preprocessing_counts_matrices.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "362edc9d",
   "metadata": {},
   "source": [
    "### Preprocessing single cell expression data\n",
    "\n",
    "Dataset: embryoid body single cell RNA seq over developmental time (https://data.mendeley.com/datasets/v6n743h5ng/)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "29c1d6ee",
   "metadata": {},
   "outputs": [],
   "source": [
    "import os\n",
    "import scprep\n",
    "import tasklogger\n",
    "import pandas as pd\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "60921bc7",
   "metadata": {},
   "outputs": [],
   "source": [
    "import pickle"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "347ef929",
   "metadata": {},
   "outputs": [],
   "source": [
    "data_path = '/Users/anuraglimdi/Desktop/Single_cell_workshop/Datasets/embryoid/'"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "ce2f12d5",
   "metadata": {},
   "outputs": [],
   "source": [
    "sns.set_theme()\n",
    "sns.set_style('ticks')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "587fc497",
   "metadata": {},
   "source": [
    "### Loading the data\n",
    "\n",
    "Using the scprep to handle inputs."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "93323f6c",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Calculating dense...\n",
      "Calculated dense in 8.23 seconds.\n",
      "Size: 1196.1MB\n"
     ]
    }
   ],
   "source": [
    "# loading data as a dense dataframe\n",
    "#using tasklogger to track how long it takes to load the data\n",
    "with tasklogger.log_task(\"dense\"):\n",
    "    data_t1 = scprep.io.load_10X(os.path.join(data_path, \"scRNAseq\", \"T0_1A\"),\n",
    "                                    sparse=False, gene_labels='both')\n",
    "\n",
    "# measure the size of the matrix with pickle\n",
    "print(\"Size: {:.1f}MB\".format(len(pickle.dumps(data_t1)) / 1024**2))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "76f545ed",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Calculating sparse...\n",
      "Calculated sparse in 7.60 seconds.\n",
      "Size: 115.6MB\n"
     ]
    }
   ],
   "source": [
    "# loading data as a sparse dataframe\n",
    "#using tasklogger to track how long it takes to load the data\n",
    "with tasklogger.log_task(\"sparse\"):\n",
    "    data_t1 = scprep.io.load_10X(os.path.join(data_path, \"scRNAseq\", \"T0_1A\"),\n",
    "                                    sparse=True, gene_labels='both')\n",
    "\n",
    "# measure the size of the matrix with pickle\n",
    "print(\"Size: {:.1f}MB\".format(len(pickle.dumps(data_t1)) / 1024**2))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5747a821",
   "metadata": {},
   "source": [
    "Turns out that the data is very sparse; most genes have zero transcripts in most cells, so a sparse representation turns out to be more efficient."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "14556594",
   "metadata": {},
   "outputs": [],
   "source": [
    "# loading the full dataset\n",
    "sparse=True\n",
    "data_time1 = scprep.io.load_10X(os.path.join(data_path, \"scRNAseq\", \"T0_1A\"), sparse=sparse, gene_labels='both')\n",
    "data_time2 = scprep.io.load_10X(os.path.join(data_path, \"scRNAseq\", \"T2_3B\"), sparse=sparse, gene_labels='both')\n",
    "data_time3 = scprep.io.load_10X(os.path.join(data_path, \"scRNAseq\", \"T4_5C\"), sparse=sparse, gene_labels='both')\n",
    "data_time4 = scprep.io.load_10X(os.path.join(data_path, \"scRNAseq\", \"T6_7D\"), sparse=sparse, gene_labels='both')\n",
    "data_time5 = scprep.io.load_10X(os.path.join(data_path, \"scRNAseq\", \"T8_9E\"), sparse=sparse, gene_labels='both')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "232f833f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(4649,)"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.shape(np.sum(data_time1,axis=1))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "bda9a2e5",
   "metadata": {},
   "source": [
    "### Library size\n",
    "\n",
    "Due to the random nature of loading droplet with cells, not all of them will have exactly one cell (in fact this should follow a Poisson distribution). We therefore need to exclude droplets that we think correspond to doublets and empty cells."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "c87233d5",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "##library size for the first timepoint\n",
    "plt.hist(np.sum(data_time1,axis=1), bins=np.linspace(0,25000,100))\n",
    "plt.title('Distribution of number of UMIs per droplet')\n",
    "sns.despine()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "587cf03d",
   "metadata": {},
   "source": [
    "While some variation is expected (in terms of number of transcripts per cell), it is likely that the right tail of this distribution would correspond to doublets/triplets etc."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "de670eaf",
   "metadata": {},
   "outputs": [],
   "source": [
    "filtered_data = []\n",
    "for batch in [data_time1, data_time2, data_time3, data_time4, data_time5]:\n",
    "    percentiles = (15, 85)\n",
    "    #using the scprep function instead of writing a new function by myself\n",
    "    batch = scprep.filter.filter_library_size(batch, percentile=percentiles)\n",
    "    filtered_data.append(batch)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "173e47e5",
   "metadata": {},
   "outputs": [],
   "source": [
    "del data_time1, data_time2, data_time3, data_time4, data_time5 # remove originally loaded data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "39141bb4",
   "metadata": {},
   "outputs": [],
   "source": [
    "data, sample_labels = scprep.utils.combine_batches(\n",
    "    filtered_data, \n",
    "    [\"Day 00-03\", \"Day 06-09\", \"Day 12-15\", \"Day 18-21\", \"Day 24-27\"]\n",
    ")\n",
    "\n",
    "del filtered_data # remove from memory\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4b80c6ed",
   "metadata": {},
   "source": [
    "### Removing dead cells\n",
    "\n",
    "In the sample processsing protocols, some cells may start dying, and we probably want to exclude these from our analysis. Luckily high expression of mitochondrial genes can serve as a marker for cell death due to apoptosis.\n",
    "\n",
    "Goal would be to identify cells with unusually high mitochondrial gene expression and remove them from analysis."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "753dd841",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "scprep.plot.plot_gene_set_expression(data, starts_with=\"MT-\",\n",
    "                                     library_size_normalize=True,\n",
    "                                     title=\"Mitochrondrial expression before filtering\")\n",
    "sns.despine()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "a7a8977a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(21460, 33694)"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cutoff = 450\n",
    "\n",
    "data_filt, sample_labels = scprep.filter.filter_gene_set_expression(\n",
    "    data, sample_labels, starts_with=\"MT-\",\n",
    "    cutoff=cutoff, keep_cells='below', library_size_normalize=True)\n",
    "data_filt.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a026c518",
   "metadata": {},
   "source": [
    "### Low expression genes\n",
    "\n",
    "Many genes are expressed in very few cells or not expressed in any cells at all; because there's so little information about them, it's difficult to make any statements based on those data. Makes sense again to exclude them"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "id": "bf40b917",
   "metadata": {},
   "outputs": [],
   "source": [
    "cells_where_expressed = np.sum(data_filt>0, axis=0)   #summing along rows; how many cells is the gene expressed in?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "id": "28ddf125",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'How many genes')"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.hist(np.log(cells_where_expressed+1), bins=40)\n",
    "plt.xlabel('log(Number of cells where expressed + 1')\n",
    "plt.ylabel('How many genes')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "id": "52784643",
   "metadata": {},
   "outputs": [],
   "source": [
    "cutoff = 5\n",
    "data_filt = scprep.filter.filter_rare_genes(data_filt, min_cells=cutoff)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "id": "19453a5a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(21460, 19655)"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data_filt.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cd515d0e",
   "metadata": {},
   "source": [
    "Over 10,000 genes have been excluded from analysis because they're barely present in the dataset"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c89c76db",
   "metadata": {},
   "source": [
    "### Normalization\n",
    "\n",
    "The library size (# UMIs/cell) can be quite variable, and comparison of counts across cells is not possible. So, we will have to normalize the number of UMIs/cell to a fixed number"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "id": "9b911ed5",
   "metadata": {},
   "outputs": [],
   "source": [
    "data_norm, library_size = scprep.normalize.library_size_normalize(data_filt, return_library_size=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "id": "dddbcb00",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>library_size</th>\n",
       "      <th>sample_labels</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>AAACATACCAGAGG-1_Day 00-03</th>\n",
       "      <td>10387.0</td>\n",
       "      <td>Day 00-03</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>AAACATTGAAAGCA-1_Day 00-03</th>\n",
       "      <td>5738.0</td>\n",
       "      <td>Day 00-03</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>AAACATTGAAGTGA-1_Day 00-03</th>\n",
       "      <td>10007.0</td>\n",
       "      <td>Day 00-03</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>AAACATTGGAGGTG-1_Day 00-03</th>\n",
       "      <td>10231.0</td>\n",
       "      <td>Day 00-03</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>AAACATTGGTTTCT-1_Day 00-03</th>\n",
       "      <td>10389.0</td>\n",
       "      <td>Day 00-03</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                            library_size sample_labels\n",
       "AAACATACCAGAGG-1_Day 00-03       10387.0     Day 00-03\n",
       "AAACATTGAAAGCA-1_Day 00-03        5738.0     Day 00-03\n",
       "AAACATTGAAGTGA-1_Day 00-03       10007.0     Day 00-03\n",
       "AAACATTGGAGGTG-1_Day 00-03       10231.0     Day 00-03\n",
       "AAACATTGGTTTCT-1_Day 00-03       10389.0     Day 00-03"
      ]
     },
     "execution_count": 38,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#metadata containing info on library size and sample info (which timepoint)\n",
    "metadata = pd.concat([library_size, sample_labels], axis=1)\n",
    "metadata.head(5)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4c2d061e",
   "metadata": {},
   "source": [
    "### Keeping most variable genes\n",
    "\n",
    "A lot of genes are housekeeping genes (involved in essential physiological processes that don't differ across cell types), and so their expression levels are likely the same. To make the amount of data we're working with more manageable, we can also restrict our analysis to genes that are most variable across the cells in the experiment."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "id": "c82d6b6b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.hist(np.mean(data_norm, axis=0), bins=50)\n",
    "plt.xlabel('Counts/gene')\n",
    "plt.ylabel('Number of genes')\n",
    "plt.yscale('log')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "id": "a7864c58",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'log(x+1) transformed data')"
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#to avoid the distribution being so long-tailed, we can transform the data\n",
    "#option 1: log(counts+1)\n",
    "plt.hist(np.mean(np.log(data_norm+1), axis=0), bins=50)\n",
    "plt.xlabel('Counts/gene')\n",
    "plt.ylabel('Number of genes')\n",
    "plt.yscale('log')\n",
    "plt.title('log(x+1) transformed data')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "id": "8d7ca118",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'sqrt(x) transformed data')"
      ]
     },
     "execution_count": 42,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#option 2: square root\n",
    "plt.hist(np.mean(np.sqrt(data_norm), axis=0), bins=50)\n",
    "plt.xlabel('Counts/gene')\n",
    "plt.ylabel('Number of genes')\n",
    "plt.yscale('log')\n",
    "plt.title('sqrt(x) transformed data')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "id": "ab0ad5b4",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<AxesSubplot:xlabel='Gene mean', ylabel='Standardized variance'>"
      ]
     },
     "execution_count": 46,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sqrt_data = np.sqrt(data_norm)\n",
    "#plotting the variability in the expression levels vs mean\n",
    "scprep.plot.plot_gene_variability(sqrt_data, percentile=90)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "85397875",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "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": "3.9.12"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}