{
    "cells": [
        {
            "cell_type": "markdown",
            "metadata": {},
            "source": [
                "# Reversible binding"
            ]
        },
        {
            "cell_type": "code",
            "execution_count": 1,
            "metadata": {
                "nbsphinx": "hidden"
            },
            "outputs": [],
            "source": [
                "import random\n",
                "random.seed(0)"
            ]
        },
        {
            "cell_type": "markdown",
            "metadata": {},
            "source": [
                "We can initialize a system of a simple reversible binding interaction as follows:"
            ]
        },
        {
            "cell_type": "code",
            "execution_count": 2,
            "metadata": {},
            "outputs": [],
            "source": [
                "from pykappa.system import System\n",
                "\n",
                "system = System.from_kappa(\n",
                "    mixture={\"A(x[.])\": 100, \"B(x[.])\": 100},\n",
                "    rules=[\n",
                "        \"A(x[.]), B(x[.]) -> A(x[1]), B(x[1]) @ 1\",\n",
                "        \"A(x[1]), B(x[1]) -> A(x[.]), B(x[.]) @ 1\",\n",
                "    ],\n",
                "    observables={\"AB\": \"|A(x[1]), B(x[1])|\"},\n",
                ")"
            ]
        },
        {
            "cell_type": "markdown",
            "metadata": {},
            "source": [
                "or equivalently from a .ka-style string:"
            ]
        },
        {
            "cell_type": "code",
            "execution_count": 3,
            "metadata": {},
            "outputs": [],
            "source": [
                "system = System.from_ka(\n",
                "    \"\"\"\n",
                "    %init: 100 A(x[.])\n",
                "    %init: 100 B(x[.])\n",
                "\n",
                "    %obs: 'AB' |A(x[1]), B(x[1])|\n",
                "\n",
                "    A(x[.]), B(x[.]) <-> A(x[1]), B(x[1]) @ 1, 1\n",
                "    \"\"\"\n",
                ")"
            ]
        },
        {
            "cell_type": "markdown",
            "metadata": {},
            "source": [
                "100 instances of molecules of type `A` and of type `B`, each with an empty binding domain `x`, are created, and we track the number of `AB` complexes.\n",
                "\n",
                "We're going to simulate this system and plot its behavior, marking certain times of interest. We'll first simulate until time 1:"
            ]
        },
        {
            "cell_type": "code",
            "execution_count": 4,
            "metadata": {},
            "outputs": [],
            "source": [
                "times = []\n",
                "while system.time < 1:\n",
                "    system.update()\n",
                "times.append(system.time)"
            ]
        },
        {
            "cell_type": "markdown",
            "metadata": {},
            "source": [
                "We'll now manually instantiate 50 new `A` and `B` molecules each, start tracking the number of free `A`, and simulate until there are no more than 10 free `A` in the mixture:"
            ]
        },
        {
            "cell_type": "code",
            "execution_count": 5,
            "metadata": {},
            "outputs": [],
            "source": [
                "system.mixture.instantiate(\"A(x[.]), B(x[.])\", 50)\n",
                "\n",
                "system[\"A\"] = \"|A(x[.])|\"\n",
                "while system[\"A\"] > 10:\n",
                "    system.update()\n",
                "times.append(system.time)"
            ]
        },
        {
            "cell_type": "markdown",
            "metadata": {},
            "source": [
                "Now let's simulate some more time:"
            ]
        },
        {
            "cell_type": "code",
            "execution_count": 6,
            "metadata": {},
            "outputs": [],
            "source": [
                "while system.time < 2:\n",
                "    system.update()\n",
                "times.append(2)"
            ]
        },
        {
            "cell_type": "markdown",
            "metadata": {},
            "source": [
                "The default simulator provides the most features since it’s written directly in Python, but models can be offloaded to [KaSim](https://github.com/Kappa-Dev/KappaTools), a compiled Kappa simulator, for faster simulation. For example, we could've run:\n",
                "```python\n",
                "system.update_via_kasim(time=1)\n",
                "```"
            ]
        },
        {
            "cell_type": "markdown",
            "metadata": {},
            "source": [
                "Finally, let’s plot the history of the quantities we tracked:"
            ]
        },
        {
            "cell_type": "code",
            "execution_count": null,
            "metadata": {},
            "outputs": [],
            "source": [
                "import matplotlib.pyplot as plt\n",
                "\n",
                "system.monitor.plot(combined=True)\n",
                "for time in times:\n",
                "    plt.axvline(time, color=\"black\", linestyle=\"dotted\")\n",
                "plt.show()"
            ]
        },
        {
            "cell_type": "markdown",
            "metadata": {},
            "source": [
                "The system equilibrates relatively early.\n",
                "Then new `A` is added and the number of `AB` complexes increases, reaching a higher equilibrium concentration."
            ]
        }
    ],
    "metadata": {
        "kernelspec": {
            "display_name": "kappa",
            "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
}