{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "<h1 id=\"Import-libraries-and-define-functions\">Import libraries and define functions<a class=\"anchor-link\" href=\"#Import-libraries-and-define-functions\">¶</a></h1>\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "\n",
    "import numpy as np #numeric library\n",
    "import matplotlib.pyplot as plt  # plotting library\n",
    "from scipy.integrate import odeint  # Integrator function\n",
    "%matplotlib inline\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "\n",
    "# Prepare a plotting function\n",
    "def plot_timeseries(s, u, alpha, beta, gamma):\n",
    "    plt.figure(None, (9,12))\n",
    "    plt.subplot(611)\n",
    "    plt.ylabel(\"alpha\")\n",
    "    try:\n",
    "        plt.plot(t, [alpha(i) for i in t], label=\"alpha\", c=\"C3\", lw=2)\n",
    "    except:\n",
    "        plt.plot(t, np.full(t.shape, alpha), label=\"alpha\", c=\"C3\", lw=2)\n",
    "    plt.xlim(t.min(), t.max())\n",
    "    plt.subplot(612)\n",
    "    plt.ylabel(\"beta\")\n",
    "    try:\n",
    "        plt.plot(t, [beta(i) for i in t], label=\"alpha\", c=\"C2\", lw=2)\n",
    "    except:\n",
    "        plt.plot(t, np.full(t.shape, beta), label=\"alpha\", c=\"C2\", lw=2)\n",
    "    plt.xlim(t.min(), t.max())\n",
    "    plt.subplot(613)\n",
    "    plt.ylabel(\"gamma\")\n",
    "    try:\n",
    "        plt.plot(t, [gamma(i) for i in t], label=\"gamma\", c=\"C4\", lw=2)\n",
    "    except:\n",
    "        plt.plot(t, np.full(t.shape, gamma), label=\"gamma\", c=\"C4\", lw=2)\n",
    "    plt.xlim(t.min(), t.max())\n",
    "    plt.subplot(614)\n",
    "    plt.ylabel(\"unspliced\")\n",
    "    plt.plot(t, u, label=\"unspliced\", c=\"#2895ae\", lw=2)\n",
    "    plt.xlim(t.min(), t.max())\n",
    "    plt.subplot(615)\n",
    "    plt.ylabel(\"spliced\")\n",
    "    plt.xlabel(\"t\")\n",
    "    plt.plot(t, s, label=\"spliced\", c=\"#eea423\", lw=2)\n",
    "    plt.xlim(t.min(), t.max())\n",
    "    ax1 = plt.subplot(616)\n",
    "    plt.ylabel(\"spliced\")\n",
    "    ax1.plot(t, s, label=\"spliced\", c=\"#eea423\", lw=2)\n",
    "    ax2 = ax1.twinx()\n",
    "    ax2.plot(t, u, label=\"unspliced\", c=\"#2895ae\", lw=2)\n",
    "    plt.ylabel(\"unspliced\")\n",
    "    plt.xlim(t.min(), t.max())\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "<h1 id=\"The-model\">The model<a class=\"anchor-link\" href=\"#The-model\">¶</a></h1>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "<p>RNA metabolism can be modelled as consisting on 3 reactions:</p>\n",
    "<p>* -&gt; pre-mRNA (transcription)</p>\n",
    "<p>pre-mRNA -&gt; mRNA (splicing)</p>\n",
    "<p>mRNA -&gt; * (degradation)</p>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "<p>The reactions can be modelled using the law of mass action. The system of differential equations are.</p>\n",
    "\\begin{align}\n",
    "\\dot{u} = \\alpha - \\beta u \\\\\n",
    "\\dot{s} = \\beta u - \\gamma s \\\\\n",
    "\\end{align}<p>Where we indicate with:</p>\n",
    "<ul>\n",
    "<li><em>u</em> - the abundance of unspliced (pre-mRNA) molecules</li>\n",
    "<li><em>s</em> - the abundance of spliced (mRNA) molecules.</li>\n",
    "<li><em>alpha</em> - the transcription rate.</li>\n",
    "<li><em>beta</em> - the splicing rate</li>\n",
    "<li><em>gamma</em> - the degratation rate of the mRNA</li>\n",
    "</ul>\n",
    "<p>Let's now write the differential equations as the following python function.</p>\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "\n",
    "def diff_equation(y, t, parameters):\n",
    "    # Let's unpack the variables and parameters vectors (that's how odeint wants the intputs)\n",
    "    u, s = y\n",
    "    alpha, beta, gamma = parameters\n",
    "    # The actual differential equation\n",
    "    du = alpha - beta * u\n",
    "    ds = beta * u - gamma * s\n",
    "    # Pack the differential as a single vector and output (that's how odeint wants the output)\n",
    "    dy = du, ds\n",
    "    return dy\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "<p>We can solve the differential equation numerically using a solver/integrator. Let's first set the simulation time and all parameters and initial condition.</p>\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [],
   "source": [
    "\n",
    "# Prepare all the input required by the solver\n",
    "t = np.linspace(0, 120, 1000) # a time of 2 hours, divided in 1000 intervals\n",
    "\n",
    "# fix the parameters\n",
    "alpha = 4\n",
    "beta = 0.4\n",
    "gamma = 0.3\n",
    "parameters = alpha, beta, gamma\n",
    "\n",
    "# fix intial conditions\n",
    "u0 = 0\n",
    "s0 = 0\n",
    "y0 = u0, s0\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "<p>The line above will perform the simulation and return the solution of the integration <em>u</em> and <em>s</em></p>\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [],
   "source": [
    "\n",
    "solution = odeint(diff_equation, y0, t, args=(parameters, ))\n",
    "u, s = solution.T\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "<p>We can plot the results of the simulation, simply by:</p>\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 648x864 with 7 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "\n",
    "plot_timeseries(s, u, alpha, beta, gamma)\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p><strong>Exercice 1</strong></p>\n",
    "\n",
    "<p>Try to answer the following questions by:\n",
    "    1. first looking at the system of differential equations \n",
    "    2. Verifing the results running simulations using the ode integrator:</p>\n",
    "<ul>\n",
    "Which parameter or set of parameters influences:<br>\n",
    "a) the steady state of the unspliced RNA  <br>\n",
    "b) the steady state of the spliced RNA (assume that unspliced RNA is at steady state)<br>\n",
    "c) the delay between unspliced and spliced (i.e. the difference between the time constants)<br>\n",
    "\n",
    "</ul>\n",
    "</li>\n",
    "</ul>\n",
    "\n",
    "\n",
    "\n",
    "<p><strong>Exercice 2</strong></p>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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sRJTGFJAIKav2yQ9VvQm3qIEJULIBpkyAFXOhflfT5/aXa6YfeDp1ge9Nh17WbM0UKQVSNvI3xWrLapj/hJvjb2m0L+otmRuDRCcYfCJccLMlflP8bORvis6ahfD7K2HzCq8lQysXdAUor4Az/9VtxpQCFaHB2juYYrJ3B/zmc7BnW9uvTVS4irePXw6nX5P/2IwJDQG1aR9TDNYshNfvhxXzsvfiaa6qD1z9F+je19XuG1NK3Jy/TfuYiHv1PnjyB26KR1Mtvy6WcKWbsThc9nvoXVOwEI0JF6v2MVG3Zzs88QNobKNfalklnHwJHFkLH/0UlHcuTHzGhJFV+5hISqXgpTvhhdthxybvRq1WlFXAoGNh/I+tt74xaTbyN5HzzE/glbugYbd3l67XWrm5Tl2gqi+cOBFOu9ISvzFpKkJD3Kp9TETs3gob34eXp/ib5rn8IRhyUmFiMyZqbORvQi/ZCI9fB7MfBok3TfwCkF5VK+ZG+8kGOOvblviNaYlaqaeJgmk/gzmPtryyVvoDYOBoOPWbMPRjrpTTGNMSq/YxIbZjA6xZ5KZ52mrGVl4JF/4Mqo8vTGzGRJpYtY8JoVQK/nw9vPkAxMsPbsjWXJ9hMP6/LPEb45cCqRxWQIjIt4HLvUO/DXwV6A88DPTCdTj+kqrW5+ykPljyj5jXfgezHnbTPK0tol5dC1c9XRJtyY3JKRWhMZGbah8RGQBcA4xU1T0i8igwATgXuFVVHxaRO4HLgDtyclKfLDVERMMeWDXP1e837G75dRJz1Tzjf2qJ35iOSor42nxKAJUikgA6A2uB04HHvOenAhfk/IfwEZQJudemwlM/dIl9347srxGBnke6G7bO/A70G1HYGI0pFu28w7e3iGSuRDjFW3/cHUt1tYj8HLeC4R5gGjAb2Kqqjd7LVgEDDjnwdrLkH3JLXoK/fL/ti7o9BsL1b9rNWsYcOkH9/0eqU9XaFo8k0hMYDwwGtgJ/AD6d5aVtrJade5b8Q0wVXvxN64k/FncXfi+61RK/MTkhOb3J60xgmapuBBCRPwHjgB4ikvBG/wOBNbk6oV+W/ENo4/vw+Hdh6cuQauHfYLzMVfIMHOPq9/sdXdgYjSlWCjTmrr3DCuBkEemMm/Y5A5gFPA9chKv4mQQ8kasT+mXJP2R21sHtZ8G+7W7kr0LWy/LxMrj6aSjvUvAQjSluIjkr9VTVN0TkMVw5ZyMwF5gC/BV4WER+4u27OycnbAdL/iEzc6or4Uwvni56cHO2ss5wzo2W+I3JBwWSOSyVU9WbgJua7V4KnJizk3SAJf8QUIUlL8DcP8AHL2XvzxMrh659oc9QOO0qGH56UNEaU/xyeZNXWFnyD4E//z+Y8xDUt1C/L0AiDpc+AEccU9DQjCk5ub7DN6ws+Qds9Vsw+8HWK3oSnWDQWEv8xhSEiHX1NPlVvwveftKtr3sQcaWbZZUwdgJ85kcFD8+YkqRAoyV/kw+7NsEfroL3noNU8sDF3UxlFXDuzTDuioKHZ0zJs2kfk3OqMGU8bHgPUg2tvRCOKXi3D2OMipASG/mbHFsxCzYvz5744+WQKHdtmydMsUVXjAmKjfxNzqSSrpxz4V9psYvHgNFw2jUw9JPQqWtBwzPGeFydf4knfxHp1drzqro5t+EUp03L4bfnwd5t7kMgW2VPWSWMvhBGfbbg4RljMomQjOWsvUNotTXyn437IBSgGtjifd8D17NicF6jKxK//xJsXwuayv58LAEV3aD2XwoblzHmYAqkKPGRv6oOBvBWmnlSVZ/2Hn8a163OtGHzCqhbkj3xx8ugUxWM/DSc/X2o7F74+IwxB7M5/wNOUNWvpx+o6jMi8uM8xVQUko3wzjOw9KXspZwAhw2G77xR2LiMMW2xap9MdSLyfeB+3G9FlwCbOnpSEekB3AWM8o53qaq+1tHjhc3OOrjjTNi5wbVsyNaWOdHJzfEbY8LF2js0NRHXle5x3J/Ni96+jroN+JuqXiQi5bh1LYvGU9+DrSsg5S3SJoDG09+4bpw9Bro+/MaYkBHasz5vZPlK/l5Vz7Ui0lVVdx7KCUWkG3Aq8BXv2PVAtgYHkbXwLwcSP3idOZNAHI79givlHH2Bu4vXGBMuitAoxV/t42tiS0TGicgiYJH3eIyI/KaD5xwCbAR+JyJzReQuETmoM72IXCEis0Rk1saNGzt4qsKqWwJvTnU3aTUnQDwGX7wTjp9gid+YMFMRX1uU+b2qcStwNt48v6rOx43eOyIBjAXuUNXjgF3A9c1fpKpTVLVWVWsPP/zwDp6qMFTh8WvhtnHwl+uALMk/loAR59g6u8aEXXrO388WZb4vaavqyma7kh085ypglaqm61wew30YRNaCP8O8R90iLA273Y1cwP7Vt8q7Qrd+cP7/BBaiMaYdUoivLcr8XvBdKSLjAPUu0F4DLO7ICVV1nYisFJHhqvoubkHjRR05Vli8frdrz9xcohzGXgwfORVGnuceG2PCTa3Us4mv4yp0BuBG7tOAqw7hvN8CHvA+SJYCXz2EYwVq1ybYtyP7c/FyOP5foDrQlTqNMe0V9VG9H36rfeqAi3N1UlWdB9Tm6nhB2LwcHrkcVs/zKnu8Ms5MsTgMOC6A4IwxHaYCDSUw8vdb7TPVuzEr/biniNyTv7DCrbEe7vwUrJwFyXqvdUNG4o+Xu0ZtX5jiWjgYY6LDTfsU/wVfv9M+o1V1a/qBqm4RkZId077zDNTvPLhfT7wcBh7v5vhrL4GeRwYTnzHm0GgEpn1EZBhwB9BXVUeJyGjgfFX9iZ/3+/3dJiYiPTNO2osSXgtgy8rs6+4m66H6BDjrRkv8xkRZSmK+toD9H3AD0ACgqm8BE/y+2W8C/x/gVRF5zHv8eeCn7QiyKGxfCzPvhWWvZn++vItL/saY6IpQS+fOqjpTmk4/Nbb04ub8XvC9T0RmAafjLm1eqKqRLs9sr5Wz4a7PQrIBkvug+Yd+vBx6VsOIc4OJzxiTK0Kj/1ugglQnIh/Bu+IoIhcBa/2+ua2VvLqp6nZvmmcd8GDGc71KaSWvx77h5vnTNAUIlHeGiu4w5iI4/Xt2gdeYqFMi09jtKmAKcLSIrAaW4Tou+9LWyP9B4DwOrOiVli5sHNKuUCNq1ybYtDTLE+p69NzwTsFDMsbkUS6nfbK1sAfeBR4BaoDlwBdUdUt7jquqS4Ezvd5oMVVt4Y6j7Npayes872tJL9eYKKfFRdcTlQUNxRiTZ4qQyu20T7YW9v8OTFfVySJyPa6/2XXtOaj3ofJl3AdIIj33r6rX+Hl/W9M+rfbcUdU5vqKMqK2rYNoP4f1priGbxJqWdyYq4aRLg4vPGJMfuSr1bKmFvYiMBz7hvWwqMIN2Jn/gaeB14G2ytpNsXVvTPq21IlPcBeCitHsT/OYU2L0ZNOkN/BOuO2eik/sQOOqTcOq1QUdqjMm1dkz79PaKYdKmqOqUjMeZLezH4KbQr8XV5q8FUNW1ItKnA2FWqOq/deB9QNvTPp/s6IGjbubdrmePeh06BdBG17LhzBth2BnQd0SgIRpj8kChPdU+daraWquadAv7b6nqGyJyG1la2HfQ70Xka8BTwL70Tr+FOL5KPUWkAvgm8DHcn81LwJ2qurfd4UbE8lddi+ZMApSVw2HVlviNKVaKkMzdBd9sLeyvB9aLSH9v1N8f2NCBY9cDtwA3cuCqpO9CHL8fb/cBHwV+BdwOjAR+364wI6bP0RDLUraZSkLPmoKHY4wpIEV8bW0eR3UdriX+cG9XuoX9k8Akb98k4IkOhPlvwFGqWqOqg73NdwWm3zt8h6vqmIzHz4vI/HaFGQGqMPMueOEW2LnhwJRPWrwc+n0U+o8OJj5jTGHk+A7fbC3sY8CjInIZsALXNaG9FgK7OxqU3+Q/V0ROVtXXAUTkJOCVjp40rJ77L3jpF241rv3EzfNLDIafAxfeEVh4xpgCUCCpuUv+rbSwP+MQD50E5onI8zSd8z/0Us8MJwFfFpEV3uNqYLGIvO3OpZEfCzfsyZL4PUNOg4sfcXfzGmOKX0R6+/zZ2zrEb/I/p6MniIrta1pYXF1hwzuW+I0pFe6CbzzoMNqkqlMP5f1+k38Cd8V6n4h8AhgN3JfZ4z/qqvplLLzeTO+hhY3FGBOsVA6nfXJNRB5V1S+kZ16aPa3Nrs+2yG+1zx+BpIgcBdwNDCajyVuUJRvgjbvgns9AZQ93UTdTWSWccWMwsRljCk+BpFfu2dYWkPStpYuBz2Zs5+N6Bvnid+SfUtVGEbkQ+KWq/kpE5rYn2jBKpeDe8bBy5oG5/ph3F6+m3IIsn/k51JwSbJzGmEISNMQj//Sdwbgyzw8znxORo/0ex2/ybxCRibgmQp/19kW+efHS52HVrKYXeVONrmfPZX+F6pODi80YE4ywL+YiIt/A3XQ7RETeyniqinZUYfpN/l8Fvg78VFWXichg4H6/JwmrD15o2qM/TZOwYqYlf2NKkSo0aKgXc3kQeAb4L5q2itjRnjVW/K7ktQi4JuPxMmCy35OEVVVfSFQc3MYhXg5degcTkzEmeCGf9tkGbAMmHspx/Pb2OQW4GTjSe4+4GPzfShw2O9dD58Mg2293sTh8dHzBQzLGhIKEetonV/xO+9wNfBvXjrSFgshoUIW//wBe+zXEOwEKEncrcoFbkvGSR91i7MaY0qOEu9QzV/wm/22q+kxeIymQBY/D67+Fxn1uAyAGPY6Ez98N/Y6BWKin+4wx+ZbL9g5h5Tf5Py8itwB/omkPicit5PXq7dCwq9nOFGxeCp17WeI3xuRuJa8wa09vH4Djva/pBdwjt5LXnhaWSI4lYO82YFBBwzHGhIyq0JAq/lFgW2v4ppcIe8r7qrglyV72Kn4iZ8RnYfNySO5ruj9eBof7vj3CGFOs3Jx/0FHkX1sfb1Xe1tXbqnCtSZ8RkQl5ji2n6nfBm3fB9hVQXulKPMG72FsJF/wa4n5/DzLGFDVV8bVFWVtr+P4o234R6QX8A3g4H0Hl2o51cOc4N+XTsBviFa6D56CT3Ipd477pLvQaY4xV+7RCVTeLZG2AHErT/t3V9aca3ePkXkBAGmxxFmPMwazOvwUicjrQwqVT38eIA7OA1ap63qEcqy3vPHUg8e+nsGYu1O+2Xv3GmANyvZJXWLV1wTdbv+hewBpck7dDcS2uJWm3QzxOm7ItxL7/ufCv2WCMKSQVkskSr/YBmo/IFdikqs0r5dtFRAYCnwF+iluBPq/GToLXf920h08sAUPPhkSnfJ/dGBMlNvIHmveKzqFfAt/DVQ9lJSJXAFcAVFdXd+gk9bvh7UfcfH9Vf9i5DjfXH4NuA+CCOzt0WGNMMVO74JsXInIesEFVZ3tLQmalqlOAKQC1tbXtrrrducFV+Oze7O7ojVe4KZ6PfRtqPgY1p9ndvMaY7KJexulHEOnvFOB8EVmOKxU9XURyvjbAsz90JZ7pVg7Jve77d/4KQz5pid8Yk50ipNTfFmUFT4GqeoOqDlTVGmAC8JyqXpLr8yx+AlINB+9fvwD2bs/12YwxxUIVGpLia4uyor2ntflC7GmCu9hrjDEtsWmfPFPVGfmq8T/+q24t3kyxBAw53er6jTGtK4Vpn6IcA+/ZCgNroe9I2LDY7ZOYq/j53JRgYzPGhJsCyVS0E7sfRZf8X74Vpt/spn006Xr0n3glDKiFwZ+wC73GmDbkYVTfvKOBiAzGFbz0AuYAX1LV+pyetA1FlQqXzoDn/sPdzLVvu+vkuX0NzP29VfgYY/xRQFP+tnZIdzRI+xlwq6oOxbXKuSxnP4BPRZUOX/+169qZSVOwbTWseyuYmIwxEaPQmIz52vzI6Ghwl/dYcAthPea9ZCpwQR5+klYV1bTP7k3Z98fiLa/gZYwxmdrZ3qG3iMzKeDzFu0E1U/OOBocBW1U13W5yFTCgg+F2WFEl/xHjYfUcaNzTdH+qAQaeEExMxpjoUf8XfOtUtbalJ1voaJDt4AVfO6yopn1qL4Me1W5lLnALtpR1hnNugfIuwcZmjImG9DKOfjYfDupogPtNoIeIpAffA3GdkguqaEb+y16Amf/nGrb1P9Y1cevaD07+JlSfHHR0xpjIUMlZqaeq3gCtc8DXAAAOiklEQVTcAOCN/L+rqheLyB+Ai3AfCJOAJ3JywnYoiuT/ws/ghckHLvaWdYF+o+DCuyDRwp2+xhiTjUIh+vlfBzwsIj8B5gJ35/uEzUU++e/cAM//FJL7Duxr2AXrFsDCP8KYicHFZoyJIIVU+8o4/R1WdQYww/t+KXBi7s/iX+Tn/Je/nL2PT8Mu19zNGGPaQ4FUSnxtURb5kX9l9+z7JQ6dexc2FmNMEVBr7xAJNae5Rm31O5ruT5RD7eXBxGSMiS4l+qN6PyI/7RNPwKSnXdO28iro1M2Vep77Czji2KCjM8ZEUR7aO4ROpEf+u+rgtdvg/Weg/yg46mzoPQyqx0GnFlcHNsaYlrnFXCI/Lm5TZJP/rjq4Y6xr6ZCu9PnwRThrMgw9O9jYjDHRlo9qn7CJ7Mfba7c1Tfzg6vyfvQHqd7f8PmOMaZW69g5+tiiLbPJ//5mmiT8tFof11sHTGNNBVuoZcl37Zd+fbIAufQobizGmiCgkbdonvE75tmvalilWBv3GQK8hwcRkjIm+dKlnsY/8I5v8h5zhLu6WdXHlnYlKOOJ4mPinoCMzxkSZKjQ2iK8tyiI57ZNKwvtPw75tcN7t0KMGuh0BvT4SdGTGmGIQ9VG9H5FL/nu2wN2nwraVrrqnrAtUdIPLXwk6MmNMUchTY7ewidy0z7M3wOYPoH6nu8OufgfsWAdPXhl0ZMaYYiEp8bVFWeRG/gv+AMn6pvs0CUunQ2O99e83xhwihXjSX2JvbPsloRW55N/iSpcFXwHTGFOMRIVEY/En/8hN+3z0IlfSmUniMPh0G/UbY3JDkv62KItc8j9rMvQcDOVd3ePyru6mrvN/G2xcxpjiIArxlPjaoixy0z6de8FV8+G9v8K6t+Cwo2DEhVBWEXRkxphiESuBap9IJf/1C+C5m2DVTOg+CD5xIwz7TNBRGWOKiSjEfF7wjbLIJP/1C+CuU1xtvyrsXAuPToRP/xKOvzTo6IwxxSTqZZx+RGbOf/r3XatmzajqadgN066DZJQvuRtjQkVUKGvwt0VZwZO/iAwSkedFZLGILBSRa/28b9VMspZzJvfBznU5DtIYU7oUYkl/W5QFMe3TCHxHVeeISBUwW0SeVdVFrb2p20DYteHg/ZqCyl75CdQYU3oEm/bJC1Vdq6pzvO93AIuBAW2977QbD27hXFYJY74E5Z2zv8cYY9pNIZ70t0VZoHP+IlIDHAe8keW5K0RklojM2rhxIyPGw9m3QEV39yGQqIDRF8O5txU6amNMMRNcqaefLcoCq/YRka7AH4F/VdXtzZ9X1SnAFIDa2loFOOFKGHspbF8NnXtDp64FDdkYUwpKpNQzkJG/iJThEv8Dqtrm8iuaguduhluPgl+NhPn3u7V6jTEm10Qh0SC+tjaP1UKBi4j0EpFnReR972vPvP9gzQRR7SPA3cBiVf2Fn/fUvQuv/By2Locty+ClyXDf2U3LPo0xJldyWO2TLnAZAZwMXCUiI4HrgemqOhSY7j0uqCBG/qcAXwJOF5F53nZua29o3AeNezMe73WtHZY9n99AjTGlRxRiKfG1taWVApfxwFTvZVOBC/L047So4HP+qvoy7pqK//ckgWbTPA17YPWbMOT03MVmjDGQn46dzQpc+qrqWnAfECLSJ/dnbF0k2jtIlt9Pyipdfx9jjMkpFd+LuQC9RWRWxuMpXrFKE80LXNzsd7Cikfzl4MeJChjxuWDiMcYUL3fB1/fL61S1ttXjZS9wWS8i/b1Rf38gyy2s+RWJ3j6HDYc+oyDeyW19R8OlM9zo3xhjckpBkuJra0srBS5PApO87ycBT+T852hDJEb+ZZVw1SzYsRYQqOoXdETGmGIl5PTu3XSBy9siMs/b9+/AZOBREbkMWAF8Pmdn9CkSyb9+J7x2K3QbAMPHBx2NMaaoae6atrVR4HJGbs7SMZFI/pveh+nXuymfxLfg0pfhsKFBR2WMKUaC3eEbGpqCZD3U74DdG+GxLwYdkTGmaClIyt8WZZEY+TehsHGRm/+v6h90MMaYYiMKZfXFP/KPXvLHlXqmbPUuY0w+5HDOP8wimfx71NgNXsaY/HBz/kFHkX+RSP6xGJCCRGeIJ+DCB4OOyBhTtEqkpXMkkn+PwTDun6HHkTBqIlQWvPmpMaZU2Mg/RCp6wFk/CzoKY0xJKJE5/0iUem75AJ79f7D5g6AjMcYUO1EhUe9vi7JIJP89W+H12+DO0bDsuaCjMcYUNc3pYi6hFYnkD5BqgIbd8PiXbQUvY0z+iCX/cNq7BbYuCzoKY0wxK4XkH4kLvplSSSjrEnQUxphiJVbqGT4ShwEnQNe+QUdijClaCon6oIPIv0gk/1gMyjtD1QC46JGgozHGFDMpkVLPSCT/7jVw8X0waNzBSzoaY0yuWfIPicqeUH1K0FEYY0qBzfmHyJ7NsLsOOvcOOhJjTCkohZF/JEo9t30Itw6CufcEHYkxpuhZnX94pFLQuBeevhq2LA06GmNMMROv2sfPFmWRSP5pqUZY8HDQURhjilmp3OEbiTn/tFTStXgwxpi8UYiVwEqBkUr+ZRUwfHzQURhjip1V+4RIWRcY/SV3h68xxuSL3eQVIl0Oh4sfg+qPBx2JMaYUWPIPie7VcOSpQUdhjCkFkop+JY8fkUj+xhhTSKUw8o9EqeeWpbD8haCjMMaUglIp9Qwk+YvIOSLyrogsEZHr23r9ni3w4Lnwyi2FiM4YU9K8Uk8/mx/tzXeFUvDkLyJx4NfAp4GRwEQRGdnW+xp2w4wfuj4/xhiTL0LuRv4dzXeFEMTI/0RgiaouVdV64GHAV/V+vBxWvJzX2IwxpS637R06nO/yLYgLvgOAlRmPVwEnNX+RiFwBXOE93HczsoDtcEMo/tj26w3UBR1EFmGNC8Ibm8XVPmGO68hDOcBaZv/9ZsRvD+EKEZmV8XiKqk7JeOwr3wUhiOSf7dY5PWiH+wOcAiAis1S1Nt+BtZfF1X5hjc3iap+Qx1VzKMdQ1XNyFA74zHdBCGLaZxUwKOPxQGBNAHEYY0y+hTbfBZH83wSGishgESkHJgBPBhCHMcbkW2jzXcGnfVS1UUSuBv4OxIF7VHVhG2+b0sbzQbG42i+ssVlc7WNx+dDBfFcQohqK6SdjjDEFFIk7fI0xxuSWJX9jjClBoU7+Yb0tWkQGicjzIrJYRBaKyLVBx5RJROIiMldEngo6ljQR6SEij4nIO96f2z8FHROAiHzb+ztcICIPiUhFgLHcIyIbRGRBxr5eIvKsiLzvfe0Zkrhu8f4u3xKRx0WkRxjiynjuuyKiIr7r9UtOaJN/mG+LBhqB76jqCOBk4KoQxQZwLbA46CCauQ34m6oeDYwhBPGJyADgGqBWVUfhLshNCDCke4HmNebXA9NVdSgw3XtcaPdycFzPAqNUdTTwHnBDoYMie1yIyCDgLGBFoQOKktAmf0J8W7SqrlXVOd73O3CJbECwUTkiMhD4DHBX0LGkiUg34FTgbgBVrVfVrcFGtV8CqBSRBNCZAGuwVfVFoHn3qvHAVO/7qcAFBQ2K7HGp6jRVTbc2ex1Xvx54XJ5bge8RkpupwirMyT/bbdGhSLCZRKQGOA54I9hI9vsl7h9+KuhAMgwBNgK/86aj7hKRLkEHpaqrgZ/jRohrgW2qOi3YqA7SV1XXght0AH0CjiebS4Fngg4CQETOB1ar6vygYwm7MCf/0N4WnSYiXYE/Av+qqttDEM95wAZVnR10LM0kgLHAHap6HLCLYKYvmvDmz8cDg4EjgC4ickmwUUWLiNyImwZ9IASxdAZuBH4YdCxREObkH9rbogFEpAyX+B9Q1T8FHY/nFOB8EVmOmyY7XUTuDzYkwP1drlLV9G9Hj+E+DIJ2JrBMVTeqagPwJ2BcwDE1t15E+gN4XzcEHM9+IjIJOA+4WMNxw9BHcB/k873/AwOBOSLSL9CoQirMyT+0t0WLiODmrxer6i+CjidNVW9Q1YFeY6sJwHOqGvhIVlXXAStFZLi36wxgUYAhpa0AThaRzt7f6RmE4EJ0M08Ck7zvJwFPBBjLfiJyDnAdcL6q7g46HgBVfVtV+6hqjfd/YBUw1vv3Z5oJbfL3Lialb4teDDwaltuicSPsL+FG1vO87dyggwq5bwEPiMhbwLHAfwYcD95vIo8Bc4C3cf8fAmsPICIPAa8Bw0VklYhcBkwGzhKR93EVLJNDEtftQBXwrPfv/86QxGV8svYOxhhTgkI78jfGGJM/lvyNMaYEWfI3xpgSZMnfGGNKkCV/Y4wpQZb8TSBE5Eavm+ZbXqngSa289mYR+a73/X+IyJk5OP+9InLRoR7HmKgq+DKOxnjtnM/D3YCzz2u7W+7nvapqt+4bkwM28jdB6A/Uqeo+AFWtU9U1IrJcRH4mIjO97ajmb8wcsYvICSLyqojM915f5a1lcIuIvOn9VnGl91oRkdtFZJGI/JVwNkgzpmAs+ZsgTAMGich7IvIbETkt47ntqnoi7g7SX7Z0AK/lxyPAtao6BtenZw9wGa475wnACcDXRGQw8DlgOHAM8DXC18PHmIKy5G8KTlV3AscDV+BaPT8iIl/xnn4o42trq30NB9aq6pveMbd7LUE+BXxZRObh2mwfBgzFrSfwkKomVXUN8FxufypjosXm/E0gVDUJzABmiMjbHGheltlvpLXeI9LC8wJ8S1X/3mSn671kvUyM8djI3xSciAwXkaEZu44FPvS+/2LG19daOcw7wBEicoJ3zCpvNa6/A9/wWm4jIsO8hWNeBCZ41wT6A5/M3U9kTPTYyN8EoSvwK2/R70ZgCW4K6Dygk4i8gRuYTGzpAKpaLyJf9I5TiZvvPxO3fGUNro+74KaVLgAeB07Hde98D3ghPz+aMdFgXT1NaHgLcNSqal3QsRhT7GzaxxhjSpCN/I0xpgTZyN8YY0qQJX9jjClBlvyNMaYEWfI3xpgSZMnfGGNK0P8H5ZXBQEERL0UAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "\n",
    "ax = plt.scatter(s,u, c=t, cmap=plt.cm.rainbow)\n",
    "plt.xlim(0,)\n",
    "plt.ylim(0,)\n",
    "plt.xlabel(\"Spliced\")\n",
    "plt.ylabel(\"Unspliced\")\n",
    "ax2 = plt.colorbar(ax); ax2.set_label(\"time\")\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "<p> 1. Notice also that at the last time points, where steady state is aproached and finally reached, the ratio unspliced/spliced has a particular value. This  can be expressed as a particularly simple fucntion of the parameters. What is it?</p>\n",
    "\n",
    "<p>2. Can this be generalized also in situations when we start from different initial conditions? Try to solve the system above from different initial conditions, to verify your prediction.</p>\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "<p>Furthermore you could have more complex situation where alpha varies as a function of time:</p>\n",
    "<p>We are going to write an example when, at the begginning, the gene is off, then it gets turned on, and then after a while again off.\n",
    "So we can observe a full cycle of upregulation and downregulation.</p>\n",
    "<p>Feel free to play with the function alpha, beta and gamma, analytic and step functions should both work well with the integrator!</p>\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "\n",
    "# The change from the code above is just to allow the transcription rate and the other parameters\n",
    "\n",
    "def alpha(t):\n",
    "    # This is a step\n",
    "    if t < 10:\n",
    "        return 0\n",
    "    elif t>=10 and t<=60:\n",
    "        return 4\n",
    "    else:\n",
    "        return 0\n",
    "    \n",
    "def beta(t):\n",
    "    # A constant\n",
    "    return 0.4\n",
    "\n",
    "def gamma(t):\n",
    "    # A constant\n",
    "    return 0.15\n",
    "    # you couuld try with a periodic function like:\n",
    "    # return 0.15 * ( np.sin(t/15.) + 1.2 ) \n",
    "\n",
    "parameters = alpha, beta, gamma\n",
    "\n",
    "u0 = 0\n",
    "s0 = 0\n",
    "y0 = u0, s0\n",
    "\n",
    "def diff_equation(y, t, parameters):\n",
    "    # Let's unpack the variables and parameters vectors\n",
    "    u, s = y\n",
    "    alpha, beta, gamma = parameters\n",
    "    # The actual differential equation\n",
    "    du = alpha(t) - beta(t) * u\n",
    "    ds = beta(t) * u - gamma(t) * s\n",
    "    # Pack the differential as a single vector and output\n",
    "    dy = du, ds\n",
    "    return dy\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "\n",
    "solution = odeint(diff_equation, y0, t, args=(parameters, ))\n",
    "u, s = solution.T\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 648x864 with 7 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "\n",
    "plot_timeseries(s, u, alpha, beta, gamma)\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "\n",
    "ax = plt.scatter(s,u, c=t, cmap=plt.cm.rainbow)\n",
    "plt.xlim(0,)\n",
    "plt.ylim(0,)\n",
    "plt.xlabel(\"Spliced\")\n",
    "plt.ylabel(\"Unspliced\")\n",
    "ax2 = plt.colorbar(ax); ax2.set_label(\"time\")\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "<h1 id=\"From-data\">From data<a class=\"anchor-link\" href=\"#From-data\">¶</a></h1>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p><strong>Exercice 3</strong></p>\n",
    "\n",
    "<p>The level of spliced and unspliced can be directly measured experimentally in many cells.\n",
    "And the model above offers an opportunity to estimate the RNA velocity</p>\n",
    "<p>For example even if the biological process we are observing is unsynchronized, and different cells are in a different phase of it, we will be able to make conclusions on whether each cell was upregulating or downregulating a gene.\n",
    "Let's see how.</p>\n",
    "<p>We start by generating a fake dataset. First add a little of white noise to the simulation.</p>\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "\n",
    "s = s + np.random.normal(0,2, size=s.shape)\n",
    "u = u + np.random.normal(0,1, size=u.shape)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "<p>Let's plot the results but from now on, remember that we are assuming that we are working with experimental data.\n",
    "So we don't know the time from the start of the process for each cell and we don't know the parameters alpha, beta, gamma and how they varied over time.</p>\n",
    "<p>We can only make use of the spliced and unspliced information form each cell and try to extract the information from there!</p>\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0,0.5,'Unspliced')"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "\n",
    "plt.scatter(s,u)\n",
    "plt.xlim(0,)\n",
    "plt.ylim(0,)\n",
    "plt.xlabel(\"Spliced\")\n",
    "plt.ylabel(\"Unspliced\")\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "<p>Then let's consider agan the original model.</p>\n",
    "\\begin{align}\n",
    "\\dot{u} = \\alpha - \\beta u \\\\\n",
    "\\dot{s}  = \\beta u - \\gamma s \\\\\n",
    "\\end{align}<p>We have no good way to estimate alpha from this data, however we can focus on the second equation, and assuming beta = 1 (or analogously writing the equation in units of beta) we get:</p>\n",
    "\\begin{align}\n",
    "\\dot{s}  = u - \\gamma s \\\\\n",
    "\\end{align}<p>Therefore if we could estimate gamma we would be able to calculate the RNA velocity (s prime) of each cell by:</p>\n",
    "\\begin{align}\n",
    "u - \\gamma s \\\\\n",
    "\\end{align}\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "<p>Therefore, considering the observation we made in the last question (about where the steady states points sit geometrically), we could try to estimate gamma  (actually gamma / beta but beta=1) from this dataset using a simple linear regression.</p>\n",
    "<p>Note that we are assuming that there are many cells in steady state (or alternatevelly as many cells upregulating and downregulating the gene), if this is not true the estimation will not work well.</p>\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "\n",
    "from scipy.optimize import leastsq\n",
    "\n",
    "# a quick linear regression\n",
    "def sum_residuals(slope):\n",
    "    return np.sum((slope*s - u)**2)\n",
    "gamma_beta = leastsq(sum_residuals, 0)[0][0]\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.36826824506703515"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "\n",
    "gamma_beta\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.37499999999999994"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "\n",
    "gamma(0) / beta(0)\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "<p>Notice how accurately we can estimate gamma / beta in this case!</p>\n",
    "<p>Then, let's estimate RNA velocity</p>\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "\n",
    "velocity = u - gamma_beta*s\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "\n",
    "ax = plt.scatter(s,u,c=velocity, cmap = plt.cm.RdBu_r)\n",
    "xs = np.linspace(0, np.max(s))\n",
    "plt.plot(xs, gamma_beta * xs, c='k')\n",
    "plt.xlim(0,); plt.ylim(0,); plt.xlabel(\"spliced\"); plt.ylabel(\"inspliced\")\n",
    "\n",
    "ax2 = plt.colorbar(ax); ax2.set_label(\"velocity\")\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "<p>1. Choose one of the data points and extrapolate the gene expression level after 20 minutes?\n",
    "You can use the following function to plot function on the plot above</p>\n",
    "<pre><code>plt.arrow(x, y, delta_x, delta_y, head_width=0.5)</code></pre>\n",
    "<p>2. Is it possible to extrapolate also for u? </p>\n",
    "<p>3. Which assumption could be made?</p>\n"
   ]
  }
 ],
 "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": "3.6.9"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}
