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January 20, 2025 04:59
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| { | |
| "cells": [ | |
| { | |
| "cell_type": "code", | |
| "execution_count": 1, | |
| "id": "a925a978", | |
| "metadata": {}, | |
| "outputs": [], | |
| "source": [ | |
| "import numpy as np\n", | |
| "from scipy.integrate import odeint\n", | |
| "import matplotlib.pyplot as plt" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "id": "f89a620f", | |
| "metadata": {}, | |
| "source": [ | |
| "Define functions. \n", | |
| "- MM_odes to integrate progress curve\n", | |
| "- MM_ts to define the characteristic timescale of the reaction, t_s" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 2, | |
| "id": "e916f49d", | |
| "metadata": {}, | |
| "outputs": [], | |
| "source": [ | |
| "def MM_odes(y,t,params):\n", | |
| " k1 = params[0]\n", | |
| " km1 = params[1]\n", | |
| " k2 = params[2]\n", | |
| " e0 = params[3]\n", | |
| " c0 = params[4]\n", | |
| " \n", | |
| " Km = (km1+k2)/k1 # Michaelis-Menton constant\n", | |
| " Ks = km1/k1 # Disassociation constant\n", | |
| " \n", | |
| " s = y[0] # Real parameters - not nondimensional!\n", | |
| " c = y[1]\n", | |
| " dsdt = k1*(-(e0+c0-c)*s+Ks*c)\n", | |
| " dcdt = k1*((e0+c0-c)*s-Km*c)\n", | |
| " \n", | |
| " return [dsdt, dcdt]\n", | |
| "\n", | |
| "def MM_ts(S0,params):\n", | |
| " k1 = params[0]\n", | |
| " km1 = params[1]\n", | |
| " k2 = params[2]\n", | |
| " E0 = params[3]\n", | |
| " Km = (km1+k2)/k1\n", | |
| " return (Km+S0)/(k2*E0)" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "id": "f9eb551c", | |
| "metadata": {}, | |
| "source": [ | |
| "Define parameters. These are within reasonable ranges. Concentration units are in M, time is in seconds" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 3, | |
| "id": "a8a3bb0b", | |
| "metadata": {}, | |
| "outputs": [], | |
| "source": [ | |
| "# set some rates for the tautomer transition:\n", | |
| "k1 = 1e5 # E + S > ES\n", | |
| "km1 = 100 # ES > E + S\n", | |
| "k2 = 1 # ES > P " | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "id": "bb66b16a", | |
| "metadata": {}, | |
| "source": [ | |
| "Calculate Km (Ks and K not used here)\n" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 4, | |
| "id": "6b8ef348", | |
| "metadata": {}, | |
| "outputs": [], | |
| "source": [ | |
| "Km = (km1+k2)/k1 #Km is about 0.001, or 1 mM" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "id": "7d95fd63", | |
| "metadata": {}, | |
| "source": [ | |
| "Set starting conditions:" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 10, | |
| "id": "8b3e6429", | |
| "metadata": {}, | |
| "outputs": [], | |
| "source": [ | |
| "E0 = 1.0e-6 # 1 µM enzyme.\n", | |
| "C0 = 0. # initially, complex conc is 0. \n", | |
| "S0 = 5.0e-3 # 10 milliMolar, approximately 5*Km " | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "id": "02e45658", | |
| "metadata": {}, | |
| "source": [ | |
| "Integrate the progress curve:" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 11, | |
| "id": "e4bacc6c", | |
| "metadata": {}, | |
| "outputs": [], | |
| "source": [ | |
| "params = [k1,km1,k2,E0,C0]\n", | |
| "y0 = [S0,C0]\n", | |
| "\n", | |
| "ts = MM_ts(S0,params)\n", | |
| "tspan = 5 # time in ts-units for simulated data/fitting\n", | |
| "Npoints = 1000\n", | |
| "time = np.linspace(0,tspan*ts,Npoints) # in seconds\n", | |
| "\n", | |
| "y, out_info1 = odeint(MM_odes,y0,time,args=(params,),full_output=1)" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "id": "ffb94b5d", | |
| "metadata": {}, | |
| "source": [ | |
| "Paper states the maximum acceleration, if S0 > Km/2, occurs at S = Km/2. Plotting this we see that it's close but not on the area of greatest curvature:" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 53, | |
| "id": "4970bc69", | |
| "metadata": {}, | |
| "outputs": [ | |
| { | |
| "data": { | |
| "text/plain": [ | |
| "<matplotlib.legend.Legend at 0x137a18500>" | |
| ] | |
| }, | |
| "execution_count": 53, | |
| "metadata": {}, | |
| "output_type": "execute_result" | |
| }, | |
| { | |
| "data": { | |
| "image/png": 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", | |
| "text/plain": [ | |
| "<Figure size 640x480 with 1 Axes>" | |
| ] | |
| }, | |
| "metadata": {}, | |
| "output_type": "display_data" | |
| } | |
| ], | |
| "source": [ | |
| "\n", | |
| "#plot substrate concentration over time:\n", | |
| "plt.plot(time, y[:,0], label='[S]')\n", | |
| "\n", | |
| "# S0 is >> Km, so the 'area of maximum acceleration' is at Km/2\n", | |
| "plt.axhline(Km/2, c='k', label='Km/2')\n", | |
| "\n", | |
| "plt.legend()" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 54, | |
| "id": "c703b06c", | |
| "metadata": {}, | |
| "outputs": [], | |
| "source": [ | |
| "from scipy.special import lambertw\n", | |
| "def MM_wfuncKmVm(t,S0,params):\n", | |
| " Km = params[0]\n", | |
| " Vmax = params[1]\n", | |
| " e0 = params[2]\n", | |
| " c0 = params[3]\n", | |
| " s = Km*lambertw(S0/Km*np.exp((S0-Vmax*t)/Km),tol=1e-12)\n", | |
| " return s\n" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 55, | |
| "id": "71438fd2", | |
| "metadata": {}, | |
| "outputs": [], | |
| "source": [ | |
| "Vmax = (E0+C0)*k2" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 56, | |
| "id": "25a874c7", | |
| "metadata": {}, | |
| "outputs": [ | |
| { | |
| "data": { | |
| "text/plain": [ | |
| "[<matplotlib.lines.Line2D at 0x132394260>]" | |
| ] | |
| }, | |
| "execution_count": 56, | |
| "metadata": {}, | |
| "output_type": "execute_result" | |
| }, | |
| { | |
| "data": { | |
| "image/png": 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", | |
| "text/plain": [ | |
| "<Figure size 640x480 with 1 Axes>" | |
| ] | |
| }, | |
| "metadata": {}, | |
| "output_type": "display_data" | |
| } | |
| ], | |
| "source": [ | |
| "golicnik = (MM_wfuncKmVm(time,S0,[Km,Vmax,E0,C0])).real\n", | |
| "plt.plot(\n", | |
| " time, golicnik\n", | |
| ")\n", | |
| "plt.plot(time, y[:,0], label='[S]')\n" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 78, | |
| "id": "7313f718", | |
| "metadata": {}, | |
| "outputs": [], | |
| "source": [ | |
| "dp = np.gradient(golicnik)\n", | |
| "d2p = np.gradient(dp)" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 88, | |
| "id": "966b81bd", | |
| "metadata": {}, | |
| "outputs": [ | |
| { | |
| "data": { | |
| "text/plain": [ | |
| "<matplotlib.lines.Line2D at 0x177673ad0>" | |
| ] | |
| }, | |
| "execution_count": 88, | |
| "metadata": {}, | |
| "output_type": "execute_result" | |
| }, | |
| { | |
| "data": { | |
| "image/png": 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", | |
| "text/plain": [ | |
| "<Figure size 1000x800 with 2 Axes>" | |
| ] | |
| }, | |
| "metadata": {}, | |
| "output_type": "display_data" | |
| } | |
| ], | |
| "source": [ | |
| "fig, ax = plt.subplots(2, 1,figsize=(10,8))\n", | |
| "ax[0].plot(time, d2p, label='Second deriv of [S]')\n", | |
| "\n", | |
| "ax[1].plot(time, y[:,0])\n", | |
| "ax[1].axhline(Km/2, c='k', label='Km/2')\n", | |
| "ax[1].axvline(time[d2p.argmax()], c='k', label='Km/2')\n" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": null, | |
| "id": "dfb01239", | |
| "metadata": {}, | |
| "outputs": [], | |
| "source": [] | |
| } | |
| ], | |
| "metadata": { | |
| "kernelspec": { | |
| "display_name": "Python 3 (ipykernel)", | |
| "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": "3.12.8" | |
| } | |
| }, | |
| "nbformat": 4, | |
| "nbformat_minor": 5 | |
| } |
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If you know the t_q, you can use this simple Km calculator, which seems to work OK even for quite noisy readouts: