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# Palmer, A.G., Kroenke, C.D. & Loria, J.P. (2001). Nuclear magnetic resonance methods for quantifying microsecond-to-millisecond motions in biological macromolecules. Meth. Enzymol. 339 http://dx.doi.org/10.1016/S0076-6879(01)39315-1
# Francesca Massi, Michael J. Grey, Arthur G. Palmer III* (2005). Microsecond timescale backbone conformational dynamics in ubiquitin studied with NMR R1ρ relaxation experiments, Protein science http://dx.doi.org/10.1110/ps.041139505
# Trott, O. and Palmer, 3rd, A. G. (2002). R1rho relaxation outside of the fast-exchange limit. J. Magn. Reson., 154(1), 157–160. (http://dx.doi.org/10.1006/jmre.2001.2466).
Different graphs.
==== The R1rho: R2 or R2eff as function of effective field in rotating frame: w_eff ====
 
Ref [2], Equation 27. Here the calculated value is noted as: R_eff: $R_{\text{eff}} = R^{0}_2 + R_{ex} = R_{1\rho}' + R_{ex} = R_{1\rho} / \sin^2(\theta) - R_1 / \tan^2(\theta)$ <br>
Ref [3], Equation 20. Figure 11+16, would be the reference. Here the calculated value is noted as: R_2: $R_{2} = R_{1\rho} / \sin^2(\theta) - R_1 / \tan^2(\theta)$. <br>
Ref [4], Equation 43. $R_{\text{eff}} = R_{1\rho} / \sin^2(\theta) - R_1 / \tan^2(\theta)$ <br>
Ref [5], Material and Methods, page 740. Figure 4 would be the wished graphs. Here the calculated value is noted as: R_2: $R_{2} = R^{0}_2 + R_{ex}$
 
'''Discussion:''' <br>
It is clear that there is no real name for the pseudo-parameter. It looks like that R_eff was Art's original way of denoting this and that he has now changed to R2 instead. <br>
But if one look at the reference for the TP02 dispersion model [[TP02]], one will see yet another notation:
 
# Trott, O. and Palmer, 3rd, A. G. (2002). R1rho relaxation outside of the fast-exchange limit. J. Magn. Reson., 154(1), 157–160. (http://dx.doi.org/10.1006/jmre.2001.2466).
Here R2 does not contain the Rex contribution. Also, Reff is absent of Rex. <br>
But in Art's Protein Science paper, the definition $R_{2} = R^{0}_2 + R_{ex}$ is used. The MP05 model reference also does not use Reff [[MP05]].
 
Ref [2], Equation 27. Here the calculated value is noted as: R_eff: $R_{\text{eff}} = R^{0}_2 + R_{ex} = R_{1\rho}' + R_{ex} = R_{1\rho} / \sin^2(\theta) - R_1 / \tan^2(\theta)$ <br>
Ref [3], Equation 20. Figure 11+16, would be the reference. Here the calculated value is noted as: R_2: $R_{2} = R_{1\rho} / \sin^2(\theta) - R_1 / \tan^2(\theta)$. <br>
Ref [4], Equation 43. $R_{\text{eff}} = R_{1\rho} / \sin^2(\theta) - R_1 / \tan^2(\theta)$ <br>
Ref [5], Material and Methods, page 740. Figure 4 would be the wished graphs. Here the calculated value is noted as: R_2: $R_{2} = R^{0}_2 + R_{ex}$
# $R_2 = R^{0}_2 + R_{ex} = R_{1\rho}' + R_{ex} = R_{1\rho} / \sin^2(\theta) - R_1 / \tan^2(\theta)$