Package lib :: Package dispersion :: Module tsmfk01
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Module tsmfk01

source code

The Tollinger et al (2001) 2-site very-slow exchange TSMFK01 model.

Description

Applicable in the limit of slow exchange, range of microsecond to second time scale, when |R2A-R2B| << 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:

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:

Functions [hide private]
 
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
Variables [hide private]
  __package__ = 'lib.dispersion'

Imports: fabs, min, sin, isfinite, sum, fix_invalid, masked_where


Function Details [hide private]

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 rank-1) - 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.