¹³C 2D MAT NMR of L-Histidine

The following is an illustration for fitting 2D MAT/PASS datasets. The example dataset is a \(^{13}\text{C}\) 2D MAT spectrum of L-Histidine from Walder et al. [1]

import numpy as np
import csdmpy as cp
import matplotlib.pyplot as plt
from lmfit import Minimizer

from mrsimulator import Simulator
from mrsimulator.method.lib import SSB2D
from mrsimulator import signal_processor as sp
from mrsimulator.utils import spectral_fitting as sf
from mrsimulator.utils import get_spectral_dimensions
from mrsimulator.utils.collection import single_site_system_generator

Import the dataset

host = "https://ssnmr.org/sites/default/files/mrsimulator/"
filename = "1H13C_CPPASS_LHistidine.csdf"
mat_dataset = cp.load(host + filename)

# For the spectral fitting, we only focus on the real part of the complex dataset.
mat_dataset = mat_dataset.real

# Convert the coordinates along each dimension from Hz to ppm.
_ = [item.to("ppm", "nmr_frequency_ratio") for item in mat_dataset.dimensions]

When using the SSB2D method, ensure the horizontal dimension of the dataset is the isotropic dimension. Here, we apply an appropriate transpose operation to the dataset.

mat_dataset = mat_dataset.T  # transpose

# plot of the dataset.
max_amp = mat_dataset.max()
levels = (np.arange(24) + 1) * max_amp / 25  # contours are drawn at these levels.
options = dict(levels=levels, alpha=0.75, linewidths=0.5)  # plot options

plt.figure(figsize=(8, 3.5))
ax = plt.subplot(projection="csdm")
ax.contour(mat_dataset, colors="k", **options)
ax.set_xlim(180, 15)
plt.grid()
plt.tight_layout()
plt.show()
plot 1 LHistidine PASS

Estimate noise statistics from the dataset

coords = mat_dataset.dimensions[0].coordinates
# noise_region = np.where(np.logical_and(coords > 65e-6, coords < 110e-6))
noise_region = np.where(np.logical_and(coords < 110e-6, coords > 65e-6))
noise_data = mat_dataset[noise_region]

plt.figure(figsize=(3.75, 2.5))
ax = plt.subplot(projection="csdm")
ax.imshow(noise_data, aspect="auto", interpolation="none")
plt.title("Noise section")
plt.axis("off")
plt.tight_layout()
plt.show()

noise_mean, sigma = noise_data.mean(), noise_data.std()
noise_mean, sigma
Noise section
(<Quantity -0.00846708>, <Quantity 0.5979741>)

Create a fitting model

Guess model

Create a guess list of spin systems.

shifts = [120, 128, 135, 175, 55, 25]  # in ppm
zeta = [-70, -65, -60, -60, -10, -10]  # in ppm
eta = [0.8, 0.4, 0.9, 0.3, 0.05, 0.05]

spin_systems = single_site_system_generator(
    isotope="13C",
    isotropic_chemical_shift=shifts,
    shielding_symmetric={"zeta": zeta, "eta": eta},
    abundance=100 / 6,
)

Method

Create the SSB2D method.

# Get the spectral dimension parameters from the experiment.
spectral_dims = get_spectral_dimensions(mat_dataset)

PASS = SSB2D(
    channels=["13C"],
    magnetic_flux_density=9.395,  # in T
    rotor_frequency=1500,  # in Hz
    spectral_dimensions=spectral_dims,
    experiment=mat_dataset,  # add the measurement to the method.
)

Guess Spectrum

# Simulation
# ----------
sim = Simulator(spin_systems=spin_systems, methods=[PASS])
sim.run()

# Post Simulation Processing
# --------------------------
processor = sp.SignalProcessor(
    operations=[
        # Lorentzian convolution along the isotropic dimensions.
        sp.FFT(dim_index=0),
        sp.apodization.Exponential(FWHM="50 Hz"),
        sp.IFFT(dim_index=0),
        sp.Scale(factor=212260),
    ]
)
processed_dataset = processor.apply_operations(dataset=sim.methods[0].simulation).real

# Plot of the guess Spectrum
# --------------------------
plt.figure(figsize=(8, 3.5))
ax = plt.subplot(projection="csdm")
ax.contour(mat_dataset, colors="k", **options)
ax.contour(processed_dataset, colors="r", linestyles="--", **options)
ax.set_xlim(180, 15)
plt.grid()
plt.tight_layout()
plt.show()
plot 1 LHistidine PASS

Least-squares minimization with LMFIT

Use the make_LMFIT_params() for a quick setup of the fitting parameters.

params = sf.make_LMFIT_params(sim, processor)
print(params.pretty_print(columns=["value", "min", "max", "vary", "expr"]))
Name                                      Value      Min      Max     Vary     Expr
SP_0_operation_1_Exponential_FWHM            50     -inf      inf     True     None
SP_0_operation_3_Scale_factor          2.123e+05     -inf      inf     True     None
sys_0_abundance                           16.67        0      100     True     None
sys_0_site_0_isotropic_chemical_shift       120     -inf      inf     True     None
sys_0_site_0_shielding_symmetric_eta        0.8        0        1     True     None
sys_0_site_0_shielding_symmetric_zeta       -70     -inf      inf     True     None
sys_1_abundance                           16.67        0      100     True     None
sys_1_site_0_isotropic_chemical_shift       128     -inf      inf     True     None
sys_1_site_0_shielding_symmetric_eta        0.4        0        1     True     None
sys_1_site_0_shielding_symmetric_zeta       -65     -inf      inf     True     None
sys_2_abundance                           16.67        0      100     True     None
sys_2_site_0_isotropic_chemical_shift       135     -inf      inf     True     None
sys_2_site_0_shielding_symmetric_eta        0.9        0        1     True     None
sys_2_site_0_shielding_symmetric_zeta       -60     -inf      inf     True     None
sys_3_abundance                           16.67        0      100     True     None
sys_3_site_0_isotropic_chemical_shift       175     -inf      inf     True     None
sys_3_site_0_shielding_symmetric_eta        0.3        0        1     True     None
sys_3_site_0_shielding_symmetric_zeta       -60     -inf      inf     True     None
sys_4_abundance                           16.67        0      100     True     None
sys_4_site_0_isotropic_chemical_shift        55     -inf      inf     True     None
sys_4_site_0_shielding_symmetric_eta       0.05        0        1     True     None
sys_4_site_0_shielding_symmetric_zeta       -10     -inf      inf     True     None
sys_5_abundance                           16.67        0      100    False 100-sys_0_abundance-sys_1_abundance-sys_2_abundance-sys_3_abundance-sys_4_abundance
sys_5_site_0_isotropic_chemical_shift        25     -inf      inf     True     None
sys_5_site_0_shielding_symmetric_eta       0.05        0        1     True     None
sys_5_site_0_shielding_symmetric_zeta       -10     -inf      inf     True     None
None

Solve the minimizer using LMFIT

opt = sim.optimize()  # Pre-compute transition pathways
minner = Minimizer(
    sf.LMFIT_min_function,
    params,
    fcn_args=(sim, processor, sigma),
    fcn_kws={"opt": opt},
)
result = minner.minimize()
result

Fit Result



The best fit solution

best_fit = sf.bestfit(sim, processor)[0].real

# Plot of the best fit solution
plt.figure(figsize=(8, 3.5))
ax = plt.subplot(projection="csdm")
ax.contour(mat_dataset, colors="k", **options)
ax.contour(best_fit, colors="r", linestyles="--", **options)
ax.set_xlim(180, 15)
plt.grid()
plt.tight_layout()
plt.show()
plot 1 LHistidine PASS

Total running time of the script: (0 minutes 32.158 seconds)

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