{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "name": "SystBio_intro.ipynb",
      "provenance": []
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    },
    "language_info": {
      "name": "python"
    }
  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Ez2vvYHxj4KX"
      },
      "source": [
        "# Exercices avec la présentation des types en python. \n",
        "On va aborder du plus simple au plus compliqué mais aussi flexible. \n",
        "\n",
        "On commence par les scalaires et non scalaires..... ;-)"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "aRsTF9j7uz6e",
        "outputId": "0daad720-2555-481c-acfb-b290ed252df6"
      },
      "source": [
        "toto = 5\n",
        "tutu = 4\n",
        "print(tutu + toto)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "9\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "fVF-szlyj3SV",
        "outputId": "9a67cba4-e8f7-440c-92af-80bb40f3009e"
      },
      "source": [
        "a = 2;\n",
        "b = 6;\n",
        "print(a*b)\n",
        "DNA = 'ATCGTGTA';\n",
        "DNA2 = 'T'*8;\n",
        "print (DNA2+DNA)\n",
        "DNA3 = DNA+DNA2;"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "12\n",
            "TTTTTTTTATCGTGTA\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "PlLUgQ58vizk",
        "outputId": "ace02ba2-e23d-48e7-f396-cded54f2f963"
      },
      "source": [
        "test = 'ATCTCGTGTGT'\n",
        "print(test[1])"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "T\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "hKrXvVoDlJx4"
      },
      "source": [
        "On va travailler ensuite sur la transcription d'une chaine d'ADN"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "ZVGn8Wk7lOLE",
        "outputId": "7f88e85d-320c-4207-8c42-91fc19437b32"
      },
      "source": [
        "DNA3 = 'TTTTTTTTTTTTTTTTTTTTTTTTTTT'\n",
        "x = len(DNA3);\n",
        "i = 0;\n",
        "RNA = '';\n",
        "while i<x:\n",
        "  print(DNA3[i])\n",
        "  if DNA3[i] == 'T':\n",
        "    RNA = RNA + 'U';\n",
        "  else:\n",
        "      RNA = RNA + DNA3[i];\n",
        "  i = i+ 1\n",
        "print('and it\\s transcription is : 5\\'-', RNA, '- 3\\'');\n"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "T\n",
            "T\n",
            "T\n",
            "T\n",
            "T\n",
            "T\n",
            "T\n",
            "T\n",
            "T\n",
            "T\n",
            "T\n",
            "T\n",
            "T\n",
            "T\n",
            "T\n",
            "T\n",
            "T\n",
            "T\n",
            "T\n",
            "T\n",
            "T\n",
            "T\n",
            "T\n",
            "T\n",
            "T\n",
            "T\n",
            "T\n",
            "and it\\s transcription is : 5'- UUUUUUUUUUUUUUUUUUUUUUUUUUU - 3'\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "e6OBXpivmjoT"
      },
      "source": [
        "Via python, on peut aussi jouer avec des structures plus complexes qui vont être très utiles. \n",
        "\n",
        "## Les Tuples\n",
        "Comme les chaines de caractères, les tuples peuvent être concaténés mais ne seront pas forcément constitués des mêmes types"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "7M_vmy3qnFbs",
        "outputId": "c003d2eb-7d0b-4b02-c659-44fa87c7ea37"
      },
      "source": [
        "t1 = ()\n",
        "t2 = (1,'two', 3)\n",
        "t1 = (1,)\n",
        "\n",
        "print((t1+t2)[2])\n",
        "print((t1+t2)[0:3])"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "two\n",
            "(1, 1, 'two')\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "vDT9p4Yan1LB"
      },
      "source": [
        "Les tuples sont idéaux pour représenter des ensembles. Il est alors possible de rechercher les éléments qui sont communs à 2 ensembles (même très grands). "
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "1tQkXKdcoCKa",
        "outputId": "7a44e617-6549-4377-892c-816d84b96320"
      },
      "source": [
        "t1 = (1,2,3,4,5,6,7,8,34,12,14,);\n",
        "t2 = (7,8,4,8,67,45,78);\n",
        "\n",
        "result = () # un tuple vide qui va stocker les resultats\n",
        "for e in t1:\n",
        "  if e in t2:\n",
        "    result +=(e,)   # on va ajouter l'element interessant au tuple resultat \n",
        "\n",
        "print(result)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "(4, 7, 8)\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Bj0p_7QYosoi"
      },
      "source": [
        "## Les Ranges\n",
        "Les ranges ne sont pas modifiables. Ils sont définis par 3 entiers : le début, la fin et le pas. On va naturellement les utiliser pour des valeurs entières"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "K82dvTNfpAId",
        "outputId": "ea6f96e2-124b-4dc4-855c-4f85e870ec8a"
      },
      "source": [
        "for i in range(1,100,3):\n",
        "  print(i)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "1\n",
            "4\n",
            "7\n",
            "10\n",
            "13\n",
            "16\n",
            "19\n",
            "22\n",
            "25\n",
            "28\n",
            "31\n",
            "34\n",
            "37\n",
            "40\n",
            "43\n",
            "46\n",
            "49\n",
            "52\n",
            "55\n",
            "58\n",
            "61\n",
            "64\n",
            "67\n",
            "70\n",
            "73\n",
            "76\n",
            "79\n",
            "82\n",
            "85\n",
            "88\n",
            "91\n",
            "94\n",
            "97\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "LVkZ2MnHpxll"
      },
      "source": [
        "## List et gestion de la modification\n",
        "Quand on travaille sur les sequences qui sont modifiables.  "
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "mGz93MnHqEUO",
        "outputId": "43332012-3ea3-437f-b384-a1cc9014cd7a"
      },
      "source": [
        "L = ['ATCG', 5, 'TTT']\n",
        "for i in range (len(L)):\n",
        "  print(i)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "0\n",
            "1\n",
            "2\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "OKwu5fZPqaAx"
      },
      "source": [
        "cela permet de contruire une structure qui mixe les types ; comme les tuples. Mais ces structures sont modifiables\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "-Ic5ihH_qktZ",
        "outputId": "302bebed-7b42-4c1d-b966-0f20c5cfa8e3"
      },
      "source": [
        "fruit = ['apple', 'cherry']\n",
        "veggie = ['potatoes', 'carrot']\n",
        "fruits = [fruit, veggie]\n",
        "print(fruits)\n",
        "fruits.append('tomato')\n",
        "print(fruits)\n",
        "\n",
        "fruits.reverse()\n",
        "print(fruits)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "[['apple', 'cherry'], ['potatoes', 'carrot']]\n",
            "[['apple', 'cherry'], ['potatoes', 'carrot'], 'tomato']\n",
            "['tomato', ['potatoes', 'carrot'], ['apple', 'cherry']]\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "hM_1mwIWrW7H"
      },
      "source": [
        "## Dictionnaires\n",
        "Comme les listes, mais les indexations se font via des clés. "
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "K4mqHdFKrg-H",
        "outputId": "24643a23-9d0a-4b58-f82c-78b3d8307de9"
      },
      "source": [
        "moisNombre = {'Jan':1, 'Feb':2, 'Mar':3,'Avr':4}\n",
        "basecomplement = {'A':'T','T':'A','C':'G','G':'C'}\n",
        "genetic_code = {'TCA':'S',\n",
        "                'TCC':'S',\n",
        "                'TCG':'S'}\n",
        "\n",
        "codon = 'TCA'\n",
        "print(codon, 'encodes for ', genetic_code[codon])"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "TCA encodes for  S\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Zi50PGQmtOoW"
      },
      "source": [
        "Pou travailler sur les différentes variables et structures, il existe de nombreuses boites à outils qu'il est possible d'appeller. Parmi beaucoup d'autres : \n",
        "\n",
        "\n",
        "*   *numpy* pour le calcul numérique sous python (au delà des simples opérations arithmétiques)\n",
        "* *matplotlib* pour les représentations graphiques\n",
        "* *scipy* pour le calcul scientifique et notamment la simulation de systèmes continus\n",
        "* *networkx* pour la manipulation de réseaux  \n",
        "\n",
        "Et regarder ce [lien vers les différents formats de figure possible sous python](https://www.python-graph-gallery.com)\n",
        "\n",
        "\n",
        "\n",
        "# Exercices sur les types en python\n",
        "Ecrire une séquence d'ADN qui peut contenir majuscules et minuscules uniquement avec des majuscules. \n",
        "\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "vZbUoHm7tjL7",
        "outputId": "96fbac9b-41e7-4610-98e3-f78a64f8a6aa"
      },
      "source": [
        "DNA = 'ATCGtGTgA'\n",
        "print(DNA.upper())"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "ATCGTGTGA\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "fl176qfTtmG_"
      },
      "source": [
        "Demander 2 séquences ADN et les afficher l'une sur l'autres tel que : \n",
        "AAAAA and TTTT will give \n",
        "\t\tAAAAATTTT\n",
        "        TTTT"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "uzgM_I88t9ff",
        "outputId": "ef8e98c6-57ae-49ec-db2b-f5226998f2ff"
      },
      "source": [
        "seq1 = input('first sequence ')\n",
        "seq2 = input('second sequence ')\n",
        "\n",
        "print(seq1+seq2)\n",
        "print(' '*len(seq1)+seq2)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "first sequence ljkhflhfqelkhql;kqeghli;\n",
            "second sequence yyyyyyyyyyyyyy\n",
            "ljkhflhfqelkhql;kqeghli;yyyyyyyyyyyyyy\n",
            "                        yyyyyyyyyyyyyy\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "psu_EvN-uS3c"
      },
      "source": [
        "Calculer le pourcentage de GC pour une séquence ADN donnée par l'utilisateur"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "-conxNYCuJZt"
      },
      "source": [
        "DNA='';\n",
        "# lecture de fichier au format fasta\n",
        "nameHandle = open('seq.fasta','r')\n",
        "for line in nameHandle:\n",
        "    DNA+=line[:-1]    # [:-1] is to avoid blank lines\n",
        "nameHandle.close()\n",
        "\n",
        "size = len(DNA)\n",
        "Gcount = DNA.count('G');\n",
        "Ccount = DNA.count('C');\n",
        "Acount = DNA.count('A');\n",
        "Tcount = DNA.count('T');\n",
        "\n",
        "print('GC content is:',(Gcount+Ccount)/size * 100, '%')\n"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "YHhs7rMqvmV5"
      },
      "source": [
        "# Exercice sur la simulation de population\n",
        "Pour cela on va faire une hypothèse de croissance exponentielle de la population bactérienne. \n",
        "$$x(t) = x_0. e^{at}$$\n",
        "avec $x_0$ la quantité initiale de bactéries, et $a$ le taux de croissance.\n",
        "\n",
        "Cela signifie que l'on peut réécrire sous la forme \n",
        "$$\\frac{dx}{dt} = a . x(t)$$"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 317
        },
        "id": "-Ef1J8qEwU61",
        "outputId": "f6638038-076f-40d2-a2c4-3bdc7660c1dd"
      },
      "source": [
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "from scipy.integrate import odeint\n",
        "\n",
        "def growth(x,t):\n",
        "    a = 0.53\n",
        "    dx = a *x\n",
        "    return dx\n",
        "\n",
        "t = np.linspace(0,10)\n",
        "x0 = [0.2]\n",
        "y = odeint(growth,x0,t)\n",
        "\n",
        "plt.figure(1)\n",
        "plt.plot(t,y[:,0],'b-')\n",
        "plt.xlabel('Temps(jours)')\n",
        "plt.ylabel('Nombres de bactéries')"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "Text(0, 0.5, 'Nombres de bactéries')"
            ]
          },
          "metadata": {},
          "execution_count": 6
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "RR0-HZH2y2TT"
      },
      "source": [
        "On va pouvoir faire la simulation d'un système plus compliqué, comme le celebre système de prédateur-proie. \n",
        "\n",
        "**Definition mathématique du système**\n",
        "\n",
        "\n",
        "$$\\frac{dx_1}{dt} = a . x_1 - b . x_1 . x_2$$,\n",
        "   \n",
        "$$\\frac{dx_2}{dt} = c . x_1 . x_2 - d . x_2$$"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 550
        },
        "id": "hit9VkXDzT4W",
        "outputId": "505891c5-d5c2-4fbc-85c1-22a820798b1b"
      },
      "source": [
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "from scipy.integrate import odeint\n",
        "\n",
        "## the model\n",
        "def f(y,t):\n",
        "    prey = y[0]\n",
        "    predator = y[1]\n",
        "    a = 1/3\n",
        "    b = 4/3\n",
        "    c = 1\n",
        "    d = 1\n",
        "    \n",
        "    ## the model equation\n",
        "    dprey = a * prey - b * prey * predator\n",
        "    dpredator = c * prey * predator - d * predator\n",
        "    return[dprey,dpredator]\n",
        "    \n",
        "t = np.linspace(0,100, 1000)\n",
        "x0 = [1,2]\n",
        "y = odeint(f,x0,t)\n",
        "\n",
        "plt.figure(1)\n",
        "plt.plot(t,y[:,0],'b-') \n",
        "plt.plot(t,y[:,1],'r-')\n",
        "\n",
        "plt.figure(2)\n",
        "plt.plot(y[:,0],y[:,1],'g-')"
      ],
      "execution_count": 1,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "[<matplotlib.lines.Line2D at 0x7fa810fcb8d0>]"
            ]
          },
          "metadata": {},
          "execution_count": 1
        },
        {
          "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",
          "data": {
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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "b9y68ih61ITS"
      },
      "source": [
        "## Analyse qualitative du système"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 282
        },
        "id": "k1GuHo3I1Mo0",
        "outputId": "a515e04b-66c5-40ff-d30e-518e69aece74"
      },
      "source": [
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "from scipy.integrate import odeint\n",
        "\n",
        "####################################################\n",
        "## the model is written here \n",
        "def f(y,t):\n",
        "    prey = y[0]\n",
        "    predator = y[1]\n",
        "    a = 2/3\n",
        "    b = 4/3\n",
        "    c = 1 \n",
        "    d = 1\n",
        "    ## the model equation\n",
        "    dprey = a * prey - b * prey * predator\n",
        "    dpredator = c * prey * predator - d * predator\n",
        "    return[dprey,dpredator]\n",
        "    \n",
        "#####################################################\n",
        "# setting up the space \n",
        "# xlabel\n",
        "y1 = np.linspace(0,4,10)\n",
        "# ylabel\n",
        "y2 = np.linspace(0,4,10)\n",
        "# making a mesh from these points\n",
        "Y1, Y2 = np.meshgrid(y1,y2)\n",
        "# one fix the time to 0 for all simulations\n",
        "t = 0\n",
        "# design of matrices full of zeros\n",
        "u,v = np.zeros(Y1.shape),np.zeros(Y2.shape)\n",
        "# size of the matrix\n",
        "NI, NJ = Y1.shape\n",
        "\n",
        "# for each point of the mesh, one computes the derivative\n",
        "for i in range(NI):\n",
        "    for j in range(NJ):\n",
        "        x = Y1[i,j]\n",
        "        y = Y2[i,j]\n",
        "        yprime = f([x,y],t)     # computing the derivative here\n",
        "        u[i,j] = yprime[0]      # size of the arrow on xlabel\n",
        "        v[i,j] = yprime[1]      # size of the arrow on ylabel\n",
        "        \n",
        "\n",
        "# just plot the arrows for each point on the mesh...\n",
        "Q = plt.quiver(Y1,Y2,u,v,color = 'r')\n",
        "\n",
        "# ploting isoclines\n",
        "# recall of the kinetics constants\n",
        "a = 2/3\n",
        "b = 4/3\n",
        "c = 1 \n",
        "d = 1\n",
        "\n",
        "# first isoclines\n",
        "plt.plot(np.ones(y1.shape)*(d/c),y2,'b')\n",
        "# second isoclines\n",
        "plt.plot(y1, np.ones(y1.shape)*(a/b),'b')\n"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "[<matplotlib.lines.Line2D at 0x7f71ca8f58d0>]"
            ]
          },
          "metadata": {},
          "execution_count": 29
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    }
  ]
}