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        {
            "cell_type": "markdown",
            "metadata": {},
            "source": [
                "# Linear polymerization\n",
                "\n",
                "This example demonstrates a simple polymerization process in which monomers `M` can bind each other to form linear chains.\n",
                "There's a lower rate of depolymerization, and chains can be terminated by capping agents `C`."
            ]
        },
        {
            "cell_type": "code",
            "execution_count": 1,
            "metadata": {
                "nbsphinx": "hidden"
            },
            "outputs": [],
            "source": [
                "import random\n",
                "random.seed(42)"
            ]
        },
        {
            "cell_type": "code",
            "execution_count": 2,
            "metadata": {},
            "outputs": [],
            "source": [
                "from pykappa.system import System\n",
                "\n",
                "system = System.from_ka(\n",
                "    \"\"\"\n",
                "    %init: 1000 M(l[.], r[.])\n",
                "\n",
                "    %obs: 'Free monomer' |M(l[.], r[.])|\n",
                "\n",
                "    M(r[.]), M(l[.]) -> M(r[1]), M(l[1]) @ 1  // Polymerization\n",
                "    M(r[1]), M(l[1]) -> M(r[.]), M(l[.]) @ 0.1  // Depolymerization\n",
                "    \n",
                "    // Chain capping\n",
                "    M(r[.]), C(m[.]) -> M(r[1]), C(m[1]) @ 0.05\n",
                "    M(l[.]), C(m[.]) -> M(l[1]), C(m[1]) @ 0.05\n",
                "    \n",
                "    // Cap removal\n",
                "    M(r[1]), C(m[1]) -> M(r[.]), C(m[.]) @ 0.01\n",
                "    M(l[1]), C(m[1]) -> M(l[.]), C(m[.]) @ 0.01\n",
                "    \"\"\"\n",
                ")"
            ]
        },
        {
            "cell_type": "markdown",
            "metadata": {},
            "source": [
                "Simulate for a bit:"
            ]
        },
        {
            "cell_type": "code",
            "execution_count": 3,
            "metadata": {},
            "outputs": [],
            "source": [
                "while system.time < 100:\n",
                "    system.update()"
            ]
        },
        {
            "cell_type": "code",
            "execution_count": null,
            "metadata": {},
            "outputs": [],
            "source": [
                "import matplotlib.pyplot as plt\n",
                "\n",
                "def polymer_len_plot(system):\n",
                "    plt.hist([len(component) for component in system.mixture if len(component) > 1])\n",
                "    plt.xlabel(\"Polymer length\")\n",
                "    plt.ylabel(\"Count\");\n",
                "\n",
                "print(f\"Free monomers: {system['Free monomer']}\")\n",
                "polymer_len_plot(system)"
            ]
        },
        {
            "cell_type": "markdown",
            "metadata": {},
            "source": [
                "Now let's add some of the capping agent:"
            ]
        },
        {
            "cell_type": "code",
            "execution_count": null,
            "metadata": {},
            "outputs": [],
            "source": [
                "system.mixture.instantiate(\"C(m[.])\", 500)\n",
                "\n",
                "while system.time < 200:\n",
                "    system.update()\n",
                "\n",
                "print(f\"Free monomers: {system['Free monomer']}\")\n",
                "polymer_len_plot(system)"
            ]
        }
    ],
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