DPL94
The Davis et al., 1994 2-site off-resonance fast exchange relaxation dispersion model for R1rho-type data. It extends the M61 model to off-resonance data, hence it collapses to this model for on-resonance data. The model is labelled as DPL94 in relax.
Contents
Equation
[math] \mathrm{R}_{1\rho}= \mathrm{R}_1\cos^2\theta + \left( \mathrm{R}_{1\rho}{´} + \frac{\Phi_\textrm{ex} \textrm{k}_\textrm{ex}}{\textrm{k}_\textrm{ex}^2 + \omega_\textrm{e}^2} \right) \sin^2\theta [/math]
Parameters
The DPL94 model has the parameters {R_{1ρ}', ..., Φ_{ex}, k_{ex}}.
Essentials
Note R_{1} should be provided in rad/s, the SI default unit for this relaxation rate. |
It is essential to read in R_{1} values before starting a calculation:
relax_data.read(ri_id='R1', ri_type='R1', frq=cdp.spectrometer_frq_list[0], file='R1_values.txt', mol_name_col=1, res_num_col=2, res_name_col=3, spin_num_col=4, spin_name_col=5, data_col=6, error_col=7)
Where the data could be stored like
# mol_name res_num res_name spin_num spin_name value error None 13 L None N 1.323940 0.146870 None 15 R None N 1.344280 0.140560 None 16 T None N 1.715140 0.136510
Parameter name space in relax
Please see the summary of the model parameters here.
Which means:
- R_{1ρ}' =
spin.r2
(Fitted) - R_{1ρ} =
spin.r2eff
(Back calculated) - Φ_{ex} =
spin.phi_ex
(Fitted) - k_{ex} =
spin.kex
(Fitted) - R_{1} =
spin.ri_data['R1']
(Loaded)
Please also see this thread: http://thread.gmane.org/gmane.science.nmr.relax.devel/5164
Equation - re-written forms
Discussed in: http://thread.gmane.org/gmane.science.nmr.relax.devel/5207
- Evenäs, J., Malmendal, A. and Akke, M. (2001). Dynamics of the transition between open and closed conformations in a calmodulin C-terminal domain mutant. Structure, 9(3), 185-195. (DOI: 10.1016/S0969-2126(01)00575-5)
- Kempf, J. G. and Loria, J. P. (2004). Measurement of intermediate exchange phenomena. Methods Mol. Biol., 278, 185-231. (DOI: 10.1385/1-59259-809-9:185)
- Massi, F., Grey, M. J., Palmer, 3rd, A. G. (2005). Microsecond timescale backbone conformational dynamics in ubiquitin studied with NMR R1ρ relaxation experiments Protein science, 14(3), 735-742. (DOI: 10.1110/ps.041139505)
- Palmer, 3rd, A. G., Kroenke, C. D., and Loria, J. P. (2001). Nuclear magnetic resonance methods for quantifying microsecond-to-millisecond motions in biological macromolecules. Methods Enzymol., 339, 204-238. (DOI: 10.1016/S0076-6879(01)39315-1)
- Palmer, 3rd, A. G. and Massi, F. (2006). Characterization of the dynamics of biomacromolecules using rotating-frame spin relaxation NMR spectroscopy. Chem. Rev., 106(5), 1700-1719. (DOI: 10.1021/cr0404287)
- Trott, O. and Palmer, 3rd, A. G. (2002). R1rho relaxation outside of the fast-exchange limit. J. Magn. Reson., 154(1), 157-160. (DOI: 10.1006/jmre.2001.2466)
Different graphs.
The R_{1ρ}: R_{2} or R_{2,eff} as function of effective field in rotating frame: ω_{e}
Discussion
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 R_{2} instead.
But if one look at the reference for the TP02 dispersion model, one will see yet another notation:
Here R_{2} does not contain the R_{ex} contribution. Also, R_{eff} is absent of R_{ex}.
But in Art's Protein Science paper (Ref [5]), the definition R_{2} = R_{2}^{0} + R_{ex} is used. The MP05 model reference also does not use R_{eff}.
The R_{eff} parameter name is confusing and it seems to have been dropped from 2005 onwards. The R_{eff} name appears to be specific to Art Palmer's group and as he himself has dropped it, then it would be best to avoid it too.
Ref [2], Equation 27. Here the calculated value is noted as: R_eff: [math]R_{\text{eff}} = R^{0}_2 + R_{ex} = R_{1\rho}' + R_{ex} = R_{1\rho} / \sin^2(\theta) - R_1 / \tan^2(\theta)[/math]
Ref [3], Equation 20. Figure 11+16, would be the reference. Here the calculated value is noted as: R_2: [math]R_{2} = R_{1\rho} / \sin^2(\theta) - R_1 / \tan^2(\theta)[/math].
Ref [4], Equation 43. [math]R_{\text{eff}} = R_{1\rho} / \sin^2(\theta) - R_1 / \tan^2(\theta)[/math]
Ref [5], Material and Methods, page 740. Figure 4 would be the wished graphs. Here the calculated value is noted as: R_2: [math]R_{2} = R^{0}_2 + R_{ex}[/math]
The following suggestions for the definition of the pseudo-parameters, which can be extracted, is then
- [math]R_2 = R^{0}_2 + R_{ex} = R_{1\rho}' + R_{ex} = R_{1\rho} / \sin^2(\theta) - R_1 / \tan^2(\theta) = \frac{R_{1\rho} - R_1\cos^2(\theta)}{\sin^2(\theta)}[/math]
Reference
The reference for the DPL94 model is:
- Davis, D. G., Perlman, M. E., and London, R. E. (1994). Direct measurements of the dissociation-rate constant for inhibitor-enzyme complexes via the T1rho and T2 (CPMG) methods. J. Magn. Reson., 104(3), 266-275. (DOI: 10.1006/jmrb.1994.1084)
Related models
The DPL94 model is simply the extension of the M61 model for off-resonance data.
Links
The implementation of the DPL94 model in relax can be seen in the: