{
    "cells": [
        {
            "cell_type": "markdown",
            "metadata": {},
            "source": [
                "# The prozone effect\n",
                "\n",
                "The prozone effect, also called the hook effect, refers to when the abundance of a molecular complex first increases then decreases as the relative concentration of a constituent molecule `E` increases.\n",
                "In this example, we will say that a complex is composed of an `L` molecule, an `M` molecule, and an `E` molecule, which connects the former two together."
            ]
        },
        {
            "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: 100 L(e[.])\n",
                "    %init: 100 M(e[.])\n",
                "\n",
                "    %obs: 'E' |E()|\n",
                "    %obs: 'Incomplete complexes' |E(l[_], m[.])| + |E(l[.], m[_])|\n",
                "    %obs: 'Complete complexes' |E(l[_], m[_])|\n",
                "\n",
                "    E(l[.]), L(e[.]) <-> E(l[1]), L(e[1]) @ 1, 1  // Bind L to E\n",
                "    E(m[.]), M(e[.]) <-> E(m[1]), M(e[1]) @ 1, 1  // Bind M to E\n",
                "    . -> E(l[.], m[.]) @ 1  // Inflow of E\n",
                "    \"\"\"\n",
                ")"
            ]
        },
        {
            "cell_type": "markdown",
            "metadata": {},
            "source": [
                "We've set up the system so that there's no `E` to start but that it flows in at a constant stochastic rate.\n",
                "Let's now simulate while tracking the corresponding number of complexes:"
            ]
        },
        {
            "cell_type": "code",
            "execution_count": null,
            "metadata": {},
            "outputs": [],
            "source": [
                "while system.time < 5 * 10 ** 2:\n",
                "    system.update()\n",
                "system.monitor.plot();"
            ]
        },
        {
            "cell_type": "markdown",
            "metadata": {},
            "source": [
                "As we introduce more `E`, at first more complexes can be formed but eventually there are so many `E` that the other components of the complex become more likely to bind separate `E` molecules.\n",
                "The result is that the full complex is less likely to form."
            ]
        }
    ],
    "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
}