{
"cells": [
{
"attachments": {},
"cell_type": "markdown",
"metadata": {},
"source": [
"# Atom-wise distances between matching AtomGroups\n",
"\n",
"Here we compare the distances between alpha-carbons of the enzyme adenylate kinase in its open and closed conformations. ``distances.dist`` can be used to calculate distances between atom groups with the *same number of atoms* within them.\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)"
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {
"execution": {
"iopub.execute_input": "2021-05-19T05:57:15.912303Z",
"iopub.status.busy": "2021-05-19T05:57:15.911769Z",
"iopub.status.idle": "2021-05-19T05:57:16.659643Z",
"shell.execute_reply": "2021-05-19T05:57:16.659995Z"
}
},
"outputs": [],
"source": [
"import MDAnalysis as mda\n",
"from MDAnalysis.tests.datafiles import PDB_small, PDB_closed\n",
"from MDAnalysis.analysis import distances\n",
"\n",
"import matplotlib.pyplot as plt\n",
"%matplotlib inline\n",
"\n",
"import warnings\n",
"# suppress some MDAnalysis warnings when writing PDB files\n",
"warnings.filterwarnings('ignore')"
]
},
{
"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) AdK has three domains: \n",
"\n",
" * CORE\n",
" * LID: an ATP-binding domain (residues 122-159)\n",
" * NMP: an AMP-binding domain (residues 30-59)\n",
" \n",
"The LID and NMP domains move around the stable CORE as the enzyme transitions between the opened and closed conformations."
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {
"execution": {
"iopub.execute_input": "2021-05-19T05:57:16.665302Z",
"iopub.status.busy": "2021-05-19T05:57:16.664753Z",
"iopub.status.idle": "2021-05-19T05:57:16.889002Z",
"shell.execute_reply": "2021-05-19T05:57:16.889497Z"
}
},
"outputs": [],
"source": [
"u1 = mda.Universe(PDB_small) # open AdK\n",
"u2 = mda.Universe(PDB_closed) # closed AdK"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Calculating the distance between CA atoms"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We select the atoms named 'CA' of each Universe."
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {
"execution": {
"iopub.execute_input": "2021-05-19T05:57:16.894787Z",
"iopub.status.busy": "2021-05-19T05:57:16.893567Z",
"iopub.status.idle": "2021-05-19T05:57:16.896802Z",
"shell.execute_reply": "2021-05-19T05:57:16.897195Z"
}
},
"outputs": [],
"source": [
"ca1 = u1.select_atoms('name CA')\n",
"ca2 = u2.select_atoms('name CA')"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"`distances.dist`([API docs](https://docs.mdanalysis.org/stable/documentation_pages/analysis/distances.html#MDAnalysis.analysis.distances.dist)) returns the residue numbers of both selections given. The `offset` keyword adds an offset to these residue numbers to help with comparison to each other and other file formats. Here we are happy with our residue numbers, so we use the default offset of 0. (See the documentation of `distances.dist` for more information.)"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {
"execution": {
"iopub.execute_input": "2021-05-19T05:57:16.902403Z",
"iopub.status.busy": "2021-05-19T05:57:16.901729Z",
"iopub.status.idle": "2021-05-19T05:57:16.903560Z",
"shell.execute_reply": "2021-05-19T05:57:16.903935Z"
}
},
"outputs": [],
"source": [
"resids1, resids2, dist = distances.dist(ca1, ca2, \n",
" offset=0) # for residue numbers"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Plotting\n",
"\n",
"Below, we plot the distance over the residue numbers and highlight the LID and NMP domains of the protein. The LID domain in particular moves a significant distance between its opened and closed conformations."
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {
"execution": {
"iopub.execute_input": "2021-05-19T05:57:16.922914Z",
"iopub.status.busy": "2021-05-19T05:57:16.917665Z",
"iopub.status.idle": "2021-05-19T05:57:17.052135Z",
"shell.execute_reply": "2021-05-19T05:57:17.052577Z"
},
"scrolled": true
},
"outputs": [
{
"data": {
"text/plain": [
""
]
},
"execution_count": 8,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
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",
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