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]
numpy float array of rank [NE][NS][NM][NO][ND][2][2]
rmmq_2site_rankN(R20A=None, R20B=None, dw=None, k_AB=None, k_BA=None, tcp=None)
The Bloch-McConnell matrix for 2-site exchange, for rank [NE][NS][NM][NO][ND][2][2].
source code
 
r2eff_ns_mmq_2site_mq(M0=None, F_vector=array([ 1., 0.]), R20A=None, R20B=None, pA=None, dw=None, dwH=None, kex=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.]), R20A=None, R20B=None, pA=None, dw=None, dwH=None, kex=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]
  m_r20a = array([[-1., 0...
  m_r20b = array([[ 0., 0...
  m_k_AB = array([[-1., 0...
  m_k_BA = array([[ 0., 1...
  m_dw = array([[ 0., 0...
  __package__ = 'lib.dispersion'

Imports: floor, array, conj, complex128, dot, einsum, float64, log, multiply, matrix_power, isNaN, matrix_exponential


Function Details [hide private]

rmmq_2site_rankN(R20A=None, R20B=None, dw=None, k_AB=None, k_BA=None, tcp=None)

source code 

The Bloch-McConnell matrix for 2-site exchange, for rank [NE][NS][NM][NO][ND][2][2].

Parameters:
  • R20A (numpy float array of rank [NE][NS][NM][NO][ND]) - The transverse, spin-spin relaxation rate for state A.
  • R20B (numpy float array of rank [NE][NS][NM][NO][ND]) - The transverse, spin-spin relaxation rate for state B.
  • dw (numpy float array of rank [NE][NS][NM][NO][ND]) - 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).
  • tcp (numpy float array of rank [NE][NS][NM][NO][ND]) - The tau_CPMG times (1 / 4.nu1).
Returns: numpy float array of rank [NE][NS][NM][NO][ND][2][2]
The relaxation matrix.

r2eff_ns_mmq_2site_mq(M0=None, F_vector=array([ 1., 0.]), R20A=None, R20B=None, pA=None, dw=None, dwH=None, kex=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.
  • R20A (numpy float array of rank [NS][NM][NO][ND]) - The transverse, spin-spin relaxation rate for state A.
  • R20B (numpy float array of rank [NS][NM][NO][ND]) - The transverse, spin-spin relaxation rate for state B.
  • pA (float) - The population of state A.
  • dw (numpy float array of rank [NS][NM][NO][ND]) - The chemical exchange difference between states A and B in rad/s.
  • dwH (numpy float array of rank [NS][NM][NO][ND]) - The proton chemical exchange difference between states A and B in rad/s.
  • kex (float) - The kex parameter value (the exchange rate in rad/s).
  • inv_tcpmg (numpy float array of rank [NS][NM][NO][ND]) - The inverse of the total duration of the CPMG element (in inverse seconds).
  • tcp (numpy float array of rank [NS][NM][NO][ND]) - The tau_CPMG times (1 / 4.nu1).
  • back_calc (numpy float array of rank [NS][NM][NO][ND]) - The array for holding the back calculated R2eff values. Each element corresponds to one of the CPMG nu1 frequencies.
  • num_points (numpy int array of rank [NS][NM][NO]) - The number of points on the dispersion curve, equal to the length of the tcp and back_calc arguments.
  • power (numpy int array of rank [NS][NM][NO][ND]) - The matrix exponential power array.

r2eff_ns_mmq_2site_sq_dq_zq(M0=None, F_vector=array([ 1., 0.]), R20A=None, R20B=None, pA=None, dw=None, dwH=None, kex=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.
  • R20A (numpy float array of rank [NS][NM][NO][ND]) - The transverse, spin-spin relaxation rate for state A.
  • R20B (numpy float array of rank [NS][NM][NO][ND]) - The transverse, spin-spin relaxation rate for state B.
  • pA (float) - The population of state A.
  • dw (numpy float array of rank [NS][NM][NO][ND]) - 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 (numpy float array of rank [NS][NM][NO][ND]) - Unused - this is simply to match the r2eff_ns_mmq_2site_mq() function arguments.
  • kex (float) - The kex parameter value (the exchange rate in rad/s).
  • inv_tcpmg (numpy float array of rank [NS][NM][NO][ND]) - The inverse of the total duration of the CPMG element (in inverse seconds).
  • tcp (numpy float array of rank [NS][NM][NO][ND]) - The tau_CPMG times (1 / 4.nu1).
  • back_calc (numpy float array of rank [NS][NM][NO][ND]) - The array for holding the back calculated R2eff values. Each element corresponds to one of the CPMG nu1 frequencies.
  • num_points (numpy int array of rank [NS][NM][NO]) - The number of points on the dispersion curve, equal to the length of the tcp and back_calc arguments.
  • power (numpy int array of rank [NS][NM][NO][ND]) - The matrix exponential power array.

Variables Details [hide private]

m_r20a

Value:
array([[-1.,  0.],
       [ 0.,  0.]])

m_r20b

Value:
array([[ 0.,  0.],
       [ 0., -1.]])

m_k_AB

Value:
array([[-1.,  0.],
       [ 1.,  0.]])

m_k_BA

Value:
array([[ 0.,  1.],
       [ 0., -1.]])

m_dw

Value:
array([[ 0.,  0.],
       [ 0.,  1.]])