Package lib :: Package dispersion :: Module ns_mmq_2site
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Module ns_mmq_2site

source code

The numeric solution for the 2-site Bloch-McConnell equations for MMQ CPMG data, the NS MMQ 2-site model.

Description

This handles proton-heteronuclear SQ, ZQ, DQ and MQ CPMG data.

References

It uses the equations of:

Links

More information on the NS MMQ 2-site model can be found in the:

Functions [hide private]
 
populate_matrix(matrix=None, R20A=None, R20B=None, dw=None, k_AB=None, k_BA=None)
The Bloch-McConnell matrix for 2-site exchange.
source code
 
r2eff_ns_mmq_2site_mq(M0=None, F_vector=array([ 1., 0.]), m1=None, m2=None, R20A=None, R20B=None, pA=None, pB=None, dw=None, dwH=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 for MQ data.
source code
 
r2eff_ns_mmq_2site_sq_dq_zq(M0=None, F_vector=array([ 1., 0.]), m1=None, m2=None, R20A=None, R20B=None, pA=None, pB=None, dw=None, dwH=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 for SQ, ZQ, and DQ data.
source code
Variables [hide private]
  __package__ = 'lib.dispersion'

Imports: floor, array, conj, dot, float64, log, isNaN, matrix_exponential, square_matrix_power


Function Details [hide private]

populate_matrix(matrix=None, R20A=None, R20B=None, dw=None, k_AB=None, k_BA=None)

source code 

The Bloch-McConnell matrix for 2-site exchange.

Parameters:
  • matrix (numpy rank-2, 2D complex64 array) - The matrix to populate.
  • R20A (float) - The transverse, spin-spin relaxation rate for state A.
  • R20B (float) - The transverse, spin-spin relaxation rate for state B.
  • dw (float) - The combined chemical exchange difference parameters between states A and B in rad/s. This can be any combination of dw and dwH.
  • 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).

r2eff_ns_mmq_2site_mq(M0=None, F_vector=array([ 1., 0.]), m1=None, m2=None, R20A=None, R20B=None, pA=None, pB=None, dw=None, dwH=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 for MQ data.

The notation used here comes from:

  • Dmitry M. Korzhnev, Philipp Neudecker, Anthony Mittermaier, Vladislav Yu. Orekhov, and Lewis E. Kay (2005). Multiple-site exchange in proteins studied with a suite of six NMR relaxation dispersion experiments: An application to the folding of a Fyn SH3 domain mutant. J. Am. Chem. Soc., 127, 15602-15611. (doi: http://dx.doi.org/10.1021/ja054550e).

and:

  • Dmitry M. Korzhnev, Philipp Neudecker, Anthony Mittermaier, Vladislav Yu. Orekhov, and Lewis E. Kay (2005). Multiple-site exchange in proteins studied with a suite of six NMR relaxation dispersion experiments: An application to the folding of a Fyn SH3 domain mutant. J. Am. Chem. Soc., 127, 15602-15611. (doi: http://dx.doi.org/10.1021/ja054550e).

This function calculates and stores the R2eff values.

Parameters:
  • 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.
  • F_vector (numpy rank-1, 2D float64 array) - The observable magnitisation vector. This defaults to [1, 0] for X observable magnitisation.
  • m1 (numpy rank-2, 2D complex64 array) - A complex numpy matrix to be populated.
  • m2 (numpy rank-2, 2D complex64 array) - A complex numpy matrix to be populated.
  • R20A (float) - The transverse, spin-spin relaxation rate for state A.
  • R20B (float) - The transverse, spin-spin relaxation rate for state B.
  • 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.
  • dwH (float) - The proton 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.

r2eff_ns_mmq_2site_sq_dq_zq(M0=None, F_vector=array([ 1., 0.]), m1=None, m2=None, R20A=None, R20B=None, pA=None, pB=None, dw=None, dwH=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 for SQ, ZQ, and DQ data.

The notation used here comes from:

  • Dmitry M. Korzhnev, Philipp Neudecker, Anthony Mittermaier, Vladislav Yu. Orekhov, and Lewis E. Kay (2005). Multiple-site exchange in proteins studied with a suite of six NMR relaxation dispersion experiments: An application to the folding of a Fyn SH3 domain mutant. J. Am. Chem. Soc., 127, 15602-15611. (doi: http://dx.doi.org/10.1021/ja054550e).

This function calculates and stores the R2eff values.

Parameters:
  • 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.
  • F_vector (numpy rank-1, 2D float64 array) - The observable magnitisation vector. This defaults to [1, 0] for X observable magnitisation.
  • m1 (numpy rank-2, 2D complex64 array) - A complex numpy matrix to be populated.
  • m2 (numpy rank-2, 2D complex64 array) - A complex numpy matrix to be populated.
  • R20A (float) - The transverse, spin-spin relaxation rate for state A.
  • R20B (float) - The transverse, spin-spin relaxation rate for state B.
  • pA (float) - The population of state A.
  • pB (float) - The population of state B.
  • dw (float) - The combined chemical exchange difference between states A and B in rad/s. It should be set to dwH for 1H SQ data, dw for heteronuclear SQ data, dwH-dw for ZQ data, and dwH+dw for DQ data.
  • dwH (float) - Unused - this is simply to match the r2eff_ns_mmq_2site_mq() function arguments.
  • 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.