{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "## Enzyme Kinetics (Part 2)\n", "\n", "We have already implemented a model in which an enzyme E aids a reaction in which a substrate S is consumed to produce a product P.\n", "\n", "\\begin{eqnarray*}\n", "\\frac{dS}{dt} &=& -k_1\\cdot S\\cdot E + k_{-1}\\cdot SE\\\\\n", "\\frac{dE}{dt} &=& -k_1S\\cdot E + k_{-1}SE + k_2\\cdot SE\\\\\n", "\\frac{dP}{dt} &=& k_2\\cdot SE\\\\\n", "\\frac{dSE}{dt} &=& k_1\\cdot S\\cdot E - k_{-1}\\cdot SE - k_2\\cdot SE\\\\\n", "\\end{eqnarray*}\n", "\n", "where SE is the compound of S and E.\n", "\n", "Our goal today is to rewrite the model with ODEs for S and P, but not E or ES.\n", "\n", "First, we rerun the model from Tuesday." ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "import scipy.integrate\n", "\n", "def enzyme_model( t, y, params ):\n", " S = y[0]\n", " E = y[1]\n", " P = y[2]\n", " SE = y[3]\n", "\n", " k1f = params[0]\n", " k1b = params[1]\n", " k2 = params[2]\n", "\n", " dydt = np.zeros( (4,) )\n", " dydt[0] = -k1f*S*E + k1b*SE # S\n", " dydt[1] = -k1f*S*E + k1b*SE + k2*SE #E\n", " dydt[2] = k2*SE #P\n", " dydt[3] = k1f*S*E - k1b*SE - k2*SE #SE\n", " return dydt" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Simulating when Enzyme concentration is low\n", "A more realistic scenario is one in which the enzyme concentration is low.\n", "\n", "Use k1f = 2, k1b=2, k2 = 3, S(0) = 100, E(0) = 1, SE(0) = 0, P(0) = 0.\n", "\n", "Simulate with from t=0 to t=100 with a timestep of 0.1" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [], "source": [ "k1f = 2\n", "k1b = 1\n", "k2 = 3\n", "params = (k1f, k1b, k2)\n", "\n", "S0 = 100\n", "E0 = 1\n", "SE0 = 0\n", "P0 = 0\n", "yinit = (S0,E0,P0,SE0)\n", "\n", "em = lambda t,y: enzyme_model(t,y,params)\n", "sol = scipy.integrate.solve_ivp( fun=em, t_span=(0,100), y0=yinit, \n", " t_eval=np.arange(0,100,1) )" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Plot the simulation over time." ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "import matplotlib.pyplot as plt \n", "\n", "plt.plot( sol.t, sol.y.T )\n", "plt.xlabel( \"Time\")\n", "plt.ylabel( \"Concentration\" )\n", "plt.legend( [\"S\",\"E\",\"P\",\"SE\"])\n", "plt.title( \"Enzyme-catalyzed reaction\");" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We are interested in learning how to express dP/dt in terms of S and have learned from the tutorial that the Michaelis-Menton equation can do that for us.\n", "\n", "The curve dP/dt vs S can be expressed as\n", "\n", "$v_{max}\\frac{S}{K_m+S}$\n", "\n", "where\n", "\n", "$v_{max} = E(0)\\cdot k_2$\n", "\n", "and \n", "\n", "$K_m = \\frac{k_{-1}+k_2}{k_1}$\n", "\n", "Plot the analytic curve (from the Michaelis-Mention model for enzyme kinetics) on the same plot as the approximated dP/dt (you can just replot the curve from above and the plot the analytic curve as well)." ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# Estimate the curve dP/dt from the simulation output\n", "P = sol.y[2,:].T\n", "S = sol.y[0,:-1].T\n", "velocity_of_P = np.divide(np.diff(P), (sol.t[1]-sol.t[0]))\n", "\n", "# Now compute it according to the Michaelis-Mention equation\n", "Km = (k1b + k2)/k1f\n", "vmax = E0*k2\n", "analytic_dPdt = vmax * np.divide( S, (S+Km) )\n", "plt.plot(S, analytic_dPdt)\n", "plt.plot( S, velocity_of_P)\n", "plt.xlabel( \"S\")\n", "plt.ylabel(\"dP/dt\")\n", "plt.legend( [\"M-M expression\",\"Simulation\"]);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Model Enzyme Kinetics with the Michaelis-Menton Equation\n", "\n", "Implement a model that uses the M-M equation" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [], "source": [ "def MM_model( t, y, params ):\n", " vmax = params[0]\n", " Km = params[1]\n", " S = y[0]\n", " P = y[1]\n", " dydt = np.zeros( (2,) )\n", " dydt[0] = -vmax * S/(S+Km)\n", " dydt[1] = vmax * S/(S+Km)\n", " return dydt" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Using the same initial conditions as above, and computing Km and vmax according to\n", "\n", "$v_{max} = E(0)\\cdot k_2$\n", "\n", "and \n", "\n", "$K_m = \\frac{k_{-1}+k_2}{k_1}$\n", "\n", "simulate the M-M model for the same time steps as the full model." ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [], "source": [ "vmax = E0*k2\n", "Km = (k1b+k2)/k1f\n", "\n", "em2 = lambda t,y: MM_model(t,y,(vmax,Km))\n", "sol2 = scipy.integrate.solve_ivp( fun=em2, t_span=(0,100), y0=(S0,P0), \n", " t_eval=np.arange(0,100,1) )" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Plot the new model's simulation results" ] }, { "cell_type": "code", "execution_count": 27, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plt.plot( sol2.t, sol2.y.T )\n", "plt.xlabel( \"Time\")\n", "plt.ylabel( \"Concentration\" )\n", "plt.legend( [\"S\",\"P\"])\n", "plt.title( \"Enzyme-catalyzed reaction\");" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now compare P from one model to the other by plotting them both" ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "P_full = sol.y[2,:]\n", "P_MM = sol2.y[1,:]\n", "plt.plot( sol.t, P_full )\n", "plt.plot( sol.t, P_MM )\n", "plt.xlabel( \"Time\")\n", "plt.ylabel( \"Concentration\" )\n", "plt.legend( [\"full model\",\"M-M model\"])\n", "plt.title( \"Product of Enzyme-catalyzed reaction\");" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Awesome, the full model and the M-M model are nearly indistinguishable. When we are modeling a process using M-M kinetics, we need two parameters, $v_{max}$ and $K_m$. Above, we saw that the two parameters depend on a larger set of parameters and the initial concentration of E. Typically, we will be assigning values directly to $v_{max}$ and $K_m$, skipping the step of determining separate parameters for forward and backward reaction rates. We should develop and intuition for how $v_{max}$ and $K_m$ affect dP/dt and P(t).\n", "\n", "We saw in the tutorial that $v_{max}$ is simply the maximum value of dP/dt.\n", "\n", "$K_m$ is often referred to as the activation threshold because it identifies the concentration of S that causes dP/dt to be at half it maximum. \n", "\n", "Make an array of S values and compute the M-M equationn for a range of values of Km. The trend is that curves with larger Km are less steep." ] }, { "cell_type": "code", "execution_count": 25, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "vmax = 1\n", "Kms = np.arange( 0.1, 10, 0.1 )\n", "fakeS = np.arange( 0, 20, 0.1 )\n", "for i in range(Kms.size):\n", " Km = Kms[i]\n", " MM = vmax * np.divide( fakeS, (fakeS+Km) )\n", " plt.plot( fakeS, MM )\n", "plt.plot( fakeS, vmax/2*np.ones(fakeS.shape));\n", "plt.xlabel( 'S')\n", "plt.ylabel( \"dPdt\")\n", "plt.title( \"Michaelis-Menton Equation with half-max velocity indicated\");" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Run the simulation with a small Km and compare it to a simulation with a large Km" ] }, { "cell_type": "code", "execution_count": 30, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "Km1 = 1\n", "Km2 = 10\n", "vmax = E0*k2\n", "\n", "em3 = lambda t,y: MM_model(t,y,(vmax,Km1))\n", "sol3 = scipy.integrate.solve_ivp( fun=em3, t_span=(0,100), y0=(S0,P0), \n", " t_eval=np.arange(0,100,1) )\n", "em4 = lambda t,y: MM_model(t,y,(vmax,Km2))\n", "sol4 = scipy.integrate.solve_ivp( fun=em4, t_span=(0,100), y0=(S0,P0), \n", " t_eval=np.arange(0,100,1) )\n", "\n", "plt.plot( sol3.t, sol3.y[1,:])\n", "plt.plot( sol3.t, sol4.y[1,:])\n", "plt.xlabel( \"Time\")\n", "plt.ylabel( \"Concentration of P\")\n", "plt.legend( ['P when Km=0.5', 'P when Km=10']);" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "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": "3.8.5" } }, "nbformat": 4, "nbformat_minor": 4 }