GutCP_delete_links.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## GutCP (Gut Cross-feeding Predictor) with deletion of links - Ecology-guided prediction of cross-feeding interactions in the human gut microbiome\n",
    "The predictive power of the trophic model heavily on a manually curated metabolic interaction network [NJS16](https://www.nature.com/articles/ncomms15393). However, the manually curated network derived from the past experiments and literature is incomplete because not all exchange reactions were revealed by experiments. The number of links in this network is only roughly one-sixth of that in a potentially over-complete cross-feeding network obtained from the genomic annotation. Here, we proposed an ecologically guided machine learning algorithm to cleverly discover metabolite exchange reactions that help to improve the predictions of the trophic level. Later, we demonstrated that the prevalent exchange reactions statistically discovered from many independent simulations are supported by the genomic evidence.\n",
    "\n",
    "GutCP only add links. An interesting direction worth trying is to delete random links and see if the performance can be improved via the deletion of false-positive links. It starts with the deletion of a random percentage of random links and sees how the performance of the trophic model is worsened by it. Then it runs the GutCP with the ability to delete random links."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "import math\n",
    "import random\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns\n",
    "from collections import Counter\n",
    "from scipy.stats import sem\n",
    "\n",
    "#%% Plot Tong's default setting\n",
    "SMALL_SIZE = 12\n",
    "MEDIUM_SIZE = 15\n",
    "BIGGER_SIZE = 15\n",
    "\n",
    "plt.rc('font', size=SMALL_SIZE, family='sans-serif', serif='Arial')          # controls default text sizes\n",
    "plt.rc('axes', titlesize=BIGGER_SIZE)     # fontsize of the axes title\n",
    "plt.rc('axes', labelsize=MEDIUM_SIZE)    # fontsize of the x and y labels\n",
    "plt.rc('xtick', labelsize=SMALL_SIZE)    # fontsize of the tick labels\n",
    "plt.rc('ytick', labelsize=SMALL_SIZE)    # fontsize of the tick labels\n",
    "plt.rc('legend', fontsize=SMALL_SIZE)    # legend fontsize\n",
    "plt.rc('figure', titlesize=BIGGER_SIZE)  # fontsize of the figure title\n",
    "plt.rc('text')\n",
    "\n",
    "from matplotlib.ticker import MaxNLocator\n",
    "my_locator = MaxNLocator(6)\n",
    "\n",
    "color_list = ['#1f77b4', '#ff7f0e', '#2ca02c', '#d62728', '#9467bd']\n",
    "\n",
    "def figure_size_setting(WIDTH):\n",
    "    #WIDTH = 700.0  # the number latex spits out\n",
    "    FACTOR = 0.8  # the fraction of the width you'd like the figure to occupy\n",
    "    fig_width_pt  = WIDTH * FACTOR\n",
    "    inches_per_pt = 1.0 / 72.27\n",
    "    golden_ratio  = (np.sqrt(5) - 1.0) / 2.0  # because it looks good\n",
    "    fig_width_in  = fig_width_pt * inches_per_pt  # figure width in inches\n",
    "    fig_height_in = fig_width_in * golden_ratio   # figure height in inches\n",
    "    fig_dims    = [fig_width_in, fig_height_in] # fig dims as a list\n",
    "    return fig_dims"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "########### import the pickled file containing all processed data which are useful for simulations (the processing is\n",
    "########### done in \"Trophic_model_for_gut_data_processing.ipynb\")\n",
    "import pickle\n",
    "pickle_in = open(\"Chia_network.pickle\",\"rb\")\n",
    "net, i_selfish, i_intake, names = pickle.load(pickle_in)\n",
    "\n",
    "pickle_in = open(\"data.pickle\",\"rb\")\n",
    "metagenome_ID, metagenome, metabolome_ID, metabolome = pickle.load(pickle_in)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Trophic model for the gut microbiome\n",
    "The human gut microbial community is complex because of 3 reasons: (1) many microbial species ($\\approx$ 570); (2) many metabolites involved ($\\approx$ 244); and (3) many microbe-metabolite interactions/links (>4400). Of all types of microbe-metabolite interactions/links, the cross-feeding makes the system more complicated to interpret. Previously, a literature-curated interspecies network of the human gut microbiota, called [NJS16](https://www.nature.com/articles/ncomms15393) is reported. This is an extensive data resource composed of ∼570 microbial species and 3 human cell types metabolically interacting through >4,400 small-molecule transport and macromolecule degradation events.\n",
    "\n",
    "Here, we devoted to building a Consumer-Resource model (CRM) with trophic levels posted in the paper \"[an evidence for a multi-level trophic organization of the human gut microbiome](https://www.biorxiv.org/content/10.1101/603365v1.full-text)\". The model is devoted to studying the complex microbe-metabolite network in human guts.\n",
    "\n",
    "In concise, a trophic level is considered as one round of carbon processing and is composed of two processes: resource allocation to microbes and the following resource/byproduct generation by microbes. The simulation is stopped after several trophic levels because the residence time of resources in the human gut is assumed to be finite."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Create maps of microbes and metabolites to their reduced matrix forms"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "#i_nonzero_microbes = net['microbes_ID'].unique()\n",
    "#i_nonzero_microbes = np.sort(i_nonzero_microbes)\n",
    "i_nonzero_microbes = metagenome_ID.values.copy()\n",
    "i_nonzero_metabolites = net['metabolites_ID'].unique()\n",
    "i_nonzero_metabolites = np.sort(i_nonzero_metabolites)\n",
    "\n",
    "\n",
    "df_metabolites = pd.DataFrame.from_dict({'oldID': i_nonzero_metabolites, 'newID':list(range(len(i_nonzero_metabolites)))})\n",
    "df_metabolites.set_index('oldID', inplace=True)\n",
    "df_microbes = pd.DataFrame.from_dict({'oldID': i_nonzero_microbes, 'newID':list(range(len(i_nonzero_microbes)))})\n",
    "df_microbes.set_index('oldID', inplace=True)\n",
    "\n",
    "\n",
    "outgoingNodes = df_metabolites.reindex(net['metabolites_ID'].values).values.flatten()\n",
    "ingoingNodesTemp = df_microbes.reindex(net['microbes_ID'].values).values.flatten()\n",
    "edge_types = net.iloc[~np.isnan(ingoingNodesTemp),2].values\n",
    "outgoingNodes = outgoingNodes[~np.isnan(ingoingNodesTemp)]\n",
    "ingoingNodes = ingoingNodesTemp[~np.isnan(ingoingNodesTemp)].astype(int)\n",
    "\n",
    "net_reduced = pd.DataFrame.from_dict({'metabolites': outgoingNodes, 'microbes':ingoingNodes, 'edgeType':edge_types})\n",
    "net = net_reduced.copy()\n",
    "net_temp = net.copy()\n",
    "net['edgeType'][net['edgeType']==5] = 2\n",
    "net_temp['edgeType'][net_temp['edgeType']==5] = 3\n",
    "net = net.append(net_temp).drop_duplicates()\n",
    "net_ori = net.copy()\n",
    "\n",
    "metagenome_ID_reduced = df_microbes.reindex(metagenome_ID).values.flatten()\n",
    "metagenome_ID = metagenome_ID_reduced[~np.isnan(metagenome_ID_reduced)].astype(int)\n",
    "\n",
    "metabolome_ID_reduced = df_metabolites.reindex(metabolome_ID).values.flatten()\n",
    "metabolome_ID = metabolome_ID_reduced[~np.isnan(metabolome_ID_reduced)].astype(int)\n",
    "\n",
    "\n",
    "i_selfish_reduced = df_microbes.reindex(i_selfish).values.flatten()\n",
    "i_selfish = i_selfish_reduced[~np.isnan(i_selfish_reduced)].astype(int)\n",
    "\n",
    "i_intake_reduced = df_metabolites.loc[i_intake].values.flatten()\n",
    "i_intake = i_intake_reduced[~np.isnan(i_intake_reduced)].astype(int)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Run the simulation with reduced matrix forms for one individual"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 3.15081328590715\n",
      "            Iterations: 16\n",
      "            Function evaluations: 338\n",
      "            Gradient evaluations: 16\n",
      "     fun: 3.15081328590715\n",
      "     jac: array([ 0.        ,  0.00985727,  0.00507495,  0.00553924,  0.06272528,\n",
      "        0.01278239,  0.03304651,  0.007664  , -0.00600949,  0.01459828,\n",
      "        0.00206959,  0.0147886 ,  0.1271221 ,  0.08330926, -0.00155351,\n",
      "        0.01078975,  0.08886302,  0.02255565, -0.01123682,  0.01378861])\n",
      " message: 'Optimization terminated successfully'\n",
      "    nfev: 338\n",
      "     nit: 16\n",
      "    njev: 16\n",
      "  status: 0\n",
      " success: True\n",
      "       x: array([5.00000000e-02, 1.10194482e-01, 4.62981925e+00, 3.86162085e-01,\n",
      "       0.00000000e+00, 1.04392453e-16, 0.00000000e+00, 7.21664222e-02,\n",
      "       3.79355536e-02, 6.36525129e-17, 4.71538944e-01, 1.65359383e-02,\n",
      "       0.00000000e+00, 2.10734346e-16, 3.52982051e-01, 2.22131630e-01,\n",
      "       0.00000000e+00, 0.00000000e+00, 2.19500120e-01, 0.00000000e+00])\n",
      "-------------------------------------------------------------------------------------------------------------\n",
      "(Correlation coefficient, P-value) of the correlation between predicted and experimentally measured metagonome:\n",
      "(0.8765075557343968, 1.169259578138045e-12)\n",
      "(Correlation coefficient, P-value) of the correlation between predicted and experimentally measured metabolome:\n",
      "(0.7502095792844012, 0.0002159956854998387)\n"
     ]
    },
    {
     "data": {
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1ZvZLwt6vTwCLgb2yNsxxnL4UWnQIsNlmm9HZ2YkkOjs76enpYfr06XWwsDIqWQmNpCGEbRnHA4cRAgXeQ/AL7ThOlSk2rvPiiy/y/PPP19iagZN2N3xOdI4ARhIWJZ4LXG9mS6tnnuM4ScaNG8fChQv75DfDeE8h0raAfg48CJwP/NjMnqueSY7jFGLRokUUimTcLOM9hSg7BhS7XfsBR5vZNxtRfCSNkvSgpOVxe4jjtBQ5lxrLli1jxowZTTneU4g0LaA1wJ2Ema++bb/GYCXwfuBr9TbEcbKmkD+fCy+8sN5mZULZFpCZrQXmA2Oqb07/MLPXfSzKaUUa2ZlYFqSdhu8GzpOUHy++YiSdERcxrpI0O69sC0k3SVohqVfSCQO9nuM0K60uPpB+EHoGMBp4WNJC4B+s9wcEgJntmbKu5wix5A8iTOMn+RawmtDa2hW4TdIjZva4pLHADQXqO8bMFqe8tuM0Be0gPpBegB6LacCY2Y0AkiYDE3L5kkYARwM7mdly4D5JtxB24J8TRWbfLGxwnEamXcQHUgqQmX2k2oYAOwBr8nwLPQJMTXOypJ8TWk1vlfQdM5td4JguQpTXpl034bQ27SQ+UPlKaBFaLW8CHjGzFRnasgmQv0N0GbBpmpPN7NAUx/QAPQCTJ0/uu6DCcepIu4kPVLAXTNLphGn4XoKP6LfG/BslfSYDW5YTVlknGQm8kkHd6/Dd8E4j0o7iA+kdkn0e+AbwXWAaG8YFu5uwTWOgzAMGS9o+kbcL8HgGda/Dd8M7jUa7ig+kbwF9AjjPzL5EaP0keZIwfpMKSYMlDQM6gA5JwyQNjt25G4ELJI2QtA9wOHB12rpTXt9bQE7D0M7iA+kFaCzwUJGytcCwCq45gxBH7BzgQ/H9jFh2OmFqfglwLXCamXkLyGlJ2l18IP0g9FOE2ag7C5TtB/wl7QXNbCYws0jZi4Qd91XDAxM6jYCLTyBtC+ibwDmSZgC5MZqtJf0b8FngP6thXDXwFpBTb1x81pN2HdD3JG1OcDx2fsz+OWET6Ewz+2GV7HOclsLFZ0NST8Ob2dcIzukPIYzdHAqMj/lNgw9CO9Uk6TB+0qRJzJkzZ12Zi09fVMjBUTswefJkmzt3br3NcFqI008/nSuuuGIDp2HDhw+np6eHadOmtaX4SHrIzCYXK0+7DujoON6T+7ytpAckvSTpJ5I2y8JYx2lW5syZ00d8AFauXMnZZ5+9gfgsWLCgaCup3UjbBZvBhquULwW2BC4Bdgeaxh+kd8GcatDd3V3QXSrAwoULNxCfZFid3t5eurq62laEUnXBJC0juGS9Q9IoYClwpJndFn32XGJmTbW707tgTpYMGjSoqABJ4p577mHKlClMmjSpYCTTzs5Onn766SpbWXsy6YJFcnd3KsFN6x3x87PAVv0zz3Fag1LeFbq7u9eN+RQLq9MMYZSrQVoBegSYHn32fAz4jZmtimUTCSuXHadtmTVrFsOHD++Tf/jhh2/gv7mYULWre5i0AvQF4EjgZUIL6PxE2RHA7zO2q2r4GJBTDaZPn05PTw+bb775uryRI0dy7LHHbnBcIaFq5rA6AyVtbPj7CC2dPYFOM0sKzpWs38vV8PhKaKda/POf/+Sll15a9/nll1/uM8CcE6pWCaszUHwdkONkwKJFi5g4cSJvvPFGn7JWHWBOQ2aD0JLeIemHkp6KUSuekjRH0s7ZmOo4zUluhXMh8YH2HWBOQ9qFiEcQ3HHsRohM8cX4ujswN5Y7TtuR3F4xZkzh0HntOsCchrTuOL4C/BQ4zhJ9NknnEoToq8DN2ZuXPe6Ow8mK/L1duUWGK1euXHdMOw8wp8LMyibCrveDipQdBKxMU08jpT322MMcp78899xztuOOO9qIESPst7/97br8a665xjo7O02SdXZ22jXXXFNHK+sPMNdKPIdpW0BzgbcDvyxQthPwx4FLoeM0B6V2tU+fPr1tZ7T6Q1EBkpRcrPBZ4DpJQwhdrSXA1oS1QR8DPlBNIx2nUXCXGtlSqgW0nA3DLwv4MnBxXh6EhYgd2ZrmOI2Fi0/2lBKgj5IX/91x2hUXn+pQVICsQGhjx2lHXHyqRyW74ZE0LjonOyW+jquWYdUi7V6wUq41nfbBxafKlJoiyyXC+M7lwOuEOGC59DrwLWBQmnoaKZWahr/mmmts+PDhRuiCGmDDhw9v+ynVdqPYVLuTHspMw6dtAZ1PGBP6AjCJEDxwUvz8UYrE+WpWuru7N1hMBsG1Znd3d50scmqNt3xqQ1oBOgmYYWZfM7MFZrYqvn6NsC3j5KpZWAfcaVTzkkXX2cWndqQVoK2BPxcp+3MsbxncaVRzMmfOnAH7W3bxqS1pBWgexRcbfgB4MhtzGgN3GtWcDLTr7OJTB0oNEOUScBxh0PkO4FTCCuiPx89rgGPT1FPNBOwF/A64B7gWGFLq+HJ7wXxPT/MhaYOJg1ySVPZcH3CuDpQZhK7kAT8wPuCrohitAh4A3pe2jmomQtTWjeP7WcAxpY73zajNT/6PxOjRowsKUEdHR8kfEBef6lFOgNJuRsXMfgX8StIgQkyw581sbYUNrqphZs8lPr5BEEmnRcmN9+S6XL29vWy00UYMGTKE119/fYNj16xZQ1dXF0CfjaKXXXYZZ555Jm+88QZjxozxiYZaU0qdqpWAMwg77FcBs/PKtgBuAlYAvcAJFda9LfAgsFGp47wF1Nx0dnYWbO2MHj3aOjo6ipYlW0wnnXRSn26br/fKFsq0gOriE1rSUYQWykGEbtPJibJrCYPj/wbsCtwG7G1mj0saS3CAls8xZrZY0kjgZ8ApZlZyYNx9Qjc3xQIBSmF/9ED+r9vZh3PWZBmYMDPM7EYzuxl4IZkf444dDXzRzJZbiMZxC3BiPG+xme1bIC2WNJgw+DyznPg4zU+ppRIDXS6Rthvm23UGTl0EqAQ7AGvMbF4i7xGCM7RyfBB4F3CepLslHZ9/gKQuSXMlzV26dGk2Fjt1odRSiWJBAtOSRsCyWHPkUJ8xoFwCLiIxBgRMARbnHXMKcHfW1/YxoOan1FKJtDNk+WNAQ4YMsdGjR5ddflFsDKqzs7Pm37WRIYtpeMK4y6FkvOm0gADtRp5/aeBzwK0ZXvMwoGe77bbL6h47TcCll15acMD5tNNOW/dgjx492jbaaKNUg9IDWXNUKc28OTorAbqHsODwOeASYMc056WoN1+ARgCrge0Tef8DXJLF9ZLJW0DtQ26dz9ChQ23MmDFFWxGVtGpq2QKqdWsrSzIRoFAPbwYuAP4exegBgj/oTdPWkahrMDCM4OL16vh+cCy7jjCYPALYB1gGvL3Sa5S4treA2oj8RYalujKVtGpq2SqpZWsrazITINvwIT4gtkxeIfiO/gGwfwXnzyxwQ2fGsi0Iju9XAAuocB1Q2uQtoNYnv+WTe2iLiUalLY1ajct4C6ivgIwAPkJYTLgWeCa+Pgzs1p86a5W8BdQeJMVn6NChBR/gXBo9erSZNe5YS6PalYZMBQiYClwVWz4vErwk7hHL3gbcCTxaSZ31St4Cal2S3a5cy6dcyj3MjTrb1Kh2laOcAKVaCS0p53RsEnAv8H3gejN7Le+4vYF7zaxhQ/QkQjOfMn/+/Hqb42RMvkuNqVOnkuZ/3Fc/V4esVkKfCvwIeKuZ7W9mV+eLT+QJgovWhsXMbjWzrlGjRtXbFCdjCsVqHzQo3b+4b0KtD2l3w080szXlDjKzFwkD0o5TUwqJT1dXF2vWlP23BdzbZb1IJUBpxMdx6kUhT4aTJk3q4x0RwmbVIUOGsHr16nV57u2yfhRtn0paKmlJ2lRLowdC2rhgTnNQzI1qqS7VlVdeSWdnJ5Lo7Oykp6enj58gpzYUHYSWNBPSh2Y2s/MzsqkmuDuOxmbOnDl0d3ezYMECJk6cyKxZs/qIRCkfzpMmTaK3t7dPvT7YXFvKDULXfTq8Xsmn4RuXNOteyrlRbea1M8065V4IqrEQsZkTvhCx4Sm38jetD+dmfJCbWTgLUU6ASnXBflxJU8vMjqvk+HrjXbDGpZS3w4ULF7Z06JxW6zqW64KVmgXbqgr2OE5ZJk6cWPAhHDduXEuLD7RfVN6iAmRm76mlIY6TY9asWRtEvADYeOONMbOWFh8oLr6tuk6p0VyyOg7Tp0+np6dn3VT5+PHj2XzzzVm2bFlLiw+0X1Te1FExJG0KHE7w2zwsv9zMzsrWtOrge8Gai3YMl5xmCUKzkMk0PPAWYDHwMsEZ2WKC58K1hMgWf0tTTyMln4ZvfNJMtTfbLFe7QZlZsLRdsP8k+P4ZA4jgH3pj4EMEh2R9IlA4zkAo1/LxqBStQVoB2hO4ghDJFELU0TVm9kPg68B/VcO4euIxn/rPQO9dmm5Xd3d3n71eK1eupLu7e0C2OzWmVPMol4CXgP3i++eBoxJl04AVaepppFSqC9Zqi8FqyUDvXdpFhs3sJ7mdIKOoGA8CJ8b3vwZ+RRiIHgLMAeanqaeRUikBamYfvPVmIPcurfgM9DpO7SgnQGm7YNcR4rQDfJEQgfRlgmvW44Gm2ohajnZbDJYl/b13lc52tdt0dctSSp2KJeBNhIilnwJ26k8d9Uqk2Avmv679pz/3rpKWTxKfBWt8yKgLth+wSZGyTYjjQ82UGnkMqJkfrErvXX/Fx2kOshKgNcCeRcr2ANakqaeRUrl1QPUSgXqLXxakvXcuPq1POQFKGxVjLfBuM3uwQNlU4Gdmtmnqfl8D0Ki74VttN3Qx2nGFczvS76gYkvaTdJ6k82LWx3KfE+li4L+BRzO2u21plQHwUmuBaiU+vparCSjWNAI+DyyNaQ3wz8TnXFpICEa4e6lmViOmRt2K0QoD4KW6kbXqdrVCV7YVIKMxoL8Du6Q5th6JsEXkAeAe4C5gm3LnNKoAtcKDU0xEx48fX7Mxn1YQ8lYgEwFq9AR0AIPi+5OBGeXOaVQBMqvuAHgtBteLrVIGajbg7CulG4NyApQ2MCGShhGm4yfQ1x2Hmdm309aVNbZh3LJNgcfrZUsWTJ8+vSruF3IbOHN7qHIbOHPXzIpiTrUk1WzAud0cezUtpdTJ1rcw9gWWENxvFEqpp+GBMwg761cBs/PKtgBuAlYAvcAJFdS7K/B74Emgs9zxjdwCqha16pYU6kYCNmPGjEyvU6kNzdaVbQXIaAzoj8DvgF2AIWnOKVHXUcARwLcLCNC1hBj0m0TRWwa8PZaNBe4rkMbm1XEccEU5O9pRgGrZLbnmmmts/Pjx6+qvpfgkbWjWBZ2tQjkBStsFeythB/wjKY8vipndCCBpMqE7R/w8AjiasLVjOXCfpFuAE4FzzGwxQZT6IGmomeVchSwD+sbkdWraLZk2bRqbbropI0aMqNs6n2p1ZZ3sSLsZ9c+EFkg12YHQlZuXyHsEeHuKc3eX9FtJvwE+A3yt0EGSuiTNlTR36dKlA7e4yajVBs5WWWTo64hqQKnmka3v1uwKPAxMTXN8yjovItEFA6YAi/OOOQW4O6trJlM7dsHMqt8taZXtFT6GlA1ktBVjKTCcMPv1OsEVR76QbV2J8Em6CJhgZifHz7sB95vZ8MQxnwP2N7PDKqm7zHXdKX2VaJWWD7TPlphqM5DAhEm+RfgVqCbzgMGStjeznDLsQsZT6mZ2K3Dr5MmTT8my3nanlcQHWmdLTKOTSoDMbGZWF5Q0OF63A+iI64veMLMVkm4ELpD0MUK373Bg76yuHa+fawFlWW1b02riA76OqFZUFJhQ0uaSpkg6QdLmMW+YpErqmQG8CpxDiKrxaswDOJ0QbWMJYUr+NDPLvAVkZl2jRo3Kstq2pRXFB9zjYs0oNUCUS4QWy1cJCwTXEjan7h7LbgPOT1NPIyRSeER00tEqA87F8HVEA4eMFiJ+hbAb/iPApChCOQHqAv6Ypp5GSu06C5ZkIA9YIfHxB9bJJysBWgR8PL7vyBOgA4CX0tTTSKndBWgg08zFxMenrZ18shKgV4H3WmEBOgR4JU09jZC8Cxbo776wYt0ud3/hFKKcAKUdPH6MMCNViEMIe8WaAvNBaKB/08ylBpx92trpD2kF6CLgNEnfA95L+HXbVdKFwMeBi6tkn1MlipLuk7oAAA/sSURBVE0nF8svN9tVaX2OA6R3SEbYZf40G7rheAY4Lm0djZDwLpiZVTZmk2a2y8eAnEKQtUdEwqbRvYEdIWzlaMbU7oPQZulmrSqZavdZMCefcgKUai9YK9KoYXkaiVZdZOjUjqz2giFpHKH7Mp7CLlnP7p+JTiPi4uPUglQCJOkDwA8AEcLxrM47xICmECDfC1YeFx+nVqR1x/FXgr/lU82sjyuOZsS7YIVx8XGypN+RUfMYDXy/VcTHKYyLj1Nr0grQjcD+VbSj4aiHO85aXzN5vQkTJjB58uSmEp9mcJnaDDbWlVJTZLlE8IZ4LfA94ATg0PyUpp5GSqWm4euxpqXW12yE0DkDoRnWHTWDjdWGjPaC7Qr8lQzigtU7kWIhYj32NdX6ms2+d6sZ7G8GG6tNOQFKOwj9p/j2C8BT9J0Fw8z6uo9rYEoNQg8aNIhC90USa9eurYo9tb5mPb5jljSD/c1gY7XJahB6B0JsrtvNbL6Z9eanbMxtDOqxr6nW1xw3blxNr5c1zbD3rBlsrDdpBehBoG3uWj3ccdbymosWLSr4y9xMLkebwWVqM9hYd0r1z2z9uMluhCCBHwLGEQalN0hp6mmkVG4vWD32NdXimsm9XTNmzGjqvVvNsPesGWysJmQ0BpTrsBY92Mw6BqSENaYdFyL6Oh+n1mS1F+yjVD8umFNFXHycRiRtXLDZVbajZrTjXjAXH6dRqSguWCtgbeaS1cXHaWSKtoAkPQicbGZ/kfQHynTBzGzPrI1zBoaLj9PolOqCPU6IhpF772NATYSLj9MMFBUgM/tI4v3JNbHGyQQXH6dZKDsGFGO/r5J0RC0McgaGi4/TTJQVIDN7DVgCvFF9cwaGpA9KWlpvO+qFi4/TbKSdBfsO8ClJQ6ppzECQNAg4hhAqqO1w8XGakbQLETcDdgKelnQn8A82HJQ2q79T+hOAG4DP1dmOmuPi4zQraVtARwOrCG44phBaGsfmpVRIOkPS3DiuNDuvbAtJN0laIalX0gkp6+wgBE78UVo7WgUXH6eZSbsSetsMr/kcIdTzQcDGeWXfIojcGIITtNskPWJmj0saS2jh5HNMrOvHZrZWUoamNjYuPk6zkzouWFaY2Y0AkiYDE3L5kkYQWlo7mdly4D5JtwAnEnwRLQb2LVSnpLcBu0n6ELC9pP82s09V+avUFRcfpxVIvRVD0s6SfiTpr7H7tHvMnyXpkAxs2YHg2nVeIu8R4O3lTjSzs83sQDM7GJhfTHwkdcXu39ylS5t3sszFx2kVUglQFJiHgLHA/wDJ2bBVwCczsGUTYFle3jJg00oqKbX138x6zGyymU3eaqut+mFi/XHxcVqJtC2gLwOzzWwqkO/O7WHCeM1AWQ6MzMsbCbySQd3rkHSYpJ5ly/K1rvFx8XFajbQCtCPrZ5jy94S9DGyRgS3zgMGStk/k7ULYh5YZzbob3sXHaUXSCtAS4M1Fyt4OLEh7QUmDJQ0DOoCOuNVjsJmtIARAvEDSCEn7AIcDV6etO+X1m64F5OLjtCppBeg6gjAkZ6FM0g7A2UAl4R5nEHbZn0PwMf1qzAM4nTA1v4QQCPE0M2vrFpCLj9PKpPUJPRT4CXAIsBjYBniWMCj9K+BIM3u9inZmRsIj4inz58+vtzklcfFxmp1yPqFTCVCisgOAA4AtgReBO83s1wO2sg40ulN6Fx+nFcjKKT0AZnYncOeArXJK4uLjtAsVCZCkA4E9CV2wRcDvm60F1OhO6V18nHYi7ULEcZJ+D/wCOIOwIfUM4JeSHpQ0voo2ZkojD0K7+DjtRtpZsB5Cq2dfMxtrZjub2ViCEI0l+AtyBoCLj9OOpBWgacBZZvZAMtPM7idMp78na8OqRSOuA3LxcdqVtAL0D9ZHyMjnVeD5bMypPo3WBXPxcdqZtAJ0MWEh4oRkZvz8JfruD3NS4OLjtDtpZ8EOBEYDf5X0R8JK5a2B3eP790p6bzzWzOz4zC1tMVx8HCe9AG0JzI8Jwi7114DcmFDT+LZohGl4Fx/HCVS0ErqVqNdKaBcfp50otxI67TqgYWXKx1VqWDvi4uM4G5J2EPphSe8qVCDpw8Bj2ZnUmrj4OE5f0grQPIKT+ItzwQklbS3pZuD7wPeqZWDW1GMdkIuP4xQmlQCZ2b8CXcBpwFxJnyZ4KnwbMMXMzqqeidlS63VALj6OU5zUm1HN7CpJfwJ+B3wD+BNha8Zr1TKu2XHxcZzSVBKW51+B2wmBBS8DdgZ+JGnrKtnW1Lj4OE550s6C/QC4GfgpsLOZfRrYG9ge+IskX3iYwMXHcdJRyWbUg83s1Og8HjObC+wGzAauqY55zYeLj+OkJ+0Y0E5m1mfayMxWAf8u6cZszWpOXHwcpzJSCVBOfGIM9j2ANwFXmtliSdsBj1bPxGyp1lYMFx/HqZy0Y0CbSPoxQWi+B1wI5FY/X0zYEd8UVGMa3sXHcfpH2jGgbxAGnd9LiNWuRNnPgYMztqtpcPFxnP6TdgzoKODTZvYbSR15Zb1AZ7ZmNQcuPo4zMNK2gDYGXihStimwJhtzmgcXH8cZOGkF6A/ASUXKjmG9X6C2wMXHcbIhbRdsBnCHpDuA6wEDDpV0JkGA9quSfamQNIkgkrk48sea2dJqXMvFx3GyI+1m1PsIIZmHErZhCDgfeDPwXjP7Q9UsTM89ZrZ/TC4+jtMEVLIZ9X5giqSNgc2Bl8xsZdUsq5x9JN0L3At0W8auHl18HCd7Um9GzWFmr5rZc/0VH0lnSJoraZWk2XllW0i6SdIKSb2STkhZ7SJgO0JXcGvCrN2AkLRBGjdunIuP42RMRbHhM+I54CLgIMLsWpJvAauBMcCuwG2SHjGzxyWNBW4oUN8xZrYYWAUQt4W8G/hJfw2UVDB/xYoVLj6OkyE1FyAzuxFA0mRgXZwxSSOAown7zpYTPDDeApwInBNFZt9CdUoaaWYvx49TgP+r4ldwHCcjKu6CVZEdgDVmNi+R9wjw9hTnTpX0UBwDGg/8sNBBkrpi92/u0qVVGad2HKcC6tEFK8YmQP6O+2WEhY4lMbNbgVtTHNcD9EAIy9MPGx3HyZBGagEtJwQ8TDISeCXLi9TDKb3jOIVpJAGaBwyWtH0ibxfWLy7MhDS74YvN4LdrEEfHqRY1FyBJg2Ogww6gQ9IwSYOjp8UbgQskjZC0D3A4cHXG10/VAjKzPslxnGypRwtoBvAqcA7wofh+Riw7nTA1vwS4FjjNzGreAnIcpza0XWz4hEfEU+bPn19vcxynpckkNnwr4S0gx2kc2k6AHMdpHNpOgHwa3nEah7YbA8ohaSnBnWyzsyXwfL2NaFL83vWftPeu08y2KlbYtgLUKkiaW2qQzymO37v+k9W9a7sumOM4jYMLkOM4dcMFqPnpqbcBTYzfu/6Tyb3zMSDHceqGt4Acx6kbLkCO49QNF6A2QdIH49onJyWS9pL0O0n3SLpW0pB629ToSJol6V5JN0gaXu54F6A2QNIgQgDJZ+ptS5PRC0wzs6nA3wjuYZwiSNoJeIuZTQHuAD5a7hwXoPbgBEJEkbX1NqSZiOGnXo0f38DvXzmmALfH97dTJIhEEhegBqIaMdMkdQDHAT+qgskNQ5XizeXO3xY4BPhZhiY3LAO4l5uz3q/7MmCLctdqJKf0ThVipsW6fmxma4vFO2sRqhJvTtJI4AfAiWa2unrmNxT9upfAP4Gcn5tRwIvlLuTrgBoQSRcBE8zs5Ph5BOGPu1MubJGkq4GFZnZOmbq+AuxG6D7sBfzAzD5VRfPrSsb3bjDwU+DrZnZXVQ1vQCq9l5LeAZxrZidI6gKGmtmlpa7hXbDmoN8x08zsbDM70MwOBua3svgUYSDx5j4IvAs4T9Ldko6vhoFNRMl7aWaPAr0xPt9BwJXlKvQuWHPQ75hpSdp05/dA4s1dTcZBEZqcsvfSzM6tpEJvATUHNYmZ1qL4vcuOzO+lC1BzUJOYaS2K37vsyPxeugA1EPWOmdbM+L3Ljprey0IB+DzVJwEzActLM2PZFsDNwApgAXBCve1tpOT3rjnvpU/DO45TN7wL5jhO3XABchynbrgAOY5TN1yAHMepGy5AjuPUDRcgx3HqhguQ4zh1wwXIaUiiUyxLfN5fkkW3n2nr6JJ0RIY27RRt2D+rOtsdFyCnWfgjwZ/RXys4pwvITICc7HF3HE5VkLSxrfenPGDM7GXgf7Oqz2kMvAXklEXS7Ogj+AhJT0h6TdJ9kt6WOMYkfVbSN2P4n0dj/jBJX5X0TPQx/IikQ/PqHyrpMkkvSXpR0n8CQ/KO6dMFk9Qh6VxJ82Ldz+Z8GEu6G9gD+HA8zySdnDj3Y5Iej+f1SjqrwPc+Pdq9QtKtwDYDv5tOEm8BOWnpBL4BfBF4FTgf+KWk7c3stXjM54HfAiey/sftBmBP4EuE7tNxwC2SJpvZw/GYS4CPAd3AX4BTgGNT2PQd4CTgq8A9hI2Sx8Sy04GfEMLpXBjz/gog6fPAxfG8uwlCdaGklWZ2WTzmcIL/4ysImy+nksLDn1Mh9d5566nxEzCbsCN670ReJyFUzanxswF/yjvvgJg/NS//t8D18f1ogqCdnSgfBDwR/j3X5e0f69opft4xfv5UCbvnArPz8kYSHGt9KS//AmAx0BE/PwjcnnfMd+M196/336RVknfBnLQsMbMHch/MrBd4iNC6yXFb3jnvJTzU90cfM4Ojo/c7gZx72HcAwwjO33N1r01+LsJ74uvsCr/HXsAI4Po8m+4iRHqYoBDKaLcCNtxY4bWcMngXzEnLkiJ5yXGRf+SVbwmMBV4vcO6a+Dq2SP2FrpdkNLDCwuB0JWwZX4t58XsTsIrwbFRqk1MhLkBOWrYukpd8kPOdS70ILKT0VPjiRF3JOFKFrpfkBWCEpJEVilDuGv9CX8EEeBJYSehe5ttQzianQlyAnLRsLWnvXDdM0kRgd+CqEufcCXwOWG5mTxQ55lHgNYJrzydi3YMoH4c9F6frJOCyIsesJnTvkvyOMOY0zszyu4zrkPRwtOGKRPZRZWxyKsQFyEnL88DVknKzYBcQuiSzS5zza+CXwK9jgMTHCYPAuwLDzOxcM3tBUg9wvqQ34jGnEELAFMXMnoznfV3S1oSB7c0IEU0/EA97AjhI0kGEFtPf4/VmAv8lqTOeN4gQ8+o9ZnZkPPdi4EZJ3wZuIsyCHZzmRjkVUO9RcE+NnwgiM5fQAphHGCO5nzgjFY8x4IwC5w4lTNk/RWiRLAZ+Abw/75jLCTGm/glcCnyWErNgMa8D+AJhqn018CxwVaL8zcAdsV4DTk6UfYgwiP5qvObvgc/m2X5GrHMl8HPgQHwWLNPkPqGdssTFfTtZewY2dKqIT8M7jlM3XIAcx6kb3gVzHKdueAvIcZy64QLkOE7dcAFyHKduuAA5jlM3XIAcx6kbLkCO49SN/w8n0WywRAXkWQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "################################# Predict metabolome from individual's metagenome.\n",
    "from numpy import array\n",
    "from scipy.sparse import csr_matrix\n",
    "import numpy.matlib\n",
    "from scipy.optimize import minimize, rosen, rosen_der\n",
    "from scipy.stats import pearsonr\n",
    "\n",
    "MAX_ID_microbes = len(i_nonzero_microbes)  # MAX_ID_microbes is the maximum of ID labels for microbes.\n",
    "MAX_ID_metabolites = len(i_nonzero_metabolites)  # MAX_ID_metabolites is the maximum of ID labels for metabolites.\n",
    "\n",
    "def Ain_out(b_real, net):\n",
    "    '''\n",
    "    Ain_out is a function used to create sparse matrices made of metabolites and microbes \n",
    "    where metabolite consumption and production is considered. The matrices created are \"m2b\" and \"b2m\":\n",
    "    (1) m2b is a matrix determines the nutrient splitting among microbes, and\n",
    "    (2) b2m is a matrix determines the byproducts generation.\n",
    "    Both matrices have rows representing bacterial species and columns representing metablolites.\n",
    "    Two matrices are created based on (1) the metabolite consumption and production network which is \n",
    "    encode in \"net\" as a dataframe, and (2) the experimentally measured bacterial abundance \"b_real\".\n",
    "    '''\n",
    "    valid_index = np.where((net['edgeType']==2) | (net['edgeType']==5))[0]\n",
    "    row = net['metabolites'].iloc[valid_index]\n",
    "    col = net['microbes'].iloc[valid_index]\n",
    "    data = np.ones((len(valid_index),))\n",
    "    m2b = csr_matrix( (data,(row,col)), shape=(MAX_ID_metabolites, MAX_ID_microbes)).toarray()#.todense()\n",
    "\n",
    "    valid_index = np.where((net['edgeType']==3) | (net['edgeType']==5))[0]\n",
    "    row = net['metabolites'].iloc[valid_index]\n",
    "    col = net['microbes'].iloc[valid_index]\n",
    "    data = np.ones((len(valid_index),))\n",
    "    b2m = csr_matrix( (data,(row,col)), shape=(MAX_ID_metabolites, MAX_ID_microbes)).toarray()#.todense()\n",
    "\n",
    "    ########## Normalize the b2m by out_degree\n",
    "    out_degree = b2m.sum(0).copy()\n",
    "    out_degree[out_degree==0]=100\n",
    "    b2m = (b2m / out_degree)\n",
    "\n",
    "    ########## Normalize the m2b by proportion of microbial abundance in each individual\n",
    "    b_real_repmat = numpy.matlib.repmat(b_real[np.newaxis,:], MAX_ID_metabolites, 1)\n",
    "    m2b = m2b * b_real_repmat\n",
    "    in_degree = m2b.sum(1)\n",
    "    in_degree[in_degree==0]=100\n",
    "    m2b = m2b / numpy.matlib.repmat(in_degree[:,np.newaxis], 1, MAX_ID_microbes)\n",
    "    m2b = np.float32(m2b)\n",
    "    b2m = np.float32(b2m)\n",
    "    return [m2b, b2m]\n",
    "\n",
    "def m2b_multiple_levels(f, m2b, b2m, numLevels_max):\n",
    "    '''\n",
    "    m2b_multiple_levels is a function used to generate matrices involving the calculation of metabolite \n",
    "    byproducts and microbial biomass after several trophic levels/layers. Those matrices are:\n",
    "    (1) m2m_layer is a conversion matrix from the nutrient intake to the metabolite byproducts at a trophic\n",
    "    level or layer.\n",
    "    (2) m2m_total is a conversion matrix from the nutrient intake to a summation of metabolite byproducts at\n",
    "    all trophic levels or layers.\n",
    "    (3) m2b_total is a conversion matrix from the nutrient intake to a summation of all microbial/bacterial \n",
    "    biomass gain at all trophic levels or layers.\n",
    "    Those matrices are computed based on (1) metabolite consumption matrix \"m2b\", (2) metabolite byproduct\n",
    "    generation matrix \"b2m\", (3) byproduct/leakage fraction \"f\", and (4) number of trophic levels/layers in the \n",
    "    simulation \"numLevels_max\".\n",
    "    '''\n",
    "    m2m_layer = np.zeros((MAX_ID_metabolites, MAX_ID_metabolites, numLevels_max));  \n",
    "    #m2b_total = np.zeros((MAX_ID_metabolites, MAX_ID_microbes));  \n",
    "    m2b_total = np.zeros((MAX_ID_metabolites, MAX_ID_metabolites));  \n",
    "    \n",
    "    f_mul = numpy.matlib.repmat(f, 1, MAX_ID_metabolites)\n",
    "    #s_step =  np.dot(b2m, m2b.T) # s_step is the conversion matrix of each trophic level/layer\n",
    "    s_step =  np.dot(b2m, f_mul*m2b.T) # s_step is the conversion matrix of each trophic level/layer\n",
    "    s_step_ii = np.eye(MAX_ID_metabolites, MAX_ID_metabolites);\n",
    "    #f_mul = numpy.matlib.repmat(f[np.newaxis,:], MAX_ID, 1)#numpy.matlib.repmat(f, 1, MAX_ID)\n",
    "    #f_mul = numpy.matlib.repmat(f, 1, MAX_ID_metabolites)\n",
    "    \n",
    "    for ii in range(numLevels_max):\n",
    "        # m2b_total is a series made of s_step of each layer\n",
    "        #m2b_total = m2b_total + f_mul**(ii) * s_step_ii\n",
    "        #m2m_layer[:,:,ii] = f_mul**(ii) * s_step_ii\n",
    "        m2b_total = m2b_total + s_step_ii\n",
    "        m2m_layer[:,:,ii] = s_step_ii\n",
    "        s_step_ii = np.dot(s_step_ii, s_step);  \n",
    "    m2m_total = m2b_total;\n",
    "    m2b_total = np.dot((1 - f_mul) * m2b.T, m2b_total) # m2b_total has an extra multiplication of m2b and (1-f).\n",
    "    return [m2b_total, m2m_total, m2m_layer]\n",
    "\n",
    "def pred_error(x, b_real, m2b_total, i_intake):\n",
    "    '''\n",
    "    pred_error is a function used to compute the logarithmic error between experimentally measured\n",
    "    metagenome and predicted metagenome computed from the model for a certain nutrient intake. It relies on \n",
    "    (1) x: the nutrient intake, (2) i_intake: IDs of the nutrient intake, (3) m2b_total: a conversion matrix \n",
    "    from thenutrient intake to the total biomass, and (4) b_real: experimentally measured metagenome. The \n",
    "    first three is used to compute the metagenome predicted by the model \"ba_pred\" and compare it with the \n",
    "    experimentally measured metagenome \"b_real\".\n",
    "    '''\n",
    "    x_full = np.zeros((MAX_ID_metabolites,));\n",
    "    x_full[i_intake] = x;\n",
    "    \n",
    "    ba_pred = np.dot(m2b_total, x_full)\n",
    "    pred_error = (np.log10(ba_pred + 1e-6) - np.log10(b_real +1e-6)) / np.log10(b_real +1e-6);\n",
    "    pred_error = np.sqrt(np.dot(pred_error, pred_error.T)) #np.sqrt(np.sum(pred_error**2))\n",
    "    return pred_error\n",
    "\n",
    "def calc_metabolome(x, m2m_layer, numLevels_max, i_intake):\n",
    "    '''\n",
    "    calc_metabolome is a function used to calculate the metabolome from the fitted nutrient intake from the\n",
    "    model. It relies on (1) x: the nutrient intake, (2) i_intake: IDs of the nutrient intake, (3) m2m_layer: \n",
    "    a conversion matrix from the nutrient intake to the metabolite byproducts at a trophic level or layer, \n",
    "    and (4) numLevels_max: the number of trophic levels/layers in the model. The metabolome in the model is \n",
    "    assumed to be composed of two parts: (1) met_levels: all metabolites in the final trophic level/layer \n",
    "    (which is considered to be reaching the end of the gut because of the finite gut length and gut motility.),\n",
    "    and (2) met_leftover_levels: all unusable metabolites from all previous trophic levels/layers. \n",
    "    '''\n",
    "    i_unused = np.where(np.sum(m2b.T,0) == 0)[0]\n",
    "    met_levels = np.zeros((MAX_ID_metabolites, numLevels_max));  \n",
    "    met_leftover_levels = np.zeros((MAX_ID_metabolites, numLevels_max));\n",
    "    \n",
    "    x_full = np.zeros((MAX_ID_metabolites,));\n",
    "    x_full[i_intake] = x;\n",
    "    \n",
    "    for ii in range(numLevels_max):\n",
    "        met_levels[:,ii] = np.dot(m2m_layer[:,:,ii], x_full)\n",
    "        if ii==0:\n",
    "            met_leftover_levels[i_unused,ii] = x_full[i_unused]\n",
    "        else:\n",
    "            met_leftover_levels[i_unused,ii] = met_levels[i_unused,ii-1]\n",
    "            \n",
    "    return [met_levels, met_leftover_levels]\n",
    "\n",
    "f_byproduct = 0.9\n",
    "f = f_byproduct * np.ones((MAX_ID_microbes,1));\n",
    "f[i_selfish] = 0.0;  # The byproduct/leakage fraction f for microbes that don't generate byproducts is set as 0.\n",
    "\n",
    "numLevels_max = 4\n",
    "\n",
    "######## Select an ID of a individual and pull out its experimentally measured metagenome:\n",
    "pa = 5; \n",
    "b_real = np.zeros((MAX_ID_microbes,))\n",
    "b_real[metagenome_ID] = metagenome.iloc[:,pa] / np.sum(metagenome.iloc[:,pa])\n",
    "\n",
    "######## Compute matrices involving the metabolite consumption and generation:\n",
    "m2b, b2m = Ain_out(b_real, net)\n",
    "m2b_total, m2m_total, m2m_layer = m2b_multiple_levels(f, m2b, b2m, numLevels_max)\n",
    "#m2b_total, m2m_total, m2m_layer = m2b_multiple_levels(i_nonzero_microbes, i_nonzero_metabolites, f, m2b, b2m, numLevels_max)\n",
    "\n",
    "######## Assign diet\n",
    "x0 = np.ones((len(i_intake),)) / len(i_intake)\n",
    "\n",
    "######## The model is converted into an optimization problem where the nutrient intake is constantly changed to\n",
    "# minimize the logarithmic error between experimentally measured metagenome and predicted metagenome computed \n",
    "# from the model for a certain nutrient intake.\n",
    "fun = lambda x: pred_error(x, b_real, m2b_total, i_intake)\n",
    "bnds = ((0, 100), ) * len(x0)\n",
    "res = minimize(fun, x0, method='SLSQP', bounds=bnds, options={'disp': True, 'maxiter': 1000}, tol=1e-3)\n",
    "#res = minimize(fun, x0, method='Nelder-Mead', bounds=bnds, options={'disp': True})\n",
    "#res = minimize(fun, x0, method='TNC', bounds=bnds, options={'disp': True, 'maxiter': 1000})\n",
    "print(res)\n",
    "\n",
    "######## As long as the optimized nutrient intake is found by using the above optimization solver, the\n",
    "# optimized nutrient intake \"res.x\" is used to generate the predict metagenome and metabolome. They are\n",
    "# visually and statistically compared to the experimentally measured metagenome and metabolome.\n",
    "x_full = np.zeros((MAX_ID_metabolites,));\n",
    "x_full[i_intake] = res.x;\n",
    "ba_pred = np.dot(m2b_total, x_full)\n",
    "\n",
    "#### Metagenome comparison\n",
    "fig, ax = plt.subplots()\n",
    "ax.loglog(ba_pred+1e-5, b_real+1e-5, 'ko')\n",
    "ax.plot([1e-5, 1], [1e-5, 1],'k-')\n",
    "ax.set_aspect('equal')\n",
    "ax.set_xlabel('predicted')\n",
    "ax.set_ylabel('experimentally observed')\n",
    "ax.set_title('Metagenome comparison')\n",
    "\n",
    "met_levels, met_leftover_levels = calc_metabolome(res.x, m2m_layer, numLevels_max, i_intake)\n",
    "metabolome_measured = np.zeros((MAX_ID_metabolites,))\n",
    "#metabolome_measured[metabolome_ID.values] = metabolome.iloc[:,pa]\n",
    "metabolome_measured[metabolome_ID] = metabolome.iloc[:,pa]\n",
    "metabolome_pred = met_levels[:, -1] + met_leftover_levels.sum(1) #np.dot(m2m_total, x_full)\n",
    "#metabolome_pred = np.dot(m2m_total, x_full)\n",
    "i_common = np.where(metabolome_measured * metabolome_pred > 1e-5)[0]\n",
    "metabolome_pred_common = metabolome_pred[i_common] / np.sum(metabolome_pred[i_common])\n",
    "metabolome_measured_common = metabolome_measured[i_common] / np.sum(metabolome_measured[i_common])\n",
    "\n",
    "#### Metabolome comparison\n",
    "fig, ax = plt.subplots()\n",
    "ax.loglog(metabolome_pred_common+1e-5, metabolome_measured_common+1e-5, 'ko')\n",
    "ax.plot([1e-5, 1], [1e-5, 1],'k-')\n",
    "ax.set_aspect('equal')\n",
    "ax.set_xlabel('predicted')\n",
    "ax.set_ylabel('experimentally observed')\n",
    "ax.set_title('Metabolome comparison')\n",
    "\n",
    "print('-------------------------------------------------------------------------------------------------------------')\n",
    "print('(Correlation coefficient, P-value) of the correlation between predicted and experimentally measured metagonome:')\n",
    "print(pearsonr(ba_pred[b_real>0], b_real[b_real>0]))\n",
    "print('(Correlation coefficient, P-value) of the correlation between predicted and experimentally measured metabolome:')\n",
    "print(pearsonr(metabolome_pred_common, metabolome_measured_common))\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Run the simulation with reduced matrix forms for all individuals for NSJ16 links"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0\n",
      "-------------------------------------------------------------------------------------------------------------\n",
      "(Correlation coefficient, P-value) of the correlation between predicted and experimentally measured metagonome:\n",
      "0.4264852667826322\n",
      "(Correlation coefficient, P-value) of the correlation between predicted and experimentally measured metabolome:\n",
      "0.6529538363213335\n",
      "1\n",
      "-------------------------------------------------------------------------------------------------------------\n",
      "(Correlation coefficient, P-value) of the correlation between predicted and experimentally measured metagonome:\n",
      "0.9011443312797254\n",
      "(Correlation coefficient, P-value) of the correlation between predicted and experimentally measured metabolome:\n",
      "0.5125407949535865\n",
      "2\n",
      "-------------------------------------------------------------------------------------------------------------\n",
      "(Correlation coefficient, P-value) of the correlation between predicted and experimentally measured metagonome:\n",
      "0.8058052669743445\n",
      "(Correlation coefficient, P-value) of the correlation between predicted and experimentally measured metabolome:\n",
      "0.7508803126168367\n",
      "3\n",
      "-------------------------------------------------------------------------------------------------------------\n",
      "(Correlation coefficient, P-value) of the correlation between predicted and experimentally measured metagonome:\n",
      "0.8249328049602644\n",
      "(Correlation coefficient, P-value) of the correlation between predicted and experimentally measured metabolome:\n",
      "0.7689774569325084\n",
      "4\n",
      "-------------------------------------------------------------------------------------------------------------\n",
      "(Correlation coefficient, P-value) of the correlation between predicted and experimentally measured metagonome:\n",
      "0.854447148040389\n",
      "(Correlation coefficient, P-value) of the correlation between predicted and experimentally measured metabolome:\n",
      "0.6821088225230025\n",
      "5\n",
      "-------------------------------------------------------------------------------------------------------------\n",
      "(Correlation coefficient, P-value) of the correlation between predicted and experimentally measured metagonome:\n",
      "0.8765075557343968\n",
      "(Correlation coefficient, P-value) of the correlation between predicted and experimentally measured metabolome:\n",
      "0.569951792281159\n",
      "6\n",
      "-------------------------------------------------------------------------------------------------------------\n",
      "(Correlation coefficient, P-value) of the correlation between predicted and experimentally measured metagonome:\n",
      "0.8164449222226515\n",
      "(Correlation coefficient, P-value) of the correlation between predicted and experimentally measured metabolome:\n",
      "0.5656970852166661\n",
      "7\n",
      "-------------------------------------------------------------------------------------------------------------\n",
      "(Correlation coefficient, P-value) of the correlation between predicted and experimentally measured metagonome:\n",
      "0.7801013436453278\n",
      "(Correlation coefficient, P-value) of the correlation between predicted and experimentally measured metabolome:\n",
      "0.5218332256188335\n",
      "8\n",
      "-------------------------------------------------------------------------------------------------------------\n",
      "(Correlation coefficient, P-value) of the correlation between predicted and experimentally measured metagonome:\n",
      "0.6825815283156419\n",
      "(Correlation coefficient, P-value) of the correlation between predicted and experimentally measured metabolome:\n",
      "0.7817900834768807\n",
      "9\n",
      "-------------------------------------------------------------------------------------------------------------\n",
      "(Correlation coefficient, P-value) of the correlation between predicted and experimentally measured metagonome:\n",
      "0.9730412745097231\n",
      "(Correlation coefficient, P-value) of the correlation between predicted and experimentally measured metabolome:\n",
      "0.5418894661381514\n",
      "10\n",
      "-------------------------------------------------------------------------------------------------------------\n",
      "(Correlation coefficient, P-value) of the correlation between predicted and experimentally measured metagonome:\n",
      "0.6793249794855232\n",
      "(Correlation coefficient, P-value) of the correlation between predicted and experimentally measured metabolome:\n",
      "0.6677576541856501\n",
      "11\n",
      "-------------------------------------------------------------------------------------------------------------\n",
      "(Correlation coefficient, P-value) of the correlation between predicted and experimentally measured metagonome:\n",
      "0.8246508928704607\n",
      "(Correlation coefficient, P-value) of the correlation between predicted and experimentally measured metabolome:\n",
      "0.5653770777636514\n",
      "12\n",
      "-------------------------------------------------------------------------------------------------------------\n",
      "(Correlation coefficient, P-value) of the correlation between predicted and experimentally measured metagonome:\n",
      "0.978326467409985\n",
      "(Correlation coefficient, P-value) of the correlation between predicted and experimentally measured metabolome:\n",
      "0.5549022140815238\n",
      "13\n",
      "-------------------------------------------------------------------------------------------------------------\n",
      "(Correlation coefficient, P-value) of the correlation between predicted and experimentally measured metagonome:\n",
      "0.6875887006717701\n",
      "(Correlation coefficient, P-value) of the correlation between predicted and experimentally measured metabolome:\n",
      "0.48940313140968145\n",
      "14\n",
      "-------------------------------------------------------------------------------------------------------------\n",
      "(Correlation coefficient, P-value) of the correlation between predicted and experimentally measured metagonome:\n",
      "0.6573005189824788\n",
      "(Correlation coefficient, P-value) of the correlation between predicted and experimentally measured metabolome:\n",
      "0.4223893032881784\n",
      "15\n",
      "-------------------------------------------------------------------------------------------------------------\n",
      "(Correlation coefficient, P-value) of the correlation between predicted and experimentally measured metagonome:\n",
      "0.9694045603660771\n",
      "(Correlation coefficient, P-value) of the correlation between predicted and experimentally measured metabolome:\n",
      "0.5654415398240481\n",
      "16\n",
      "-------------------------------------------------------------------------------------------------------------\n",
      "(Correlation coefficient, P-value) of the correlation between predicted and experimentally measured metagonome:\n",
      "0.6592519660121644\n",
      "(Correlation coefficient, P-value) of the correlation between predicted and experimentally measured metabolome:\n",
      "0.7310204743635058\n",
      "17\n",
      "-------------------------------------------------------------------------------------------------------------\n",
      "(Correlation coefficient, P-value) of the correlation between predicted and experimentally measured metagonome:\n",
      "0.953785465689431\n",
      "(Correlation coefficient, P-value) of the correlation between predicted and experimentally measured metabolome:\n",
      "0.5519902009997193\n",
      "18\n",
      "-------------------------------------------------------------------------------------------------------------\n",
      "(Correlation coefficient, P-value) of the correlation between predicted and experimentally measured metagonome:\n",
      "0.7565291161563831\n",
      "(Correlation coefficient, P-value) of the correlation between predicted and experimentally measured metabolome:\n",
      "0.7304309608075412\n",
      "19\n",
      "-------------------------------------------------------------------------------------------------------------\n",
      "(Correlation coefficient, P-value) of the correlation between predicted and experimentally measured metagonome:\n",
      "0.9031879630590502\n",
      "(Correlation coefficient, P-value) of the correlation between predicted and experimentally measured metabolome:\n",
      "0.6832822607229561\n",
      "20\n",
      "-------------------------------------------------------------------------------------------------------------\n",
      "(Correlation coefficient, P-value) of the correlation between predicted and experimentally measured metagonome:\n",
      "0.7630536986250274\n",
      "(Correlation coefficient, P-value) of the correlation between predicted and experimentally measured metabolome:\n",
      "0.5774059673776893\n",
      "21\n",
      "-------------------------------------------------------------------------------------------------------------\n",
      "(Correlation coefficient, P-value) of the correlation between predicted and experimentally measured metagonome:\n",
      "0.7700035345916794\n",
      "(Correlation coefficient, P-value) of the correlation between predicted and experimentally measured metabolome:\n",
      "0.6679272882344236\n",
      "22\n",
      "-------------------------------------------------------------------------------------------------------------\n",
      "(Correlation coefficient, P-value) of the correlation between predicted and experimentally measured metagonome:\n",
      "0.902676084804102\n",
      "(Correlation coefficient, P-value) of the correlation between predicted and experimentally measured metabolome:\n",
      "0.7102119626324975\n",
      "23\n",
      "-------------------------------------------------------------------------------------------------------------\n",
      "(Correlation coefficient, P-value) of the correlation between predicted and experimentally measured metagonome:\n",
      "0.8927271129828811\n",
      "(Correlation coefficient, P-value) of the correlation between predicted and experimentally measured metabolome:\n",
      "0.7756813437783495\n",
      "24\n",
      "-------------------------------------------------------------------------------------------------------------\n",
      "(Correlation coefficient, P-value) of the correlation between predicted and experimentally measured metagonome:\n",
      "0.96935779901318\n",
      "(Correlation coefficient, P-value) of the correlation between predicted and experimentally measured metabolome:\n",
      "0.5352094201755129\n",
      "25\n",
      "-------------------------------------------------------------------------------------------------------------\n",
      "(Correlation coefficient, P-value) of the correlation between predicted and experimentally measured metagonome:\n",
      "0.4050883391885774\n",
      "(Correlation coefficient, P-value) of the correlation between predicted and experimentally measured metabolome:\n",
      "0.3812994999489509\n",
      "26\n",
      "-------------------------------------------------------------------------------------------------------------\n",
      "(Correlation coefficient, P-value) of the correlation between predicted and experimentally measured metagonome:\n",
      "0.9698716333153009\n",
      "(Correlation coefficient, P-value) of the correlation between predicted and experimentally measured metabolome:\n",
      "0.701931276913292\n",
      "27\n",
      "-------------------------------------------------------------------------------------------------------------\n",
      "(Correlation coefficient, P-value) of the correlation between predicted and experimentally measured metagonome:\n",
      "0.8330615223184958\n",
      "(Correlation coefficient, P-value) of the correlation between predicted and experimentally measured metabolome:\n",
      "0.5939302913346534\n",
      "28\n",
      "-------------------------------------------------------------------------------------------------------------\n",
      "(Correlation coefficient, P-value) of the correlation between predicted and experimentally measured metagonome:\n",
      "0.899763586164664\n",
      "(Correlation coefficient, P-value) of the correlation between predicted and experimentally measured metabolome:\n",
      "0.5305577891294646\n",
      "29\n",
      "-------------------------------------------------------------------------------------------------------------\n",
      "(Correlation coefficient, P-value) of the correlation between predicted and experimentally measured metagonome:\n",
      "0.7790605038069409\n",
      "(Correlation coefficient, P-value) of the correlation between predicted and experimentally measured metabolome:\n",
      "0.7376868336415021\n",
      "30\n",
      "-------------------------------------------------------------------------------------------------------------\n",
      "(Correlation coefficient, P-value) of the correlation between predicted and experimentally measured metagonome:\n",
      "0.17689971639403446\n",
      "(Correlation coefficient, P-value) of the correlation between predicted and experimentally measured metabolome:\n",
      "0.5040594387290794\n",
      "31\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "-------------------------------------------------------------------------------------------------------------\n",
      "(Correlation coefficient, P-value) of the correlation between predicted and experimentally measured metagonome:\n",
      "0.7108908874329506\n",
      "(Correlation coefficient, P-value) of the correlation between predicted and experimentally measured metabolome:\n",
      "0.5878886369468715\n",
      "32\n",
      "-------------------------------------------------------------------------------------------------------------\n",
      "(Correlation coefficient, P-value) of the correlation between predicted and experimentally measured metagonome:\n",
      "0.8864630454585144\n",
      "(Correlation coefficient, P-value) of the correlation between predicted and experimentally measured metabolome:\n",
      "0.6961391678417423\n",
      "33\n",
      "-------------------------------------------------------------------------------------------------------------\n",
      "(Correlation coefficient, P-value) of the correlation between predicted and experimentally measured metagonome:\n",
      "0.986176875879008\n",
      "(Correlation coefficient, P-value) of the correlation between predicted and experimentally measured metabolome:\n",
      "0.592952328995068\n",
      "34\n",
      "-------------------------------------------------------------------------------------------------------------\n",
      "(Correlation coefficient, P-value) of the correlation between predicted and experimentally measured metagonome:\n",
      "0.5908428407623538\n",
      "(Correlation coefficient, P-value) of the correlation between predicted and experimentally measured metabolome:\n",
      "0.5871530829855477\n",
      "35\n",
      "-------------------------------------------------------------------------------------------------------------\n",
      "(Correlation coefficient, P-value) of the correlation between predicted and experimentally measured metagonome:\n",
      "0.3354147936534358\n",
      "(Correlation coefficient, P-value) of the correlation between predicted and experimentally measured metabolome:\n",
      "0.45756681663310456\n",
      "36\n",
      "-------------------------------------------------------------------------------------------------------------\n",
      "(Correlation coefficient, P-value) of the correlation between predicted and experimentally measured metagonome:\n",
      "0.9029675099569258\n",
      "(Correlation coefficient, P-value) of the correlation between predicted and experimentally measured metabolome:\n",
      "0.7655944139627233\n",
      "37\n",
      "-------------------------------------------------------------------------------------------------------------\n",
      "(Correlation coefficient, P-value) of the correlation between predicted and experimentally measured metagonome:\n",
      "0.16592525731382513\n",
      "(Correlation coefficient, P-value) of the correlation between predicted and experimentally measured metabolome:\n",
      "0.4624534356331108\n",
      "38\n",
      "-------------------------------------------------------------------------------------------------------------\n",
      "(Correlation coefficient, P-value) of the correlation between predicted and experimentally measured metagonome:\n",
      "0.8287701911734202\n",
      "(Correlation coefficient, P-value) of the correlation between predicted and experimentally measured metabolome:\n",
      "0.5758689820996707\n",
      "39\n",
      "-------------------------------------------------------------------------------------------------------------\n",
      "(Correlation coefficient, P-value) of the correlation between predicted and experimentally measured metagonome:\n",
      "0.852832426091764\n",
      "(Correlation coefficient, P-value) of the correlation between predicted and experimentally measured metabolome:\n",
      "0.6230555463679136\n",
      "40\n",
      "-------------------------------------------------------------------------------------------------------------\n",
      "(Correlation coefficient, P-value) of the correlation between predicted and experimentally measured metagonome:\n",
      "0.8433786381374087\n",
      "(Correlation coefficient, P-value) of the correlation between predicted and experimentally measured metabolome:\n",
      "0.6681193791876443\n"
     ]
    }
   ],
   "source": [
    "net = net_reduced.copy()\n",
    "\n",
    "corr_list = np.zeros((metabolome.shape[1],2))\n",
    "diet_list = np.zeros((metabolome.shape[1], 20))\n",
    "for pa in range(metabolome.shape[1]):\n",
    "    print(pa)\n",
    "    ######## Select an ID of a individual and pull out its experimentally measured metagenome:\n",
    "    b_real = np.zeros((MAX_ID_microbes,))\n",
    "    b_real[metagenome_ID] = metagenome.iloc[:,pa] / np.sum(metagenome.iloc[:,pa])\n",
    "\n",
    "    ######## Compute matrices involving the metabolite consumption and generation:\n",
    "    m2b, b2m = Ain_out(b_real, net)\n",
    "    m2b_total, m2m_total, m2m_layer = m2b_multiple_levels(f, m2b, b2m, numLevels_max)\n",
    "\n",
    "    ######## Assign diet\n",
    "    x0 = np.ones((len(i_intake),)) / len(i_intake)\n",
    "\n",
    "    ######## The model is converted into an optimization problem where the nutrient intake is constantly changed to\n",
    "    # minimize the logarithmic error between experimentally measured metagenome and predicted metagenome computed \n",
    "    # from the model for a certain nutrient intake.\n",
    "    fun = lambda x: pred_error(x, b_real, m2b_total, i_intake)\n",
    "    bnds = ((0, 100), ) * len(x0)\n",
    "    res = minimize(fun, x0, method='SLSQP', bounds=bnds, options={'maxiter': 1000}, tol=1e-3)\n",
    "\n",
    "    ######## As long as the optimized nutrient intake is found by using the above optimization solver, the\n",
    "    # optimized nutrient intake \"res.x\" is used to generate the predict metagenome and metabolome. They are\n",
    "    # visually and statistically compared to the experimentally measured metagenome and metabolome.\n",
    "    x_full = np.zeros((MAX_ID_metabolites,));\n",
    "    x_full[i_intake] = res.x;\n",
    "    ba_pred = np.dot(m2b_total, x_full)\n",
    "\n",
    "    met_levels, met_leftover_levels = calc_metabolome(res.x, m2m_layer, numLevels_max, i_intake)\n",
    "    metabolome_measured = np.zeros((MAX_ID_metabolites,))\n",
    "    metabolome_measured[metabolome_ID] = metabolome.iloc[:,pa]\n",
    "    metabolome_pred = met_levels[:, -1] + met_leftover_levels.sum(1)\n",
    "    i_common = np.where(metabolome_measured * metabolome_pred > 1e-5)[0]\n",
    "    metabolome_pred_common = metabolome_pred[i_common] / np.sum(metabolome_pred[i_common])\n",
    "    metabolome_measured_common = metabolome_measured[i_common] / np.sum(metabolome_measured[i_common])\n",
    "    if i_common.shape[0] >= 2:\n",
    "        corr_list[pa, 0] = pearsonr(ba_pred[b_real>0], b_real[b_real>0])[0]\n",
    "        corr_list[pa, 1] = pearsonr(np.log10(metabolome_pred_common+1e-5), np.log10(metabolome_measured_common+1e-5))[0]\n",
    "    else:\n",
    "        corr_list[pa, 0] = -1\n",
    "        corr_list[pa, 1] = -1\n",
    "    diet_list[pa, :] = res.x\n",
    "\n",
    "    print('-------------------------------------------------------------------------------------------------------------')\n",
    "    print('(Correlation coefficient, P-value) of the correlation between predicted and experimentally measured metagonome:')\n",
    "    print(corr_list[pa, 0])\n",
    "    print('(Correlation coefficient, P-value) of the correlation between predicted and experimentally measured metabolome:')\n",
    "    print(corr_list[pa, 1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The mean Pearson correlation coefficient is 0.610812453562786\n"
     ]
    }
   ],
   "source": [
    "print(\"The mean Pearson correlation coefficient is\", np.mean(corr_list[:,1]))\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Run the simulation with reduced matrix forms for all individuals for NSJ16 links with random proportion of links deleted"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.0\n",
      "0.1\n",
      "0.2\n",
      "0.30000000000000004\n",
      "0.4\n",
      "0.5\n"
     ]
    }
   ],
   "source": [
    "pDel_list = np.linspace(0,0.5,6)\n",
    "corr_array = np.zeros((pDel_list.shape[0], 50))\n",
    "\n",
    "for pDel in pDel_list:\n",
    "    print(pDel)\n",
    "    for which_replicate in range(50):\n",
    "        net = net_ori.copy()\n",
    "        i_x = np.random.choice(range(len(net_ori)), int(len(net_ori) * pDel))\n",
    "        net.drop(net.index[i_x], inplace=True)\n",
    "\n",
    "        corr_list = np.zeros((metabolome.shape[1],2))\n",
    "        diet_list = np.zeros((metabolome.shape[1], 20))\n",
    "        for pa in range(metabolome.shape[1]):\n",
    "            ######## Select an ID of a individual and pull out its experimentally measured metagenome:\n",
    "            b_real = np.zeros((MAX_ID_microbes,))\n",
    "            b_real[metagenome_ID] = metagenome.iloc[:,pa] / np.sum(metagenome.iloc[:,pa])\n",
    "\n",
    "            ######## Compute matrices involving the metabolite consumption and generation:\n",
    "            m2b, b2m = Ain_out(b_real, net)\n",
    "            m2b_total, m2m_total, m2m_layer = m2b_multiple_levels(f, m2b, b2m, numLevels_max)\n",
    "\n",
    "            ######## Assign diet\n",
    "            x0 = np.ones((len(i_intake),)) / len(i_intake)\n",
    "\n",
    "            ######## The model is converted into an optimization problem where the nutrient intake is constantly changed to\n",
    "            # minimize the logarithmic error between experimentally measured metagenome and predicted metagenome computed \n",
    "            # from the model for a certain nutrient intake.\n",
    "            fun = lambda x: pred_error(x, b_real, m2b_total, i_intake)\n",
    "            bnds = ((0, 100), ) * len(x0)\n",
    "            res = minimize(fun, x0, method='SLSQP', bounds=bnds, options={'maxiter': 1000}, tol=1e-3)\n",
    "\n",
    "            ######## As long as the optimized nutrient intake is found by using the above optimization solver, the\n",
    "            # optimized nutrient intake \"res.x\" is used to generate the predict metagenome and metabolome. They are\n",
    "            # visually and statistically compared to the experimentally measured metagenome and metabolome.\n",
    "            x_full = np.zeros((MAX_ID_metabolites,));\n",
    "            x_full[i_intake] = res.x;\n",
    "            ba_pred = np.dot(m2b_total, x_full)\n",
    "\n",
    "            met_levels, met_leftover_levels = calc_metabolome(res.x, m2m_layer, numLevels_max, i_intake)\n",
    "            metabolome_measured = np.zeros((MAX_ID_metabolites,))\n",
    "            metabolome_measured[metabolome_ID] = metabolome.iloc[:,pa]\n",
    "            metabolome_pred = met_levels[:, -1] + met_leftover_levels.sum(1)\n",
    "            i_common = np.where(metabolome_measured * metabolome_pred > 1e-5)[0]\n",
    "            metabolome_pred_common = metabolome_pred[i_common] / np.sum(metabolome_pred[i_common])\n",
    "            metabolome_measured_common = metabolome_measured[i_common] / np.sum(metabolome_measured[i_common])\n",
    "            if i_common.shape[0] >= 2:\n",
    "                corr_list[pa, 0] = pearsonr(ba_pred[b_real>0], b_real[b_real>0])[0]\n",
    "                corr_list[pa, 1] = pearsonr(np.log10(metabolome_pred_common+1e-5), np.log10(metabolome_measured_common+1e-5))[0]\n",
    "            else:\n",
    "                corr_list[pa, 0] = -1\n",
    "                corr_list[pa, 1] = -1\n",
    "            diet_list[pa, :] = res.x\n",
    "            '''\n",
    "            print('-------------------------------------------------------------------------------------------------------------')\n",
    "            print('(Correlation coefficient, P-value) of the correlation between predicted and experimentally measured metagonome:')\n",
    "            print(corr_list[pa, 0])\n",
    "            print('(Correlation coefficient, P-value) of the correlation between predicted and experimentally measured metabolome:')\n",
    "            print(corr_list[pa, 1])\n",
    "            '''\n",
    "            corr_array[np.where(pDel_list == pDel)[0], which_replicate] = np.mean(corr_list[:,1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "from scipy.stats import kruskal\n",
    "from scipy.stats import ttest_ind\n",
    "def annotate_kruskal_wallis_test(i1, i2, y, axes):\n",
    "    x1, x2 = i1+1, i2+1\n",
    "    #plt.plot([x1, x2], [y, y], lw=1.0, c='k')\n",
    "    h=0.02\n",
    "    plt.plot([x1, x1, x2, x2], [y, y+h, y+h, y], lw=1.0, c='k')\n",
    "    pvalue = ttest_ind(corr_array.transpose()[:,i1], corr_array.transpose()[:,i2])[1]\n",
    "    if pvalue > 0.05:\n",
    "        axes.text((x1+x2)*.5, y+h*0.8, \"ns\", ha='center', va='bottom', color='k', fontsize=14)\n",
    "    elif pvalue > 0.01:\n",
    "        axes.text((x1+x2)*.5, y+h*0.5, \"*\", ha='center', va='bottom', color='k', fontsize=14)\n",
    "    elif pvalue > 0.001:\n",
    "        axes.text((x1+x2)*.5, y+h*0.5, \"**\", ha='center', va='bottom', color='k', fontsize=14)\n",
    "    else:\n",
    "        axes.text((x1+x2)*.5, y+h*0.5, \"***\", ha='center', va='bottom', color='k', fontsize=14)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 102,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 557.908x344.806 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig_dims = figure_size_setting(700)\n",
    "fig, axes = plt.subplots(1, 1, figsize=fig_dims, sharex=True)\n",
    "axes.boxplot(corr_array.transpose());\n",
    "axes.set_xticks(np.array(list(range(len(pDel_list))))+1);\n",
    "axes.set_xticklabels(np.round(pDel_list,2));\n",
    "axes.set_xlabel('Fraction of deleted links')\n",
    "#axes.set_ylabel('Correlation coefficients')\n",
    "axes.set_ylabel('Correlation between predicted and \\n experimentally measured metabolome')\n",
    "\n",
    "'''\n",
    "annotate_kruskal_wallis_test(0, 1, 0.7, axes)\n",
    "annotate_kruskal_wallis_test(0, 2, 0.75, axes)\n",
    "annotate_kruskal_wallis_test(0, 3, 0.8, axes)\n",
    "annotate_kruskal_wallis_test(0, 4, 0.85, axes)\n",
    "annotate_kruskal_wallis_test(0, 5, 0.9, axes)\n",
    "axes.text(1.5, 0.38, \"***: P < $10^{-3}$\", ha='center', va='bottom', color='k', fontsize=14)\n",
    "axes.text(1.5, 0.35, \"**: P < $10^{-2}$\", ha='center', va='bottom', color='k', fontsize=14)\n",
    "axes.text(1.5, 0.32, \"ns: P > 0.05\", ha='center', va='bottom', color='k', fontsize=14)\n",
    "'''\n",
    "\n",
    "fig.subplots_adjust(left=.13, bottom=.11, right=.97, top=.97, hspace=0.2)\n",
    "fig.savefig(\"./performance_degradation_random_links_deleted.pdf\", dpi=600)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Show one example of running algorithms with deletion of links"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "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>metabolites</th>\n",
       "      <th>microbes</th>\n",
       "      <th>edgeType</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>117</td>\n",
       "      <td>2</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>10</td>\n",
       "      <td>69</td>\n",
       "      <td>3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>219</td>\n",
       "      <td>63</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>182</td>\n",
       "      <td>71</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>55</td>\n",
       "      <td>6</td>\n",
       "      <td>3</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   metabolites  microbes  edgeType\n",
       "0          117         2         2\n",
       "1           10        69         3\n",
       "2          219        63         2\n",
       "3          182        71         2\n",
       "4           55         6         3"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_added = pd.read_csv(\"added_links_prior_distribution_run1.csv\", index_col=0)\n",
    "df_added['metabolites'] = df_metabolites.loc[df_added['metabolite ID']].values\n",
    "df_added['microbes'] = df_microbes.loc[df_added['microbes ID']].values\n",
    "df_added_net = df_added[['metabolites','microbes','edgeType']]\n",
    "df_added_net.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "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>metabolites</th>\n",
       "      <th>microbes</th>\n",
       "      <th>edgeType</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>47</td>\n",
       "      <td>9</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>159</td>\n",
       "      <td>61</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>147</td>\n",
       "      <td>47</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>55</td>\n",
       "      <td>13</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>153</td>\n",
       "      <td>56</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   metabolites  microbes  edgeType\n",
       "0           47         9         2\n",
       "1          159        61         2\n",
       "2          147        47         2\n",
       "3           55        13         2\n",
       "4          153        56         2"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_deleted = pd.read_csv(\"deleted_links_prior_distribution_run1.csv\", index_col=0)\n",
    "df_deleted['metabolites'] = df_metabolites.loc[df_deleted['metabolite ID']].values\n",
    "df_deleted['microbes'] = df_microbes.loc[df_deleted['microbes ID']].values\n",
    "df_deleted_net = df_deleted[['metabolites','microbes','edgeType']]\n",
    "df_deleted_net.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "def compute_error(net):\n",
    "    corr_list = np.zeros((metabolome.shape[1],2))\n",
    "    diet_list = np.zeros((metabolome.shape[1], 20))\n",
    "    for pa in range(metabolome.shape[1]):\n",
    "        ######## Select an ID of a individual and pull out its experimentally measured metagenome:\n",
    "        b_real = np.zeros((MAX_ID_microbes,))\n",
    "        b_real[metagenome_ID] = metagenome.iloc[:,pa] / np.sum(metagenome.iloc[:,pa])\n",
    "\n",
    "        ######## Compute matrices involving the metabolite consumption and generation:\n",
    "        m2b, b2m = Ain_out(b_real, net)\n",
    "        m2b_total, m2m_total, m2m_layer = m2b_multiple_levels(f, m2b, b2m, numLevels_max)\n",
    "\n",
    "        ######## Assign diet\n",
    "        x0 = np.ones((len(i_intake),)) / len(i_intake)\n",
    "\n",
    "        ######## The model is converted into an optimization problem where the nutrient intake is constantly changed to\n",
    "        # minimize the logarithmic error between experimentally measured metagenome and predicted metagenome computed \n",
    "        # from the model for a certain nutrient intake.\n",
    "        fun = lambda x: pred_error(x, b_real, m2b_total, i_intake)\n",
    "        bnds = ((0, 100), ) * len(x0)\n",
    "        res = minimize(fun, x0, method='SLSQP', bounds=bnds, options={'maxiter': 1000}, tol=1e-3)\n",
    "\n",
    "        ######## As long as the optimized nutrient intake is found by using the above optimization solver, the\n",
    "        # optimized nutrient intake \"res.x\" is used to generate the predict metagenome and metabolome. They are\n",
    "        # visually and statistically compared to the experimentally measured metagenome and metabolome.\n",
    "        x_full = np.zeros((MAX_ID_metabolites,));\n",
    "        x_full[i_intake] = res.x;\n",
    "        ba_pred = np.dot(m2b_total, x_full)\n",
    "\n",
    "        met_levels, met_leftover_levels = calc_metabolome(res.x, m2m_layer, numLevels_max, i_intake)\n",
    "        metabolome_measured = np.zeros((MAX_ID_metabolites,))\n",
    "        metabolome_measured[metabolome_ID] = metabolome.iloc[:,pa]\n",
    "        metabolome_pred = met_levels[:, -1] + met_leftover_levels.sum(1)\n",
    "        i_common = np.where(metabolome_measured * metabolome_pred > 1e-5)[0]\n",
    "        metabolome_pred_common = metabolome_pred[i_common] / np.sum(metabolome_pred[i_common])\n",
    "        metabolome_measured_common = metabolome_measured[i_common] / np.sum(metabolome_measured[i_common])\n",
    "        if i_common.shape[0] >= 2:\n",
    "            corr_list[pa, 0] = pearsonr(ba_pred[b_real>0], b_real[b_real>0])[0]\n",
    "            corr_list[pa, 1] = pearsonr(np.log10(metabolome_pred_common+1e-5), np.log10(metabolome_measured_common+1e-5))[0]\n",
    "        else:\n",
    "            corr_list[pa, 0] = -1\n",
    "            corr_list[pa, 1] = -1\n",
    "        diet_list[pa, :] = res.x\n",
    "        \n",
    "    return list(corr_list[:,1])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Only use links from NSJ16"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The mean Pearson correlation coefficient is 0.6176332806699286\n"
     ]
    }
   ],
   "source": [
    "net = net_ori.copy()\n",
    "net = net.drop_duplicates(keep=False)\n",
    "corr_list = compute_error(net)\n",
    "print(\"The mean Pearson correlation coefficient is\", np.mean(corr_list))\n",
    "corr_all_cases = []\n",
    "corr_all_cases = corr_all_cases + [corr_list]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Use links from NJS16 + addition of links + deletion of links"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The mean Pearson correlation coefficient is 0.7499376185754689\n"
     ]
    }
   ],
   "source": [
    "net = net_ori.copy()\n",
    "net = pd.concat([net, df_added_net])\n",
    "net = pd.concat([net, df_deleted_net])\n",
    "net = net.drop_duplicates(keep=False)\n",
    "corr_list = compute_error(net)\n",
    "print(\"The mean Pearson correlation coefficient is\", np.mean(corr_list))\n",
    "corr_all_cases = corr_all_cases + [corr_list]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Use links from NJS16 + addition of links (deleted links ignored)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The mean Pearson correlation coefficient is 0.7474089316067004\n"
     ]
    }
   ],
   "source": [
    "net = net_ori.copy()\n",
    "net = pd.concat([net, df_added_net])\n",
    "net = net.drop_duplicates(keep=False)\n",
    "corr_list = compute_error(net)\n",
    "print(\"The mean Pearson correlation coefficient is\", np.mean(corr_list))\n",
    "corr_all_cases = corr_all_cases + [corr_list]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Use links from NJS16 + deletion of links (added links ignored)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The mean Pearson correlation coefficient is 0.6273303975291333\n"
     ]
    }
   ],
   "source": [
    "net = net_ori.copy()\n",
    "net = pd.concat([net, df_deleted_net])\n",
    "net = net.drop_duplicates(keep=False)\n",
    "corr_list = compute_error(net)\n",
    "print(\"The mean Pearson correlation coefficient is\", np.mean(corr_list))\n",
    "corr_all_cases = corr_all_cases + [corr_list]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Visulation of effects of addition vs deletion"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [],
   "source": [
    "from scipy.stats import kruskal\n",
    "def annotate_kruskal_wallis_test(i1, i2, y, axes):\n",
    "    x1, x2 = i1+1, i2+1\n",
    "    #plt.plot([x1, x2], [y, y], lw=1.0, c='k')\n",
    "    h=0.02\n",
    "    plt.plot([x1, x1, x2, x2], [y, y+h, y+h, y], lw=1.0, c='k')\n",
    "    pvalue = kruskal(corr_all_cases[i1], corr_all_cases[i2])[1]\n",
    "    print(pvalue)\n",
    "    if pvalue > 0.05:\n",
    "        axes.text((x1+x2)*.5, y+h*0.8, \"ns\", ha='center', va='bottom', color='k', fontsize=14)\n",
    "    elif pvalue > 0.01:\n",
    "        axes.text((x1+x2)*.5, y+h*0.5, \"*\", ha='center', va='bottom', color='k', fontsize=14)\n",
    "    elif pvalue > 0.001:\n",
    "        axes.text((x1+x2)*.5, y+h*0.5, \"**\", ha='center', va='bottom', color='k', fontsize=14)\n",
    "    else:\n",
    "        axes.text((x1+x2)*.5, y+h*0.5, \"***\", ha='center', va='bottom', color='k', fontsize=14)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.4905046813159105e-07\n",
      "2.0135257523371715e-07\n",
      "0.7141236735146556\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 797.011x492.58 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig_dims = figure_size_setting(1000)\n",
    "fig, axes = plt.subplots(1, 1, figsize=fig_dims, sharex=True)\n",
    "axes.boxplot(corr_all_cases);\n",
    "#axes.set_xlabel('Number of microbial species')\n",
    "axes.set_ylabel('Correlation between predicted and \\n experimentally measured metabolome')\n",
    "axes.set_xticks(range(1,5))\n",
    "axes.set_xticklabels(['NJS16', 'NJS16 + GutCP added links\\n - GutCP deleted links', 'NJS16 + GutCP \\n added links only', 'NJS16 - GutCP \\n deleted links'])\n",
    "\n",
    "annotate_kruskal_wallis_test(0, 1, 0.9, axes)\n",
    "annotate_kruskal_wallis_test(0, 2, 0.95, axes)\n",
    "annotate_kruskal_wallis_test(0, 3, 1.0, axes)\n",
    "axes.text(2.5, 0.43, \"***: P < $10^{-3}$\", ha='center', va='bottom', color='k', fontsize=14)\n",
    "axes.text(2.5, 0.4, \"ns: P > 0.05\", ha='center', va='bottom', color='k', fontsize=14)\n",
    "\n",
    "fig.subplots_adjust(left=.13, bottom=.11, right=.97, top=.95, hspace=0.2)\n",
    "fig.savefig(\"./performance_addition_versus_deletion.pdf\", dpi=600)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## GutCP with deletion of links: Markov Chain Monte Carlo algorithm of proposing random links (exchange reactions) to add or delete and accepting according to the change in performance"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Training-test splitting"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The original error is 0.9182052265414039\n",
      "0\n",
      "Addition accepted, error is 0.9175311694870872\n",
      "Deletion accepted, error is 0.9165079300725743\n",
      "Deletion accepted, error is 0.9043564298444301\n",
      "50\n",
      "Addition accepted, error is 0.8892252654664162\n",
      "Addition accepted, error is 0.8892075559051827\n",
      "Deletion accepted, error is 0.887315819713606\n",
      "Addition accepted, error is 0.8842133835779072\n",
      "Deletion accepted, error is 0.8687378181662895\n",
      "Addition accepted, error is 0.86647611817689\n",
      "Addition accepted, error is 0.8668925074871296\n",
      "Deletion accepted, error is 0.866249194817257\n",
      "Deletion accepted, error is 0.8656684668717608\n",
      "100\n",
      "Addition accepted, error is 0.8583394076615627\n",
      "Addition accepted, error is 0.8366011108749529\n",
      "Addition accepted, error is 0.8342472396994547\n",
      "Deletion accepted, error is 0.8352472396994547\n",
      "Addition accepted, error is 0.8355107859008006\n",
      "Deletion accepted, error is 0.8353051015520842\n",
      "150\n",
      "Addition accepted, error is 0.8343157659620405\n",
      "Deletion accepted, error is 0.8320037436213769\n",
      "Deletion accepted, error is 0.8306554279444452\n",
      "Deletion accepted, error is 0.8191938450825904\n",
      "Addition accepted, error is 0.8182151205648311\n",
      "200\n",
      "Addition accepted, error is 0.8014461799018083\n",
      "Deletion accepted, error is 0.8010283084711881\n",
      "Deletion accepted, error is 0.799811210852096\n",
      "Addition accepted, error is 0.7983726100784387\n",
      "250\n",
      "Deletion accepted, error is 0.7981683009031245\n",
      "Addition accepted, error is 0.7983537151257128\n",
      "Addition accepted, error is 0.797151776036384\n",
      "Addition accepted, error is 0.7922727332415588\n",
      "Addition accepted, error is 0.7742763197430444\n",
      "Addition accepted, error is 0.7663708894128102\n",
      "Addition accepted, error is 0.7651033874329671\n",
      "Deletion accepted, error is 0.7644855295510179\n",
      "300\n",
      "Deletion accepted, error is 0.7644636428325285\n",
      "350\n",
      "Addition accepted, error is 0.7654725727130938\n",
      "Addition accepted, error is 0.7623052765755418\n",
      "Addition accepted, error is 0.7563286656600694\n",
      "Addition accepted, error is 0.7561857429380873\n",
      "Addition accepted, error is 0.7549104889507577\n",
      "Addition accepted, error is 0.7546981616355624\n",
      "400\n",
      "Addition accepted, error is 0.7508876825486077\n",
      "Addition accepted, error is 0.7505664673201212\n",
      "Addition accepted, error is 0.7506150667893515\n",
      "Deletion accepted, error is 0.7488943251371865\n",
      "Addition accepted, error is 0.7412292025628403\n",
      "Addition accepted, error is 0.7378639783884746\n",
      "450\n",
      "Deletion accepted, error is 0.7366737084117884\n",
      "Addition accepted, error is 0.734728554712356\n",
      "500\n",
      "Addition accepted, error is 0.7342907645566642\n",
      "Addition accepted, error is 0.7340060680486639\n",
      "Addition accepted, error is 0.7305472051715367\n",
      "550\n",
      "Addition accepted, error is 0.7285491987993227\n",
      "Addition accepted, error is 0.7284929492425364\n",
      "600\n",
      "Deletion accepted, error is 0.7280759333155447\n",
      "Deletion accepted, error is 0.7263458209084568\n",
      "Addition accepted, error is 0.7241534598000604\n",
      "Addition accepted, error is 0.7233140940210826\n",
      "Deletion accepted, error is 0.7229223657764748\n",
      "650\n",
      "Addition accepted, error is 0.716144946557009\n",
      "Addition accepted, error is 0.7161729620764254\n",
      "Deletion accepted, error is 0.7151820582021762\n",
      "Addition accepted, error is 0.7096380828152998\n",
      "Addition accepted, error is 0.7090900682632205\n",
      "700\n",
      "750\n",
      "Addition accepted, error is 0.706223548979306\n",
      "Deletion accepted, error is 0.7065718456272613\n",
      "800\n",
      "Addition accepted, error is 0.7059727962287977\n",
      "Addition accepted, error is 0.7056721856988489\n",
      "850\n",
      "Addition accepted, error is 0.7007725682101988\n",
      "900\n",
      "Addition accepted, error is 0.7006846768549504\n",
      "Addition accepted, error is 0.6987115394560562\n",
      "950\n",
      "Addition accepted, error is 0.6986230856770507\n",
      "Addition accepted, error is 0.6973514678550535\n",
      "Addition accepted, error is 0.6937956914909997\n",
      "1000\n",
      "Deletion accepted, error is 0.6933201778484009\n",
      "Addition accepted, error is 0.689935602715093\n",
      "Addition accepted, error is 0.6901323710235474\n",
      "1050\n",
      "Addition accepted, error is 0.6898983976759543\n",
      "Addition accepted, error is 0.6905456873601353\n",
      "1100\n",
      "Deletion accepted, error is 0.6901306224355845\n",
      "Addition accepted, error is 0.6886854564340035\n",
      "1150\n",
      "Addition accepted, error is 0.6876919726491175\n",
      "Addition accepted, error is 0.6878889088201107\n",
      "1200\n",
      "Deletion accepted, error is 0.6875481275820702\n",
      "Deletion accepted, error is 0.6871768124250845\n",
      "Deletion accepted, error is 0.6872841354317485\n",
      "Deletion accepted, error is 0.6875163259245886\n",
      "Addition accepted, error is 0.6755387927844779\n",
      "Deletion accepted, error is 0.6752645623478818\n",
      "1250\n",
      "Addition accepted, error is 0.6733316823143303\n",
      "1300\n",
      "Deletion accepted, error is 0.6743316823143303\n",
      "Addition accepted, error is 0.6736872413178056\n",
      "1350\n",
      "1400\n",
      "Deletion accepted, error is 0.6732132644402804\n",
      "Addition accepted, error is 0.6731800476131894\n",
      "1450\n",
      "1500\n",
      "Addition accepted, error is 0.6728326114096341\n",
      "1550\n",
      "1600\n",
      "Deletion accepted, error is 0.6726589717327787\n",
      "Deletion accepted, error is 0.6720810586749276\n",
      "1650\n",
      "Deletion accepted, error is 0.6727595114421269\n",
      "Addition accepted, error is 0.6727699413420035\n",
      "Addition accepted, error is 0.6728344496219075\n",
      "1700\n",
      "Deletion accepted, error is 0.6738344496219075\n",
      "Addition accepted, error is 0.6737648322570906\n"
     ]
    }
   ],
   "source": [
    "import random\n",
    "######## Select all microbes in the Thai data:\n",
    "b_real = np.zeros((MAX_ID_microbes,))\n",
    "b_real[metagenome_ID] = 0.05\n",
    "\n",
    "######## Compute matrices involving the metabolite consumption and generation:\n",
    "m2b, b2m = Ain_out(b_real, net)\n",
    "\n",
    "m2b_ori = (m2b!=0).astype(int).copy()\n",
    "b2m_ori = (b2m!=0).astype(int).copy()\n",
    "x_ori = np.concatenate([m2b_ori.flatten(), b2m_ori.flatten()])\n",
    "net_ori = net.copy()\n",
    "\n",
    "def pred_error_addingLinks(i_train, x, m2b_ori, b2m_ori, x_ori):\n",
    "    '''\n",
    "    pred_error_addingLinks is a function used to compute the logarithmic error between experimentally measured\n",
    "    metagenome and predicted metagenome computed from the model for a certain nutrient intake. It relies on \n",
    "    (1) x: the nutrient intake, (2) i_intake: IDs of the nutrient intake, (3) m2b_total: a conversion matrix \n",
    "    from thenutrient intake to the total biomass, and (4) b_real: experimentally measured metagenome. The \n",
    "    first three is used to compute the metagenome predicted by the model \"ba_pred\" and compare it with the \n",
    "    experimentally measured metagenome \"b_real\".\n",
    "    '''\n",
    "    max_links = m2b_ori.shape[0] * m2b_ori.shape[1] # maximal number of links = numberr of specis * number of metabolites\n",
    "    \n",
    "    ######## Convert x to net structure (convert the adjacency matrix into the edge list):\n",
    "    thres = 0.1\n",
    "    x = x - x_ori\n",
    "    ### delete links:\n",
    "    net_ori_deleted = net_ori.copy()\n",
    "    m2b_deleted = x[:max_links].reshape((m2b_ori.shape[0], m2b_ori.shape[1]))\n",
    "    a = df_metabolites['newID'].values[np.where(m2b_deleted <= -thres)[0]]\n",
    "    b = metagenome_ID[np.where(m2b_deleted <= -thres)[1]]\n",
    "    c = [2] * np.where(m2b_deleted <= -thres)[1].shape[0]\n",
    "    net_deleted = pd.DataFrame({net_ori.columns[0]:list(a), net_ori.columns[1]:list(b), net_ori.columns[2]:c})\n",
    "    net_ori_deleted = pd.concat([net_ori_deleted, net_deleted]).drop_duplicates(keep=False)\n",
    "    ### consumption links:\n",
    "    m2b_added = x[:max_links].reshape((m2b_ori.shape[0], m2b_ori.shape[1]))\n",
    "    a = df_metabolites['newID'].values[np.where(m2b_added >= thres)[0]]\n",
    "    b = metagenome_ID[np.where(m2b_added >= thres)[1]]\n",
    "    c = [2] * np.where(m2b_added >= thres)[1].shape[0]\n",
    "    net_added_consumption = pd.DataFrame({net_ori.columns[0]:list(a), net_ori.columns[1]:list(b), net_ori.columns[2]:c})\n",
    "    ### production links:\n",
    "    b2m_added = x[max_links:].reshape((m2b_ori.shape[0], m2b_ori.shape[1]))\n",
    "    a = df_metabolites['newID'].values[np.where(b2m_added >= thres)[0]]\n",
    "    b = metagenome_ID[np.where(b2m_added >= thres)[1]]\n",
    "    c = [3] * np.where(b2m_added >= thres)[1].shape[0]\n",
    "    net_added_production = pd.DataFrame({net_ori.columns[0]:list(a), net_ori.columns[1]:list(b), net_ori.columns[2]:c})\n",
    "    ### overall edge list of the new network\n",
    "    net = pd.concat([net_ori_deleted, net_added_consumption, net_added_production])\n",
    "    \n",
    "    f_byproduct = 0.9\n",
    "    f = f_byproduct * np.ones((MAX_ID_microbes,1));\n",
    "    f[i_selfish] = 0.0;  # The byproduct/leakage fraction f for microbes that don't generate byproducts is set as 0.\n",
    "\n",
    "    numLevels_max = 4\n",
    "\n",
    "    corr_list_aveDiet = np.zeros((i_train.shape[0], 2))\n",
    "    log_list_aveDiet = np.zeros((i_train.shape[0], 2))\n",
    "    order_dev_list = np.zeros((i_train.shape[0], MAX_ID_metabolites)) ## order difference in metabolome\n",
    "    order_dev_metagenome_list = np.zeros((i_train.shape[0], MAX_ID_microbes)) ## order difference in metagenome\n",
    "    numMetabolites_list = np.zeros((i_train.shape[0]))\n",
    "    for pa in range(i_train.shape[0]):\n",
    "        ######## Select an ID of a individual and pull out its experimentally measured metagenome:\n",
    "        b_real = np.zeros((MAX_ID_microbes,))\n",
    "        b_real[metagenome_ID] = metagenome.iloc[:, i_train[pa]] / np.sum(metagenome.iloc[:, i_train[pa]])\n",
    "\n",
    "        ######## Compute matrices involving the metabolite consumption and generation:\n",
    "        m2b, b2m = Ain_out(b_real, net)\n",
    "        #m2b_total, m2m_total, m2m_layer = m2b_multiple_levels(f, m2b, b2m, numLevels_max)\n",
    "        m2b_total, m2m_total, m2m_layer = m2b_multiple_levels(f, m2b, b2m, numLevels_max)\n",
    "\n",
    "        ######## As long as the optimized nutrient intake is found by using the above optimization solver, the\n",
    "        # optimized nutrient intake \"res.x\" is used to generate the predict metagenome and metabolome. They are\n",
    "        # visually and statistically compared to the experimentally measured metagenome and metabolome.\n",
    "        \n",
    "        ######## Assign diet\n",
    "        x0 = np.ones((len(i_intake),)) / len(i_intake)\n",
    "\n",
    "        ######## The model is converted into an optimization problem where the nutrient intake is constantly changed to\n",
    "        # minimize the logarithmic error between experimentally measured metagenome and predicted metagenome computed \n",
    "        # from the model for a certain nutrient intake.\n",
    "        fun2 = lambda y: pred_error(y, b_real, m2b_total, i_intake)\n",
    "        bnds = ((0, 100), ) * len(x0)\n",
    "        res = minimize(fun2, x0, method='SLSQP', bounds=bnds, options={'disp': False, 'maxiter': 1000}, tol=1e-3, callback=None)\n",
    "\n",
    "        ######## As long as the optimized nutrient intake is found by using the above optimization solver, the\n",
    "        # optimized nutrient intake \"res.x\" is used to generate the predict metagenome and metabolome. They are\n",
    "        # visually and statistically compared to the experimentally measured metagenome and metabolome.\n",
    "        x_full = np.zeros((MAX_ID_metabolites,));\n",
    "        x_full[i_intake] = res.x;\n",
    "        ba_pred = np.dot(m2b_total, x_full)\n",
    "\n",
    "        met_levels, met_leftover_levels = calc_metabolome(res.x, m2m_layer, numLevels_max, i_intake)\n",
    "        metabolome_measured = np.zeros((MAX_ID_metabolites,))\n",
    "        metabolome_measured[metabolome_ID] = metabolome.iloc[:, i_train[pa]]\n",
    "        metabolome_pred = met_levels[:, -1] + met_leftover_levels.sum(1) #np.dot(m2m_total, x_full)\n",
    "        i_common = np.where(metabolome_measured * metabolome_pred > 1e-5)[0]\n",
    "        metabolome_pred_common = metabolome_pred[i_common] / np.sum(metabolome_pred[i_common])\n",
    "        metabolome_measured_common = metabolome_measured[i_common] / np.sum(metabolome_measured[i_common])\n",
    "        ######## compute the bias of the order of magnitude\n",
    "        order_dev_metagenome_list[pa, :] = np.log10(b_real + 1e-5) - np.log10(ba_pred + 1e-5)\n",
    "        order_dev_list[pa, i_common] = np.log10(metabolome_measured_common + 1e-5) - np.log10(metabolome_pred_common + 1e-5)\n",
    "        numMetabolites_list[pa] = i_common.shape[0]\n",
    "            \n",
    "        if i_common.shape[0] >= 2:\n",
    "            corr_list_aveDiet[pa, 0] = pearsonr(ba_pred[b_real>0], b_real[b_real>0])[0]\n",
    "            corr_list_aveDiet[pa, 1] = pearsonr(metabolome_pred_common, metabolome_measured_common)[0]\n",
    "            log_list_aveDiet[pa, 0] = np.mean(np.abs(np.log10(ba_pred[b_real>0]+1e-6) - np.log10(b_real[b_real>0]+1e-6)))\n",
    "            log_list_aveDiet[pa, 1] = np.mean(np.abs(np.log10(metabolome_pred_common+1e-6) - np.log10(metabolome_measured_common+1e-6)))\n",
    "\n",
    "        else:\n",
    "            corr_list_aveDiet[pa, 0] = -1\n",
    "            corr_list_aveDiet[pa, 1] = -1\n",
    "            log_list_aveDiet[pa, 0] = 5\n",
    "            log_list_aveDiet[pa, 1] = 5\n",
    "            \n",
    "    x_full = np.zeros((MAX_ID_metabolites,));\n",
    "    x_full[i_intake] = res.x;\n",
    "    \n",
    "    ba_pred = np.dot(m2b_total, x_full)\n",
    "    \n",
    "    pred_error1 = np.mean(log_list_aveDiet[:,0])\n",
    "    pred_error2 = np.mean(log_list_aveDiet[:,1])\n",
    "    pred_error3 = np.sum(np.abs(x))\n",
    "    pred_error4 = np.mean(numMetabolites_list)\n",
    "    hyper_reg = 0.001\n",
    "    pred_errorTotal = pred_error2 + hyper_reg * pred_error3 - (pred_error4 - 20) * 0.003 # with reward\n",
    "    \n",
    "    return [pred_errorTotal, np.abs(np.sum(order_dev_list, 0)), np.sum(order_dev_metagenome_list, 0)]\n",
    "\n",
    "i_train = np.sort(np.random.choice(range(metabolome.shape[1]), 30, replace=False))\n",
    "i_test = np.setdiff1d(range(metabolome.shape[1]), i_train)\n",
    "\n",
    "error_list = []\n",
    "current_step_list = []\n",
    "pos_x_list = []\n",
    "metID_list = []\n",
    "microbeID_list = []\n",
    "prior_list = []\n",
    "fun = lambda x: pred_error_addingLinks(i_train, x, m2b_ori, b2m_ori, x_ori)\n",
    "max_links = m2b.shape[0]*m2b.shape[1]\n",
    "x = x_ori.copy()\n",
    "error_before, bias_metabolome, bias_metagenome = fun(x)\n",
    "bias_metabolome_ori = bias_metabolome.copy()\n",
    "prior_prob1 = np.matlib.repmat(np.exp(3 * (bias_metagenome) / metabolome.shape[1])[np.newaxis, :], m2b.shape[0], 1) * np.matlib.repmat(np.exp(3 * bias_metabolome_ori / metabolome.shape[1])[:, np.newaxis], 1, m2b.shape[1])\n",
    "prior_prob2 = np.matlib.repmat(np.exp(3 * bias_metabolome_ori / metabolome.shape[1])[:, np.newaxis], 1, m2b.shape[1])\n",
    "prior_prob = np.concatenate([prior_prob1.flatten(), prior_prob2.flatten()]) + 0.1\n",
    "prior_prob = prior_prob / np.sum(prior_prob)\n",
    "print('The original error is', error_before)\n",
    "error_list.append(error_before)\n",
    "\n",
    "inverseKT = 5000\n",
    "Twindow = 500\n",
    "numStepsNotAdded = 0\n",
    "error_window = []\n",
    "# MCMC\n",
    "for i in range(10000):\n",
    "    if i%50==0:\n",
    "        print(i)\n",
    "    if np.random.uniform(0,1,1)[0] < 0.5:\n",
    "        i_x = np.random.choice(np.where(x==0)[0], 1, p=prior_prob[x==0]/np.sum(prior_prob[x==0]))[0]\n",
    "    else:\n",
    "        p_delete = 1.0 / prior_prob[x==1]\n",
    "        p_delete = p_delete / np.sum(p_delete)\n",
    "        i_x = np.random.choice(np.where(x==1)[0], 1, p=p_delete)[0]\n",
    "        #i_x = np.random.choice(np.where(x==1)[0], 1)[0]\n",
    "    x[i_x] = 1 - x[i_x]\n",
    "    error_after, bias_metabolome, bias_metagenome = fun(x)\n",
    "    ## Consumption links:\n",
    "    prior_prob1 = np.matlib.repmat(np.exp(3 * (bias_metagenome) / metabolome.shape[1])[np.newaxis, :], m2b.shape[0], 1) * np.matlib.repmat(np.exp(3 * bias_metabolome_ori / metabolome.shape[1])[:, np.newaxis], 1, m2b.shape[1])\n",
    "    ## Production links:\n",
    "    prior_prob2 = np.matlib.repmat(np.exp(3 * bias_metabolome_ori / metabolome.shape[1])[:, np.newaxis], 1, m2b.shape[1])\n",
    "    prior_prob = np.concatenate([prior_prob1.flatten(), prior_prob2.flatten()]) + 0.1\n",
    "    prior_prob = prior_prob / np.sum(prior_prob)\n",
    "    if np.random.uniform(0,1,1)[0] <= np.min([1, np.exp((inverseKT)*(error_before - error_after))]): \n",
    "        error_before = error_after\n",
    "        if x[i_x] == 1:\n",
    "            print('Addition accepted, error is', error_before)\n",
    "        else:\n",
    "            print('Deletion accepted, error is', error_before)\n",
    "        error_list.append(error_before)\n",
    "        current_step_list.append(i)\n",
    "        pos_x_list.append(i_x)\n",
    "        prior_list.append(prior_prob[i_x])\n",
    "        if i_x < max_links:\n",
    "            row_num = i_x // m2b_ori.shape[1]\n",
    "            col_num = i_x - row_num * m2b_ori.shape[1]\n",
    "        elif i_x >= max_links:\n",
    "            i_x = i_x - m2b_ori.shape[0] * m2b_ori.shape[1]\n",
    "            row_num = i_x // b2m_ori.shape[1]\n",
    "            col_num = i_x - row_num * b2m_ori.shape[1]\n",
    "        metID_list.append(row_num)\n",
    "        microbeID_list.append(col_num)\n",
    "        numStepsNotAdded = 0\n",
    "    else:  ## not accepted   \n",
    "        x[i_x] = 1 - x[i_x]\n",
    "        numStepsNotAdded += 1\n",
    "    error_window.append(error_before)\n",
    "    if (i > Twindow) and ((error_window[-1] - error_window[-Twindow]) > -(np.sqrt(Twindow) / inverseKT)):\n",
    "        break"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Convert x to network structure and add it to *net*"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The original network has 2254 links\n",
      "There are 14 links added\n",
      "There are 5 links deleted\n"
     ]
    }
   ],
   "source": [
    "######## Convert x to net structure:\n",
    "a = np.array(metID_list)\n",
    "b = np.array(microbeID_list)\n",
    "c = np.ones([len(metID_list)], dtype = int) * 3\n",
    "c[np.where(np.array(pos_x_list) < max_links)[0]] = 2\n",
    "net_modified = pd.DataFrame({net_ori.columns[0]:list(a), net_ori.columns[1]:list(b), net_ori.columns[2]:c})\n",
    "i_added = x[pos_x_list].astype(bool)\n",
    "i_deleted = ~x[pos_x_list].astype(bool)\n",
    "net_added = net_modified[i_added]\n",
    "net_deleted = net_modified[i_deleted]\n",
    "net_new = pd.concat([net_ori, net_added, net_deleted]).drop_duplicates(keep=False)\n",
    "\n",
    "print('The original network has',len(net_ori),'links')\n",
    "print('There are',len(net_added),'links added')\n",
    "print('There are',len(net_deleted),'links deleted')\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Show the performance on the data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The average Pearson correlation coefficient for the test set:\n",
      "0.012132676935017435\n",
      "The average log error for the test set:\n",
      "0.0\n"
     ]
    }
   ],
   "source": [
    "corr_list = np.zeros((i_test.shape[0], 2))\n",
    "diet_list = np.zeros((i_test.shape[0], 20))\n",
    "log_list = np.zeros((i_test.shape[0], 2))\n",
    "for pa in range(i_test.shape[0]):\n",
    "    ######## Select an ID of a individual and pull out its experimentally measured metagenome:\n",
    "    b_real = np.zeros((MAX_ID_microbes,))\n",
    "    b_real[metagenome_ID] = metagenome.iloc[:, i_test[pa]] / np.sum(metagenome.iloc[:, i_test[pa]])\n",
    "\n",
    "    ######## Compute matrices involving the metabolite consumption and generation:\n",
    "    m2b, b2m = Ain_out(b_real, net_new)\n",
    "    m2b_total, m2m_total, m2m_layer = m2b_multiple_levels(f, m2b, b2m, numLevels_max)\n",
    "\n",
    "    ######## Assign diet\n",
    "    x0 = np.ones((len(i_intake),)) / len(i_intake)\n",
    "\n",
    "    ######## The model is converted into an optimization problem where the nutrient intake is constantly changed to\n",
    "    # minimize the logarithmic error between experimentally measured metagenome and predicted metagenome computed \n",
    "    # from the model for a certain nutrient intake.\n",
    "    fun = lambda x: pred_error(x, b_real, m2b_total, i_intake)\n",
    "    bnds = ((0, 100), ) * len(x0)\n",
    "    res = minimize(fun, x0, method='SLSQP', bounds=bnds, options={'maxiter': 1000}, tol=1e-3)\n",
    "\n",
    "    ######## As long as the optimized nutrient intake is found by using the above optimization solver, the\n",
    "    # optimized nutrient intake \"res.x\" is used to generate the predict metagenome and metabolome. They are\n",
    "    # visually and statistically compared to the experimentally measured metagenome and metabolome.\n",
    "    x_full = np.zeros((MAX_ID_metabolites,));\n",
    "    x_full[i_intake] = res.x;\n",
    "    ba_pred = np.dot(m2b_total, x_full)\n",
    "\n",
    "    met_levels, met_leftover_levels = calc_metabolome(res.x, m2m_layer, numLevels_max, i_intake)\n",
    "    metabolome_measured = np.zeros((MAX_ID_metabolites,))\n",
    "    metabolome_measured[metabolome_ID] = metabolome.iloc[:, i_test[pa]]\n",
    "    metabolome_pred = met_levels[:, -1] + met_leftover_levels.sum(1) #np.dot(m2m_total, x_full)\n",
    "    i_common = np.where(metabolome_measured * metabolome_pred > 1e-5)[0]\n",
    "    metabolome_pred_common = metabolome_pred[i_common] / np.sum(metabolome_pred[i_common])\n",
    "    metabolome_measured_common = metabolome_measured[i_common] / np.sum(metabolome_measured[i_common])\n",
    "    if i_common.shape[0] >= 2:\n",
    "        corr_list[pa, 0] = pearsonr(ba_pred[b_real>0], b_real[b_real>0])[0]\n",
    "        corr_list[pa, 1] = pearsonr(np.log10(metabolome_pred_common+1e-5), np.log10(metabolome_measured_common+1e-5))[0]\n",
    "    else:\n",
    "        corr_list[pa, 0] = -1\n",
    "        corr_list[pa, 1] = -1\n",
    "    diet_list[pa, :] = res.x\n",
    "    \n",
    "print('The average Pearson correlation coefficient for the test set:')\n",
    "print(np.mean(corr_list[:,1]))\n",
    "print('The average log error for the test set:')\n",
    "print(np.mean(log_list[:,1]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Construct the added links to a pandas data frame"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 117,
   "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>metabolite ID</th>\n",
       "      <th>metabolite names</th>\n",
       "      <th>microbes ID</th>\n",
       "      <th>microbes names</th>\n",
       "      <th>edgeType</th>\n",
       "      <th>error reduced</th>\n",
       "      <th>step added</th>\n",
       "      <th>position in x</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>2122</td>\n",
       "      <td>Isovalerate (3-Methylbutanoic acid)</td>\n",
       "      <td>464</td>\n",
       "      <td>Faecalibacterium prausnitzii</td>\n",
       "      <td>3</td>\n",
       "      <td>1.844743e-02</td>\n",
       "      <td>325</td>\n",
       "      <td>23660</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>2116</td>\n",
       "      <td>Inosine</td>\n",
       "      <td>134</td>\n",
       "      <td>Bacteroides thetaiotaomicron</td>\n",
       "      <td>3</td>\n",
       "      <td>1.332175e-02</td>\n",
       "      <td>271</td>\n",
       "      <td>23200</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>2012</td>\n",
       "      <td>5-Aminovalerate</td>\n",
       "      <td>329</td>\n",
       "      <td>Collinsella aerofaciens (Eubacterium aerofaciens)</td>\n",
       "      <td>3</td>\n",
       "      <td>1.320793e-02</td>\n",
       "      <td>30</td>\n",
       "      <td>16736</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>2065</td>\n",
       "      <td>D-Galacturonate</td>\n",
       "      <td>454</td>\n",
       "      <td>Eubacterium eligens</td>\n",
       "      <td>3</td>\n",
       "      <td>1.196131e-02</td>\n",
       "      <td>113</td>\n",
       "      <td>19982</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>30</th>\n",
       "      <td>2133</td>\n",
       "      <td>L-Glutamate (L-Glutamic acid, Glutamate, D-Glu...</td>\n",
       "      <td>123</td>\n",
       "      <td>Bacteroides dorei</td>\n",
       "      <td>3</td>\n",
       "      <td>1.128696e-02</td>\n",
       "      <td>996</td>\n",
       "      <td>24345</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>22</th>\n",
       "      <td>2127</td>\n",
       "      <td>L-Arginine (Arginine)</td>\n",
       "      <td>129</td>\n",
       "      <td>Bacteroides ovatus</td>\n",
       "      <td>3</td>\n",
       "      <td>9.566429e-03</td>\n",
       "      <td>558</td>\n",
       "      <td>23917</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>35</th>\n",
       "      <td>2137</td>\n",
       "      <td>L-Homoserine</td>\n",
       "      <td>968</td>\n",
       "      <td>Ruminococcus obeum</td>\n",
       "      <td>3</td>\n",
       "      <td>8.807495e-03</td>\n",
       "      <td>1146</td>\n",
       "      <td>24688</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17</th>\n",
       "      <td>2049</td>\n",
       "      <td>Cholic acid (Cholate)</td>\n",
       "      <td>338</td>\n",
       "      <td>Coprococcus comes</td>\n",
       "      <td>3</td>\n",
       "      <td>7.812703e-03</td>\n",
       "      <td>379</td>\n",
       "      <td>19041</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>2068</td>\n",
       "      <td>D-Glucose (Glucose)</td>\n",
       "      <td>878</td>\n",
       "      <td>Prevotella salivae</td>\n",
       "      <td>2</td>\n",
       "      <td>7.025520e-03</td>\n",
       "      <td>78</td>\n",
       "      <td>4304</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>58</th>\n",
       "      <td>2133</td>\n",
       "      <td>L-Glutamate (L-Glutamic acid, Glutamate, D-Glu...</td>\n",
       "      <td>457</td>\n",
       "      <td>Eubacterium rectale</td>\n",
       "      <td>2</td>\n",
       "      <td>6.083423e-03</td>\n",
       "      <td>2209</td>\n",
       "      <td>8465</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>2107</td>\n",
       "      <td>H2 (Hydrogen)</td>\n",
       "      <td>338</td>\n",
       "      <td>Coprococcus comes</td>\n",
       "      <td>2</td>\n",
       "      <td>5.915619e-03</td>\n",
       "      <td>334</td>\n",
       "      <td>6873</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>52</th>\n",
       "      <td>2133</td>\n",
       "      <td>L-Glutamate (L-Glutamic acid, Glutamate, D-Glu...</td>\n",
       "      <td>454</td>\n",
       "      <td>Eubacterium eligens</td>\n",
       "      <td>3</td>\n",
       "      <td>5.881095e-03</td>\n",
       "      <td>1866</td>\n",
       "      <td>24374</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>32</th>\n",
       "      <td>2067</td>\n",
       "      <td>D-Glucosamine (Glucosamine)</td>\n",
       "      <td>157</td>\n",
       "      <td>Bifidobacterium longum (Bifidobacterium infant...</td>\n",
       "      <td>3</td>\n",
       "      <td>5.329910e-03</td>\n",
       "      <td>1039</td>\n",
       "      <td>20111</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>2040</td>\n",
       "      <td>Cadaverine</td>\n",
       "      <td>1007</td>\n",
       "      <td>Shigella sonnei</td>\n",
       "      <td>3</td>\n",
       "      <td>5.329638e-03</td>\n",
       "      <td>240</td>\n",
       "      <td>18570</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>23</th>\n",
       "      <td>2105</td>\n",
       "      <td>Guanine</td>\n",
       "      <td>968</td>\n",
       "      <td>Ruminococcus obeum</td>\n",
       "      <td>3</td>\n",
       "      <td>5.252280e-03</td>\n",
       "      <td>598</td>\n",
       "      <td>22672</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>2217</td>\n",
       "      <td>Succinate</td>\n",
       "      <td>1099</td>\n",
       "      <td>Sutterella wadsworthensis</td>\n",
       "      <td>2</td>\n",
       "      <td>5.223751e-03</td>\n",
       "      <td>222</td>\n",
       "      <td>14111</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>26</th>\n",
       "      <td>2134</td>\n",
       "      <td>L-Glutamine (D-Glutamine, Glutamine)</td>\n",
       "      <td>157</td>\n",
       "      <td>Bifidobacterium longum (Bifidobacterium infant...</td>\n",
       "      <td>2</td>\n",
       "      <td>4.961538e-03</td>\n",
       "      <td>707</td>\n",
       "      <td>8519</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>41</th>\n",
       "      <td>2239</td>\n",
       "      <td>Uridine</td>\n",
       "      <td>964</td>\n",
       "      <td>Ruminococcus bromii</td>\n",
       "      <td>3</td>\n",
       "      <td>4.586705e-03</td>\n",
       "      <td>1341</td>\n",
       "      <td>31525</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16</th>\n",
       "      <td>2009</td>\n",
       "      <td>3-phenylpropionic acid (Phenylpropanoate, 3-ph...</td>\n",
       "      <td>124</td>\n",
       "      <td>Bacteroides eggerthii</td>\n",
       "      <td>3</td>\n",
       "      <td>4.146937e-03</td>\n",
       "      <td>368</td>\n",
       "      <td>16498</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>60</th>\n",
       "      <td>2125</td>\n",
       "      <td>L-Alanine (D-Alanine, Alanine)</td>\n",
       "      <td>464</td>\n",
       "      <td>Faecalibacterium prausnitzii</td>\n",
       "      <td>3</td>\n",
       "      <td>3.942222e-03</td>\n",
       "      <td>2428</td>\n",
       "      <td>23804</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>29</th>\n",
       "      <td>2240</td>\n",
       "      <td>Valerate (Pentanoic acid, Pentanoate)</td>\n",
       "      <td>456</td>\n",
       "      <td>Eubacterium limosum</td>\n",
       "      <td>3</td>\n",
       "      <td>3.358106e-03</td>\n",
       "      <td>970</td>\n",
       "      <td>31576</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>44</th>\n",
       "      <td>2053</td>\n",
       "      <td>Citrate</td>\n",
       "      <td>137</td>\n",
       "      <td>Bacteroides xylanisolvens</td>\n",
       "      <td>3</td>\n",
       "      <td>2.997298e-03</td>\n",
       "      <td>1373</td>\n",
       "      <td>19242</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>40</th>\n",
       "      <td>2185</td>\n",
       "      <td>Orotic acid (Orotate)</td>\n",
       "      <td>125</td>\n",
       "      <td>Bacteroides finegoldii (Alistipes finegoldii)</td>\n",
       "      <td>3</td>\n",
       "      <td>2.743548e-03</td>\n",
       "      <td>1247</td>\n",
       "      <td>27875</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>55</th>\n",
       "      <td>2201</td>\n",
       "      <td>Propanoate (Propionate)</td>\n",
       "      <td>135</td>\n",
       "      <td>Bacteroides uniformis</td>\n",
       "      <td>2</td>\n",
       "      <td>2.401912e-03</td>\n",
       "      <td>2045</td>\n",
       "      <td>12977</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>19</th>\n",
       "      <td>2226</td>\n",
       "      <td>Thiamine (Vitamin B1, Thiamin)</td>\n",
       "      <td>137</td>\n",
       "      <td>Bacteroides xylanisolvens</td>\n",
       "      <td>3</td>\n",
       "      <td>2.389538e-03</td>\n",
       "      <td>408</td>\n",
       "      <td>30618</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>2203</td>\n",
       "      <td>Putrescine</td>\n",
       "      <td>54</td>\n",
       "      <td>Alistipes putredinis</td>\n",
       "      <td>2</td>\n",
       "      <td>2.235055e-03</td>\n",
       "      <td>189</td>\n",
       "      <td>13106</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>34</th>\n",
       "      <td>2049</td>\n",
       "      <td>Cholic acid (Cholate)</td>\n",
       "      <td>54</td>\n",
       "      <td>Alistipes putredinis</td>\n",
       "      <td>2</td>\n",
       "      <td>2.117413e-03</td>\n",
       "      <td>1133</td>\n",
       "      <td>3098</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>2193</td>\n",
       "      <td>Pentanol</td>\n",
       "      <td>870</td>\n",
       "      <td>Prevotella copri</td>\n",
       "      <td>3</td>\n",
       "      <td>1.897985e-03</td>\n",
       "      <td>318</td>\n",
       "      <td>28423</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>49</th>\n",
       "      <td>2201</td>\n",
       "      <td>Propanoate (Propionate)</td>\n",
       "      <td>454</td>\n",
       "      <td>Eubacterium eligens</td>\n",
       "      <td>3</td>\n",
       "      <td>1.593203e-03</td>\n",
       "      <td>1754</td>\n",
       "      <td>28910</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>39</th>\n",
       "      <td>2241</td>\n",
       "      <td>Xanthine</td>\n",
       "      <td>608</td>\n",
       "      <td>Lactococcus lactis</td>\n",
       "      <td>3</td>\n",
       "      <td>1.451015e-03</td>\n",
       "      <td>1209</td>\n",
       "      <td>31657</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>69</th>\n",
       "      <td>2032</td>\n",
       "      <td>beta-alanine (3-Aminopropionate)</td>\n",
       "      <td>158</td>\n",
       "      <td>Bifidobacterium pseudocatenulatum</td>\n",
       "      <td>3</td>\n",
       "      <td>5.594825e-04</td>\n",
       "      <td>2678</td>\n",
       "      <td>18024</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>43</th>\n",
       "      <td>2011</td>\n",
       "      <td>4-Aminobutyrate (GABA)</td>\n",
       "      <td>1064</td>\n",
       "      <td>Streptococcus salivarius</td>\n",
       "      <td>3</td>\n",
       "      <td>4.415987e-04</td>\n",
       "      <td>1354</td>\n",
       "      <td>16701</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>2175</td>\n",
       "      <td>N-Acetylneuraminic acid (N-acetylneuraminate, ...</td>\n",
       "      <td>121</td>\n",
       "      <td>Bacteroides coprocola</td>\n",
       "      <td>3</td>\n",
       "      <td>4.179560e-04</td>\n",
       "      <td>204</td>\n",
       "      <td>27223</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>51</th>\n",
       "      <td>2185</td>\n",
       "      <td>Orotic acid (Orotate)</td>\n",
       "      <td>137</td>\n",
       "      <td>Bacteroides xylanisolvens</td>\n",
       "      <td>3</td>\n",
       "      <td>4.090147e-04</td>\n",
       "      <td>1843</td>\n",
       "      <td>27882</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15</th>\n",
       "      <td>2122</td>\n",
       "      <td>Isovalerate (3-Methylbutanoic acid)</td>\n",
       "      <td>135</td>\n",
       "      <td>Bacteroides uniformis</td>\n",
       "      <td>2</td>\n",
       "      <td>2.675129e-04</td>\n",
       "      <td>361</td>\n",
       "      <td>7721</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>33</th>\n",
       "      <td>2238</td>\n",
       "      <td>Urea</td>\n",
       "      <td>54</td>\n",
       "      <td>Alistipes putredinis</td>\n",
       "      <td>3</td>\n",
       "      <td>2.313251e-04</td>\n",
       "      <td>1092</td>\n",
       "      <td>31394</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>53</th>\n",
       "      <td>2153</td>\n",
       "      <td>L-Threonine (Threonine)</td>\n",
       "      <td>454</td>\n",
       "      <td>Eubacterium eligens</td>\n",
       "      <td>3</td>\n",
       "      <td>2.172182e-04</td>\n",
       "      <td>1874</td>\n",
       "      <td>25814</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>65</th>\n",
       "      <td>2081</td>\n",
       "      <td>Deoxycholic acid</td>\n",
       "      <td>952</td>\n",
       "      <td>Roseburia intestinalis</td>\n",
       "      <td>2</td>\n",
       "      <td>2.166116e-04</td>\n",
       "      <td>2531</td>\n",
       "      <td>5243</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>2229</td>\n",
       "      <td>Thymine</td>\n",
       "      <td>965</td>\n",
       "      <td>Ruminococcus flavefaciens</td>\n",
       "      <td>3</td>\n",
       "      <td>1.830720e-04</td>\n",
       "      <td>15</td>\n",
       "      <td>30878</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>38</th>\n",
       "      <td>2024</td>\n",
       "      <td>alpha-Tocopherol (Vitamin E, alpha-Tocotrienol)</td>\n",
       "      <td>401</td>\n",
       "      <td>Desulfovibrio piger</td>\n",
       "      <td>3</td>\n",
       "      <td>9.154606e-05</td>\n",
       "      <td>1205</td>\n",
       "      <td>17531</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>56</th>\n",
       "      <td>2136</td>\n",
       "      <td>L-Histidine (Histidine)</td>\n",
       "      <td>309</td>\n",
       "      <td>Clostridium difficile</td>\n",
       "      <td>3</td>\n",
       "      <td>4.180515e-05</td>\n",
       "      <td>2054</td>\n",
       "      <td>24580</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>45</th>\n",
       "      <td>2233</td>\n",
       "      <td>Trimethylamine</td>\n",
       "      <td>329</td>\n",
       "      <td>Collinsella aerofaciens (Eubacterium aerofaciens)</td>\n",
       "      <td>2</td>\n",
       "      <td>1.594808e-05</td>\n",
       "      <td>1413</td>\n",
       "      <td>15152</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50</th>\n",
       "      <td>2155</td>\n",
       "      <td>L-Tyrosine (Tyrosine)</td>\n",
       "      <td>457</td>\n",
       "      <td>Eubacterium rectale</td>\n",
       "      <td>3</td>\n",
       "      <td>6.671989e-06</td>\n",
       "      <td>1802</td>\n",
       "      <td>25961</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>2233</td>\n",
       "      <td>Trimethylamine</td>\n",
       "      <td>608</td>\n",
       "      <td>Lactococcus lactis</td>\n",
       "      <td>2</td>\n",
       "      <td>7.552419e-07</td>\n",
       "      <td>42</td>\n",
       "      <td>15169</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>27</th>\n",
       "      <td>2060</td>\n",
       "      <td>D-Arabinose (L-Arabinose, Arabinose, L-Arabino...</td>\n",
       "      <td>968</td>\n",
       "      <td>Ruminococcus obeum</td>\n",
       "      <td>2</td>\n",
       "      <td>-4.737172e-05</td>\n",
       "      <td>856</td>\n",
       "      <td>3736</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>2019</td>\n",
       "      <td>Adenosylcobalamin (Vitamin B12, Cobamide coenz...</td>\n",
       "      <td>455</td>\n",
       "      <td>Eubacterium hallii</td>\n",
       "      <td>3</td>\n",
       "      <td>-7.774698e-05</td>\n",
       "      <td>118</td>\n",
       "      <td>17247</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>28</th>\n",
       "      <td>2090</td>\n",
       "      <td>Ethanolamine (Phosphatidylethanolamine)</td>\n",
       "      <td>968</td>\n",
       "      <td>Ruminococcus obeum</td>\n",
       "      <td>3</td>\n",
       "      <td>-8.808849e-05</td>\n",
       "      <td>961</td>\n",
       "      <td>21736</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>66</th>\n",
       "      <td>2116</td>\n",
       "      <td>Inosine</td>\n",
       "      <td>968</td>\n",
       "      <td>Ruminococcus obeum</td>\n",
       "      <td>2</td>\n",
       "      <td>-8.995019e-05</td>\n",
       "      <td>2577</td>\n",
       "      <td>7336</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>47</th>\n",
       "      <td>2044</td>\n",
       "      <td>Cellotetraose (Cellohexaose, Cellopentaose, Ce...</td>\n",
       "      <td>952</td>\n",
       "      <td>Roseburia intestinalis</td>\n",
       "      <td>2</td>\n",
       "      <td>-1.575806e-04</td>\n",
       "      <td>1494</td>\n",
       "      <td>2939</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20</th>\n",
       "      <td>2233</td>\n",
       "      <td>Trimethylamine</td>\n",
       "      <td>952</td>\n",
       "      <td>Roseburia intestinalis</td>\n",
       "      <td>2</td>\n",
       "      <td>-1.592162e-04</td>\n",
       "      <td>470</td>\n",
       "      <td>15179</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>31</th>\n",
       "      <td>2061</td>\n",
       "      <td>D-Fructose (Fructose)</td>\n",
       "      <td>969</td>\n",
       "      <td>Ruminococcus torques</td>\n",
       "      <td>2</td>\n",
       "      <td>-2.764878e-04</td>\n",
       "      <td>1029</td>\n",
       "      <td>3809</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25</th>\n",
       "      <td>2038</td>\n",
       "      <td>Butyrate</td>\n",
       "      <td>966</td>\n",
       "      <td>Ruminococcus gnavus</td>\n",
       "      <td>2</td>\n",
       "      <td>-2.960926e-04</td>\n",
       "      <td>645</td>\n",
       "      <td>2583</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>68</th>\n",
       "      <td>2067</td>\n",
       "      <td>D-Glucosamine (Glucosamine)</td>\n",
       "      <td>314</td>\n",
       "      <td>Clostridium leptum</td>\n",
       "      <td>3</td>\n",
       "      <td>-4.485705e-04</td>\n",
       "      <td>2669</td>\n",
       "      <td>20117</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>36</th>\n",
       "      <td>2036</td>\n",
       "      <td>Butanol</td>\n",
       "      <td>55</td>\n",
       "      <td>Alistipes shahii</td>\n",
       "      <td>3</td>\n",
       "      <td>-6.393945e-04</td>\n",
       "      <td>1171</td>\n",
       "      <td>18291</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>61</th>\n",
       "      <td>2239</td>\n",
       "      <td>Uridine</td>\n",
       "      <td>964</td>\n",
       "      <td>Ruminococcus bromii</td>\n",
       "      <td>2</td>\n",
       "      <td>-7.083394e-04</td>\n",
       "      <td>2470</td>\n",
       "      <td>15613</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>42</th>\n",
       "      <td>2037</td>\n",
       "      <td>Butylamine</td>\n",
       "      <td>260</td>\n",
       "      <td>Catenibacterium mitsuokai</td>\n",
       "      <td>3</td>\n",
       "      <td>-7.774267e-04</td>\n",
       "      <td>1345</td>\n",
       "      <td>18387</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>62</th>\n",
       "      <td>2122</td>\n",
       "      <td>Isovalerate (3-Methylbutanoic acid)</td>\n",
       "      <td>260</td>\n",
       "      <td>Catenibacterium mitsuokai</td>\n",
       "      <td>3</td>\n",
       "      <td>-9.306140e-04</td>\n",
       "      <td>2502</td>\n",
       "      <td>23643</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>54</th>\n",
       "      <td>2062</td>\n",
       "      <td>D-Fructuronate</td>\n",
       "      <td>123</td>\n",
       "      <td>Bacteroides dorei</td>\n",
       "      <td>2</td>\n",
       "      <td>-1.000000e-03</td>\n",
       "      <td>2011</td>\n",
       "      <td>3825</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>63</th>\n",
       "      <td>2195</td>\n",
       "      <td>Phenylacetate</td>\n",
       "      <td>46</td>\n",
       "      <td>Akkermansia muciniphila</td>\n",
       "      <td>3</td>\n",
       "      <td>-1.000000e-03</td>\n",
       "      <td>2510</td>\n",
       "      <td>28513</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>67</th>\n",
       "      <td>2207</td>\n",
       "      <td>Retinoate</td>\n",
       "      <td>460</td>\n",
       "      <td>Eubacterium siraeum</td>\n",
       "      <td>2</td>\n",
       "      <td>-1.000000e-03</td>\n",
       "      <td>2606</td>\n",
       "      <td>13434</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>70 rows × 8 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "    metabolite ID                                   metabolite names  \\\n",
       "13           2122                Isovalerate (3-Methylbutanoic acid)   \n",
       "11           2116                                            Inosine   \n",
       "1            2012                                    5-Aminovalerate   \n",
       "5            2065                                    D-Galacturonate   \n",
       "30           2133  L-Glutamate (L-Glutamic acid, Glutamate, D-Glu...   \n",
       "22           2127                              L-Arginine (Arginine)   \n",
       "35           2137                                       L-Homoserine   \n",
       "17           2049                              Cholic acid (Cholate)   \n",
       "4            2068                                D-Glucose (Glucose)   \n",
       "58           2133  L-Glutamate (L-Glutamic acid, Glutamate, D-Glu...   \n",
       "14           2107                                      H2 (Hydrogen)   \n",
       "52           2133  L-Glutamate (L-Glutamic acid, Glutamate, D-Glu...   \n",
       "32           2067                        D-Glucosamine (Glucosamine)   \n",
       "10           2040                                         Cadaverine   \n",
       "23           2105                                            Guanine   \n",
       "9            2217                                          Succinate   \n",
       "26           2134               L-Glutamine (D-Glutamine, Glutamine)   \n",
       "41           2239                                            Uridine   \n",
       "16           2009  3-phenylpropionic acid (Phenylpropanoate, 3-ph...   \n",
       "60           2125                     L-Alanine (D-Alanine, Alanine)   \n",
       "29           2240              Valerate (Pentanoic acid, Pentanoate)   \n",
       "44           2053                                            Citrate   \n",
       "40           2185                              Orotic acid (Orotate)   \n",
       "55           2201                            Propanoate (Propionate)   \n",
       "19           2226                     Thiamine (Vitamin B1, Thiamin)   \n",
       "7            2203                                         Putrescine   \n",
       "34           2049                              Cholic acid (Cholate)   \n",
       "12           2193                                           Pentanol   \n",
       "49           2201                            Propanoate (Propionate)   \n",
       "39           2241                                           Xanthine   \n",
       "..            ...                                                ...   \n",
       "69           2032                   beta-alanine (3-Aminopropionate)   \n",
       "43           2011                             4-Aminobutyrate (GABA)   \n",
       "8            2175  N-Acetylneuraminic acid (N-acetylneuraminate, ...   \n",
       "51           2185                              Orotic acid (Orotate)   \n",
       "15           2122                Isovalerate (3-Methylbutanoic acid)   \n",
       "33           2238                                               Urea   \n",
       "53           2153                            L-Threonine (Threonine)   \n",
       "65           2081                                   Deoxycholic acid   \n",
       "0            2229                                            Thymine   \n",
       "38           2024    alpha-Tocopherol (Vitamin E, alpha-Tocotrienol)   \n",
       "56           2136                            L-Histidine (Histidine)   \n",
       "45           2233                                     Trimethylamine   \n",
       "50           2155                              L-Tyrosine (Tyrosine)   \n",
       "2            2233                                     Trimethylamine   \n",
       "27           2060  D-Arabinose (L-Arabinose, Arabinose, L-Arabino...   \n",
       "6            2019  Adenosylcobalamin (Vitamin B12, Cobamide coenz...   \n",
       "28           2090            Ethanolamine (Phosphatidylethanolamine)   \n",
       "66           2116                                            Inosine   \n",
       "47           2044  Cellotetraose (Cellohexaose, Cellopentaose, Ce...   \n",
       "20           2233                                     Trimethylamine   \n",
       "31           2061                              D-Fructose (Fructose)   \n",
       "25           2038                                           Butyrate   \n",
       "68           2067                        D-Glucosamine (Glucosamine)   \n",
       "36           2036                                            Butanol   \n",
       "61           2239                                            Uridine   \n",
       "42           2037                                         Butylamine   \n",
       "62           2122                Isovalerate (3-Methylbutanoic acid)   \n",
       "54           2062                                     D-Fructuronate   \n",
       "63           2195                                      Phenylacetate   \n",
       "67           2207                                          Retinoate   \n",
       "\n",
       "    microbes ID                                     microbes names  edgeType  \\\n",
       "13          464                       Faecalibacterium prausnitzii         3   \n",
       "11          134                       Bacteroides thetaiotaomicron         3   \n",
       "1           329  Collinsella aerofaciens (Eubacterium aerofaciens)         3   \n",
       "5           454                                Eubacterium eligens         3   \n",
       "30          123                                  Bacteroides dorei         3   \n",
       "22          129                                 Bacteroides ovatus         3   \n",
       "35          968                                 Ruminococcus obeum         3   \n",
       "17          338                                  Coprococcus comes         3   \n",
       "4           878                                 Prevotella salivae         2   \n",
       "58          457                                Eubacterium rectale         2   \n",
       "14          338                                  Coprococcus comes         2   \n",
       "52          454                                Eubacterium eligens         3   \n",
       "32          157  Bifidobacterium longum (Bifidobacterium infant...         3   \n",
       "10         1007                                    Shigella sonnei         3   \n",
       "23          968                                 Ruminococcus obeum         3   \n",
       "9          1099                          Sutterella wadsworthensis         2   \n",
       "26          157  Bifidobacterium longum (Bifidobacterium infant...         2   \n",
       "41          964                                Ruminococcus bromii         3   \n",
       "16          124                              Bacteroides eggerthii         3   \n",
       "60          464                       Faecalibacterium prausnitzii         3   \n",
       "29          456                                Eubacterium limosum         3   \n",
       "44          137                          Bacteroides xylanisolvens         3   \n",
       "40          125      Bacteroides finegoldii (Alistipes finegoldii)         3   \n",
       "55          135                              Bacteroides uniformis         2   \n",
       "19          137                          Bacteroides xylanisolvens         3   \n",
       "7            54                               Alistipes putredinis         2   \n",
       "34           54                               Alistipes putredinis         2   \n",
       "12          870                                   Prevotella copri         3   \n",
       "49          454                                Eubacterium eligens         3   \n",
       "39          608                                 Lactococcus lactis         3   \n",
       "..          ...                                                ...       ...   \n",
       "69          158                  Bifidobacterium pseudocatenulatum         3   \n",
       "43         1064                           Streptococcus salivarius         3   \n",
       "8           121                              Bacteroides coprocola         3   \n",
       "51          137                          Bacteroides xylanisolvens         3   \n",
       "15          135                              Bacteroides uniformis         2   \n",
       "33           54                               Alistipes putredinis         3   \n",
       "53          454                                Eubacterium eligens         3   \n",
       "65          952                             Roseburia intestinalis         2   \n",
       "0           965                          Ruminococcus flavefaciens         3   \n",
       "38          401                                Desulfovibrio piger         3   \n",
       "56          309                              Clostridium difficile         3   \n",
       "45          329  Collinsella aerofaciens (Eubacterium aerofaciens)         2   \n",
       "50          457                                Eubacterium rectale         3   \n",
       "2           608                                 Lactococcus lactis         2   \n",
       "27          968                                 Ruminococcus obeum         2   \n",
       "6           455                                 Eubacterium hallii         3   \n",
       "28          968                                 Ruminococcus obeum         3   \n",
       "66          968                                 Ruminococcus obeum         2   \n",
       "47          952                             Roseburia intestinalis         2   \n",
       "20          952                             Roseburia intestinalis         2   \n",
       "31          969                               Ruminococcus torques         2   \n",
       "25          966                                Ruminococcus gnavus         2   \n",
       "68          314                                 Clostridium leptum         3   \n",
       "36           55                                   Alistipes shahii         3   \n",
       "61          964                                Ruminococcus bromii         2   \n",
       "42          260                          Catenibacterium mitsuokai         3   \n",
       "62          260                          Catenibacterium mitsuokai         3   \n",
       "54          123                                  Bacteroides dorei         2   \n",
       "63           46                            Akkermansia muciniphila         3   \n",
       "67          460                                Eubacterium siraeum         2   \n",
       "\n",
       "    error reduced  step added  position in x  \n",
       "13   1.844743e-02         325          23660  \n",
       "11   1.332175e-02         271          23200  \n",
       "1    1.320793e-02          30          16736  \n",
       "5    1.196131e-02         113          19982  \n",
       "30   1.128696e-02         996          24345  \n",
       "22   9.566429e-03         558          23917  \n",
       "35   8.807495e-03        1146          24688  \n",
       "17   7.812703e-03         379          19041  \n",
       "4    7.025520e-03          78           4304  \n",
       "58   6.083423e-03        2209           8465  \n",
       "14   5.915619e-03         334           6873  \n",
       "52   5.881095e-03        1866          24374  \n",
       "32   5.329910e-03        1039          20111  \n",
       "10   5.329638e-03         240          18570  \n",
       "23   5.252280e-03         598          22672  \n",
       "9    5.223751e-03         222          14111  \n",
       "26   4.961538e-03         707           8519  \n",
       "41   4.586705e-03        1341          31525  \n",
       "16   4.146937e-03         368          16498  \n",
       "60   3.942222e-03        2428          23804  \n",
       "29   3.358106e-03         970          31576  \n",
       "44   2.997298e-03        1373          19242  \n",
       "40   2.743548e-03        1247          27875  \n",
       "55   2.401912e-03        2045          12977  \n",
       "19   2.389538e-03         408          30618  \n",
       "7    2.235055e-03         189          13106  \n",
       "34   2.117413e-03        1133           3098  \n",
       "12   1.897985e-03         318          28423  \n",
       "49   1.593203e-03        1754          28910  \n",
       "39   1.451015e-03        1209          31657  \n",
       "..            ...         ...            ...  \n",
       "69   5.594825e-04        2678          18024  \n",
       "43   4.415987e-04        1354          16701  \n",
       "8    4.179560e-04         204          27223  \n",
       "51   4.090147e-04        1843          27882  \n",
       "15   2.675129e-04         361           7721  \n",
       "33   2.313251e-04        1092          31394  \n",
       "53   2.172182e-04        1874          25814  \n",
       "65   2.166116e-04        2531           5243  \n",
       "0    1.830720e-04          15          30878  \n",
       "38   9.154606e-05        1205          17531  \n",
       "56   4.180515e-05        2054          24580  \n",
       "45   1.594808e-05        1413          15152  \n",
       "50   6.671989e-06        1802          25961  \n",
       "2    7.552419e-07          42          15169  \n",
       "27  -4.737172e-05         856           3736  \n",
       "6   -7.774698e-05         118          17247  \n",
       "28  -8.808849e-05         961          21736  \n",
       "66  -8.995019e-05        2577           7336  \n",
       "47  -1.575806e-04        1494           2939  \n",
       "20  -1.592162e-04         470          15179  \n",
       "31  -2.764878e-04        1029           3809  \n",
       "25  -2.960926e-04         645           2583  \n",
       "68  -4.485705e-04        2669          20117  \n",
       "36  -6.393945e-04        1171          18291  \n",
       "61  -7.083394e-04        2470          15613  \n",
       "42  -7.774267e-04        1345          18387  \n",
       "62  -9.306140e-04        2502          23643  \n",
       "54  -1.000000e-03        2011           3825  \n",
       "63  -1.000000e-03        2510          28513  \n",
       "67  -1.000000e-03        2606          13434  \n",
       "\n",
       "[70 rows x 8 columns]"
      ]
     },
     "execution_count": 117,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "NUMADDED = len(net_added)\n",
    "\n",
    "df_added_metabolites = names.loc[df_metabolites.reset_index().set_index('newID').loc[net_added.iloc[-NUMADDED:,0]].values.flatten()]\n",
    "df_added_metabolites.reset_index(inplace=True)\n",
    "df_added_metabolites.columns = ['metabolite ID', 'metabolite names'] \n",
    "\n",
    "df_added_microbes = names.loc[df_microbes.reset_index().set_index('newID').loc[net_added.iloc[-NUMADDED:,1]].values.flatten()]\n",
    "df_added_microbes.reset_index(inplace=True)\n",
    "df_added_microbes.columns = ['microbes ID', 'microbes names'] \n",
    "\n",
    "df_added_edgeTypes = net_added.iloc[-NUMADDED:,2]\n",
    "df_added_edgeTypes = pd.DataFrame(df_added_edgeTypes)\n",
    "df_added_edgeTypes.index = range(NUMADDED)\n",
    "\n",
    "df_added_errorReduced = -np.diff(error_list)[i_added]\n",
    "df_added_errorReduced = pd.DataFrame(df_added_errorReduced)\n",
    "df_added_errorReduced.index = range(NUMADDED)\n",
    "df_added_errorReduced.columns = ['error reduced'] \n",
    "\n",
    "df_added_step = np.array(current_step_list)[i_added]\n",
    "df_added_step = pd.DataFrame(df_added_step)\n",
    "df_added_step.index = range(NUMADDED)\n",
    "df_added_step.columns = ['step added'] \n",
    "\n",
    "df_added_pos = np.array(pos_x_list)[i_added]\n",
    "df_added_pos = pd.DataFrame(df_added_pos)\n",
    "df_added_pos.index = range(NUMADDED)\n",
    "df_added_pos.columns = ['position in x'] \n",
    "\n",
    "df_added_tables = pd.concat([df_added_metabolites, df_added_microbes, df_added_edgeTypes,  df_added_errorReduced, df_added_step, df_added_pos], axis=1, sort=False)\n",
    "df_added_tables.sort_values(by = 'error reduced', ascending=False)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Construct the added links to a pandas data frame"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 118,
   "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>metabolite ID</th>\n",
       "      <th>metabolite names</th>\n",
       "      <th>microbes ID</th>\n",
       "      <th>microbes names</th>\n",
       "      <th>edgeType</th>\n",
       "      <th>error reduced</th>\n",
       "      <th>step deleted</th>\n",
       "      <th>position in x</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>2122</td>\n",
       "      <td>Isovalerate (3-Methylbutanoic acid)</td>\n",
       "      <td>952</td>\n",
       "      <td>Roseburia intestinalis</td>\n",
       "      <td>3</td>\n",
       "      <td>0.019988</td>\n",
       "      <td>286</td>\n",
       "      <td>23675</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>2107</td>\n",
       "      <td>H2 (Hydrogen)</td>\n",
       "      <td>161</td>\n",
       "      <td>Blautia hansenii (Ruminococcus hansenii)</td>\n",
       "      <td>2</td>\n",
       "      <td>0.011876</td>\n",
       "      <td>275</td>\n",
       "      <td>6866</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>2055</td>\n",
       "      <td>CO2</td>\n",
       "      <td>123</td>\n",
       "      <td>Bacteroides dorei</td>\n",
       "      <td>2</td>\n",
       "      <td>0.005725</td>\n",
       "      <td>479</td>\n",
       "      <td>3393</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17</th>\n",
       "      <td>2055</td>\n",
       "      <td>CO2</td>\n",
       "      <td>137</td>\n",
       "      <td>Bacteroides xylanisolvens</td>\n",
       "      <td>2</td>\n",
       "      <td>0.004862</td>\n",
       "      <td>572</td>\n",
       "      <td>3402</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>26</th>\n",
       "      <td>2238</td>\n",
       "      <td>Urea</td>\n",
       "      <td>1064</td>\n",
       "      <td>Streptococcus salivarius</td>\n",
       "      <td>3</td>\n",
       "      <td>0.003845</td>\n",
       "      <td>819</td>\n",
       "      <td>31461</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>2098</td>\n",
       "      <td>Glycerol</td>\n",
       "      <td>966</td>\n",
       "      <td>Ruminococcus gnavus</td>\n",
       "      <td>2</td>\n",
       "      <td>0.003131</td>\n",
       "      <td>28</td>\n",
       "      <td>6255</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>2204</td>\n",
       "      <td>Pyridoxal (Vitamin B6, Pyridoxine, Pyridoxamin...</td>\n",
       "      <td>964</td>\n",
       "      <td>Ruminococcus bromii</td>\n",
       "      <td>2</td>\n",
       "      <td>0.002847</td>\n",
       "      <td>488</td>\n",
       "      <td>13237</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>2163</td>\n",
       "      <td>Menaquinone (Vitamin K2)</td>\n",
       "      <td>513</td>\n",
       "      <td>Haemophilus parainfluenzae</td>\n",
       "      <td>2</td>\n",
       "      <td>0.002550</td>\n",
       "      <td>421</td>\n",
       "      <td>10631</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>46</th>\n",
       "      <td>2133</td>\n",
       "      <td>L-Glutamate (L-Glutamic acid, Glutamate, D-Glu...</td>\n",
       "      <td>131</td>\n",
       "      <td>Bacteroides plebeius</td>\n",
       "      <td>2</td>\n",
       "      <td>0.002350</td>\n",
       "      <td>1588</td>\n",
       "      <td>8438</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>21</th>\n",
       "      <td>2072</td>\n",
       "      <td>D-Mannose (Mannose)</td>\n",
       "      <td>968</td>\n",
       "      <td>Ruminococcus obeum</td>\n",
       "      <td>2</td>\n",
       "      <td>0.002256</td>\n",
       "      <td>671</td>\n",
       "      <td>4600</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>2019</td>\n",
       "      <td>Adenosylcobalamin (Vitamin B12, Cobamide coenz...</td>\n",
       "      <td>964</td>\n",
       "      <td>Ruminococcus bromii</td>\n",
       "      <td>2</td>\n",
       "      <td>0.001469</td>\n",
       "      <td>461</td>\n",
       "      <td>1357</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>2065</td>\n",
       "      <td>D-Galacturonate</td>\n",
       "      <td>126</td>\n",
       "      <td>Bacteroides fragilis</td>\n",
       "      <td>2</td>\n",
       "      <td>0.001191</td>\n",
       "      <td>220</td>\n",
       "      <td>4044</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>56</th>\n",
       "      <td>2203</td>\n",
       "      <td>Putrescine</td>\n",
       "      <td>55</td>\n",
       "      <td>Alistipes shahii</td>\n",
       "      <td>3</td>\n",
       "      <td>0.001175</td>\n",
       "      <td>2344</td>\n",
       "      <td>29019</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>36</th>\n",
       "      <td>2108</td>\n",
       "      <td>H2O2</td>\n",
       "      <td>895</td>\n",
       "      <td>Pseudoflavonifractor capillosus</td>\n",
       "      <td>2</td>\n",
       "      <td>0.001126</td>\n",
       "      <td>1062</td>\n",
       "      <td>6970</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15</th>\n",
       "      <td>2002</td>\n",
       "      <td>1,2-diacylglycerol (1-acylglycerol, Monoacylgl...</td>\n",
       "      <td>161</td>\n",
       "      <td>Blautia hansenii (Ruminococcus hansenii)</td>\n",
       "      <td>2</td>\n",
       "      <td>0.001000</td>\n",
       "      <td>528</td>\n",
       "      <td>98</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>22</th>\n",
       "      <td>2109</td>\n",
       "      <td>H2S (HS-)</td>\n",
       "      <td>460</td>\n",
       "      <td>Eubacterium siraeum</td>\n",
       "      <td>3</td>\n",
       "      <td>0.000988</td>\n",
       "      <td>732</td>\n",
       "      <td>22938</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>49</th>\n",
       "      <td>2028</td>\n",
       "      <td>Ascorbic acid (Vitamin C, L-Ascorbate, Ascorbate)</td>\n",
       "      <td>152</td>\n",
       "      <td>Bifidobacterium bifidum</td>\n",
       "      <td>3</td>\n",
       "      <td>0.000973</td>\n",
       "      <td>1727</td>\n",
       "      <td>17733</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>53</th>\n",
       "      <td>2099</td>\n",
       "      <td>Glycochenodeoxycholate</td>\n",
       "      <td>54</td>\n",
       "      <td>Alistipes putredinis</td>\n",
       "      <td>3</td>\n",
       "      <td>0.000964</td>\n",
       "      <td>1906</td>\n",
       "      <td>22178</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>60</th>\n",
       "      <td>2060</td>\n",
       "      <td>D-Arabinose (L-Arabinose, Arabinose, L-Arabino...</td>\n",
       "      <td>461</td>\n",
       "      <td>Eubacterium ventriosum</td>\n",
       "      <td>3</td>\n",
       "      <td>0.000903</td>\n",
       "      <td>2638</td>\n",
       "      <td>19627</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>27</th>\n",
       "      <td>2055</td>\n",
       "      <td>CO2</td>\n",
       "      <td>119</td>\n",
       "      <td>Bacteroides caccae</td>\n",
       "      <td>2</td>\n",
       "      <td>0.000876</td>\n",
       "      <td>821</td>\n",
       "      <td>3390</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>2122</td>\n",
       "      <td>Isovalerate (3-Methylbutanoic acid)</td>\n",
       "      <td>952</td>\n",
       "      <td>Roseburia intestinalis</td>\n",
       "      <td>3</td>\n",
       "      <td>0.000798</td>\n",
       "      <td>390</td>\n",
       "      <td>23675</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>43</th>\n",
       "      <td>2098</td>\n",
       "      <td>Glycerol</td>\n",
       "      <td>966</td>\n",
       "      <td>Ruminococcus gnavus</td>\n",
       "      <td>2</td>\n",
       "      <td>0.000777</td>\n",
       "      <td>1525</td>\n",
       "      <td>6255</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>28</th>\n",
       "      <td>2157</td>\n",
       "      <td>Lactose</td>\n",
       "      <td>812</td>\n",
       "      <td>Parabacteroides distasonis</td>\n",
       "      <td>2</td>\n",
       "      <td>0.000717</td>\n",
       "      <td>892</td>\n",
       "      <td>10204</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>31</th>\n",
       "      <td>2061</td>\n",
       "      <td>D-Fructose (Fructose)</td>\n",
       "      <td>134</td>\n",
       "      <td>Bacteroides thetaiotaomicron</td>\n",
       "      <td>2</td>\n",
       "      <td>0.000669</td>\n",
       "      <td>974</td>\n",
       "      <td>3760</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>23</th>\n",
       "      <td>2203</td>\n",
       "      <td>Putrescine</td>\n",
       "      <td>55</td>\n",
       "      <td>Alistipes shahii</td>\n",
       "      <td>3</td>\n",
       "      <td>0.000664</td>\n",
       "      <td>748</td>\n",
       "      <td>29019</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>57</th>\n",
       "      <td>2178</td>\n",
       "      <td>NH3 (Ammonia, NH4+, Ammonium)</td>\n",
       "      <td>425</td>\n",
       "      <td>Eggerthella lenta</td>\n",
       "      <td>2</td>\n",
       "      <td>0.000633</td>\n",
       "      <td>2360</td>\n",
       "      <td>11485</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16</th>\n",
       "      <td>2178</td>\n",
       "      <td>NH3 (Ammonia, NH4+, Ammonium)</td>\n",
       "      <td>965</td>\n",
       "      <td>Ruminococcus flavefaciens</td>\n",
       "      <td>2</td>\n",
       "      <td>0.000497</td>\n",
       "      <td>560</td>\n",
       "      <td>11510</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>2236</td>\n",
       "      <td>Tyramine</td>\n",
       "      <td>126</td>\n",
       "      <td>Bacteroides fragilis</td>\n",
       "      <td>2</td>\n",
       "      <td>0.000487</td>\n",
       "      <td>247</td>\n",
       "      <td>15348</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>51</th>\n",
       "      <td>2238</td>\n",
       "      <td>Urea</td>\n",
       "      <td>1064</td>\n",
       "      <td>Streptococcus salivarius</td>\n",
       "      <td>3</td>\n",
       "      <td>0.000413</td>\n",
       "      <td>1890</td>\n",
       "      <td>31461</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>44</th>\n",
       "      <td>2099</td>\n",
       "      <td>Glycochenodeoxycholate</td>\n",
       "      <td>54</td>\n",
       "      <td>Alistipes putredinis</td>\n",
       "      <td>3</td>\n",
       "      <td>0.000402</td>\n",
       "      <td>1554</td>\n",
       "      <td>22178</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>2109</td>\n",
       "      <td>H2S (HS-)</td>\n",
       "      <td>460</td>\n",
       "      <td>Eubacterium siraeum</td>\n",
       "      <td>3</td>\n",
       "      <td>0.000293</td>\n",
       "      <td>401</td>\n",
       "      <td>22938</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>59</th>\n",
       "      <td>2141</td>\n",
       "      <td>L-Lactate ([S]-Lactate, Lactate, D-Lactate, [R...</td>\n",
       "      <td>401</td>\n",
       "      <td>Desulfovibrio piger</td>\n",
       "      <td>2</td>\n",
       "      <td>0.000237</td>\n",
       "      <td>2623</td>\n",
       "      <td>9035</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>45</th>\n",
       "      <td>2122</td>\n",
       "      <td>Isovalerate (3-Methylbutanoic acid)</td>\n",
       "      <td>457</td>\n",
       "      <td>Eubacterium rectale</td>\n",
       "      <td>2</td>\n",
       "      <td>0.000221</td>\n",
       "      <td>1563</td>\n",
       "      <td>7745</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20</th>\n",
       "      <td>2196</td>\n",
       "      <td>Phenylethylamine</td>\n",
       "      <td>119</td>\n",
       "      <td>Bacteroides caccae</td>\n",
       "      <td>2</td>\n",
       "      <td>0.000004</td>\n",
       "      <td>655</td>\n",
       "      <td>12678</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>54</th>\n",
       "      <td>2238</td>\n",
       "      <td>Urea</td>\n",
       "      <td>158</td>\n",
       "      <td>Bifidobacterium pseudocatenulatum</td>\n",
       "      <td>2</td>\n",
       "      <td>-0.000016</td>\n",
       "      <td>2032</td>\n",
       "      <td>15504</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>18</th>\n",
       "      <td>2196</td>\n",
       "      <td>Phenylethylamine</td>\n",
       "      <td>119</td>\n",
       "      <td>Bacteroides caccae</td>\n",
       "      <td>2</td>\n",
       "      <td>-0.000068</td>\n",
       "      <td>615</td>\n",
       "      <td>12678</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>19</th>\n",
       "      <td>2133</td>\n",
       "      <td>L-Glutamate (L-Glutamic acid, Glutamate, D-Glu...</td>\n",
       "      <td>131</td>\n",
       "      <td>Bacteroides plebeius</td>\n",
       "      <td>2</td>\n",
       "      <td>-0.000116</td>\n",
       "      <td>637</td>\n",
       "      <td>8438</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>2082</td>\n",
       "      <td>Dextrin (Maltotriose, Maltodextrin, Maltohexao...</td>\n",
       "      <td>134</td>\n",
       "      <td>Bacteroides thetaiotaomicron</td>\n",
       "      <td>2</td>\n",
       "      <td>-0.000116</td>\n",
       "      <td>373</td>\n",
       "      <td>5272</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>29</th>\n",
       "      <td>2204</td>\n",
       "      <td>Pyridoxal (Vitamin B6, Pyridoxine, Pyridoxamin...</td>\n",
       "      <td>608</td>\n",
       "      <td>Lactococcus lactis</td>\n",
       "      <td>2</td>\n",
       "      <td>-0.000131</td>\n",
       "      <td>925</td>\n",
       "      <td>13225</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>40</th>\n",
       "      <td>2122</td>\n",
       "      <td>Isovalerate (3-Methylbutanoic acid)</td>\n",
       "      <td>457</td>\n",
       "      <td>Eubacterium rectale</td>\n",
       "      <td>2</td>\n",
       "      <td>-0.000141</td>\n",
       "      <td>1384</td>\n",
       "      <td>7745</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>30</th>\n",
       "      <td>2049</td>\n",
       "      <td>Cholic acid (Cholate)</td>\n",
       "      <td>314</td>\n",
       "      <td>Clostridium leptum</td>\n",
       "      <td>2</td>\n",
       "      <td>-0.000148</td>\n",
       "      <td>936</td>\n",
       "      <td>3125</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>47</th>\n",
       "      <td>2238</td>\n",
       "      <td>Urea</td>\n",
       "      <td>323</td>\n",
       "      <td>Clostridium scindens</td>\n",
       "      <td>2</td>\n",
       "      <td>-0.000151</td>\n",
       "      <td>1589</td>\n",
       "      <td>15510</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>24</th>\n",
       "      <td>2055</td>\n",
       "      <td>CO2</td>\n",
       "      <td>124</td>\n",
       "      <td>Bacteroides eggerthii</td>\n",
       "      <td>2</td>\n",
       "      <td>-0.000363</td>\n",
       "      <td>754</td>\n",
       "      <td>3394</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25</th>\n",
       "      <td>2061</td>\n",
       "      <td>D-Fructose (Fructose)</td>\n",
       "      <td>129</td>\n",
       "      <td>Bacteroides ovatus</td>\n",
       "      <td>2</td>\n",
       "      <td>-0.000363</td>\n",
       "      <td>805</td>\n",
       "      <td>3757</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>2236</td>\n",
       "      <td>Tyramine</td>\n",
       "      <td>126</td>\n",
       "      <td>Bacteroides fragilis</td>\n",
       "      <td>2</td>\n",
       "      <td>-0.000500</td>\n",
       "      <td>122</td>\n",
       "      <td>15348</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>42</th>\n",
       "      <td>2161</td>\n",
       "      <td>Maltose</td>\n",
       "      <td>329</td>\n",
       "      <td>Collinsella aerofaciens (Eubacterium aerofaciens)</td>\n",
       "      <td>2</td>\n",
       "      <td>-0.000518</td>\n",
       "      <td>1463</td>\n",
       "      <td>10472</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>34</th>\n",
       "      <td>2068</td>\n",
       "      <td>D-Glucose (Glucose)</td>\n",
       "      <td>814</td>\n",
       "      <td>Parabacteroides merdae</td>\n",
       "      <td>2</td>\n",
       "      <td>-0.000551</td>\n",
       "      <td>1038</td>\n",
       "      <td>4302</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>37</th>\n",
       "      <td>2028</td>\n",
       "      <td>Ascorbic acid (Vitamin C, L-Ascorbate, Ascorbate)</td>\n",
       "      <td>152</td>\n",
       "      <td>Bifidobacterium bifidum</td>\n",
       "      <td>3</td>\n",
       "      <td>-0.000591</td>\n",
       "      <td>1066</td>\n",
       "      <td>17733</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>55</th>\n",
       "      <td>2178</td>\n",
       "      <td>NH3 (Ammonia, NH4+, Ammonium)</td>\n",
       "      <td>425</td>\n",
       "      <td>Eggerthella lenta</td>\n",
       "      <td>2</td>\n",
       "      <td>-0.000619</td>\n",
       "      <td>2243</td>\n",
       "      <td>11485</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>35</th>\n",
       "      <td>2157</td>\n",
       "      <td>Lactose</td>\n",
       "      <td>796</td>\n",
       "      <td>Odoribacter splanchnicus</td>\n",
       "      <td>2</td>\n",
       "      <td>-0.000699</td>\n",
       "      <td>1046</td>\n",
       "      <td>10202</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50</th>\n",
       "      <td>2014</td>\n",
       "      <td>Acetate</td>\n",
       "      <td>952</td>\n",
       "      <td>Roseburia intestinalis</td>\n",
       "      <td>2</td>\n",
       "      <td>-0.000707</td>\n",
       "      <td>1759</td>\n",
       "      <td>995</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>52</th>\n",
       "      <td>2082</td>\n",
       "      <td>Dextrin (Maltotriose, Maltodextrin, Maltohexao...</td>\n",
       "      <td>964</td>\n",
       "      <td>Ruminococcus bromii</td>\n",
       "      <td>2</td>\n",
       "      <td>-0.000864</td>\n",
       "      <td>1891</td>\n",
       "      <td>5317</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>41</th>\n",
       "      <td>2038</td>\n",
       "      <td>Butyrate</td>\n",
       "      <td>314</td>\n",
       "      <td>Clostridium leptum</td>\n",
       "      <td>3</td>\n",
       "      <td>-0.001000</td>\n",
       "      <td>1405</td>\n",
       "      <td>18461</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>39</th>\n",
       "      <td>2240</td>\n",
       "      <td>Valerate (Pentanoic acid, Pentanoate)</td>\n",
       "      <td>75</td>\n",
       "      <td>Anaerostipes caccae</td>\n",
       "      <td>3</td>\n",
       "      <td>-0.001000</td>\n",
       "      <td>1367</td>\n",
       "      <td>31540</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>32</th>\n",
       "      <td>2073</td>\n",
       "      <td>D-Psicose</td>\n",
       "      <td>129</td>\n",
       "      <td>Bacteroides ovatus</td>\n",
       "      <td>2</td>\n",
       "      <td>-0.001000</td>\n",
       "      <td>977</td>\n",
       "      <td>4621</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>2002</td>\n",
       "      <td>1,2-diacylglycerol (1-acylglycerol, Monoacylgl...</td>\n",
       "      <td>161</td>\n",
       "      <td>Blautia hansenii (Ruminococcus hansenii)</td>\n",
       "      <td>2</td>\n",
       "      <td>-0.001000</td>\n",
       "      <td>372</td>\n",
       "      <td>98</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>48</th>\n",
       "      <td>2014</td>\n",
       "      <td>Acetate</td>\n",
       "      <td>880</td>\n",
       "      <td>Prevotella timonensis</td>\n",
       "      <td>3</td>\n",
       "      <td>-0.001000</td>\n",
       "      <td>1655</td>\n",
       "      <td>16905</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>58</th>\n",
       "      <td>2034</td>\n",
       "      <td>Bicarbonate (HCO3-, H2CO3, Carbonic acid, Carb...</td>\n",
       "      <td>964</td>\n",
       "      <td>Ruminococcus bromii</td>\n",
       "      <td>2</td>\n",
       "      <td>-0.001000</td>\n",
       "      <td>2426</td>\n",
       "      <td>2293</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>2060</td>\n",
       "      <td>D-Arabinose (L-Arabinose, Arabinose, L-Arabino...</td>\n",
       "      <td>461</td>\n",
       "      <td>Eubacterium ventriosum</td>\n",
       "      <td>3</td>\n",
       "      <td>-0.001022</td>\n",
       "      <td>333</td>\n",
       "      <td>19627</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>33</th>\n",
       "      <td>2108</td>\n",
       "      <td>H2O2</td>\n",
       "      <td>895</td>\n",
       "      <td>Pseudoflavonifractor capillosus</td>\n",
       "      <td>2</td>\n",
       "      <td>-0.001144</td>\n",
       "      <td>1013</td>\n",
       "      <td>6970</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>61 rows × 8 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "    metabolite ID                                   metabolite names  \\\n",
       "5            2122                Isovalerate (3-Methylbutanoic acid)   \n",
       "4            2107                                      H2 (Hydrogen)   \n",
       "13           2055                                                CO2   \n",
       "17           2055                                                CO2   \n",
       "26           2238                                               Urea   \n",
       "0            2098                                           Glycerol   \n",
       "14           2204  Pyridoxal (Vitamin B6, Pyridoxine, Pyridoxamin...   \n",
       "11           2163                           Menaquinone (Vitamin K2)   \n",
       "46           2133  L-Glutamate (L-Glutamic acid, Glutamate, D-Glu...   \n",
       "21           2072                                D-Mannose (Mannose)   \n",
       "12           2019  Adenosylcobalamin (Vitamin B12, Cobamide coenz...   \n",
       "2            2065                                    D-Galacturonate   \n",
       "56           2203                                         Putrescine   \n",
       "36           2108                                               H2O2   \n",
       "15           2002  1,2-diacylglycerol (1-acylglycerol, Monoacylgl...   \n",
       "22           2109                                          H2S (HS-)   \n",
       "49           2028  Ascorbic acid (Vitamin C, L-Ascorbate, Ascorbate)   \n",
       "53           2099                             Glycochenodeoxycholate   \n",
       "60           2060  D-Arabinose (L-Arabinose, Arabinose, L-Arabino...   \n",
       "27           2055                                                CO2   \n",
       "9            2122                Isovalerate (3-Methylbutanoic acid)   \n",
       "43           2098                                           Glycerol   \n",
       "28           2157                                            Lactose   \n",
       "31           2061                              D-Fructose (Fructose)   \n",
       "23           2203                                         Putrescine   \n",
       "57           2178                      NH3 (Ammonia, NH4+, Ammonium)   \n",
       "16           2178                      NH3 (Ammonia, NH4+, Ammonium)   \n",
       "3            2236                                           Tyramine   \n",
       "51           2238                                               Urea   \n",
       "44           2099                             Glycochenodeoxycholate   \n",
       "..            ...                                                ...   \n",
       "10           2109                                          H2S (HS-)   \n",
       "59           2141  L-Lactate ([S]-Lactate, Lactate, D-Lactate, [R...   \n",
       "45           2122                Isovalerate (3-Methylbutanoic acid)   \n",
       "20           2196                                   Phenylethylamine   \n",
       "54           2238                                               Urea   \n",
       "18           2196                                   Phenylethylamine   \n",
       "19           2133  L-Glutamate (L-Glutamic acid, Glutamate, D-Glu...   \n",
       "8            2082  Dextrin (Maltotriose, Maltodextrin, Maltohexao...   \n",
       "29           2204  Pyridoxal (Vitamin B6, Pyridoxine, Pyridoxamin...   \n",
       "40           2122                Isovalerate (3-Methylbutanoic acid)   \n",
       "30           2049                              Cholic acid (Cholate)   \n",
       "47           2238                                               Urea   \n",
       "24           2055                                                CO2   \n",
       "25           2061                              D-Fructose (Fructose)   \n",
       "1            2236                                           Tyramine   \n",
       "42           2161                                            Maltose   \n",
       "34           2068                                D-Glucose (Glucose)   \n",
       "37           2028  Ascorbic acid (Vitamin C, L-Ascorbate, Ascorbate)   \n",
       "55           2178                      NH3 (Ammonia, NH4+, Ammonium)   \n",
       "35           2157                                            Lactose   \n",
       "50           2014                                            Acetate   \n",
       "52           2082  Dextrin (Maltotriose, Maltodextrin, Maltohexao...   \n",
       "41           2038                                           Butyrate   \n",
       "39           2240              Valerate (Pentanoic acid, Pentanoate)   \n",
       "32           2073                                          D-Psicose   \n",
       "7            2002  1,2-diacylglycerol (1-acylglycerol, Monoacylgl...   \n",
       "48           2014                                            Acetate   \n",
       "58           2034  Bicarbonate (HCO3-, H2CO3, Carbonic acid, Carb...   \n",
       "6            2060  D-Arabinose (L-Arabinose, Arabinose, L-Arabino...   \n",
       "33           2108                                               H2O2   \n",
       "\n",
       "    microbes ID                                     microbes names  edgeType  \\\n",
       "5           952                             Roseburia intestinalis         3   \n",
       "4           161           Blautia hansenii (Ruminococcus hansenii)         2   \n",
       "13          123                                  Bacteroides dorei         2   \n",
       "17          137                          Bacteroides xylanisolvens         2   \n",
       "26         1064                           Streptococcus salivarius         3   \n",
       "0           966                                Ruminococcus gnavus         2   \n",
       "14          964                                Ruminococcus bromii         2   \n",
       "11          513                         Haemophilus parainfluenzae         2   \n",
       "46          131                               Bacteroides plebeius         2   \n",
       "21          968                                 Ruminococcus obeum         2   \n",
       "12          964                                Ruminococcus bromii         2   \n",
       "2           126                               Bacteroides fragilis         2   \n",
       "56           55                                   Alistipes shahii         3   \n",
       "36          895                    Pseudoflavonifractor capillosus         2   \n",
       "15          161           Blautia hansenii (Ruminococcus hansenii)         2   \n",
       "22          460                                Eubacterium siraeum         3   \n",
       "49          152                            Bifidobacterium bifidum         3   \n",
       "53           54                               Alistipes putredinis         3   \n",
       "60          461                             Eubacterium ventriosum         3   \n",
       "27          119                                 Bacteroides caccae         2   \n",
       "9           952                             Roseburia intestinalis         3   \n",
       "43          966                                Ruminococcus gnavus         2   \n",
       "28          812                         Parabacteroides distasonis         2   \n",
       "31          134                       Bacteroides thetaiotaomicron         2   \n",
       "23           55                                   Alistipes shahii         3   \n",
       "57          425                                  Eggerthella lenta         2   \n",
       "16          965                          Ruminococcus flavefaciens         2   \n",
       "3           126                               Bacteroides fragilis         2   \n",
       "51         1064                           Streptococcus salivarius         3   \n",
       "44           54                               Alistipes putredinis         3   \n",
       "..          ...                                                ...       ...   \n",
       "10          460                                Eubacterium siraeum         3   \n",
       "59          401                                Desulfovibrio piger         2   \n",
       "45          457                                Eubacterium rectale         2   \n",
       "20          119                                 Bacteroides caccae         2   \n",
       "54          158                  Bifidobacterium pseudocatenulatum         2   \n",
       "18          119                                 Bacteroides caccae         2   \n",
       "19          131                               Bacteroides plebeius         2   \n",
       "8           134                       Bacteroides thetaiotaomicron         2   \n",
       "29          608                                 Lactococcus lactis         2   \n",
       "40          457                                Eubacterium rectale         2   \n",
       "30          314                                 Clostridium leptum         2   \n",
       "47          323                               Clostridium scindens         2   \n",
       "24          124                              Bacteroides eggerthii         2   \n",
       "25          129                                 Bacteroides ovatus         2   \n",
       "1           126                               Bacteroides fragilis         2   \n",
       "42          329  Collinsella aerofaciens (Eubacterium aerofaciens)         2   \n",
       "34          814                             Parabacteroides merdae         2   \n",
       "37          152                            Bifidobacterium bifidum         3   \n",
       "55          425                                  Eggerthella lenta         2   \n",
       "35          796                           Odoribacter splanchnicus         2   \n",
       "50          952                             Roseburia intestinalis         2   \n",
       "52          964                                Ruminococcus bromii         2   \n",
       "41          314                                 Clostridium leptum         3   \n",
       "39           75                                Anaerostipes caccae         3   \n",
       "32          129                                 Bacteroides ovatus         2   \n",
       "7           161           Blautia hansenii (Ruminococcus hansenii)         2   \n",
       "48          880                              Prevotella timonensis         3   \n",
       "58          964                                Ruminococcus bromii         2   \n",
       "6           461                             Eubacterium ventriosum         3   \n",
       "33          895                    Pseudoflavonifractor capillosus         2   \n",
       "\n",
       "    error reduced  step deleted  position in x  \n",
       "5        0.019988           286          23675  \n",
       "4        0.011876           275           6866  \n",
       "13       0.005725           479           3393  \n",
       "17       0.004862           572           3402  \n",
       "26       0.003845           819          31461  \n",
       "0        0.003131            28           6255  \n",
       "14       0.002847           488          13237  \n",
       "11       0.002550           421          10631  \n",
       "46       0.002350          1588           8438  \n",
       "21       0.002256           671           4600  \n",
       "12       0.001469           461           1357  \n",
       "2        0.001191           220           4044  \n",
       "56       0.001175          2344          29019  \n",
       "36       0.001126          1062           6970  \n",
       "15       0.001000           528             98  \n",
       "22       0.000988           732          22938  \n",
       "49       0.000973          1727          17733  \n",
       "53       0.000964          1906          22178  \n",
       "60       0.000903          2638          19627  \n",
       "27       0.000876           821           3390  \n",
       "9        0.000798           390          23675  \n",
       "43       0.000777          1525           6255  \n",
       "28       0.000717           892          10204  \n",
       "31       0.000669           974           3760  \n",
       "23       0.000664           748          29019  \n",
       "57       0.000633          2360          11485  \n",
       "16       0.000497           560          11510  \n",
       "3        0.000487           247          15348  \n",
       "51       0.000413          1890          31461  \n",
       "44       0.000402          1554          22178  \n",
       "..            ...           ...            ...  \n",
       "10       0.000293           401          22938  \n",
       "59       0.000237          2623           9035  \n",
       "45       0.000221          1563           7745  \n",
       "20       0.000004           655          12678  \n",
       "54      -0.000016          2032          15504  \n",
       "18      -0.000068           615          12678  \n",
       "19      -0.000116           637           8438  \n",
       "8       -0.000116           373           5272  \n",
       "29      -0.000131           925          13225  \n",
       "40      -0.000141          1384           7745  \n",
       "30      -0.000148           936           3125  \n",
       "47      -0.000151          1589          15510  \n",
       "24      -0.000363           754           3394  \n",
       "25      -0.000363           805           3757  \n",
       "1       -0.000500           122          15348  \n",
       "42      -0.000518          1463          10472  \n",
       "34      -0.000551          1038           4302  \n",
       "37      -0.000591          1066          17733  \n",
       "55      -0.000619          2243          11485  \n",
       "35      -0.000699          1046          10202  \n",
       "50      -0.000707          1759            995  \n",
       "52      -0.000864          1891           5317  \n",
       "41      -0.001000          1405          18461  \n",
       "39      -0.001000          1367          31540  \n",
       "32      -0.001000           977           4621  \n",
       "7       -0.001000           372             98  \n",
       "48      -0.001000          1655          16905  \n",
       "58      -0.001000          2426           2293  \n",
       "6       -0.001022           333          19627  \n",
       "33      -0.001144          1013           6970  \n",
       "\n",
       "[61 rows x 8 columns]"
      ]
     },
     "execution_count": 118,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "NUMdeleted = len(net_deleted)\n",
    "\n",
    "df_deleted_metabolites = names.loc[df_metabolites.reset_index().set_index('newID').loc[net_deleted.iloc[-NUMdeleted:,0]].values.flatten()]\n",
    "df_deleted_metabolites.reset_index(inplace=True)\n",
    "df_deleted_metabolites.columns = ['metabolite ID', 'metabolite names'] \n",
    "\n",
    "df_deleted_microbes = names.loc[df_microbes.reset_index().set_index('newID').loc[net_deleted.iloc[-NUMdeleted:,1]].values.flatten()]\n",
    "df_deleted_microbes.reset_index(inplace=True)\n",
    "df_deleted_microbes.columns = ['microbes ID', 'microbes names'] \n",
    "\n",
    "df_deleted_edgeTypes = net_deleted.iloc[-NUMdeleted:,2]\n",
    "df_deleted_edgeTypes = pd.DataFrame(df_deleted_edgeTypes)\n",
    "df_deleted_edgeTypes.index = range(NUMdeleted)\n",
    "\n",
    "df_deleted_errorReduced = -np.diff(error_list)[i_deleted]\n",
    "df_deleted_errorReduced = pd.DataFrame(df_deleted_errorReduced)\n",
    "df_deleted_errorReduced.index = range(NUMdeleted)\n",
    "df_deleted_errorReduced.columns = ['error reduced'] \n",
    "\n",
    "df_deleted_step = np.array(current_step_list)[i_deleted]\n",
    "df_deleted_step = pd.DataFrame(df_deleted_step)\n",
    "df_deleted_step.index = range(NUMdeleted)\n",
    "df_deleted_step.columns = ['step deleted'] \n",
    "\n",
    "df_deleted_pos = np.array(pos_x_list)[i_deleted]\n",
    "df_deleted_pos = pd.DataFrame(df_deleted_pos)\n",
    "df_deleted_pos.index = range(NUMdeleted)\n",
    "df_deleted_pos.columns = ['position in x'] \n",
    "\n",
    "df_deleted_tables = pd.concat([df_deleted_metabolites, df_deleted_microbes, df_deleted_edgeTypes,  df_deleted_errorReduced, df_deleted_step, df_deleted_pos], axis=1, sort=False)\n",
    "df_deleted_tables.sort_values(by = 'error reduced', ascending=False)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Visualize error reduction over time and rank plot of error reduction"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 119,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 0, 'number of links added')"
      ]
     },
     "execution_count": 119,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure()\n",
    "plt.plot(np.cumsum(np.sort(df_added_tables['error reduced'].values))[::-1])\n",
    "plt.yscale('log')\n",
    "plt.ylabel('per link error reduction')\n",
    "plt.xlabel('rank of links')\n",
    "\n",
    "plt.figure()\n",
    "plt.plot(error_list)\n",
    "plt.ylabel('error')\n",
    "plt.xlabel('number of links added')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Generate p-value by comparing the added links to links in the MAMBO"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 120,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "3217 30749\n",
      "0.1046212884971869\n",
      "Of 48 valid links existing in MAMBO, there are 25 found by the GutCP.\n",
      "The p-value of this is 5.116521195613899e-08\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "chia_microbes_in_Thai = df_microbes.reset_index().set_index('newID').loc[metagenome_ID].values.flatten()\n",
    "chia_metabolites_in_Thai = df_metabolites.reset_index().set_index('newID').loc[df_metabolites['newID']].values.flatten()\n",
    "\n",
    "df_MAMBO = pd.read_csv(\"mambo_curated.txt\", sep = '\\t')\n",
    "df_MAMBO_filtered = df_MAMBO[df_MAMBO['microbe_ID'].apply(lambda x: x in chia_microbes_in_Thai)]\n",
    "df_MAMBO_filtered = df_MAMBO_filtered[df_MAMBO_filtered['metabolite_ID'].apply(lambda x: x in chia_metabolites_in_Thai)]\n",
    "\n",
    "df_MAMBO_filtered_newID = df_MAMBO_filtered[['microbe_ID', 'metabolite_ID']].copy()\n",
    "df_MAMBO_filtered_newID.columns = ['microbes', 'metabolites']\n",
    "df_MAMBO_filtered_newID['microbes'] = df_microbes.loc[df_MAMBO_filtered_newID['microbes']].values\n",
    "df_MAMBO_filtered_newID['metabolites'] = df_metabolites.loc[df_MAMBO_filtered_newID['metabolites']].values\n",
    "s1 = df_MAMBO_filtered_newID\n",
    "s2 = net[['metabolites', 'microbes']]\n",
    "numOverlap = len(pd.merge(s1, s2, how='inner'))\n",
    "\n",
    "print((len(df_MAMBO_filtered)-numOverlap), (x.shape[0] - len(net_ori)))\n",
    "print((len(df_MAMBO_filtered)-numOverlap) / (x.shape[0] - len(net_ori)) )\n",
    "\n",
    "k = 0\n",
    "l = 0\n",
    "ifIncluded = np.zeros((NUMADDED))\n",
    "ifCovered = np.zeros((NUMADDED))\n",
    "for i in range(NUMADDED):\n",
    "    if (np.sum((df_MAMBO['microbe_ID'] == df_added_tables['microbes ID'].iloc[i])) >=1 and \n",
    "       np.sum((df_MAMBO['metabolite_ID'] == df_added_tables['metabolite ID'].iloc[i]))>=1):\n",
    "        ifCovered[i] = 1\n",
    "        l += 1\n",
    "    if np.sum((df_MAMBO['microbe_ID'] == df_added_tables['microbes ID'].iloc[i]) & \n",
    "       (df_MAMBO['metabolite_ID'] == df_added_tables['metabolite ID'].iloc[i]))>=1:\n",
    "        ifIncluded[i] = 1\n",
    "        k += 1\n",
    "print('Of '+str(l)+' valid links existing in MAMBO, there are '+str(k)+' found by the GutCP.')\n",
    "\n",
    "from scipy.stats import bernoulli, binom\n",
    "xx = range(NUMADDED)\n",
    "p = len(df_MAMBO_filtered) / x.shape[0]\n",
    "#prob = bernoulli.cdf(xx, p)\n",
    "probCum = binom.cdf(xx, NUMADDED, p)\n",
    "prob = binom.pmf(xx, NUMADDED, p)\n",
    "plt.plot(xx, prob, 'o')\n",
    "plt.plot([k, k], [0, np.max(prob)], '-.')\n",
    "plt.xlabel('Number of predicted links in MAMBO')\n",
    "plt.ylabel('Probability')\n",
    "p_value = 1 - probCum[k]\n",
    "print('The p-value of this is',str(p_value))\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernel_info": {
   "name": "python3"
  },
  "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": "3.7.3"
  },
  "nteract": {
   "version": "0.15.0"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}