Author: bugman
Date: Tue Jun 4 15:47:28 2013
New Revision: 19859
URL: http://svn.gna.org/viewcvs/relax?rev=19859&view=rev
Log:
Added the M61 model equations to the relax library.
This is for the Meiboom 1961 2-site fast exchange model for R1rho-type
experiments.
Added:
branches/relax_disp/lib/dispersion/m61.py
- copied, changed from r19858,
branches/relax_disp/lib/dispersion/lm63.py
Modified:
branches/relax_disp/lib/dispersion/__init__.py
Modified: branches/relax_disp/lib/dispersion/__init__.py
URL:
http://svn.gna.org/viewcvs/relax/branches/relax_disp/lib/dispersion/__init__.py?rev=19859&r1=19858&r2=19859&view=diff
==============================================================================
--- branches/relax_disp/lib/dispersion/__init__.py (original)
+++ branches/relax_disp/lib/dispersion/__init__.py Tue Jun 4 15:47:28 2013
@@ -26,4 +26,5 @@
'cr72',
'equations',
'lm63'
+ 'm61'
]
Copied: branches/relax_disp/lib/dispersion/m61.py (from r19858,
branches/relax_disp/lib/dispersion/lm63.py)
URL:
http://svn.gna.org/viewcvs/relax/branches/relax_disp/lib/dispersion/m61.py?p2=branches/relax_disp/lib/dispersion/m61.py&p1=branches/relax_disp/lib/dispersion/lm63.py&r1=19858&r2=19859&rev=19859&view=diff
==============================================================================
--- branches/relax_disp/lib/dispersion/lm63.py (original)
+++ branches/relax_disp/lib/dispersion/m61.py Tue Jun 4 15:47:28 2013
@@ -21,41 +21,43 @@
###############################################################################
# Module docstring.
-"""The Luz and Meiboom (1963) 2-site fast exchange model.
+"""The Meiboom (1961) 2-site fast exchange R1rho model.
-This module is for the function, gradient and Hessian of the LM63 model.
The model is named after the reference:
+This module is for the function, gradient and Hessian of the M61 model. The
model is named after the reference:
- Luz, S. and Meiboom S., (1963) Nuclear Magnetic Resonance study of
protolysis of trimethylammonium ion in aqueous solution - order of reaction
with respect to solvent, J. Chem. Phys. 39, 366-370 (U{DOI:
10.1063/1.1734254<http://dx.doi.org/10.1063/1.1734254>}).
+ Meiboom S. (1961). Nuclear magnetic resonance study of the proton
transfer in water. J. Chem. Phys., 34, 375-388. (U{DOI:
10.1063/1.1700960<http://dx.doi.org/10.1063/1.1700960>}).
The equation used is:
- phi_ex / 4 * nu_cpmg / kex \ \
- R2eff = R20 + ------ * | 1 - ----------- * tanh | ----------- | | ,
- kex \ kex \ 4 * nu_cpmg / /
+ phi_ex * kex
+ R1rho = R1rho' + sin^2(theta) * ----------------- ,
+ kex^2 + omega_e^2
-where:
+where R1rho' is the R1rho value in the absence of exchange, theta is the
rotating frame tilt angle,
phi_ex = pA * pB * delta_omega^2 ,
-kex is the chemical exchange rate constant, pA and pB are the populations of
states A and B, and delta_omega is the chemical shift difference between the
two states.
+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_e is the effective field in the rotating frame.
"""
# Python module imports.
-from math import tanh
+from math import pi, sin
-def r2eff_LM63(r20=None, phi_ex=None, kex=None, cpmg_frqs=None,
back_calc=None, num_points=None):
- """Calculate the R2eff values for the LM63 model.
+def r2eff_M61(r1rho0=None, phi_ex=None, kex=None, theta=pi/2,
cpmg_frqs=None, back_calc=None, num_points=None):
+ """Calculate the R2eff values for the M61 model.
See the module docstring for details.
- @keyword r20: The R20 parameter value (R2 with no exchange).
- @type r20: float
+ @keyword r1rho0: The R1rho0 parameter value (R1rho with no
exchange).
+ @type r1rho0: float
@keyword phi_ex: The phi_ex parameter value (pA * pB *
delta_omega^2).
@type phi_ex: float
@keyword kex: The kex parameter value (the exchange rate in
rad/s).
@type kex: float
+ @keyword theta: The rotating frame tilt angle.
+ @type theta: float
@keyword cpmg_frqs: The CPMG nu1 frequencies.
@type cpmg_frqs: numpy rank-1 float array
@keyword back_calc: The array for holding the back calculated R2eff
values. Each element corresponds to one of the CPMG nu1 frequencies.
@@ -66,14 +68,14 @@
# Loop over the time points, back calculating the R2eff values.
for i in range(num_points):
- # Catch zeros.
- if phi_ex == 0.0:
+ # Catch zeros (to avoid pointless mathematical operations).
+ if phi_ex == 0.0 or kex == 0.0:
back_calc[i] = r20
# Avoid divide by zero.
- elif kex == 0.0:
+ elif kex == 0.0 and cpmg_frqs[i] == 0.0:
back_calc[i] = 1e100
# The full formula.
else:
- back_calc[i] = r20 + phi_ex / kex * (1.0 - (4.0 * cpmg_frqs[i] /
kex) * tanh(kex / (4 * cpmg_frqs[i])))
+ back_calc[i] = r1rho0 + sin(theta) * phi_ex * kex / (kex**2 +
cpmg_frqs[i]**2)
r19859 - in /branches/relax_disp/lib/dispersion: __init__.py m61.py