Difference between revisions of "DPL94"

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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.
+
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 [[Relaxation dispersion citation for relax|relax]].
  
 
== Equation ==
 
== Equation ==
 
<math>
 
<math>
\mathrm{R}_{1\rho}= \mathrm{R}_1\cos^2\theta + \left( \mathrm{R}_{ex}}{\textrm{k}_\textrm{ex}^2 + \omega_\textrm{e}^2} \right) \sin^2\theta
+
\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>
 
</math>
  
 
== Parameters ==
 
== Parameters ==
  
The DPL94 model has the parameters {$R_{1\rho}'$, $...$, $\Phi_{ex}$, $k_{ex}$}.
+
The DPL94 model has the parameters {{{:R1rhoprime}}, ..., {{:Phiex}}, {{:kex}}}.
 +
 
 +
== Essentials ==
 +
 
 +
{{note|{{:R1}} should be provided in rad/s, the SI default unit for this relaxation rate.}}
 +
 
 +
It is essential to read in {{:R1}} values before starting a calculation:<br>
 +
<source lang="python">
 +
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)
 +
</source>
 +
 
 +
Where the data could be stored like
 +
<source lang="text">
 +
# 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
 +
</source>
 +
 
 +
== Parameter name space in relax ==
 +
 
 +
{{collapsible script
 +
| type  = relax script
 +
| title  = At time of writing (March 2014) the parameters in relax were stored as demonstrated in this script.
 +
| lang  = python
 +
| script =
 +
# Load the outcome from an analysis
 +
state.load(state="results.bz2", dir="results/final")
 +
 
 +
# import spin functions
 +
from pipe_control.mol_res_spin import return_spin, spin_loop
 +
 
 +
# Alias one spin
 +
s13 = return_spin(":13@N")
 +
 
 +
# See attributes
 +
dir(s13)
 +
 
 +
# See parameters
 +
print(s13.params)
 +
['r2', 'phi_ex', 'kex']
 +
 
 +
# Print parameters
 +
print(s13.r2)
 +
{'R1rho - 799.77739910 MHz': xx.yy}
 +
print(s13.phi_ex)
 +
print(s13.kex)
 +
 
 +
# See Ri data (ri_type:  The relaxation data type, i.e. 'R1', 'R2', 'NOE', or 'R2eff'. )
 +
print(s13.ri_data)
 +
{'R1': 1.3239399999999999}
 +
 
 +
# Print all spin id
 +
for curspin, mol_name, res_num, res_name, spin_id in spin_loop(full_info=True, return_id=True, skip_desel=False):
 +
    if curspin.select == False:
 +
        print(mol_name, res_num, res_name, spin_id)
 +
    else:
 +
        print(mol_name, res_num, res_name, spin_id, curspin.r2, curspin.phi_ex, curspin.kex)
 +
}}
 +
 
 +
[http://www.nmr-relax.com/manual/Dispersion_model_summary.html Please see the summary of the model parameters here.]
 +
 
 +
Which means:
 +
# {{:R1rhoprime}} = <code>spin.r2</code> (Fitted)
 +
# {{:R1rho}} = <code>spin.r2eff</code> (Back calculated)
 +
# {{:Phiex}} = <code>spin.phi_ex</code> (Fitted)
 +
# {{:kex}} = <code>spin.kex</code> (Fitted)
 +
# {{:R1}} = <code>spin.ri_data['R1']</code> (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
 +
 
 +
* {{#lst:Citations|Evenäs01}}
 +
* {{#lst:Citations|KempfLoria04}}
 +
* {{#lst:Citations|Massi05}}
 +
* {{#lst:Citations|Palmer01}}
 +
* {{#lst:Citations|PalmerMassi06}}
 +
* {{#lst:Citations|TrottPalmer02}}
 +
 
 +
Different graphs.
 +
 
 +
== The {{:R1rho}}: {{:R2}} or {{:R2eff}} as function of effective field in rotating frame: {{:omegaeff}} ==
 +
 
 +
=== Discussion ===
 +
It is clear that there is no real name for the pseudo-parameter.  It looks like that {{:Reff}} 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|TP02 dispersion model]], one will see yet another notation:
 +
 
 +
Here {{:R2}} does not contain the {{:Rex}} contribution.  Also, {{:Reff}} is absent of {{:Rex}}. <br>
 +
But in Art's Protein Science paper (Ref [5]), the definition {{:R2}} = {{:R2zero}} + {{:Rex}} is used.  The [[MP05|MP05 model reference]] also does not use {{:Reff}}.
 +
 
 +
The {{:Reff}} parameter name is confusing and it seems to have been dropped from 2005 onwards.  The {{:Reff}} 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> <br>
 +
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>. <br>
 +
Ref [4], Equation 43. <math>R_{\text{eff}} =  R_{1\rho} / \sin^2(\theta) - R_1 / \tan^2(\theta)</math> <br>
 +
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 ==
 
== Reference ==
Line 14: Line 114:
 
The reference for the DPL94 model is:
 
The reference for the DPL94 model is:
  
* Davis, D., Perlman, M., and London, R. (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. ([http://dx.doi.org/10.1006/jmrb.1994.1084 10.1006/jmrb.1994.1084])
+
* {{#lst:Citations|Davis94}}
  
 
== Related models ==
 
== Related models ==
Line 22: Line 122:
 
== Links ==
 
== Links ==
  
The implementation of the DPL94 model in relax can be seen in the:
+
The [[Relaxation dispersion citation for relax|implementation of the DPL94 model in relax]] can be seen in the:
* [http://www.nmr-relax.com/manual/DPL94_2_site_fast_exchange_R1_model.html relax manual],  
+
* [http://www.nmr-relax.com/manual/The_DPL94_2_site_fast_exchange_R1_rho_model.html relax manual],  
 
* [http://www.nmr-relax.com/api/3.1/lib.dispersion.dpl94-module.html API documentation],
 
* [http://www.nmr-relax.com/api/3.1/lib.dispersion.dpl94-module.html API documentation],
 
* [http://www.nmr-relax.com/analyses/relaxation_dispersion.html#DPL94 relaxation dispersion page of the relax website].
 
* [http://www.nmr-relax.com/analyses/relaxation_dispersion.html#DPL94 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 15:01, 18 November 2015

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.

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', ..., Φex, kex}.

Essentials

Note  R1 should be provided in rad/s, the SI default unit for this relaxation rate.

It is essential to read in R1 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:

  1. R' = spin.r2 (Fitted)
  2. R = spin.r2eff (Back calculated)
  3. Φex = spin.phi_ex (Fitted)
  4. kex = spin.kex (Fitted)
  5. R1 = 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: R2 or R2,eff as function of effective field in rotating frame: ωe

Discussion

It is clear that there is no real name for the pseudo-parameter. It looks like that Reff was Art's original way of denoting this and that he has now changed to R2 instead.
But if one look at the reference for the TP02 dispersion model, one will see yet another notation:

Here R2 does not contain the Rex contribution. Also, Reff is absent of Rex.
But in Art's Protein Science paper (Ref [5]), the definition R2 = R20 + Rex is used. The MP05 model reference also does not use Reff.

The Reff parameter name is confusing and it seems to have been dropped from 2005 onwards. The Reff 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:

See also