Module dpl94

The Davis, Perlman and London (1994) 2-site fast exchange R1rho DPL94 model.

Description

This module is for the function, gradient and Hessian of the DPL94 model.

References

The model is named after the reference:

• Davis, D. G., Perlman, M. E. and London, R. E. (1994). Direct measurements of the dissociation-rate constant for inhibitor-enzyme complexes via the T1rho and T2 (CPMG) methods. J. Magn. Reson., Series B, 104, 266-275. (DOI: 10.1006/jmrb.1994.1084)

Equations

The equation used is:

                                                                     phi_ex * kex
   R1rho = R1.cos^2(theta) + R1rho'.sin^2(theta) + sin^2(theta) * ------------------ ,
                                                                  kex^2 + omega_sl^2

where theta is the rotating frame tilt angle, and:

   phi_ex = pA * pB * delta_omega^2 ,

kex is the chemical exchange rate constant, pA and pB are the populations of states A and B, delta_omega is the chemical shift difference between the two states, and omega_sl is the spin-lock field strength.

Links

More information on the DPL94 model can be found in the:

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

Functions

r1rho_DPL94(r1rho_prime=None, phi_ex=None, kex=None, theta=None, R1=0.0, spin_lock_fields2=None, back_calc=None)
Calculate the R1rho values for the DPL94 model.

Variables

__package__ = 'lib.dispersion'

Imports: any, cos, isfinite, min, sin, sum, fix_invalid, masked_where

Function Details

r1rho_DPL94(r1rho_prime=None, phi_ex=None, kex=None, theta=None, R1=0.0, spin_lock_fields2=None, back_calc=None)

Calculate the R1rho values for the DPL94 model.

See the module docstring for details.

Parameters:

• r1rho_prime (numpy float array of rank [NE][NS][NM][NO][ND]) - The R1rho_prime parameter value (R1rho with no exchange).
• phi_ex (numpy float array of rank [NE][NS][NM][NO][ND]) - The phi_ex parameter value (pA * pB * delta_omega^2).
• kex (float) - The kex parameter value (the exchange rate in rad/s).
• theta (numpy float array of rank [NE][NS][NM][NO][ND]) - The rotating frame tilt angles for each dispersion point.
• R1 (numpy float array of rank [NE][NS][NM][NO][ND]) - The R1 relaxation rate.
• spin_lock_fields2 (numpy float array of rank [NE][NS][NM][NO][ND]) - The R1rho spin-lock field strengths squared (in rad^2.s^-2).
• back_calc (numpy float array of rank [NE][NS][NM][NO][ND]) - The array for holding the back calculated R1rho values. Each element corresponds to the combination of theta and spin lock field.