Package lib :: Package dispersion :: Module ns_cpmg_2site_3d
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Module ns_cpmg_2site_3d

source code

The numerical fit of 2-site Bloch-McConnell equations for CPMG-type experiments, the NS CPMG 2-site 3D and NS CPMG 2-site 3D full models.

Description

The function uses an explicit matrix that contains relaxation, exchange and chemical shift terms. It does the 180deg pulses in the CPMG train. The approach of Bloch-McConnell can be found in chapter 3.1 of Palmer, A. G. Chem Rev 2004, 104, 3623-3640. This function was written, initially in MATLAB, in 2010.

Code origin

This is the model of the numerical solution for the 2-site Bloch-McConnell equations. It originates as optimization function number 1 from the fitting_main_kex.py script from Mathilde Lescanne, Paul Schanda, and Dominique Marion (see http://thread.gmane.org/gmane.science.nmr.relax.devel/4138, https://gna.org/task/?7712#comment2 and https://gna.org/support/download.php?file_id=18262).

Links

More information on the NS CPMG 2-site 3D model can be found in the:

More information on the NS CPMG 2-site 3D full model can be found in the:

Functions [hide private]
 
r2eff_ns_cpmg_2site_3D(r180x=None, M0=None, r10a=0.0, r10b=0.0, r20a=None, r20b=None, pA=None, pB=None, dw=None, k_AB=None, k_BA=None, inv_tcpmg=None, tcp=None, back_calc=None, num_points=None, power=None)
The 2-site numerical solution to the Bloch-McConnell equation.
source code
Variables [hide private]
  __package__ = 'lib.dispersion'

Imports: log, dot, rcpmg_3d, isNaN, matrix_exponential


Function Details [hide private]

r2eff_ns_cpmg_2site_3D(r180x=None, M0=None, r10a=0.0, r10b=0.0, r20a=None, r20b=None, pA=None, pB=None, dw=None, k_AB=None, k_BA=None, inv_tcpmg=None, tcp=None, back_calc=None, num_points=None, power=None)

source code 

The 2-site numerical solution to the Bloch-McConnell equation.

This function calculates and stores the R2eff values.

Parameters:
  • r180x (numpy float64, rank-2, 7D array) - The X-axis pi-pulse propagator.
  • M0 (numpy float64, rank-1, 7D array) - This is a vector that contains the initial magnetizations corresponding to the A and B state transverse magnetizations.
  • r10a (float) - The R1 value for state A.
  • r10b (float) - The R1 value for state B.
  • r20a (float) - The R2 value for state A in the absence of exchange.
  • r20b (float) - The R2 value for state B in the absence of exchange.
  • pA (float) - The population of state A.
  • pB (float) - The population of state B.
  • dw (float) - The chemical exchange difference between states A and B in rad/s.
  • k_AB (float) - The rate of exchange from site A to B (rad/s).
  • k_BA (float) - The rate of exchange from site B to A (rad/s).
  • inv_tcpmg (float) - The inverse of the total duration of the CPMG element (in inverse seconds).
  • tcp (numpy rank-1 float array) - The tau_CPMG times (1 / 4.nu1).
  • 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 tcp and back_calc arguments.
  • power (numpy int16, rank-1 array) - The matrix exponential power array.