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,
k_AB=None,
tcp=None,
back_calc=None,
num_points=None)
Calculate the R2eff values for the TSMFK01 model. 
source code



__package__ = ' lib.dispersion '

Imports:
array,
min,
sin,
isfinite,
sum
r2eff_TSMFK01(r20a=None,
dw=None,
k_AB=None,
tcp=None,
back_calc=None,
num_points=None)
 source code

Calculate the R2eff values for the TSMFK01 model.
See the module docstring for details.
 Parameters:
r20a (float)  The R20 parameter value of state A (R2 with no exchange).
dw (float)  The chemical exchange difference between states A and B in rad/s.
k_AB (float)  The k_AB parameter value (the forward exchange rate in rad/s).
tcp (numpy rank1 float array.)  The tau_CPMG times (1 / 4.nu1).
back_calc (numpy rank1 float array)  The array for holding the back calculated R2eff values. Each
element corresponds to one of the CPMG nu1 frequencies.
num_points (int)  The number of points on the dispersion curve, equal to the length
of the cpmg_frqs and back_calc arguments.
