Module lm63_3site

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:

• 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:

• 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:

• relax wiki,
• relax manual,
• relaxation dispersion page of the relax website.

Functions

r2eff_LM63_3site(r20=None, rex_B=None, rex_C=None, quart_kB=None, quart_kC=None, cpmg_frqs=None, back_calc=None, num_points=None)
Calculate the R2eff values for the LM63 3-site model.

Variables

__package__ = 'lib.dispersion'

Imports: tanh

Function Details

r2eff_LM63_3site(r20=None, rex_B=None, rex_C=None, quart_kB=None, quart_kC=None, cpmg_frqs=None, back_calc=None, num_points=None)

Calculate the R2eff values for the LM63 3-site model.

See the module docstring for details.

Parameters:

• r20 (float) - The R20 parameter value (R2 with no exchange).
• rex_B (float) - The phi_ex_B / kB parameter value.
• rex_C (float) - The phi_ex_C / kC parameter value.
• quart_kB (float) - Approximate chemical exchange rate constant between sites A and B (the exchange rate in rad/s) divided by 4.
• quart_kC (float) - Approximate chemical exchange rate constant between sites A and C (the exchange rate in rad/s) divided by 4.
• cpmg_frqs (numpy rank-1 float array) - The CPMG nu1 frequencies.
• back_calc (numpy rank-1 float array) - The array for holding the back calculated R2eff values. Each element corresponds to one of the CPMG nu1 frequencies.
• num_points (int) - The number of points on the dispersion curve, equal to the length of the cpmg_frqs and back_calc arguments.