{
"cells": [
{
"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 executed:** May 18, 2021 with MDAnalysis 1.1.1\n",
"\n",
"**Last updated:** January 2020\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"
]
},
{
"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": 5,
"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": 1,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
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\n",
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