Source Code for Module lib.dispersion.dpl94

  1  ############################################################################### 
  2  #                                                                             # 
  3  # Copyright (C) 2009 Sebastien Morin                                          # 
  4  # Copyright (C) 2013-2014 Edward d'Auvergne                                   # 
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 22   
 23  # Module docstring. 
 24  """The Davis, Perlman and London (1994) 2-site fast exchange R1rho U{DPL94<http://wiki.nmr-relax.com/DPL94>} model. 
 25   
 26  Description 
 27  =========== 
 28   
 29  This module is for the function, gradient and Hessian of the U{DPL94<http://wiki.nmr-relax.com/DPL94>} model. 
 30   
 31   
 32  References 
 33  ========== 
 34   
 35  The model is named after the reference: 
 36   
 37      - Davis, D. G., Perlman, M. E. and London, R. E. (1994).  Direct measurements of the dissociation-rate constant for inhibitor-enzyme complexes via the T1rho and T2 (CPMG) methods.  I{J. Magn. Reson.}, Series B, B{104}, 266-275.  (U{DOI: 10.1006/jmrb.1994.1084<http://dx.doi.org/10.1006/jmrb.1994.1084>}) 
 38   
 39  Equations 
 40  ========= 
 41   
 42  The equation used is:: 
 43   
 44                                                                        phi_ex * kex 
 45      R1rho = R1.cos^2(theta) + R1rho'.sin^2(theta) + sin^2(theta) * ------------------ , 
 46                                                                     kex^2 + omega_sl^2 
 47   
 48  where theta is the rotating frame tilt angle, and:: 
 49   
 50      phi_ex = pA * pB * delta_omega^2 , 
 51   
 52  kex is the chemical exchange rate constant, pA and pB are the populations of states A and B, delta_omega is the chemical shift difference between the two states, and omega_sl is the spin-lock field strength. 
 53   
 54   
 55  Links 
 56  ===== 
 57   
 58  More information on the DPL94 model can be found in the: 
 59   
 60      - U{relax wiki<http://wiki.nmr-relax.com/DPL94>}, 
 61      - U{relax manual<http://www.nmr-relax.com/manual/DPL94_2_site_fast_exchange_R1_model.html>}, 
 62      - U{relaxation dispersion page of the relax website<http://www.nmr-relax.com/analyses/relaxation_dispersion.html#DPL94>}. 
 63  """ 
 64   
 65  # Python module imports. 
 66  from numpy import abs, array, cos, isfinite, min, sin, sum 
 67   
 68   
 69 -def r1rho_DPL94(r1rho_prime=None, phi_ex=None, kex=None, theta=None, R1=0.0, spin_lock_fields2=None, back_calc=None, num_points=None): 
 70      """Calculate the R1rho values for the DPL94 model. 
 71   
 72      See the module docstring for details. 
 73   
 74   
 75      @keyword r1rho_prime:       The R1rho_prime parameter value (R1rho with no exchange). 
 76      @type r1rho_prime:          float 
 77      @keyword phi_ex:            The phi_ex parameter value (pA * pB * delta_omega^2). 
 78      @type phi_ex:               float 
 79      @keyword kex:               The kex parameter value (the exchange rate in rad/s). 
 80      @type kex:                  float 
 81      @keyword theta:             The rotating frame tilt angles for each dispersion point. 
 82      @type theta:                numpy rank-1 float array 
 83      @keyword R1:                The R1 relaxation rate. 
 84      @type R1:                   float 
 85      @keyword spin_lock_fields2: The R1rho spin-lock field strengths squared (in rad^2.s^-2). 
 86      @type spin_lock_fields2:    numpy rank-1 float array 
 87      @keyword back_calc:         The array for holding the back calculated R1rho values.  Each element corresponds to the combination of theta and spin lock field. 
 88      @type back_calc:            numpy rank-1 float array 
 89      @keyword num_points:        The number of points on the dispersion curve, equal to the length of the spin_lock_fields and back_calc arguments. 
 90      @type num_points:           int 
 91      """ 
 92   
 93      # Repetitive calculations (to speed up calculations). 
 94      kex2 = kex**2 
 95   
 96      # The non-Rex factors. 
 97      sin_theta2 = sin(theta)**2 
 98      R1_R2 = R1 * cos(theta)**2  +  r1rho_prime * sin_theta2 
 99   
100      # The numerator. 
101      numer = sin_theta2 * phi_ex * kex 
102   
103      # Catch zeros (to avoid pointless mathematical operations). 
104      # This will result in no exchange, returning flat lines. 
105      if min(numer) == 0.0: 
106          back_calc[:] = R1_R2 
107          return 
108   
109      # Denominator. 
110      denom = kex2 + spin_lock_fields2 
111   
112      # Catch math domain error of dividing with 0. 
113      # This is when denom =0. 
114      if min(abs(denom)) == 0: 
115          back_calc[:] = array([1e100]*num_points) 
116          return 
117   
118      # R1rho calculation. 
119      R1rho = R1_R2 + numer / denom 
120   
121      # Catch errors, taking a sum over array is the fastest way to check for 
122      # +/- inf (infinity) and nan (not a number). 
123      if not isfinite(sum(R1rho)): 
124          R1rho = array([1e100]*num_points) 
125   
126      back_calc[:] = R1rho 
127