GREMLIN_TF1_simple.ipynb

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      "name": "GREMLIN_TF1_simple.ipynb",
      "provenance": [],
      "collapsed_sections": [],
      "include_colab_link": true
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    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
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    "accelerator": "GPU"
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  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
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      "source": [
        "<a href=\"https://colab.research.google.com/github/sokrypton/GREMLIN_CPP/blob/master/GREMLIN_TF1_simple.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "3SHD25hwV_FA",
        "colab_type": "text"
      },
      "source": [
        "## GREMLIN_TF1_simple\n",
        "\n",
        "This is a bare minimum version of GREMLIN (no gap removal, etc), intended for educational/demo purposes.\n",
        "\n",
        "For the NEW version designed to integrate with TF2+Keras [see here](https://colab.research.google.com/github/sokrypton/GREMLIN_CPP/blob/master/GREMLIN_TF_simple.ipynb)."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "dyhXMSv5HbpK",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "# ------------------------------------------------------------\n",
        "# \"THE BEERWARE LICENSE\" (Revision 42):\n",
        "# <so@g.harvard.edu> and <koo@cshl.edu> wrote this code.\n",
        "# As long as you retain this notice, you can do whatever you want\n",
        "# with this stuff. If we meet someday, and you think this stuff\n",
        "# is worth it, you can buy us a beer in return.\n",
        "# --Sergey Ovchinnikov and Peter Koo\n",
        "# ------------------------------------------------------------"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "2R1EtdXxSPTW",
        "colab_type": "text"
      },
      "source": [
        "Select tensorflow version for Google Colab"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "S4iwIoJyLpn8",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "%tensorflow_version 1.x"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ZdGBxCYlURSw",
        "colab_type": "text"
      },
      "source": [
        "## Load some libraries"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "aJcHKRLQQAS4",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "import numpy as np\n",
        "import tensorflow as tf\n",
        "import matplotlib.pylab as plt\n",
        "import string\n",
        "\n",
        "# importing functions specific to tensorflow v1\n",
        "import tensorflow.compat.v1 as tf1\n",
        "\n",
        "# disable eager execuation (if using tensorflow v2)\n",
        "tf1.disable_eager_execution()"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ijbQXxzlYKAk",
        "colab_type": "text"
      },
      "source": [
        "## Convert FASTA to MSA np.array()"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "wU8Gzh1FQEZl",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "def parse_fasta(filename, a3m=False):\n",
        "  '''function to parse fasta file'''\n",
        "  \n",
        "  if a3m:\n",
        "    # for a3m files the lowercase letters are removed\n",
        "    # as these do not align to the query sequence\n",
        "    rm_lc = str.maketrans(dict.fromkeys(string.ascii_lowercase))\n",
        "    \n",
        "  header, sequence = [],[]\n",
        "  lines = open(filename, \"r\")\n",
        "  for line in lines:\n",
        "    line = line.rstrip()\n",
        "    if line[0] == \">\":\n",
        "      header.append(line[1:])\n",
        "      sequence.append([])\n",
        "    else:\n",
        "      if a3m: line = line.translate(rm_lc)\n",
        "      else: line = line.upper()\n",
        "      sequence[-1].append(line)\n",
        "  lines.close()\n",
        "  sequence = [''.join(seq) for seq in sequence]\n",
        "  \n",
        "  return header, sequence\n",
        "  \n",
        "def mk_msa(seqs):\n",
        "  '''one hot encode msa'''\n",
        "  alphabet = \"ARNDCQEGHILKMFPSTWYV-\"\n",
        "  states = len(alphabet)  \n",
        "  a2n = {a:n for n,a in enumerate(alphabet)}\n",
        "  msa_ori = np.array([[a2n.get(aa, states-1) for aa in seq] for seq in seqs])\n",
        "  return np.eye(states)[msa_ori]"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "z8j_kpFSUeFT",
        "colab_type": "text"
      },
      "source": [
        "## load example"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Nn5oow4zP9ht",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "!wget -q -nc https://gremlin2.bakerlab.org/db/PDB_EXP/fasta/4FAZA.fas"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "ipoWnWOCQryY",
        "colab_type": "code",
        "outputId": "f822b213-a36d-4629-d487-20c6596a2a0a",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        }
      },
      "source": [
        "names, seqs = parse_fasta(\"4FAZA.fas\")\n",
        "msa = mk_msa(seqs)\n",
        "\n",
        "print(msa.shape)"
      ],
      "execution_count": 6,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "(817, 62, 21)\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "H-PcQ6EORuZP",
        "colab_type": "text"
      },
      "source": [
        "### compute weight for each sequence\n",
        "if your alignment has many redundant sequences, these should be downweighted!\n",
        "For example, if two sequences share more 80% identity, they are effectively one sequence, and thus each would get a weight of 0.5."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "fG2loW_9RteN",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "from scipy.spatial.distance import pdist, squareform\n",
        "def get_eff(msa, eff_cutoff=0.8):\n",
        "  if msa.ndim == 3: msa = msa.argmax(-1)    \n",
        "  # pairwise identity  \n",
        "  msa_sm = 1.0 - squareform(pdist(msa,\"hamming\"))\n",
        "  # weight for each sequence\n",
        "  msa_w = (msa_sm >= eff_cutoff).astype(np.float)\n",
        "  msa_w = 1/np.sum(msa_w,-1)\n",
        "  \n",
        "  return msa_w"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "7vmvo-T7Rx3R",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "msa_weights = get_eff(msa)"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "eNAbmgeOQ1UK",
        "colab_type": "text"
      },
      "source": [
        "## GREMLIN\n",
        "GREMLIN is technically an \"autoencoder\" with a single dense (or fully-connected) layer between the input and output, with no hidden variables. GREMLIN tries to minimize the difference between the input and output.  The \"latent\" variables are the (w)eights/(b)ias of the dense layer.\n",
        "\n",
        "* loss = categorical_crossentropy(msa,  softmax(dot(msa, w) + b))\n",
        " - the math is identical to computing the \"pseudolikelihood\" as in GREMLIN()\n",
        " \n",
        "* msa\n",
        " - msa.shape = (batch, L x 21)\n",
        " - 21 =  (20 amino acids + 1 gap) categories\n",
        "* w = weight\n",
        " - w.shape = (L x 21, L x 21)\n",
        " -  aka two-body term of the MRF (aka co-evolution)\n",
        " -  note: the w matrix is symmetrized and the diagional is set to zero\n",
        "* b = bias \n",
        " - b.shape = (L x 21)\n",
        " - aka one-body-term of the MRF (aka conservation)"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "bYFxhwGoQxyT",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "def GREMLIN_simple(msa, msa_weights=None, opt_iter=100):\n",
        "  \n",
        "  # collecting some information about input msa\n",
        "  N = msa.shape[0] # number of sequences\n",
        "  L = msa.shape[1] # length of sequence\n",
        "  A = msa.shape[2] # number of states (or categories)\n",
        "  \n",
        "  # weights\n",
        "  if msa_weights is None:\n",
        "    msa_weights = np.ones(N)\n",
        "\n",
        "  # kill any existing tensorflow graph\n",
        "  tf1.reset_default_graph()\n",
        "\n",
        "  # setting up weights\n",
        "  b = tf1.get_variable(\"b\", [L,A])\n",
        "  w = tf1.get_variable(\"w\", [L,A,L,A], initializer=tf.initializers.zeros)\n",
        "\n",
        "  # symmetrize w\n",
        "  w = w * np.reshape(1-np.eye(L),(L,1,L,1))\n",
        "  w = w + tf.transpose(w,[2,3,0,1])\n",
        "  \n",
        "  # input\n",
        "  MSA = tf.constant(msa,dtype=tf.float32)\n",
        "  MSA_weights = tf.constant(msa_weights,dtype=tf.float32)\n",
        "\n",
        "  # dense layer + softmax activation\n",
        "  MSA_pred = tf.nn.softmax(tf.tensordot(MSA,w,2)+b,-1)\n",
        "\n",
        "  # loss = categorical crossentropy (aka pseudo-likelihood)\n",
        "  loss = tf.reduce_sum(tf.keras.losses.categorical_crossentropy(MSA,MSA_pred),-1)\n",
        "  loss = tf.reduce_sum(loss * MSA_weights)\n",
        "\n",
        "  # add L2 regularization\n",
        "  reg_b = 0.01 * tf.reduce_sum(tf.square(b))\n",
        "  reg_w = 0.01 * tf.reduce_sum(tf.square(w)) * 0.5 * (L-1) * (A-1)\n",
        "  loss = loss + reg_b + reg_w\n",
        "\n",
        "  # setup optimizer\n",
        "  learning_rate = 0.1 * np.log(N)/L\n",
        "  opt = tf1.train.AdamOptimizer(learning_rate).minimize(loss)\n",
        "\n",
        "  # optimize!\n",
        "  with tf1.Session() as sess:\n",
        "    sess.run(tf1.global_variables_initializer())\n",
        "\n",
        "    # initialize bias\n",
        "    pc = 0.01 * np.log(N)\n",
        "    b_ini = np.log(np.sum(msa,0) + pc)\n",
        "    b_ini = b_ini - np.mean(b_ini,-1,keepdims=True)\n",
        "    sess.run(b.assign(b_ini))\n",
        "    \n",
        "    print(\"starting\",sess.run(loss))\n",
        "\n",
        "    for i in range(opt_iter):\n",
        "      sess.run(opt)\n",
        "      if (i+1) % int(opt_iter/10) == 0:\n",
        "        print((i+1),sess.run(loss))\n",
        "\n",
        "    # save the weights (aka V and W parameters of the MRF)\n",
        "    V = sess.run(b)\n",
        "    W = sess.run(w)\n",
        "  return(V,W) "
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "BEnCFJg1XBaf",
        "colab_type": "code",
        "outputId": "dbf32a0b-69fc-4645-b07f-3402bef6f744",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 238
        }
      },
      "source": [
        "%%time\n",
        "V,W = GREMLIN_simple(msa, msa_weights)"
      ],
      "execution_count": 14,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "starting 51558.387\n",
            "10 30474.594\n",
            "20 28137.197\n",
            "30 27369.766\n",
            "40 27132.457\n",
            "50 27029.05\n",
            "60 26978.797\n",
            "70 26952.555\n",
            "80 26937.062\n",
            "90 26926.297\n",
            "100 26917.89\n",
            "CPU times: user 1.24 s, sys: 243 ms, total: 1.48 s\n",
            "Wall time: 1.48 s\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "2VYRfajHSgv1",
        "colab_type": "text"
      },
      "source": [
        "## get contacts"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "mTw-NPuCSESQ",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "def get_mtx(W):\n",
        "  # l2norm of 20x20 matrices (note: we ignore gaps)\n",
        "  raw = np.sqrt(np.sum(np.square(W[:,:-1,:,:-1]),(1,3)))\n",
        "\n",
        "  # apc (average product correction)\n",
        "  ap = np.sum(raw,0,keepdims=True)*np.sum(raw,1,keepdims=True)/np.sum(raw)\n",
        "  apc = raw - ap\n",
        "  np.fill_diagonal(apc,0)\n",
        "  \n",
        "  return(raw,apc)"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "hjJrppRvS2pV",
        "colab_type": "code",
        "outputId": "75838872-453f-4139-8a42-72f8393379f4",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 318
        }
      },
      "source": [
        "raw, apc = get_mtx(W)\n",
        "\n",
        "plt.figure(figsize=(10,5))\n",
        "plt.subplot(1,2,1)\n",
        "plt.imshow(raw)\n",
        "plt.grid(False)\n",
        "plt.title(\"raw\")\n",
        "plt.subplot(1,2,2)\n",
        "plt.imshow(apc)\n",
        "plt.grid(False)\n",
        "plt.title(\"apc\")\n",
        "plt.show()"
      ],
      "execution_count": 12,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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3XRRFeZnynfpAfVFEfkJEfufc///jRR3leWKiG+u4zTiuZzZTrHPB7axxacbc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\nUIZhGIZhGE1iD1CGYRiGYRhN8v8BucPC5PFkVSQAAAAASUVORK5CYII=\n",
            "text/plain": [
              "<Figure size 720x360 with 2 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    }
  ]
}