class02a_igraph_R.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# CSX46: Class session 2\n",
    "## *Introduction to the igraph package and the Pathway Commons network in SIF format*\n",
    "\n",
    "### Objective: load a network of human molecular interactions and create three igraph `Graph` objects from it (one for protein-protein interactions, one for metabolism interactions, and one for directed protein-protein interactions)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "OK, we are going to read in the Pathway Commons data in SIF format. Recall that a SIF file is a tab-separated value file. You can find the file as `shared/pathway_commons.sif`. Load it into a data frame `pcdf` using the built-in function `read.table`. Don't forget to specify that the separator is the tab `\\t`, and that there is no quoting allowed (`quote=\"\"`). Use the `col.names` argument to name the three columns `species1`, `interaction_type`, and `species2`. Make sure to specify that there is no header and that `stringsAsFactors=FALSE`.\n",
    "\n",
    "For help on using `read.table`, just type ?read.table\n",
    "\n",
    "Note: for each row, the `interaction_type` column contains one of 11 different interaction types (identified by a string, like `interacts-with` or `controls-production-of`). "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "pcdf <- read.table(\"shared/pathway_commons.sif\",\n",
    "                    sep=\"\\t\",\n",
    "                    quote=\"\",\n",
    "                    comment.char=\"\",\n",
    "                    stringsAsFactors=FALSE,\n",
    "                    header=FALSE,\n",
    "                    col.names=c(\"species1\",\"interaction_type\",\"species2\"))\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's take a peek at `pcdf` using the `head` function:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<caption>A data.frame: 6 × 3</caption>\n",
       "<thead>\n",
       "\t<tr><th scope=col>species1</th><th scope=col>interaction_type</th><th scope=col>species2</th></tr>\n",
       "\t<tr><th scope=col>&lt;chr&gt;</th><th scope=col>&lt;chr&gt;</th><th scope=col>&lt;chr&gt;</th></tr>\n",
       "</thead>\n",
       "<tbody>\n",
       "\t<tr><td>A1BG</td><td>controls-expression-of     </td><td>A2M   </td></tr>\n",
       "\t<tr><td>A1BG</td><td>interacts-with             </td><td>ABCC6 </td></tr>\n",
       "\t<tr><td>A1BG</td><td>controls-phosphorylation-of</td><td>AKT1  </td></tr>\n",
       "\t<tr><td>A1BG</td><td>controls-state-change-of   </td><td>AKT1  </td></tr>\n",
       "\t<tr><td>A1BG</td><td>interacts-with             </td><td>ANXA7 </td></tr>\n",
       "\t<tr><td>A1BG</td><td>interacts-with             </td><td>CDKN1A</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "A data.frame: 6 × 3\n",
       "\\begin{tabular}{r|lll}\n",
       " species1 & interaction\\_type & species2\\\\\n",
       " <chr> & <chr> & <chr>\\\\\n",
       "\\hline\n",
       "\t A1BG & controls-expression-of      & A2M   \\\\\n",
       "\t A1BG & interacts-with              & ABCC6 \\\\\n",
       "\t A1BG & controls-phosphorylation-of & AKT1  \\\\\n",
       "\t A1BG & controls-state-change-of    & AKT1  \\\\\n",
       "\t A1BG & interacts-with              & ANXA7 \\\\\n",
       "\t A1BG & interacts-with              & CDKN1A\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "A data.frame: 6 × 3\n",
       "\n",
       "| species1 &lt;chr&gt; | interaction_type &lt;chr&gt; | species2 &lt;chr&gt; |\n",
       "|---|---|---|\n",
       "| A1BG | controls-expression-of      | A2M    |\n",
       "| A1BG | interacts-with              | ABCC6  |\n",
       "| A1BG | controls-phosphorylation-of | AKT1   |\n",
       "| A1BG | controls-state-change-of    | AKT1   |\n",
       "| A1BG | interacts-with              | ANXA7  |\n",
       "| A1BG | interacts-with              | CDKN1A |\n",
       "\n"
      ],
      "text/plain": [
       "  species1 interaction_type            species2\n",
       "1 A1BG     controls-expression-of      A2M     \n",
       "2 A1BG     interacts-with              ABCC6   \n",
       "3 A1BG     controls-phosphorylation-of AKT1    \n",
       "4 A1BG     controls-state-change-of    AKT1    \n",
       "5 A1BG     interacts-with              ANXA7   \n",
       "6 A1BG     interacts-with              CDKN1A  "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "head(pcdf)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\n",
      "Attaching package: ‘igraph’\n",
      "\n",
      "\n",
      "The following objects are masked from ‘package:stats’:\n",
      "\n",
      "    decompose, spectrum\n",
      "\n",
      "\n",
      "The following object is masked from ‘package:base’:\n",
      "\n",
      "    union\n",
      "\n",
      "\n"
     ]
    }
   ],
   "source": [
    "library(igraph)\n",
    "\n",
    "interaction_types_ppi <- c(\"interacts-with\",\n",
    "                           \"in-complex-with\",\n",
    "                           \"neighbor-of\")\n",
    "\n",
    "interaction_types_metab <- c(\"controls-production-of\",\n",
    "                             \"consumption-controlled-by\",\n",
    "                             \"controls-production-of\",\n",
    "                             \"controls-transport-of-chemical\")\n",
    "\n",
    "interaction_types_ppd <- c(\"catalysis-precedes\",\n",
    "                           \"controls-phosphorylation-of\",\n",
    "                           \"controls-state-change-of\",\n",
    "                           \"controls-transport-of\",\n",
    "                           \"controls-expression-of\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Subset data frame `pcdf` to obtain only the rows whose interactions are in `interaction_types_ppi`, and select only columns 1 and 3:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "pcdf_ppi <- pcdf[pcdf$interaction_type %in% interaction_types_ppi,c(1,3)]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Use the `igraph` function `graph_from_data_farme` to build a network from the edge-list data in `pcdf_ppi`; use `print` to see a summary of the graph:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "IGRAPH ba9e496 UN-- 17020 523498 -- \n",
      "+ attr: name (v/c)\n",
      "+ edges from ba9e496 (vertex names):\n",
      " [1] A1BG--ABCC6   A1BG--ANXA7   A1BG--CDKN1A  A1BG--CRISP3  A1BG--GDPD1  \n",
      " [6] A1BG--GRB2    A1BG--GRB7    A1BG--HNF4A   A1BG--ONECUT1 A1BG--PIK3CA \n",
      "[11] A1BG--PIK3R1  A1BG--PRDX4   A1BG--PTPN11  A1BG--SETD7   A1BG--SMN1   \n",
      "[16] A1BG--SMN2    A1BG--SNCA    A1BG--SOS1    A1BG--TK1     A1CF--ACBD3  \n",
      "[21] A1CF--ACLY    A1CF--APOBEC1 A1CF--APOBEC1 A1CF--ATF2    A1CF--CELF2  \n",
      "[26] A1CF--CTNNB1  A1CF--E2F1    A1CF--E2F3    A1CF--E2F4    A1CF--FHL3   \n",
      "[31] A1CF--HNF1A   A1CF--HNF4A   A1CF--JUN     A1CF--KAT5    A1CF--KHSRP  \n",
      "[36] A1CF--MBD2    A1CF--MBD3    A1CF--NRF1    A1CF--RBL2    A1CF--REL    \n",
      "+ ... omitted several edges\n"
     ]
    }
   ],
   "source": [
    "graph_ppi <- graph_from_data_frame(pcdf_ppi,\n",
    "                                   directed=FALSE)\n",
    "print(graph_ppi)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Do the same for the metabolic network:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "IGRAPH 77472bf DN-- 7620 38145 -- \n",
      "+ attr: name (v/c)\n",
      "+ edges from 77472bf (vertex names):\n",
      " [1] A4GALT->CHEBI:17659 A4GALT->CHEBI:17950 A4GALT->CHEBI:18307\n",
      " [4] A4GALT->CHEBI:18313 A4GALT->CHEBI:58223 A4GALT->CHEBI:67119\n",
      " [7] A4GNT ->CHEBI:17659 A4GNT ->CHEBI:58223 AAAS  ->CHEBI:1604 \n",
      "[10] AAAS  ->CHEBI:2274  AACS  ->CHEBI:13705 AACS  ->CHEBI:15345\n",
      "[13] AACS  ->CHEBI:17369 AACS  ->CHEBI:18361 AACS  ->CHEBI:29888\n",
      "[16] AACS  ->CHEBI:57286 AACS  ->CHEBI:57287 AACS  ->CHEBI:57288\n",
      "[19] AACS  ->CHEBI:57392 AACS  ->CHEBI:58280 AADAC ->CHEBI:17790\n",
      "[22] AADAC ->CHEBI:40574 AADAC ->CHEBI:4743  AADAC ->CHEBI:85505\n",
      "+ ... omitted several edges\n"
     ]
    }
   ],
   "source": [
    "pcdf_metab <- pcdf[pcdf$interaction_type %in% interaction_types_metab, c(1,3)]\n",
    "graph_metab <- graph_from_data_frame(pcdf_metab,\n",
    "                                     directed=TRUE)\n",
    "print(graph_metab)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Do the same for the directed protein-protein interactions:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "IGRAPH DN-- 16063 359713 -- \n",
      "+ attr: name (v/c), interaction_type (e/c)\n",
      "IGRAPH DN-- 16063 359713 -- \n",
      "+ attr: name (v/c), interaction_type (e/c)\n",
      "+ edges (vertex names):\n",
      " [1] A1BG  ->A2M      A1BG  ->AKT1     A1BG  ->AKT1     A2M   ->APOA1   \n",
      " [5] A2M   ->CDC42    A2M   ->RAC1     A2M   ->RAC2     A2M   ->RAC3    \n",
      " [9] A2M   ->RHOA     A2M   ->RHOBTB1  A2M   ->RHOBTB2  A2M   ->RHOB    \n",
      "[13] A2M   ->RHOC     A2M   ->RHOD     A2M   ->RHOF     A2M   ->RHOG    \n",
      "[17] A2M   ->RHOH     A2M   ->RHOJ     A2M   ->RHOQ     A2M   ->RHOT1   \n",
      "[21] A2M   ->RHOT2    A2M   ->RHOU     A2M   ->RHOV     A4GALT->ABO     \n",
      "[25] A4GALT->AK3      A4GALT->B3GALNT1 A4GALT->B3GALT1  A4GALT->B3GALT2 \n",
      "[29] A4GALT->B3GALT4  A4GALT->B3GALT5  A4GALT->B3GALT6  A4GALT->B3GAT2  \n",
      "+ ... omitted several edges\n"
     ]
    }
   ],
   "source": [
    "pcdf_ppd <- pcdf[pcdf$interaction_type %in% interaction_types_ppd, c(1,3)]\n",
    "graph_ppd <- graph_from_data_frame(pcdf_ppd,\n",
    "                                   directed=TRUE)\n",
    "print(graph_ppd)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "Question: of the three networks that you just created, which has the most edges?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Next, we need to create a small graph. Let's make a three-vertex undirected graph from an edge-list. Let's connect all vertices to all other vertices: 1<->2, 2<->3, 3<->1. We'll once again use graph_from_data_farme to do this:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "testgraph <- graph_from_data_frame(data.frame(c(1,2,3), c(2,3,1)), directed=FALSE)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now let's plot the small test graph:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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b1e39raOjg46HK5tFqt7GkAapEQorGxkS9BqkTYAeWSzWbD4fBKzxkMBpfLRc8B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\n0n4qZ2IAAAAASUVORK5CYII=",
      "text/plain": [
       "Plot with title “”"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 420,
       "width": 420
      },
      "text/plain": {
       "height": 420,
       "width": 420
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot(testgraph)"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "R",
   "language": "R",
   "name": "ir"
  },
  "language_info": {
   "codemirror_mode": "r",
   "file_extension": ".r",
   "mimetype": "text/x-r-source",
   "name": "R",
   "pygments_lexer": "r",
   "version": "3.6.1"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}