Difference between revisions of "CR72 full"
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| − | \zeta = 2 \Delta \omega \, (R_2^A - R_2^B - | + | \alpha_- = R_2^A - R_2^B + k_{\textrm{AB}} - k_{\textrm{BA}} \\ |
| − | \Psi = (R_2^A - R_2^B - p_A k_{\textrm{EX}} + p_B k_{\textrm{ | + | \zeta = 2 \Delta \omega \, (R_2^A - R_2^B +k_{\textrm{AB}} - k_{\textrm{BA}} ) \\ |
| − | \eta_+ = \frac{1}{2\sqrt{2}\nu_{\textrm{cpmg}}}\sqrt{+\Psi + \sqrt{\Psi^2 + \zeta^2}} \\ | + | \phantom{\zeta} = 2 \Delta \omega \, (R_2^A - R_2^B + p_B k_{\textrm{EX}} - p_A k_{\textrm{EX}} ) \\ |
| − | \eta_- = \frac{1}{2\sqrt{2}\nu_{\textrm{cpmg}}}\sqrt{-\Psi + \sqrt{\Psi^2 + \zeta^2}} \\ | + | \phantom{\zeta} = 2 \Delta \omega \alpha_- \\ |
| + | \Psi = (R_2^A - R_2^B + p_B k_{\textrm{EX}} - p_A k_{\textrm{EX}} )^2 - \Delta \omega^2 + 4 p_A p_B k_{\textrm{ex}}^2 \\ | ||
| + | \phantom{\Psi} = \alpha_-^2 - \Delta \omega^2 + 4 p_A p_B k_{\textrm{ex}}^2 \\ | ||
| + | \eta_+ = \frac{1}{2\sqrt{2} \, \nu_{\textrm{cpmg}}}\sqrt{+\Psi + \sqrt{\Psi^2 + \zeta^2}} \\ | ||
| + | \eta_- = \frac{1}{2\sqrt{2} \, \nu_{\textrm{cpmg}}}\sqrt{-\Psi + \sqrt{\Psi^2 + \zeta^2}} \\ | ||
D_+=\frac{1}{2}\left(1+\frac{\Psi+2\Delta \omega^2}{\sqrt{\Psi^2+\zeta^2}} \right) \\ | D_+=\frac{1}{2}\left(1+\frac{\Psi+2\Delta \omega^2}{\sqrt{\Psi^2+\zeta^2}} \right) \\ | ||
D_-=\frac{1}{2}\left(-1+\frac{\Psi+2\Delta \omega^2}{\sqrt{\Psi^2+\zeta^2}} \right) | D_-=\frac{1}{2}\left(-1+\frac{\Psi+2\Delta \omega^2}{\sqrt{\Psi^2+\zeta^2}} \right) | ||
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== Parameters == | == Parameters == | ||
| − | The CR72 full model has the parameters { | + | The CR72 full model has the parameters {{{:R2Azero}}, {{:R2Bzero}}, ..., {{:pA}}, {{:Deltaomega}}, {{:kex}}}. |
== Reference == | == Reference == | ||
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The reference for the CR72 full model is: | The reference for the CR72 full model is: | ||
| − | * | + | * {{#lst:Citations|CarverRichards72}} |
== Related models == | == Related models == | ||
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The [[Relaxation dispersion citation for relax|implementation of the CR72 full model in relax]] can be seen in the: | The [[Relaxation dispersion citation for relax|implementation of the CR72 full model in relax]] can be seen in the: | ||
| − | * [http://www.nmr-relax.com/manual/ | + | * [http://www.nmr-relax.com/manual/The_full_CR72_2_site_CPMG_model.html relax manual], |
* [http://www.nmr-relax.com/api/3.1/lib.dispersion.cr72-module.html API documentation], | * [http://www.nmr-relax.com/api/3.1/lib.dispersion.cr72-module.html API documentation], | ||
* [http://www.nmr-relax.com/analyses/relaxation_dispersion.html#CR72_full relaxation dispersion page of the relax website]. | * [http://www.nmr-relax.com/analyses/relaxation_dispersion.html#CR72_full relaxation dispersion page of the relax website]. | ||
== See also == | == See also == | ||
| − | [[Category:Relaxation_dispersion]] | + | [[Category:Models]] |
| + | [[Category:Dispersion models]] | ||
| + | [[Category:Relaxation_dispersion analysis]] | ||
Latest revision as of 16:44, 6 November 2015
The full Carver and Richards 1972 2-site relaxation dispersion model for SQ CPMG-type data for most time scales. This model is labelled as CR72 full in relax.
Equation
Please see the summary of the model parameters here.
- relax manual http://www.nmr-relax.com/manual/full_CR72_2_site_CPMG_model.html
- relaxation dispersion page of the relax website http://www.nmr-relax.com/analyses/relaxation_dispersion.html#CR72_full
[math] R_{2,\textrm{eff}} = \frac{R_2^A+R_2^B+k_{\textrm{EX}}}{2} - \nu_{\textrm{cpmg}} \cosh^{-1} (D_+\cosh(\eta_+) - D_-\cos(\eta_-)) [/math]
Which have the following definitions
[math] \alpha_- = R_2^A - R_2^B + k_{\textrm{AB}} - k_{\textrm{BA}} \\ \zeta = 2 \Delta \omega \, (R_2^A - R_2^B +k_{\textrm{AB}} - k_{\textrm{BA}} ) \\ \phantom{\zeta} = 2 \Delta \omega \, (R_2^A - R_2^B + p_B k_{\textrm{EX}} - p_A k_{\textrm{EX}} ) \\ \phantom{\zeta} = 2 \Delta \omega \alpha_- \\ \Psi = (R_2^A - R_2^B + p_B k_{\textrm{EX}} - p_A k_{\textrm{EX}} )^2 - \Delta \omega^2 + 4 p_A p_B k_{\textrm{ex}}^2 \\ \phantom{\Psi} = \alpha_-^2 - \Delta \omega^2 + 4 p_A p_B k_{\textrm{ex}}^2 \\ \eta_+ = \frac{1}{2\sqrt{2} \, \nu_{\textrm{cpmg}}}\sqrt{+\Psi + \sqrt{\Psi^2 + \zeta^2}} \\ \eta_- = \frac{1}{2\sqrt{2} \, \nu_{\textrm{cpmg}}}\sqrt{-\Psi + \sqrt{\Psi^2 + \zeta^2}} \\ D_+=\frac{1}{2}\left(1+\frac{\Psi+2\Delta \omega^2}{\sqrt{\Psi^2+\zeta^2}} \right) \\ D_-=\frac{1}{2}\left(-1+\frac{\Psi+2\Delta \omega^2}{\sqrt{\Psi^2+\zeta^2}} \right) [/math]
[math]k_{\textrm{EX}}[/math] is the chemical exchange rate constant, [math]p_A[/math] and [math]p_B[/math] are the populations of states A and B, and [math]\Delta \omega[/math] is the chemical shift difference between the two states in ppm.
Parameters
The CR72 full model has the parameters {R2A0, R2B0, ..., pA, Δω, kex}.
Reference
The reference for the CR72 full model is:
- Carver, J. P. and Richards, R. E. (1972). General 2-site solution for chemical exchange produced dependence of T2 upon Carr-Purcell pulse separation. J. Magn. Reson., 6(1), 89-105. (DOI: 10.1016/0022-2364(72)90090-X)
Related models
The CR72 model is a parametric restriction of this model.
Links
The implementation of the CR72 full model in relax can be seen in the:
