lib.dispersion.ns_cpmg_2site

Source Code for Module lib.dispersion.ns_cpmg_2site_3d

1 ############################################################################### 2 # # 3 # Copyright (C) 2010-2013 Paul Schanda (https://web.archive.org/web/https://gna.org/users/pasa) # 4 # Copyright (C) 2013 Mathilde Lescanne # 5 # Copyright (C) 2013 Dominique Marion # 6 # Copyright (C) 2013-2014 Edward d'Auvergne # 7 # # 8 # This file is part of the program relax (http://www.nmr-relax.com). # 9 # # 10 # This program is free software: you can redistribute it and/or modify # 11 # it under the terms of the GNU General Public License as published by # 12 # the Free Software Foundation, either version 3 of the License, or # 13 # (at your option) any later version. # 14 # # 15 # This program is distributed in the hope that it will be useful, # 16 # but WITHOUT ANY WARRANTY; without even the implied warranty of # 17 # MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the # 18 # GNU General Public License for more details. # 19 # # 20 # You should have received a copy of the GNU General Public License # 21 # along with this program. If not, see <http://www.gnu.org/licenses/>. # 22 # # 23 ############################################################################### 24 25 # Module docstring. 26 """The numerical fit of 2-site Bloch-McConnell equations for CPMG-type experiments, the U{NS CPMG 2-site 3D<http://wiki.nmr-relax.com/NS_CPMG_2-site_3D>} and U{NS CPMG 2-site 3D full<http://wiki.nmr-relax.com/NS_CPMG_2-site_3D_full>} models. 27 28 Description 29 =========== 30 31 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. 32 33 34 Code origin 35 =========== 36 37 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 U{http://thread.gmane.org/gmane.science.nmr.relax.devel/4138}, U{https://web.archive.org/web/https://gna.org/task/?7712#comment2} and U{https://web.archive.org/web/https://gna.org/support/download.php?file_id=18262}). 38 39 40 Links 41 ===== 42 43 More information on the NS CPMG 2-site 3D model can be found in the: 44 45 - U{relax wiki<http://wiki.nmr-relax.com/NS_CPMG_2-site_3D>}, 46 - U{relax manual<http://www.nmr-relax.com/manual/reduced_NS_2_site_3D_CPMG_model.html>}, 47 - U{relaxation dispersion page of the relax website<http://www.nmr-relax.com/analyses/relaxation_dispersion.html#NS_CPMG_2-site_3D>}. 48 49 More information on the NS CPMG 2-site 3D full model can be found in the: 50 51 - U{relax wiki<http://wiki.nmr-relax.com/NS_CPMG_2-site_3D_full>}, 52 - U{relax manual<http://www.nmr-relax.com/manual/full_NS_2_site_3D_CPMG_model.html>}, 53 - U{relaxation dispersion page of the relax website<http://www.nmr-relax.com/analyses/relaxation_dispersion.html#NS_CPMG_2-site_3D_full>}. 54 """ 55 56 # Python module imports. 57 from math import log 58 from numpy import dot 59 60 # relax module imports. 61 from lib.dispersion.ns_matrices import rcpmg_3d 62 from lib.float import isNaN 63 from lib.linear_algebra.matrix_exponential import matrix_exponential 64 65

66 -def 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):

67 """The 2-site numerical solution to the Bloch-McConnell equation. 68 69 This function calculates and stores the R2eff values. 70 71 72 @keyword r180x: The X-axis pi-pulse propagator. 73 @type r180x: numpy float64, rank-2, 7D array 74 @keyword M0: This is a vector that contains the initial magnetizations corresponding to the A and B state transverse magnetizations. 75 @type M0: numpy float64, rank-1, 7D array 76 @keyword r10a: The R1 value for state A. 77 @type r10a: float 78 @keyword r10b: The R1 value for state B. 79 @type r10b: float 80 @keyword r20a: The R2 value for state A in the absence of exchange. 81 @type r20a: float 82 @keyword r20b: The R2 value for state B in the absence of exchange. 83 @type r20b: float 84 @keyword pA: The population of state A. 85 @type pA: float 86 @keyword pB: The population of state B. 87 @type pB: float 88 @keyword dw: The chemical exchange difference between states A and B in rad/s. 89 @type dw: float 90 @keyword k_AB: The rate of exchange from site A to B (rad/s). 91 @type k_AB: float 92 @keyword k_BA: The rate of exchange from site B to A (rad/s). 93 @type k_BA: float 94 @keyword inv_tcpmg: The inverse of the total duration of the CPMG element (in inverse seconds). 95 @type inv_tcpmg: float 96 @keyword tcp: The tau_CPMG times (1 / 4.nu1). 97 @type tcp: numpy rank-1 float array 98 @keyword back_calc: The array for holding the back calculated R2eff values. Each element corresponds to one of the CPMG nu1 frequencies. 99 @type back_calc: numpy rank-1 float array 100 @keyword num_points: The number of points on the dispersion curve, equal to the length of the tcp and back_calc arguments. 101 @type num_points: int 102 @keyword power: The matrix exponential power array. 103 @type power: numpy int16, rank-1 array 104 """ 105 106 # Catch parameter values that will result in no exchange, returning flat R2eff = R20 lines (when kex = 0.0, k_AB = 0.0). 107 if dw == 0.0 or pA == 1.0 or k_AB == 0.0: 108 for i in range(num_points): 109 back_calc[i] = r20a 110 return 111 112 # The matrix R that contains all the contributions to the evolution, i.e. relaxation, exchange and chemical shift evolution. 113 R = rcpmg_3d(R1A=r10a, R1B=r10b, R2A=r20a, R2B=r20b, pA=pA, pB=pB, dw=dw, k_AB=k_AB, k_BA=k_BA) 114 115 # Loop over the time points, back calculating the R2eff values. 116 for i in range(num_points): 117 # Initial magnetisation. 118 Mint = M0 119 120 # This matrix is a propagator that will evolve the magnetization with the matrix R for a delay tcp. 121 Rexpo = matrix_exponential(R*tcp[i]) 122 123 # Loop over the CPMG elements, propagating the magnetisation. 124 for j in range(2*power[i]): 125 Mint = dot(Rexpo, Mint) 126 Mint = dot(r180x, Mint) 127 Mint = dot(Rexpo, Mint) 128 129 # The next lines calculate the R2eff using a two-point approximation, i.e. assuming that the decay is mono-exponential. 130 Mx = Mint[1] / pA 131 if Mx <= 0.0 or isNaN(Mx): 132 back_calc[i] = r20a 133 else: 134 back_calc[i]= -inv_tcpmg * log(Mx)

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