FUN_HETRELAX_MODELS module
- t1t2ne.scripts.fun_hetrelax_models.J(J_func, w, f_args)[source]
General function to calculate the spectral density J using a given J_func. Supports: - Isotropic Lipari-Szabo: J_func =
LS_iso(), f_args = (S2s, taus) - Anisotropic Lipari-Szabo: J_func =LS_aniso(), f_args = (S2s, taus, D_comp, r_pdb) - Freed outer sphere: J_func =J_Freed(), f_args = (d, D_target, D_cosolute, tau_1, tau_2)
- t1t2ne.scripts.fun_hetrelax_models.J_Freed(w, d, D_target, D_cosolute, tau_1=1e-09, tau_2=None)[source]
Freed spectral density function for outer sphere relaxation. Equations 6.42, 6.48 and 6.50 in Bertini et al. 2016.
\[\tau_D = \frac{d^2}{D_{target} + D_{cosolute}} z = \sqrt{2 |\omega| \tau_D + \frac{\tau_D}{\tau_1}} J(\omega) = \frac{2}{5} \frac{1 + \frac{5 z}{8} + \frac{z^2}{8}}{1 + z + \frac{z^2}{2} + \frac{z^3}{6} + \frac{4 z^4}{81} + \frac{z^5}{81} + \frac{z^6}{648}}\]- Parameters:
w (float) – Larmor frequency in rad/s
d (float) – distance of closest approach of the paramagnetic center and the nucleus in meters
D_target (float) – diffusion coefficient of the target molecule in m^2/s
D_cosolute (float) – diffusion coefficient of the cosolute in m^2/s
tau_1 (float) – longitudinal correlation time of the electron in seconds
tau_2 (float or None) – transverse correlation time of the electron in seconds (default None, will be set to tau_1 if not provided)
- Returns:
J – spectral density
- Return type:
float
- t1t2ne.scripts.fun_hetrelax_models.J_omega_tau_aniso(w, D_comp, r_pdb)[source]
Function to calculate the anisotropic spectral density J, given the tensor D and the orientation r
- t1t2ne.scripts.fun_hetrelax_models.J_omega_tau_iso(w, tau)[source]
Function to calculate the spectral density J for isotropic tumbling, given the Larmor frequency w and the correlation time \(\tau\)
- t1t2ne.scripts.fun_hetrelax_models.LS_aniso(w, S2s, taus, D_comp, r_pdb)[source]
Anisotropic reorientation extended model-free Lipari-Szabo density function, given the Larmor frequency w, the order parameters S2s, the correlation times taus, the diffusion tensor components D_comp and the orientation r_pdb. S2s should be as long as taus, as the first term corresponds to the anisotropic contribution and the rest to the isotropic contributions. The function calculates the weights for each term based on the S2s and then sums up the contributions from each term using the J_omega_tau_aniso and J_omega_tau_iso functions.
- t1t2ne.scripts.fun_hetrelax_models.LS_iso(w, S2s, taus)[source]
Isotropic reorientation extended model-free Lipari-Szabo density function, given the Larmor frequency w, the order parameters S2s and the correlation times taus. S2s should be one less than taus, as the last term corresponds to the global tumbling. The function calculates the weights for each term based on the S2s and then sums up the contributions from each term using the J_omega_tau_iso function.
- t1t2ne.scripts.fun_hetrelax_models.R1R2nOe(B, r=1.02e-10, nuc1='1H', nuc2='15N', Deltasigma=-160, func=<function LS_iso>, f_args=([0.9], [1e-09, 1e-11]), Rex=0)[source]
H-X relaxation rates R1, R2 and NOE enhancement factor eta, given the magnetic field strength B, the distance r between the nuclei, the types of nuclei nuc1 and nuc2, the CSA value Deltasigma, the function to calculate the spectral density func and its arguments f_args, and an optional Rex contribution to R2. The function calculates the dipole-dipole coupling constant d and the CSA constant c, then uses them to calculate R1, R2 and eta based on the formulas reported by Fushman:
\[R_1 = d^2 (J(\omega_H - \omega_X) + 6 J(\omega_H + \omega_X)) + 3 (c^2 B^2 + d^2) J(\omega_X)\]\[R_2 = R_{ex} + \frac{1}{2} d^2 (J(\omega_H - \omega_X) + 6 J(\omega_H + \omega_X) + 6 J(\omega_H)) + \frac{1}{2} (c^2 B^2 + d^2) (4 J(0) + 3 J(\omega_X))\]\[\eta = 1 - \frac{d^2 \gamma_1}{\gamma_2} \frac{6 J(\omega_H + \omega_X) - J(\omega_H - \omega_X)}{R_1}\]
- t1t2ne.scripts.fun_hetrelax_models.c(Deltasigma=-160, nuc='15N')[source]
function to calculate the CSA constant c
\[c = -\frac{\Delta \sigma \gamma}{3}\]
- t1t2ne.scripts.fun_hetrelax_models.d(r=1.02e-10, nuc1='1H', nuc2='15N')[source]
Function to calculate dipole-dipole coupling constant d
\[d = \frac{\mu_0 h \gamma_1 \gamma_2}{16 \pi^2 r^3}\]
- t1t2ne.scripts.fun_hetrelax_models.eta_z_eta_xy(B, r=1.02e-10, nuc1='1H', nuc2='15N', Deltasigma=-160, theta=0.29670597283903605, func=<function LS_iso>, f_args=([0.9], [1e-09, 1e-11]))[source]
Compute cross-correlated relaxation rates eta_z and eta_xy for a given magnetic field strength B, distance r between the nuclei, types of nuclei nuc1 and nuc2, CSA value Deltasigma, angle theta between the NH bond and the magnetic field, function to calculate the spectral density func and its arguments f_args. The function calculates the dipole-dipole coupling constant d and the CSA constant c, then uses them to calculate eta_z and eta_xy based on the formulas reported by Salvi:
\[\eta_z = \frac{1}{15} P_2(\cos\theta) d c B 6 J(\omega_X)\]\[\eta_{xy} = \frac{1}{15} P_2(\cos\theta) d c B (4 J(0) + 3 J(\omega_X))\]