{
    "cells": [
        {
            "cell_type": "markdown",
            "metadata": {},
            "source": [
                "# Chemostat\n",
                "\n",
                "A chemostat can maintain a concentration of nutrients in a container by flowing in and flowing out nutrients each at a constant rate.\n",
                "Here we will set up a simulatable chemostat with a clonal and unevolving unicellular organism, and adjust the flow rate to observe the effect on the growth rate of the cells.\n",
                "More specifically, we will assume that a cell `C` replicates following metabolism of three units of the nutrient `N`, and that cells die memorylessly at a constant stochastic rate."
            ]
        },
        {
            "cell_type": "code",
            "execution_count": 1,
            "metadata": {
                "nbsphinx": "hidden"
            },
            "outputs": [],
            "source": [
                "import random\n",
                "random.seed(0)"
            ]
        },
        {
            "cell_type": "code",
            "execution_count": 2,
            "metadata": {},
            "outputs": [],
            "source": [
                "from pykappa.system import System\n",
                "\n",
                "system = System.from_ka(\n",
                "    \"\"\"\n",
                "    %init: 10 C(n{0})  // Start with a few cells\n",
                "\n",
                "    %obs: 'C' |C()|\n",
                "\n",
                "    . -> N() @ 1  // Nutrient inflow\n",
                "    N() -> . @ 0.1  // Nutrient outflow\n",
                "\n",
                "    // Metabolism\n",
                "    C(n{0}), N() -> C(n{1}), . @ 0.5\n",
                "    C(n{1}), N() -> C(n{2}), . @ 0.5\n",
                "    C(n{2}), N() -> C(n{3}), . @ 0.5\n",
                "\n",
                "    C(n{3}), . -> C(n{0}), C(n{0}) @ 0.1 // Cell division\n",
                "    C() -> . @ 0.01  // Cell death\n",
                "    \"\"\"\n",
                ")"
            ]
        },
        {
            "cell_type": "markdown",
            "metadata": {},
            "source": [
                "If we started with only, say, one cell, it would be reasonably likely that the population would die out before replicating sufficiently to virtually preclude extinction."
            ]
        },
        {
            "cell_type": "markdown",
            "metadata": {},
            "source": [
                "Let's start the chemostat and observe the population size:"
            ]
        },
        {
            "cell_type": "code",
            "execution_count": null,
            "metadata": {},
            "outputs": [],
            "source": [
                "while system.time < 10 ** 3:\n",
                "    system.update()\n",
                "system.monitor.plot();"
            ]
        },
        {
            "cell_type": "markdown",
            "metadata": {},
            "source": [
                "Now let's increase inflow of the nutrient without changing the outflow rate and observe that the population size increases:"
            ]
        },
        {
            "cell_type": "code",
            "execution_count": null,
            "metadata": {},
            "outputs": [],
            "source": [
                "system.add_rule(\". -> N() @ 1\")\n",
                "\n",
                "while system.time < 5 * 10 ** 3:\n",
                "    system.update()\n",
                "system.monitor.plot();"
            ]
        }
    ],
    "metadata": {
        "kernelspec": {
            "display_name": "standard",
            "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": "3.12.3"
        }
    },
    "nbformat": 4,
    "nbformat_minor": 2
}