Module tsmfk01

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:

• Tollinger, M., Skrynnikov, N. R., Mulder, F. A. A., Forman-Kay, 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:

• relax wiki,
• relax manual,
• relaxation dispersion page of the relax website.

Functions

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.

Variables

__package__ = 'lib.dispersion'

Imports: array, min, sin, isfinite, sum

Function Details

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.

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 rank-1 float array.) - The tau_CPMG times (1 / 4.nu1).
• back_calc (numpy rank-1 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.