Module mp05

The Miloushev and Palmer (2005) 2-site exchange R1rho MP05 model.

Description

This module is for the function, gradient and Hessian of the MP05 model.

References

The model is named after the reference:

• Miloushev V. Z. and Palmer A. (2005). R1rho relaxation for two-site chemical exchange: General approximations and some exact solutions. J. Magn. Reson., 177, 221-227. (DOI: 10.1016/j.jmr.2005.07.023).

Code origin

The code was copied from the TP02 model, hence it originates as the funTrottPalmer.m Matlab file from the sim_all.tar file attached to task #7712 (https://web.archive.org/web/https://gna.org/task/?7712). This is code from Nikolai Skrynnikov and Martin Tollinger.

Links to the copyright licensing agreements from all authors are:

• Nikolai Skrynnikov, http://article.gmane.org/gmane.science.nmr.relax.devel/4279,
• Martin Tollinger, http://article.gmane.org/gmane.science.nmr.relax.devel/4276.

Links

More information on the MP05 model can be found in the:

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

Functions

r1rho_MP05(r1rho_prime=None, omega=None, offset=None, pA=None, dw=None, kex=None, R1=0.0, spin_lock_fields=None, spin_lock_fields2=None, back_calc=None)
Calculate the R1rho' values for the TP02 model.

Variables

__package__ = 'lib.dispersion'

Imports: arctan2, isfinite, min, sin, sum, fix_invalid, masked_where

Function Details

r1rho_MP05(r1rho_prime=None, omega=None, offset=None, pA=None, dw=None, kex=None, R1=0.0, spin_lock_fields=None, spin_lock_fields2=None, back_calc=None)

Calculate the R1rho' values for the TP02 model.

See the module docstring for details. This is the Miloushev and Palmer (2005) equation according to Korzhnev (J. Biomol. NMR (2003), 26, 39-48).

Parameters:

• r1rho_prime (numpy float array of rank [NE][NS][NM][NO][ND]) - The R1rho_prime parameter value (R1rho with no exchange).
• omega (numpy float array of rank [NE][NS][NM][NO][ND]) - The chemical shift for the spin in rad/s.
• offset (numpy float array of rank [NE][NS][NM][NO][ND]) - The spin-lock offsets for the data.
• pA (float) - The population of state A.
• dw (numpy float array of rank [NE][NS][NM][NO][ND]) - The chemical exchange difference between states A and B in rad/s.
• kex (float) - The kex parameter value (the exchange rate in rad/s).
• R1 (numpy float array of rank [NE][NS][NM][NO][ND]) - The R1 relaxation rate.
• spin_lock_fields (numpy float array of rank [NE][NS][NM][NO][ND]) - The R1rho spin-lock field strengths (in rad.s^-1).
• spin_lock_fields2 (numpy float array of rank [NE][NS][NM][NO][ND]) - The R1rho spin-lock field strengths squared (in rad^2.s^-2). This is for speed.
• back_calc (numpy float array of rank [NE][NS][NM][NO][ND]) - The array for holding the back calculated R1rho values. Each element corresponds to the combination of offset and spin lock field.