Module it99

The Ishima and Torchia (1999) 2-site all time scale exchange (with pA >> pB) IT99 model.

Description

This module is for the function, gradient and Hessian of the IT99 model.

References

The model is named after the reference:

• Ishima R. and Torchia D.A. (1999). Estimating the time scale of chemical exchange of proteins from measurements of transverse relaxation rates in solution. J. Biomol. NMR, 14, 369-372. (DOI: 10.1023/A:1008324025406).

Equations

The equation used is:

             phi_ex * tex
   Rex ~= ------------------- ,
          1 + omega_a^2*tex^2

   phi_ex = pA * pB * delta_omega^2 ,

   omega_a^2 = sqrt(omega_1eff^4 + pA^2*delta_omega^4) ,

   R2eff = R20 + Rex ,

where tex = 1/(2kex), 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. The effective rotating frame field for a CPMG-type experiment is given by:

   omega_1eff = 4*sqrt(3) * nu_cpmg

and therefore:

   omega_1eff^4 = 2304 * nu_cpmg^4

Links

More information on the IT99 model can be found in the:

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

Functions

r2eff_IT99(r20=None, pA=None, dw=None, dw_orig=None, tex=None, cpmg_frqs=None, back_calc=None)
Calculate the R2eff values for the IT99 model.

Variables

__package__ = 'lib.dispersion'

Imports: isfinite, fabs, sqrt, sum, fix_invalid, masked_where

Function Details

r2eff_IT99(r20=None, pA=None, dw=None, dw_orig=None, tex=None, cpmg_frqs=None, back_calc=None)

Calculate the R2eff values for the IT99 model.

See the module docstring for details.

Parameters:

• r20 (numpy float array of rank [NE][NS][NM][NO][ND]) - The R20 parameter value (R2 with no exchange).
• pA (float) - The population of state A.
• 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.
• tex (float) - The tex parameter value (the time of exchange in s/rad).
• cpmg_frqs (numpy float array of rank [NE][NS][NM][NO][ND]) - The CPMG nu1 frequencies.
• 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.