{
"cells": [
{
"cell_type": "markdown",
"id": "e0687262",
"metadata": {},
"source": [
"# Chemical Exchange Saturation Transfer (CEST)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"
"
]
},
{
"cell_type": "markdown",
"id": "f92703e1",
"metadata": {},
"source": [
"Sometimes, a system undergoes chemical exchange, but with one large population and one very small population, such that the peak of the latter is difficult or impossible to observe directly. However, if we apply a low-power saturating field to magnetization in the z-direction, it is possible to saturate the magnetization when the applied field is on-resonant with the invisible peak. This is referred to as the Chemical Exchange Saturation Transfer experiment (CEST).$^1$ This allows us to observed \"invisible\" resonances in exchange with the main resonance.\n",
"\n",
"[1] S. Forsén, R.A. Hoffman. [*J. Chem. Phys.*](https://doi.org/10.1063/1.1734121), **1963**, 39, 2892-2901."
]
},
{
"cell_type": "markdown",
"id": "dc8bdb8c",
"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": "0db1dd6e",
"metadata": {},
"outputs": [],
"source": [
"import SLEEPY as sl\n",
"import numpy as np\n",
"import matplotlib.pyplot as plt\n",
"sl.Defaults['verbose']=False"
]
},
{
"cell_type": "markdown",
"id": "d7926839",
"metadata": {},
"source": [
"## Build the spin system"
]
},
{
"cell_type": "code",
"execution_count": 3,
"id": "4b6b174b",
"metadata": {},
"outputs": [],
"source": [
"ex0=sl.ExpSys(v0H=600,Nucs='13C',T_K=298) #We need a description of the experiment for both states (ex0, ex1)\n",
"ex1=ex0.copy()\n",
"ex0.set_inter(Type='CS',i=0,ppm=-7)\n",
"_=ex1.set_inter(Type='CS',i=0,ppm=7)"
]
},
{
"cell_type": "markdown",
"id": "a534ea71",
"metadata": {},
"source": [
"## Build the Liouvillian\n",
"For CEST to work, we need to be able saturate the spins, which requires $T_2$ relaxation. For a more realistic behavior, we also include $T_1$ recovery of the magnetization, which can inhibit the saturation. Finally, we will allow the magnetization to recover towards its thermal equilibrium. These terms are all added via the `L.add_relax(...)` functionality of the Liouvillian."
]
},
{
"cell_type": "code",
"execution_count": 4,
"id": "28a95966",
"metadata": {},
"outputs": [],
"source": [
"L=sl.Liouvillian((ex0,ex1)) #Builds the two different Hamiltonians and exports them to Liouville space\n",
"\n",
"tc=1e-3 #Correlation time\n",
"p1=0.95 #Population of state 1\n",
"\n",
"L.kex=sl.Tools.twoSite_kex(tc=tc,p1=p1) #Add exchange to the Liouvillian\n",
"\n",
"L.add_relax(Type='T1',i=0,T1=1.5) #Add T1 relaxation to the system\n",
"L.add_relax(Type='T2',i=0,T2=.05) #Add T2 relaxation to the system\n",
"_=L.add_relax(Type='recovery') #This brings the spins back into thermal equilibrium"
]
},
{
"cell_type": "markdown",
"id": "f69ec89f",
"metadata": {},
"source": [
"## Calculate the required propagators\n",
"We'll simulate this system by starting with magnetization along the z-axis and saturating at some frequency, which will be swept. After the saturation period, we'll apply a $\\pi/2$-pulse along the y-axis to get x-magnetization. This will be allowed to evolve, and will then be Fourier transformed. We then integrate the main peak to determine the amount of saturation that has occured."
]
},
{
"cell_type": "markdown",
"id": "89873027",
"metadata": {},
"source": [
"## Run the sequence, with sweep over $\\nu_1$\n",
"\n",
"For each offset frequency, we start with a 25 Hz saturating field for 500 ms, followed by a $\\pi/2$ pulse (defined in the sequence `seq`). Then, we evolve (using the sequence `evol`) to get a spectrum (which we will later integrate the main peak)"
]
},
{
"cell_type": "code",
"execution_count": 5,
"id": "75c1f25e",
"metadata": {},
"outputs": [],
"source": [
"rho=sl.Rho(rho0='13Cz',detect='13Cp') #Initial density matrix\n",
"\n",
"# Make a sequence for saturation\n",
"seq=L.Sequence() #Saturation and pi/2 pulse\n",
"t=[0,0.5,0.5+2.5e-6] #Preparation sequence (500 ms saturation, 100 kHz pi-pulse)\n",
"\n",
"# Make a sequence for detection\n",
"Dt=1/(4*10*150) #Broad enough to capture 10 ppm\n",
"evol=L.Sequence(Dt=Dt) #Evolution sequence\n",
"\n",
"voff0=np.linspace(-20,20,500)*ex0.v0[0]/1e6 #5 ppm*150 MHz / 1e6 =750 Hz\n",
"spec=list()\n",
"for voff in voff0:\n",
" seq.add_channel('13C',t=t,v1=[25,100e3],\n",
" voff=[voff,0],phase=[0,np.pi/2])\n",
" rho.clear()\n",
" (seq*rho).DetProp(evol,n=1024)\n",
" spec.append(rho.FT[0].real)"
]
},
{
"cell_type": "markdown",
"id": "a8517a47",
"metadata": {},
"source": [
"## Plot one of the spectra\n",
"We first plot a spectrum, where we observe that the weaker peak is nearly invisible (it appears if we zoom in around 5 ppm, but would be quite difficult to see in a real spectrum).\n",
"\n",
"Note that later we integrate the spectrum by selecting a range of points in the spectrum. In this case, it may be useful to set `axis='points'` to more easily determine what range of points to sum over."
]
},
{
"cell_type": "code",
"execution_count": 6,
"id": "afc86042",
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"ax=rho.plot(FT=True,axis='ppm')\n",
"_=ax.set_yticklabels('')"
]
},
{
"cell_type": "markdown",
"id": "5315d50e",
"metadata": {},
"source": [
"## Integrate spectrum for all values of $\\nu_1$ and plot results\n",
"We integrate over the strong peak and plot the peak intensity"
]
},
{
"cell_type": "code",
"execution_count": 7,
"id": "5073de40",
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"spec=np.array(spec) #Convert the list of spectra to a numpy array\n",
"I=spec[:,400:620].sum(1) #Integrate over the main peak\n",
"\n",
"ax=plt.subplots()[1]\n",
"ax.plot(voff0*1e6/ex0.v0[0],I)\n",
"ax.set_xlabel(r'$\\nu_{off}$ / ppm')\n",
"ax.set_ylabel('I / a.u.')\n",
"ax.invert_xaxis()"
]
},
{
"cell_type": "markdown",
"id": "f3c92942",
"metadata": {},
"source": [
"## Investigate CEST as a function of exchange rate\n",
"We repeat the above setup, while varying the exchange rate"
]
},
{
"cell_type": "code",
"execution_count": 8,
"id": "a635c3eb",
"metadata": {},
"outputs": [],
"source": [
"p1=0.95 #Population of state 1\n",
"p2=1-p1 #Population of state 2\n",
"\n",
"rho=sl.Rho(rho0='13Cz',detect='13Cp')\n",
"\n",
"# Make a sequence for saturation\n",
"seq=L.Sequence() \n",
"t=[0,0.5,0.5+2.5e-6] #Preparation sequence (500 ms saturation, 100 kHz pi-pulse)\n",
"\n",
"# Make a sequence for detection\n",
"Dt=1/(4*10*150) #Broad enough to capture 10 ppm\n",
"evol=L.Sequence(Dt=Dt) #Evolution sequence\n",
"\n",
"tc0=np.logspace(0,-5.5,12)\n",
"I=list()\n",
"for tc in tc0:\n",
" L.kex=sl.Tools.twoSite_kex(tc=tc,p1=p1) #Add exchange to the Liouvillian\n",
" \n",
" voff0=np.linspace(-20,20,500)*ex0.v0[0]/1e6 #5 ppm*150 MHz / 1e6 =750 Hz\n",
" spec=list()\n",
" for voff in voff0:\n",
" seq.add_channel('13C',t=t,v1=[25,100e3],\n",
" voff=[voff,0],phase=[0,np.pi/2])\n",
" rho.clear()\n",
" (seq*rho).DetProp(evol,n=1024)\n",
" spec.append(rho.FT[0].real)\n",
"\n",
" spec=np.array(spec) #Convert to a numpy array\n",
" I.append(spec[:,400:620].sum(1)) #Integrate over the main peak"
]
},
{
"cell_type": "markdown",
"id": "fafe70cc",
"metadata": {},
"source": [
"We plot the results below, where we see that the saturation behavior depends strongly on the exchange rate. Note that if the exchange is too fast or too slow, the CEST experiment is no longer as effective, since it either becomes difficult to saturate the main peak via the minor peak, or because the two peaks coalesce."
]
},
{
"cell_type": "code",
"execution_count": 9,
"id": "d8e99520",
"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(3,4,figsize=[8,6])\n",
"ax=ax.reshape(ax.size)\n",
"\n",
"for a,I0,tc in zip(ax,I,tc0):\n",
" a.plot(voff0*1e6/ex0.v0[0],I0)\n",
" if a.is_last_row():\n",
" a.set_xlabel(r'$\\nu_{off}$ / ppm')\n",
" if a.is_first_col():\n",
" a.set_ylabel('I / a.u.')\n",
" a.invert_xaxis()\n",
" a.set_yticklabels('')\n",
" a.set_ylim([0,a.get_ylim()[1]])\n",
" a.text(20,a.get_ylim()[1]*.05,r'$\\tau_c$'+f' = \\n{tc:.1e} s')\n",
"fig.tight_layout()"
]
}
],
"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
}