Module lm63_3site
source code
The Luz and Meiboom (1963) 3-site fast exchange LM63
3-site model.
Description
This module is for the function, gradient and Hessian of the LM63
3-site model.
References
The model is named after the reference:
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Luz, S. and Meiboom S., (1963) Nuclear Magnetic Resonance study of
protolysis of trimethylammonium ion in aqueous solution - order of
reaction with respect to solvent, J. Chem. Phys. 39,
366-370 (DOI: 10.1063/1.1734254).
Equations
The equation used is:
_3_
\ phi_ex_i / 4 * nu_cpmg / ki \ \
R2eff = R20 + > -------- * | 1 - ----------- * tanh | ----------- | | .
/__ ki \ ki \ 4 * nu_cpmg / /
i=2
For deconvoluting the parameters, see the relax user manual or the
reference:
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O'Connell, N. E., Grey, M. J., Tang, Y., Kosuri, P., Miloushev, V.
Z., Raleigh, D. P., and Palmer, 3rd, A. G. (2009). Partially folded
equilibrium intermediate of the villin headpiece HP67 defined by
13C relaxation dispersion. J. Biomol. NMR, 45(1-2),
85-98. (DOI: 10.1007/s10858-009-9340-0).
Links
More information on the LM63 3-site model can be found in the:
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r2eff_LM63_3site(r20=None,
phi_ex_B=None,
phi_ex_C=None,
kB=None,
kC=None,
cpmg_frqs=None,
back_calc=None)
Calculate the R2eff values for the LM63 3-site model. |
source code
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__package__ = ' lib.dispersion '
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Imports:
fabs,
min,
tanh,
isfinite,
sum,
fix_invalid,
masked_where
r2eff_LM63_3site(r20=None,
phi_ex_B=None,
phi_ex_C=None,
kB=None,
kC=None,
cpmg_frqs=None,
back_calc=None)
| source code
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Calculate the R2eff values for the LM63 3-site model.
See the module docstring for details.
- Parameters:
r20 (numpy float array of rank [NS][NM][NO][ND]) - The R20 parameter value (R2 with no exchange).
phi_ex_B (numpy float array of rank [NS][NM][NO][ND]) - The fast exchange factor between sites A and B (ppm^2)
phi_ex_C (numpy float array of rank [NE][NS][NM][NO][ND]) - The fast exchange factor between sites A and C (ppm^2)
kB (float) - Approximate chemical exchange rate constant between sites A and B
(the exchange rate in rad/s).
kC (float) - Approximate chemical exchange rate constant between sites A and C
(the exchange rate in rad/s).
cpmg_frqs (numpy float array of rank [NE][NS][NM][NO][ND]) - The CPMG nu1 frequencies.
back_calc (numpy float array of rank [NE][NS][NM][NO][ND]) - The array for holding the back calculated R2eff values. Each
element corresponds to one of the CPMG nu1 frequencies.
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