{
"cells": [
{
"cell_type": "markdown",
"id": "b4058066",
"metadata": {},
"source": [
"# Quadrupolar phenomena"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
""
]
},
{
"cell_type": "markdown",
"id": "a895635c",
"metadata": {},
"source": [
"SLEEPY can be used to simulate quadrupolar nuclei, both in the rotating and lab frames. We start with an example on deuterium in exchange.\n",
"\n",
"Membrane properties are often characterized by measurement of residual dipole or quadrupole couplings. For example, the $^2$H quadrupole spliting (difference between maxima) in a membrane aliphatic chain is approximately 167 kHz when rigid, but symmetric rotation about the membrane normal already reduces that value by half. Additional motion reduces this value further, yielding order parameters (scaling factors) from 0.01-0.2 in pure POPC.\n",
"\n",
"In more complex membranes, it can be the case that lipids exchange environments, leading to complex lineshapes coming from both environments, with potential broadening depending on the rate of exchange. Here, we simulate a deuterium nucleus, with exchange of the quadrupole coupling."
]
},
{
"cell_type": "markdown",
"id": "296a92d7",
"metadata": {},
"source": [
"## Setup"
]
}
,
{
"cell_type": "code",
"execution_count": 0,
"metadata": {"tags": [
"remove-cell"
]},
"outputs": [],
"source": [
"# SETUP SLEEPY\n",
"import sys\n",
"if 'google.colab' in sys.modules:\n",
" !pip install sleepy-nmr"
]
},
{
"cell_type": "code",
"execution_count": 2,
"id": "84d1cf3c",
"metadata": {},
"outputs": [],
"source": [
"import SLEEPY as sl\n",
"import numpy as np\n",
"import matplotlib.pyplot as plt"
]
},
{
"cell_type": "markdown",
"id": "69c2b445",
"metadata": {},
"source": [
"## Build the system\n",
"We start with a reference peak-to-peak width (`DelPP`) of 167 kHz, and scale it with order parameters of 0.15 and 0.3."
]
},
{
"cell_type": "code",
"execution_count": 3,
"id": "a1284e00",
"metadata": {},
"outputs": [],
"source": [
"ex0=sl.ExpSys(v0H=600,Nucs='2H',vr=0,pwdavg='bcr400')\n",
"ex0.set_inter('quadrupole',i=0,DelPP=167e3*.15)\n",
"ex1=ex0.copy()\n",
"ex1.set_inter('quadrupole',i=0,DelPP=167e3*.3)\n",
"\n",
"L=sl.Liouvillian(ex0,ex1,kex=sl.Tools.twoSite_kex(tc=5e-5,p1=.5))"
]
},
{
"cell_type": "markdown",
"id": "870e98be",
"metadata": {},
"source": [
"## Propagate the system, plot"
]
},
{
"cell_type": "code",
"execution_count": 4,
"id": "d8b9ef80",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"State-space reduction: 18->4\n"
]
},
{
"data": {
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\n",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"seq=L.Sequence(Dt=5e-6)\n",
"rho=sl.Rho('2Hx','2Hp')\n",
"\n",
"rho.DetProp(seq,n=4096)\n",
"rho.apod_pars['WDW']='em'\n",
"rho.apod_pars['LB']=100\n",
"_=rho.plot(FT=True,apodize=True)"
]
},
{
"cell_type": "markdown",
"id": "b04bbe4d",
"metadata": {},
"source": [
"Note the behavior at the central frequency comes from couplings oriented near the magic angle, where the change in the size of the quadrupole coupling has little influence on the resonance frequency, and so very little relaxation is induced at these orientations. \n",
"\n",
"If we change the exchange rate, we can obtain two well-separated lineshapes (slow exchange) or a single well-resolved lineshape (fast exchange)."
]
},
{
"cell_type": "code",
"execution_count": 5,
"id": "a3a04795",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"State-space reduction: 18->4\n",
"State-space reduction: 18->4\n"
]
},
{
"data": {
"image/png": 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\n",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"#seq=L.Sequence(Dt=5e-6)\n",
"\n",
"fig,ax=plt.subplots(1,2,figsize=[8,4])\n",
"\n",
"L.kex=sl.Tools.twoSite_kex(tc=1e-7)\n",
"\n",
"rho=sl.Rho('2Hx','2Hp')\n",
"\n",
"rho.DetProp(seq,n=4096)\n",
"rho.apod_pars['WDW']='em'\n",
"rho.apod_pars['LB']=500\n",
"rho.plot(FT=True,apodize=True,ax=ax[0])\n",
"\n",
"L.kex=sl.Tools.twoSite_kex(tc=1e-1)\n",
"\n",
"rho=sl.Rho('2Hx','2Hp')\n",
"\n",
"rho.DetProp(seq,n=4096)\n",
"rho.apod_pars['WDW']='em'\n",
"rho.apod_pars['LB']=500\n",
"_=rho.plot(FT=True,apodize=True,ax=ax[1])"
]
},
{
"cell_type": "markdown",
"id": "3e8e4942",
"metadata": {},
"source": [
"## Second order quadrupolar broadening in the lab frame\n",
"Half-integer spins produce a narrow peak in the middle of the quadrupolar spectrum. However, this peak is broadened by the second-order quadrupole coupling. Simulating this broadening presents a challenge, because it is a rank-4 tensor, making its transformation under rotation different than the rank-2 tensors that most simulation packages are setup to handle. However, if the quadrupolar interaction is simulated in the lab frame, the second order quadrupole coupling arises naturally. We demonstrate here, with one simulation in the rotating frame, and one in the lab frame."
]
},
{
"cell_type": "code",
"execution_count": 6,
"id": "2c191b64",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"State-space reduction: 36->5\n",
"Prop: 32 steps per every 1 rotor period\n",
"Prop: 32 steps per every 1 rotor period\n"
]
}
],
"source": [
"exRF=sl.ExpSys(250,Nucs='17O',vr=60000,pwdavg=sl.PowderAvg('bcr100',gamma_encoded=True))\n",
"exRF.set_inter('quadrupole',i=0,delta=150000)\n",
"seqRF=exRF.Liouvillian().Sequence()\n",
"rhoRF=sl.Rho('17Ox','17Op')\n",
"rhoRF.DetProp(seqRF,n=16000,n_per_seq=32)\n",
"\n",
"exLF=sl.ExpSys(250,Nucs='17O',vr=60000,LF=True,pwdavg=sl.PowderAvg('bcr100',gamma_encoded=True))\n",
"exLF.set_inter('quadrupole',i=0,delta=150000)\n",
"seqLF=exLF.Liouvillian().Sequence()\n",
"rhoLF=sl.Rho('17Ox','17Op')\n",
"_=rhoLF.DetProp(seqLF,n=16000,n_per_seq=32)"
]
},
{
"cell_type": "markdown",
"id": "3bf8d7dd",
"metadata": {},
"source": [
"Note that if we observe transverse magnetization when it is in the lab frame, it will oscillate near the Larmor frequency of the spin. The center frequency of the spectrum will then be incorrect. This may be corrected by downmixing the signal before plotting (`rho.downmix()`)."
]
},
{
"cell_type": "code",
"execution_count": 7,
"id": "359ed626",
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"fig,ax=plt.subplots(1,2,figsize=[8,4])\n",
"rhoRF.plot(FT=True,apodize=True,axis='kHz',ax=ax[0])\n",
"rhoRF.plot(FT=True,apodize=True,axis='kHz',ax=ax[1])\n",
"rhoLF.downmix()\n",
"rhoLF.plot(FT=True,apodize=True,axis='kHz',ax=ax[0])\n",
"rhoLF.plot(FT=True,apodize=True,axis='kHz',ax=ax[1])\n",
"ax[1].set_xlim([12,-12])\n",
"ax[1].set_ylim([-50,200])\n",
"fig.tight_layout()"
]
},
{
"cell_type": "markdown",
"id": "107f08a9",
"metadata": {},
"source": [
"A benefit of high-field magnets is that they narrow the second-order quadrupole broadening. We demonstrate that here, by comparing the spectrum from 250 MHz to that using a 1.2 GHz magnet."
]
},
{
"cell_type": "code",
"execution_count": 8,
"id": "a22bdd4a",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Prop: 32 steps per every 1 rotor period\n"
]
}
],
"source": [
"exHF=sl.ExpSys(1200,Nucs='17O',vr=60000,LF=True,pwdavg=sl.PowderAvg('bcr100',gamma_encoded=True))\n",
"exHF.set_inter('quadrupole',i=0,delta=150000)\n",
"seqHF=exHF.Liouvillian().Sequence()\n",
"rhoHF=sl.Rho('17Ox','17Op')\n",
"rhoHF.DetProp(seqHF,n=16000,n_per_seq=32)\n",
"_=rhoHF.downmix()"
]
},
{
"cell_type": "code",
"execution_count": 9,
"id": "8bc4b0a6",
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"ax=rhoHF.plot(FT=True,apodize=True,axis='kHz')\n",
"rhoLF.plot(FT=True,apodize=True,axis='kHz',ax=ax)\n",
"ax.legend(['1.2 GHz','250 MHz'])\n",
"_=ax.set_xlim([12,-12])"
]
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 3",
"language": "python",
"name": "python3"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 3
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.7.3"
}
},
"nbformat": 4,
"nbformat_minor": 5
}