{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Tyson1991\n", "\n", "This model is described in the article:\n", "\n", "- J.J. Tyson, \"Modeling the cell division cycle: cdc2 and cyclin interactions.\", Proc. Natl. Acad. Sci. U.S.A., 88(16), 7328-32, 1991.\n", "\n", "Abstract:\n", "The proteins cdc2 and cyclin form a heterodimer (maturation promoting factor) that controls the major events of the cell cycle. A mathematical model for the interactions of cdc2 and cyclin is constructed. Simulation and analysis of the model show that the control system can operate in three modes: as a steady state with high maturation promoting factor activity, as a spontaneous oscillator, or as an excitable switch. We associate the steady state with metaphase arrest in unfertilized eggs, the spontaneous oscillations with rapid division cycles in early embryos, and the excitable switch with growth-controlled division cycles typical of nonembryonic cells." ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "collapsed": true }, "outputs": [], "source": [ "%matplotlib inline\n", "from ecell4 import *" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "collapsed": true }, "outputs": [], "source": [ "with reaction_rules():\n", " YT = Y + YP + M + pM\n", " CT = C2 + CP + M + pM\n", "\n", " ~Y > Y | 0.015 / CT\n", " Y > ~Y | 0.0 * Y\n", " CP + Y > pM | 200.0 * CP * Y / CT\n", " pM > M | pM * (0.018 + 180 * ((M / CT) ** 2))\n", " M > pM | 0.0 * M\n", " M > C2 + YP | 1.0 * M\n", " YP > ~YP | 0.6 * YP\n", " C2 > CP | 1000000.0 * C2\n", " CP > C2 | 1000.0 * CP\n", "\n", "m = get_model()" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "C2+CP+M+pM>Y+C2+CP+M+pM|(0.015/(C2+CP+M+pM))\n", "Y>|(0.0*Y)\n", "CP+Y+C2+M>pM+C2+M|((200.0*CP*Y)/(C2+CP+M+pM))\n", "pM+C2+CP>M+C2+CP|(pM*(0.018+(180*((M/(C2+CP+M+pM))**2))))\n", "M>pM|(0.0*M)\n", "M>C2+YP|(1.0*M)\n", "YP>|(0.6*YP)\n", "C2>CP|(1000000.0*C2)\n", "CP>C2|(1000.0*CP)\n" ] } ], "source": [ "for rr in m.reaction_rules():\n", " print(rr.as_string())" ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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JKWUpsAi4s8IxqYBv2de+QIaU0nY9KjpKykki0i+yXlVNKxJCMKnXJFY9uIoX1r3A1NVT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\nbY3sS48lNjOWv9yCMQ6LF+e4Semi+OwOsv93Dfq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