, a number between 0 and 1." I guess, in this light, what I use are reduced spectral densities (?) or is that yet something else entirely? What affect does this have on what we want to do?
> For isotropic diffusion, no angular/asymmetry parameters are necessary. In
> fact, for a spherical molecule, the current state of the equations is
> perfect and no changes need to be made. Unfortunately, I don't know how
> often a molecule is perfectly spherical.
Without the previous assumption, surely the non-collinearity of the DD
and CSA interactions together with certain anisotropic motions of the
XH bond would be of concern in spherical diffusion? As for a
macromolecule diffusing as a perfect sphere, despite that assumption
for many published model-free analyses, I can't see it as ever being
statistically significant.
I'm still not sure I understand. In model free analysis, aren't the internal motions assumed isotropic? To my knowledge, no one has attempted to address anisotropic internal motions, whether the interaction is symmetric (dipole) or not (csa). However, I am certain that, assuming isotropic tumbling and model free as it currently is used, the non-collinearity is not necessary for the understanding of auto-relaxation. If cross-correlated relaxation were to be added to relax, that would be a different story altogether ...
Alex Hansen
Re: Improving expressions for the CSA interaction