Difference between revisions of "CR72"
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| − | The Carver and Richards 1972 2-site relaxation dispersion model for [[SQ CPMG-type data]] for most time scales whereby the simplification | + | The Carver and Richards 1972 2-site relaxation dispersion model for [[SQ CPMG-type data]] for most time scales whereby the simplification {{:R2Azero}} = {{:R2Bzero}} is assumed. This model is labelled as '''CR72''' in [[Relaxation dispersion citation for relax|relax]]. |
| + | |||
| + | == Equation == | ||
| + | [http://www.nmr-relax.com/manual/Dispersion_model_summary.html Please see the summary of the model parameters here.] | ||
| + | |||
| + | <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_-)) \\ | ||
| + | \phantom{R_{2,\textrm{eff}}} = R_2 + \frac{k_{\textrm{EX}}}{2} - \nu_{\textrm{cpmg}} \cosh^{-1} (D_+\cosh(\eta_+) - D_-\cos(\eta_-)) | ||
| + | </math> | ||
| + | |||
| + | Which have the following definitions | ||
| + | |||
| + | <math> | ||
| + | \zeta = 2 \Delta \omega \, (R_2^A - R_2^B - p_A k_{\textrm{EX}} + p_B k_{\textrm{EX}}) \\ | ||
| + | \phantom{\zeta} = - 2 \Delta \omega \, ( p_A k_{\textrm{EX}} - p_B k_{\textrm{EX}}) \\ | ||
| + | \phantom{\zeta} = - 2 \Delta \omega \, ( k_{\textrm{BA}} - k_{\textrm{AB}}) \\ | ||
| + | \phantom{\zeta} = - 2 \Delta \omega \, k_{\textrm{EX}} ( 2p_A - 1) \\ | ||
| + | \Psi = (p_B k_{\textrm{EX}} - p_A k_{\textrm{EX}})^2 + 4 p_A p_B k_{\textrm{ex}}^2 - \Delta \omega^2 \\ | ||
| + | \phantom{\Psi} = ( p_A k_{\textrm{EX}} + p_B k_{\textrm{EX}} )^2 - \Delta \omega^2 \\ | ||
| + | \phantom{\Psi} = k_{\textrm{ex}}^2 - \Delta \omega^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> | ||
| + | |||
| + | {{:kex}} is the chemical exchange rate constant, {{:pA}} and {{:pB}} are the populations of states A and B, and {{:Deltaomega}} is the chemical shift difference between the two states in ppm. | ||
== Parameters == | == Parameters == | ||
| − | The CR72 model has the parameters { | + | The CR72 model has the parameters {{{:R2zero}}, ..., {{:pA}}, {{:Deltaomega}}, {{:kex}}}. |
| + | == Code == | ||
| + | |||
| + | The library code: {{relax url|path=lib/dispersion/cr72.py}} | ||
== Reference == | == Reference == | ||
| Line 10: | Line 39: | ||
The reference for the CR72 model is: | The reference for the CR72 model is: | ||
| − | * | + | * {{#lst:Citations|CarverRichards72}} |
| + | |||
| + | == Related models == | ||
| + | The CR72 model is a parametric restriction of the [[CR72 full]] model. | ||
== Links == | == Links == | ||
| − | The implementation of the | + | The [[Relaxation dispersion citation for relax|implementation of the CR72 model in relax]] can be seen in the: |
| − | * [http://www.nmr-relax.com/manual/ | + | * [http://www.nmr-relax.com/manual/The_reduced_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 relaxation dispersion page of the relax website]. | + | * [http://www.nmr-relax.com/analyses/relaxation_dispersion.html#CR72 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 12:15, 27 October 2017
The Carver and Richards 1972 2-site relaxation dispersion model for SQ CPMG-type data for most time scales whereby the simplification R2A0 = R2B0 is assumed. This model is labelled as CR72 in relax.
Equation
Please see the summary of the model parameters here.
[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_-)) \\ \phantom{R_{2,\textrm{eff}}} = R_2 + \frac{k_{\textrm{EX}}}{2} - \nu_{\textrm{cpmg}} \cosh^{-1} (D_+\cosh(\eta_+) - D_-\cos(\eta_-)) [/math]
Which have the following definitions
[math] \zeta = 2 \Delta \omega \, (R_2^A - R_2^B - p_A k_{\textrm{EX}} + p_B k_{\textrm{EX}}) \\ \phantom{\zeta} = - 2 \Delta \omega \, ( p_A k_{\textrm{EX}} - p_B k_{\textrm{EX}}) \\ \phantom{\zeta} = - 2 \Delta \omega \, ( k_{\textrm{BA}} - k_{\textrm{AB}}) \\ \phantom{\zeta} = - 2 \Delta \omega \, k_{\textrm{EX}} ( 2p_A - 1) \\ \Psi = (p_B k_{\textrm{EX}} - p_A k_{\textrm{EX}})^2 + 4 p_A p_B k_{\textrm{ex}}^2 - \Delta \omega^2 \\ \phantom{\Psi} = ( p_A k_{\textrm{EX}} + p_B k_{\textrm{EX}} )^2 - \Delta \omega^2 \\ \phantom{\Psi} = k_{\textrm{ex}}^2 - \Delta \omega^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]
kex is the chemical exchange rate constant, pA and pB are the populations of states A and B, and Δω is the chemical shift difference between the two states in ppm.
Parameters
The CR72 model has the parameters {R20, ..., pA, Δω, kex}.
Code
The library code: https://sourceforge.net/p/nmr-relax/code/ci/master/tree/lib/dispersion/cr72.py
Reference
The reference for the CR72 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 the CR72 full model.
Links
The implementation of the CR72 model in relax can be seen in the:
