> I thought that tc term (relax uses the tm notation) would be
> problematic! Doh. Is there an alternative equation (probably an
> intermediate in it's derivation) in which the (w.tc)^2 term is
> replaced by J(w). I'm assuming that the intermediate equations depend
> on J(w) and assumptions are made to replace it with (w.tc)^2. If you
> did use J(w) instead, the equation would be much more accurate and it
> would be a lot easier to implement the equations into relax (as the
> J(w) terms will already be calculated by the time you reach the R1,
> R2, and NOE relaxation equations). Then again, the tm value will be
> accessible at that time as well. Therefore the only benefit of using
> J(w) over (w.tc)^2 would be that no assumptions about the global
> tumbling and internal motions are made. Actually, now that I think a
> little more about it, you would need the J(w) component parallel to
> the CC vector for each CC interaction. That would significantly
> complicate the situation over the isotropic assumption of (w.tc)^2.
> Forget I just wrote that paragraph!
Ok ... paragraph forgotten :) One thing though. Correct me if I'm wrong,
but I think of tau( c ) and tau( m ) interchangeably. In fact tau( e ),
tau( f ), and tau( s ) are pretty much the same thing to me too. Just to be
clear, the expression I gave is a huge approximation and drops about 4 J(w)
terms, keeping only the dominant one for D_cc and D_ch relaxation (J(0) and
J(w_c) respectively). It also assumes (for J(w_c)) that ( w.tc)^2 >> 1,
which is pretty true. The expression is for a rigid interaction.
tau_c and tau_m are the same thing, they both represent the isotropic
global correlation time. Both notations are used in the literature.
I'm not sure about the origin of each symbol, although Lipari and
Szabo used the tm (tau_m) notation for model-free analysis which is
why relax uses tm for model-free analysis ;) As for te, tf, and ts,
these are all different. However they can approximate each other in
the different model-free models!
In the equation you gave, is isotropic diffusion assumed? The term
(w.tc)^2 appears to suggest that assumption.
> Therefore it's obvious that the separation of the R1 rates is not
> possible prior to analysis because it depends on the Brownian
> rotational diffusion. It would therefore be useful to have an option
> so that the user can select between uniform labelling and natural
> abundance when inputting the 13C R1 values.
I agree. Also, for uniformly labeled, it would be useful to choose if the
spin was detected selectively or not. If selective, one can use
heteronuclear dipolar equations to calculate the relaxation rate. If
nonselective (ie you hit both Ca and CO, or C5 and C6) then you need to use
the homonuclear expressions for dipolar relaxation.
Maybe we should have two options. The default could be called
'standard' or maybe 'isolated system', the other called something like
'CC coupled', 'non-isolated', 'spin-diffusion', etc. There's no point
having an option such as 'NC dipolar interations' for doubly labelled
proteins until relax can handle that situation (if it ever will).
a) R1 like spins:
0.1 d^2 [ 3 J(w_i) + 12 J(2 w_i) ]
b) R1 unlike spins (should be familiar):
0.1 d^2 [ J (w_i - w_s) + 3 J (w_i) + 6 J(w_i + w_s) ]
c) R1 of like spins, treated as unlike (selective excitation):
0.1 d^2 [ J ( 0 ) + 3 J (w_i) + 6 J(2 w_i) ]
d = (mu0 * gam_i * gam_s * h)/(8 pi^2 * r^3)
J = extended model free
These I determined from using the Spiess reference I keep talking about :)
[NMR Basic Principles and Progress (1978) 15, 55-214]
Do you think spin diffusion will be much of an issue for carbons?
Edward
Re: Improving expressions for the CSA interaction