Difference between revisions of "CR72"

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= Intro =
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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 {{:R2Azero}} = {{:R2Bzero}} is assumed.  This model is labelled as '''CR72''' in [[Relaxation dispersion citation for relax|relax]].
 
 
The Carver and Richards 1972 2-site relaxation dispersion model for [[SQ CPMG-type data]] for most time scales whereby the simplification $R_{2A}^0$ = $R_{2B}^0$ is assumed.  This model is labelled as '''CR72''' in [[Relaxation dispersion citation for relax|relax]].
 
  
 
== Equation ==
 
== Equation ==
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</math>
 
</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.
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{{: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 {$R_2^0$, $...$, $p_A$, $\Delta\omega$, $k_{ex}$}.
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The CR72 model has the parameters {{{:R2zero}}, ..., {{:pA}}, {{:Deltaomega}}, {{:kex}}}.
  
 
== Code ==
 
== Code ==
  
The library code.<br>
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The library code: {{relax url|path=lib/dispersion/cr72.py}}
http://svn.gna.org/viewcvs/*checkout*/relax/trunk/lib/dispersion/cr72.py?revision=HEAD
 
  
 
== Reference ==
 
== Reference ==
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The reference for the CR72 model is:
 
The reference for the CR72 model is:
  
* Carver, J. and Richards, R. (1972).  General 2-site solution for chemical exchange produced dependence of T2 upon Carr-Purcell pulse separation. ''J. Magn. Reson.'', '''6'''(1), 89-105. ([http://dx.doi.org/10.1016/0022-2364(72)90090-X 10.1016/0022-2364(72)90090-X]).
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* {{#lst:Citations|CarverRichards72}}
  
 
== Related models ==
 
== Related models ==
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The [[Relaxation dispersion citation for relax|implementation of the CR72 model in relax]] can be seen in 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/reduced_CR72_2_site_CPMG_model.html relax manual],
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* [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#CR72 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]]
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[[Category:Models]]
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[[Category:Dispersion models]]
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[[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:

See also