Relax disp.spin lock offset+field

Setting up relax_disp.spin_lock_offset and relax_disp.spin_lock_field

Refer to the manual for parameter explanation

This page is a little help to understand how to use the functions:

1. relax_disp.spin_lock_offset()
2. relax_disp.spin_lock_field()

spin lock offset

Manual on relax_disp.spin_lock_offset
The relax function relax_disp.spin_lock_offset() requires the values to be provided in ppm.

relax_disp.spin_lock_offset(spectrum_id=None, offset=None)

spin lock field

Manual on relax_disp.spin_lock_field
The relax function relax_disp.spin_lock_field() requires the values to be provided in Hz.

relax_disp.spin_lock_field(spectrum_id=None, field=None)

Literature comments

See Figure 1 and 10 in the reference:

• Palmer, 3rd, A. G. and Massi, F. (2006). Characterization of the dynamics of biomacromolecules using rotating-frame spin relaxation NMR spectroscopy. Chem. Rev., 106(5), 1700-1719. (DOI: 10.1021/cr0404287)

Try to reproduce Figure 1.

Figure produced with script found here.

Calculations in relax

spin lock offset

In the literature, the values are often stated as "offset", "carrier offset", "offset of the spin-lock pulse" with values given in Hz, and can have values from 0-500 to 10-20.000 Hz.
These values reflects offset frequencies to the carrier frequency, and in relax is noted as "Spin-lock offset, the frequency of of the rf field" : ω_rf.

Relax needs input for ω_rf in ppm, and during calculations converts to the rad/s, with the following function call.

offsets[ei][si][mi][oi] = frequency_to_rad_per_s(frq=cdp.spin_lock_offset[id], B0=frq, isotope=spin.isotope)

If you need to convert to ppm from Hz values, consider during this in your relax script.
If for example you have recorded at a 800 MHz spectrometer, you could find the Carrier position for ¹⁵N (Value of yCar in NMRPipe scripts). If yCAR = 118.078 ppm, then

from lib.nmr import frequency_to_Hz, frequency_to_ppm

# Spectrometer frequency
sfrq = 799.7773991 # MHz
# Carrier position
yCAR = 118.078 # ppm 

# We take the absolute value, since the gyromagnetic ratio of N15 is negative.
yCAR_Hz = abs(frequency_to_Hz(frq=yCAR, B0=sfrq*1E6, isotope='15N'))
# We add the offset (deltadof2 in varian pulse sequences) in Hz, and from 0 to 10.000
yCar_offset_Hz = yCAR_Hz + float(deltadof2)
# The convert back from Hz to ppm. Again absolute value, because of the gyromagnetic ratio of N15 is negative.
yCar_offset_ppm = abs(frequency_to_ppm(frq=yCar_offset_Hz, B0=sfrq*1E6, isotope='15N'))

relax_disp.spin_lock_offset(spectrum_id=sp_id, offset=yCar_offset_ppm)

Offset in the literature

The offset is in the literature noted as Ω_S, where Ω_S is the (Ex. ¹⁵N) resonance offset from the spin-lock carrier.

Note that Ω_S is dependent of the chemical shifts δ in ppm for the nuclei of interest.

The Chemical Shifts δ in ppm for nuclei of interest (ex. ¹⁵N and which have been loaded in with relax function chemical_shift_read from a peak list formatted file) is first converted to to the rad/s with the following function calls.

[math] \bar{\omega}_{S,i} = 2\pi \cdot \delta_{S,i} \cdot B_0 \cdot \frac{\gamma_{^{15}N}}{\gamma_{^{1}H}} [/math]

shifts[ei][si][mi] = frequency_to_rad_per_s(frq=shift, B0=frq, isotope=spin.isotope)

Then Ω_S is calculated with: Ω_S,i = Ω_S,i - ω_rf, where Ω is the population averaged Larmor frequency of the spin and comes from the conversion of the Chemical Shifts δ_S,i to frequency Ω_S,i.

Delta_omega = shifts[ei][si][mi] - offsets[ei][si][mi][oi]

spin lock field

The spin lock field strength is noted ν₁, and relax requires these to be provided in unit of rad/s.

The spin lock field strength is converted to rad/s, with the following function call.

[math] \omega_{S,1} = 2\pi \cdot \nu_{S,1} [/math]

omega1 = point * 2.0 * pi

Then the Rotating frame tilt angle θ is calculated.

[math] \theta = \tan^{-1} \left( \frac{\omega_1}{\bar{\Omega}_{S,i}} \right) [/math]

if Delta_omega == 0.0:
    theta[ei][si][mi][oi].append(pi / 2.0)
# Calculate the theta angle describing the tilted rotating frame relative to the laboratory.
# If Delta_omega is negative, there follow the symmetry of atan, that atan(-x) = - atan(x).
# Then it should be: theta = pi + atan(-x) = pi - atan(x) = pi - abs(atan( +/- x))
elif omega1 / Delta_omega > 0 :
    theta[ei][si][mi][oi].append(atan(omega1 / Delta_omega))
else:
    theta[ei][si][mi][oi].append(pi + atan(omega1 / Delta_omega))

Code reference calculations in relax

The code which is called resides in:

lib/nmr.py

frequency_to_rad_per_s(frq=None, B0=None, isotope=None):

"""Convert the given frequency from ppm to rad/s units."""
return frq * 2.0 * pi * B0 / g1H * return_gyromagnetic_ratio(isotope) * 1e-6

specific_analyses/relax_disp/disp_data.py

return_offset_data(spins=None, spin_ids=None, field_count=None, fields=None):

Data structures

"""
The data structures consist of many different index types.  These are:

- Ei:  The index for each experiment type.
- Si:  The index for each spin of the spin cluster.
- Mi:  The index for each magnetic field strength.
- Oi:  The index for each spin-lock offset.
- Di:  The index for each dispersion point, the spin-lock field strength.
"""

Spectrometer notes

Varian / VnmrJ

In some pulse sequences, the following is seen:

'trim' is a basic timeunit and the total spinlock time is calculated as 2.0*ncyc*trim
b1 = getval("b1"),                      /* spin-lock field, Hz! */  
deltadof2 = getval("deltadof2"),        /* offset for N15 spinlock */