View source for 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 [[Relaxation dispersion citation for relax|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 {{{: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 ==

The reference for the DPL94 model is:

* {{#lst:Citations|Davis94}}

== Related models ==

The DPL94 model is simply the extension of the [[M61]] model for off-resonance data.

== Links ==

The [[Relaxation dispersion citation for relax|implementation of the DPL94 model in relax]] can be seen in the:
* [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/analyses/relaxation_dispersion.html#DPL94 relaxation dispersion page of the relax website].

== See also ==
[[Category:Models]]
[[Category:Dispersion models]]
[[Category:Relaxation dispersion analysis]]