Figure 1a.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/mnt/kauffman/nbserver/jupyter-run-software/anaconda3/lib/python3.6/importlib/_bootstrap.py:219: RuntimeWarning: numpy.dtype size changed, may indicate binary incompatibility. Expected 96, got 88\n",
      "  return f(*args, **kwds)\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "from scipy import stats\n",
    "from numpy import mean\n",
    "from numpy.random import beta, poisson\n",
    "from scipy.special import j_roots\n",
    "from scipy.special import beta as beta_fun\n",
    "from matplotlib import pyplot as plt\n",
    "import pandas as pd"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "test = pd.read_pickle('data/SS3_c57_UMIs_concat_vs_SS3_cast_UMIs_concat_TEST.pkl')\n",
    "c57 = pd.read_csv('data/SS3_c57_UMIs_concat.csv', index_col=0)\n",
    "cast = pd.read_csv('data/SS3_cast_UMIs_concat.csv', index_col=0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# moment-based inference\n",
    "def MomentInference(vals, export_moments=False):\n",
    "    # code from Anton Larsson's R implementation\n",
    "    from scipy import stats # needs imports inside function when run in ipyparallel\n",
    "    import numpy as np\n",
    "    m1 = float(np.mean(vals))\n",
    "    m2 = float(sum(vals*(vals - 1))/len(vals))\n",
    "    m3 = float(sum(vals*(vals - 1)*(vals - 2))/len(vals))\n",
    "    \n",
    "    # sanity check on input (e.g. need at least on expression level)\n",
    "    if sum(vals) == 0: return np.nan\n",
    "    if m1 == 0: return np.nan\n",
    "    if m2 == 0: return np.nan\n",
    "    \n",
    "    r1=m1\n",
    "    r2=m2/m1\n",
    "    r3=m3/m2\n",
    "    \n",
    "    if (r1*r2-2*r1*r3 + r2*r3) == 0: return np.nan\n",
    "    if ((r1*r2 - 2*r1*r3 + r2*r3)*(r1-2*r2+r3)) == 0: return np.nan\n",
    "    if (r1 - 2*r2 + r3) == 0: return np.nan\n",
    "        \n",
    "    lambda_est = (2*r1*(r3-r2))/(r1*r2-2*r1*r3 + r2*r3)\n",
    "    mu_est = (2*(r3-r2)*(r1-r3)*(r2-r1))/((r1*r2 - 2*r1*r3 + r2*r3)*(r1-2*r2+r3))\n",
    "    v_est = (2*r1*r3 - r1*r2 - r2*r3)/(r1 - 2*r2 + r3)\n",
    "    \n",
    "    if export_moments:\n",
    "        return np.array([lambda_est, mu_est, v_est, r1, r2, r3])\n",
    "    \n",
    "    return np.array([lambda_est, mu_est, v_est])\n",
    "def MaximumLikelihood(vals, export_asymp_ci = False, fix = 0, export_fun = False):\n",
    "    from scipy.interpolate import interp1d\n",
    "    from scipy.optimize import minimize\n",
    "    from scipy import special\n",
    "    from scipy.stats import poisson,norm\n",
    "    from scipy.special import j_roots\n",
    "    from scipy.special import beta as beta_fun    \n",
    "    import numpy as np\n",
    "    if len(vals) == 0:\n",
    "        return np.array([np.nan, np.nan, np.nan])\n",
    "    def dBP(at, alpha, bet, lam):\n",
    "        at.shape = (len(at), 1)\n",
    "        np.repeat(at, 50, axis = 1)\n",
    "        def fun(at, m):\n",
    "            if(max(m) < 1e6):\n",
    "                return(poisson.pmf(at,m))\n",
    "            else:\n",
    "                return(norm.pdf(at,loc=m,scale=sqrt(m)))\n",
    "        \n",
    "        x,w = j_roots(50,alpha = bet - 1, beta = alpha - 1)\n",
    "        gs = np.sum(w*fun(at, m = lam*(1+x)/2), axis=1)\n",
    "        prob = 1/beta_fun(alpha, bet)*2**(-alpha-bet+1)*gs\n",
    "        return(prob)\n",
    "    def LogLikelihood(x, vals):\n",
    "        kon = x[0]\n",
    "        koff = x[1]\n",
    "        ksyn = x[2]\n",
    "        return(-np.sum(np.log( dBP(vals,kon,koff,ksyn) + 1e-10) ) )\n",
    "    x0 = MomentInference(vals)\n",
    "    if np.isnan(x0).any():\n",
    "        x0 = np.array([10,10,10])\n",
    "    bnds = ((1e-3,1e3),(1e-3,1e3), (1, 1e10))\n",
    "    vals_ = np.copy(vals) # Otherwise the structure is violated.\n",
    "    try:\n",
    "        ll = minimize(LogLikelihood, x0, args = (vals_), method='L-BFGS-B', bounds = bnds)\n",
    "    except:\n",
    "        if export_fun:\n",
    "            return np.array([np.nan,np.nan,np.nan]), np.nan\n",
    "        return np.array([np.nan,np.nan,np.nan])\n",
    "    #se = ll.hess_inv.todense().diagonal()\n",
    "    if export_fun:\n",
    "        return ll.x, ll.fun\n",
    "    estim = ll.x\n",
    "    return estim"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "cells = 222"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def dBP(at, alpha, bet, lam):\n",
    "    at.shape = (len(at),1)\n",
    "    np.repeat(at, 50, axis = 1)\n",
    "    def fun(at, m):\n",
    "        if(max(m) < 1e6):\n",
    "            return(stats.poisson.pmf(at,m))\n",
    "        else:\n",
    "            return(stats.norm.pdf(at,loc=m,scale=sqrt(m)))\n",
    "    if alpha <= 0 or bet <= 0:\n",
    "        return np.nan\n",
    "    x,w = j_roots(50,alpha = bet-1, beta = alpha - 1)\n",
    "    gs = np.sum(w*fun(at, m = lam*(1+x)/2), axis=1)\n",
    "    prob = 1/beta_fun(alpha, bet)*2**(-alpha-bet+1)*gs\n",
    "    return(prob)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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EZCvOhal9PA7FFBDr0TbGGGOMMcYP7GJIY4wxxhhj/MASbWOMMcYYY/ygWI3Rjo6O1ri4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\n",
      "text/plain": [
       "<Figure size 864x216 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "gene = 'Mbnl2'\n",
    "mat = c57.loc[gene][pd.notnull(c57.loc[gene])]\n",
    "pat = cast.loc[gene][pd.notnull(cast.loc[gene])]\n",
    "fig = plt.figure(figsize=(12,3))\n",
    "plt.subplot(121)\n",
    "tot_kon,tot_koff, tot_ksyn = test.loc[gene][0]\n",
    "plt.hist(mat, bins=40, label='c57', color='orange')\n",
    "plt.plot(cells*dBP(np.arange(35), tot_kon, tot_koff, tot_ksyn),'g--',linewidth=2)\n",
    "plt.xlabel(\"Maternal Expression\")\n",
    "plt.ylabel(\"Cells\")\n",
    "plt.title(\"kon=%.2f, koff=%.2f, ksyn=%.2f\" % (tot_kon, tot_koff, tot_ksyn))\n",
    "plt.legend(loc='best')\n",
    "plt.subplot(122)\n",
    "tot_kon,tot_koff, tot_ksyn = test.loc[gene][1]\n",
    "plt.hist(pat, bins=32, label='Cast', color='blue')\n",
    "plt.plot(cells*dBP(np.arange(35), tot_kon, tot_koff, tot_ksyn), 'g--',linewidth=2)\n",
    "plt.xlabel(\"Paternal Expression\")\n",
    "plt.ylabel(\"Cells\")\n",
    "plt.legend(loc='best')\n",
    "plt.title(\"kon=%.2f, koff=%.2f, ksyn=%.2f\" % (tot_kon, tot_koff, tot_ksyn))\n",
    "plt.savefig(\"figures/Fig1a_{}_allelic.pdf\".format(gene))\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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AJ8A30xiDiIi0UmlLUO4+EbDtbD42Xa8rIiK5QT1JiIhIVlKCEhGRrKQEJSIiWUkJSkRE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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "tot_kon, tot_koff, tot_ksyn = MaximumLikelihood(mat+pat)\n",
    "plt.hist(mat+pat, bins=40, label='total', color='black')\n",
    "plt.plot(cells*dBP(np.arange(60), tot_kon, tot_koff, tot_ksyn),'g--',linewidth=2)\n",
    "plt.xlabel(\"Total Expression\")\n",
    "plt.ylabel(\"Cells\")\n",
    "plt.title(\"kon=%.2f, koff=%.2f, ksyn=%.2f\" % (tot_kon, tot_koff, tot_ksyn))\n",
    "plt.legend(loc='best')\n",
    "plt.tight_layout()\n",
    "plt.savefig('figures/Fig1a_{}_total.pdf'.format(gene))\n",
    "plt.show()"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}