Module tsmfk01
source code
The Tollinger et al (2001) 2site veryslow exchange TSMFK01
model.
Description
Applicable in the limit of slow exchange, range of microsecond to
second time scale, when R2AR2B << k_AB, kB << 1/tau_CP.
R20A is the transverse relaxation rate of site A in the absence of
exchange. 2*tau_CP is is the time between successive 180 degree
pulses.
This module is for the function, gradient and Hessian of the TSMFK01
model
References
The model is named after the reference:

Tollinger, M., Skrynnikov, N. R., Mulder, F. A. A., FormanKay, J.
D. and Kay, L. E. (2001). Slow Dynamics in Folded and Unfolded
States of an SH3 Domain, J. Am. Chem. Soc., 123 (46)
(DOI:
10.1021/ja011300z).
Equations
The equation used is:
sin(delta_omega * tau_CP)
R2Aeff = R20A + k_AB  k_AB *  ,
delta_omega * tau_CP
where:
tau_CP = 1.0/(4*nu_cpmg) ,
R20A is the transverse relaxation rate of site A in the absence of
exchange, 2*tau_CP is is the time between successive 180 deg. pulses,
k_AB is the forward chemical exchange rate constant, delta_omega is the
chemical shift difference between the two states.
Links
More information on the TSMFK01 model can be found in the:

r2eff_TSMFK01(r20a=None,
dw=None,
dw_orig=None,
k_AB=None,
tcp=None,
back_calc=None)
Calculate the R2eff values for the TSMFK01 model. 
source code



__package__ = ' lib.dispersion '

Imports:
fabs,
min,
sin,
isfinite,
sum,
fix_invalid,
masked_where
r2eff_TSMFK01(r20a=None,
dw=None,
dw_orig=None,
k_AB=None,
tcp=None,
back_calc=None)
 source code

Calculate the R2eff values for the TSMFK01 model.
See the module docstring for details.
 Parameters:
r20a (numpy float array of rank [NE][NS][NM][NO][ND])  The R20 parameter value of state A (R2 with no exchange).
dw (numpy float array of rank [NE][NS][NM][NO][ND])  The chemical exchange difference between states A and B in rad/s.
dw_orig (numpy float array of rank1)  The chemical exchange difference between states A and B in ppm.
This is only for faster checking of zero value, which result in
no exchange.
k_AB (float)  The k_AB parameter value (the forward exchange rate in rad/s).
tcp (numpy float array of rank [NE][NS][NM][NO][ND])  The tau_CPMG times (1 / 4.nu1).
back_calc (numpy float array of rank [NE][NS][NM][NO][ND])  The array for holding the back calculated R2eff values. Each
element corresponds to one of the CPMG nu1 frequencies.
