{
"cells": [
{
"attachments": {},
"cell_type": "markdown",
"metadata": {},
"source": [
"# Calculating the RDF atom-to-atom\n",
"\n",
"We calculate the site-specific radial distribution functions of solvent around certain atoms.\n",
"\n",
"**Last updated:** December 2022 with MDAnalysis 2.4.0-dev0\n",
"\n",
"**Minimum version of MDAnalysis:** 0.19.0\n",
"\n",
"**Packages required:**\n",
" \n",
"* MDAnalysis (Michaud-Agrawal *et al.*, 2011, Gowers *et al.*, 2016)\n",
"* MDAnalysisTests\n",
"\n",
"**Optional packages for visualisation:**\n",
"\n",
"* [matplotlib](https://matplotlib.org)\n"
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {
"execution": {
"iopub.execute_input": "2021-05-19T05:58:29.353011Z",
"iopub.status.busy": "2021-05-19T05:58:29.352352Z",
"iopub.status.idle": "2021-05-19T05:58:30.289550Z",
"shell.execute_reply": "2021-05-19T05:58:30.290032Z"
}
},
"outputs": [],
"source": [
"import MDAnalysis as mda\n",
"from MDAnalysis.tests.datafiles import TPR, XTC\n",
"from MDAnalysis.analysis import rdf\n",
"import matplotlib.pyplot as plt\n",
"import numpy as np\n",
"%matplotlib inline"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Loading files"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The test files we will be working with here feature adenylate kinase (AdK), a phosophotransferase enzyme. (Beckstein *et al.*, 2009)"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {
"execution": {
"iopub.execute_input": "2021-05-19T05:58:30.294493Z",
"iopub.status.busy": "2021-05-19T05:58:30.293625Z",
"iopub.status.idle": "2021-05-19T05:58:31.229943Z",
"shell.execute_reply": "2021-05-19T05:58:31.229178Z"
}
},
"outputs": [],
"source": [
"u = mda.Universe(TPR, XTC)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Calculating the site-specific radial distribution function"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"A radial distribution function $g_{ab}(r)$ describes the time-averaged density of particles in $b$ from the reference group $a$ at distance $r$. It is normalised so that it becomes 1 for large separations in a homogenous system. See [the tutorial on averaged RDFs](average_rdf.ipynb) for more information. The `InterRDF_s` class ([API docs](https://docs.mdanalysis.org/stable/documentation_pages/analysis/rdf.html#MDAnalysis.analysis.rdf.InterRDF_s)) allows you to compute RDFs on an atom-to-atom basis, rather than simply giving the averaged RDF as in `InterRDF`.\n",
"\n",
"Below, I calculate the RDF between selected alpha-carbons and the water atoms within 15 angstroms of CA60, *in the first frame of the trajectory*. The water group does not update over the trajectory as the water moves towards and away from the alpha-carbon. \n",
"\n",
"The RDF is limited to a spherical shell around each atom by `range`. Note that the range is defined around *each atom*, rather than the center-of-mass of the entire group.\n",
"\n",
"If `density=True`, the final RDF is over the average density of the selected atoms in the trajectory box, making it comparable to the output of `rdf.InterRDF`. If `density=False`, the density is not taken into account. This can make it difficult to compare RDFs between AtomGroups that contain different numbers of atoms."
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {
"execution": {
"iopub.execute_input": "2021-05-19T05:58:31.235366Z",
"iopub.status.busy": "2021-05-19T05:58:31.234786Z",
"iopub.status.idle": "2021-05-19T05:58:31.854793Z",
"shell.execute_reply": "2021-05-19T05:58:31.855177Z"
}
},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"/home/pbarletta/mambaforge/envs/guide/lib/python3.9/site-packages/MDAnalysis/analysis/rdf.py:531: DeprecationWarning: The `u` attribute is superflous and will be removed in MDAnalysis 3.0.0.\n",
" warnings.warn(\"The `u` attribute is superflous and will be removed \"\n"
]
},
{
"data": {
"text/plain": [
""
]
},
"execution_count": 3,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"ca60 = u.select_atoms('resid 61 and name CA')\n",
"ca61 = u.select_atoms('resid 62 and name CA')\n",
"ca62 = u.select_atoms('resid 63 and name CA')\n",
"water = u.select_atoms('resname SOL and sphzone 15 group sel_a', sel_a=ca60)\n",
"\n",
"ags = [[ca60+ca61, water], [ca62, water]]\n",
"\n",
"ss_rdf = rdf.InterRDF_s(u, ags,\n",
" nbins=75, # default\n",
" range=(0.0, 15.0), # distance\n",
" norm='density',\n",
" )\n",
"ss_rdf.run()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Like `rdf.InterRDF`, the distance bins are available at `ss_rdf.bins`."
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {
"execution": {
"iopub.execute_input": "2021-05-19T05:58:31.859860Z",
"iopub.status.busy": "2021-05-19T05:58:31.859307Z",
"iopub.status.idle": "2021-05-19T05:58:31.861752Z",
"shell.execute_reply": "2021-05-19T05:58:31.862184Z"
}
},
"outputs": [
{
"data": {
"text/plain": [
"array([ 0.1, 0.3, 0.5, 0.7, 0.9, 1.1, 1.3, 1.5, 1.7, 1.9, 2.1,\n",
" 2.3, 2.5, 2.7, 2.9, 3.1, 3.3, 3.5, 3.7, 3.9, 4.1, 4.3,\n",
" 4.5, 4.7, 4.9, 5.1, 5.3, 5.5, 5.7, 5.9, 6.1, 6.3, 6.5,\n",
" 6.7, 6.9, 7.1, 7.3, 7.5, 7.7, 7.9, 8.1, 8.3, 8.5, 8.7,\n",
" 8.9, 9.1, 9.3, 9.5, 9.7, 9.9, 10.1, 10.3, 10.5, 10.7, 10.9,\n",
" 11.1, 11.3, 11.5, 11.7, 11.9, 12.1, 12.3, 12.5, 12.7, 12.9, 13.1,\n",
" 13.3, 13.5, 13.7, 13.9, 14.1, 14.3, 14.5, 14.7, 14.9])"
]
},
"execution_count": 4,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"ss_rdf.results.bins"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"`ss_rdf.rdf` contains the atom-pairwise RDF for each of your pairs of AtomGroups. It is a list with the same length as your list of pairs `ags`. A result array has the shape `(len(ag1), len(ag2), nbins)` for the AtomGroup pair `(ag1, ag2)`. "
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {
"execution": {
"iopub.execute_input": "2021-05-19T05:58:31.867176Z",
"iopub.status.busy": "2021-05-19T05:58:31.866041Z",
"iopub.status.idle": "2021-05-19T05:58:31.868917Z",
"shell.execute_reply": "2021-05-19T05:58:31.868467Z"
},
"scrolled": true
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"There are 1041 water atoms\n",
"The first result array has shape: (2, 1041, 75)\n",
"The second result array has shape: (1, 1041, 75)\n"
]
}
],
"source": [
"print('There are {} water atoms'.format(len(water)))\n",
"print('The first result array has shape: {}'.format(ss_rdf.results.rdf[0].shape))\n",
"print('The second result array has shape: {}'.format(ss_rdf.results.rdf[1].shape))"
]
},
{
"attachments": {},
"cell_type": "markdown",
"metadata": {},
"source": [
"Index the results array to get the RDF for a particular pair of atoms. `ss_rdf.rdf[i][j][k]` will return the RDF between atoms $j$ and $k$ in the $i$-th pair of atom groups. For example, below we get the RDF between the alpha-carbon in residue 61 (i.e. the second atom of the first atom group) and the 571st atom of water."
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {
"execution": {
"iopub.execute_input": "2021-05-19T05:58:31.872815Z",
"iopub.status.busy": "2021-05-19T05:58:31.872315Z",
"iopub.status.idle": "2021-05-19T05:58:31.874585Z",
"shell.execute_reply": "2021-05-19T05:58:31.874939Z"
},
"scrolled": true
},
"outputs": [
{
"data": {
"text/plain": [
"array([0. , 0. , 0. , 0. , 0. ,\n",
" 0. , 0. , 0. , 0. , 0. ,\n",
" 0. , 0. , 0. , 0. , 0. ,\n",
" 0. , 0. , 0. , 0. , 0. ,\n",
" 0.0023665 , 0. , 0. , 0. , 0. ,\n",
" 0. , 0. , 0. , 0. , 0.00114292,\n",
" 0.00106921, 0. , 0.00094167, 0. , 0. ,\n",
" 0. , 0.0007466 , 0. , 0. , 0. ,\n",
" 0. , 0. , 0.00055068, 0. , 0. ,\n",
" 0. , 0. , 0. , 0. , 0. ,\n",
" 0. , 0. , 0. , 0. , 0. ,\n",
" 0. , 0.0003116 , 0. , 0. , 0. ,\n",
" 0. , 0. , 0.00025464, 0.00024669, 0. ,\n",
" 0. , 0. , 0. , 0. , 0. ,\n",
" 0. , 0. , 0. , 0. , 0. ])"
]
},
"execution_count": 6,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"ca61_h2o_571 = ss_rdf.results.rdf[0][1][570]\n",
"ca61_h2o_571"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {
"execution": {
"iopub.execute_input": "2021-05-19T05:58:31.889621Z",
"iopub.status.busy": "2021-05-19T05:58:31.888908Z",
"iopub.status.idle": "2021-05-19T05:58:31.994719Z",
"shell.execute_reply": "2021-05-19T05:58:31.995133Z"
}
},
"outputs": [
{
"data": {
"text/plain": [
"Text(0.5, 1.0, 'RDF between CA61 and MW6365')"
]
},
"execution_count": 7,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
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",
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