{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "***Note: this is the Cooperative.ipynb notebook. The\n", "PDF version \"Cooperative Enzyme-catalysed Reactions\"\n", "is available [here](Cooperative.pdf).***" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Introduction\n", "\"For many enzymes, the reaction velocity is not a simple hyperbolic curve, as predicted\n", "by the Michaelis–Menten model, but often has a sigmoidal character. This can result from cooperative effects, in which the enzyme can bind more than one substrate\n", "molecule but the binding of one substrate molecule affects the binding of subsequent\n", "ones\" (Keener and Sneyd, 2009), Section 1.4.4.\n", "\n", "This note gives a bond graph (Gawthrop and Crampin, 2014) interpretation of such cooperativity and uses the iterative properties of [BondGraphTools](https://pypi.org/project/BondGraphTools/) (Cudmore et. al., 2019) to build high-order cooperative systems. These systems are simulated to give steady-state behavior as the order of cooperativity increases.\n", "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Import some python code\n", "The bond graph analysis uses a number of Python modules:" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "## Some useful imports\n", "\n", "import BondGraphTools as bgt\n", "import numpy as np\n", "import sympy as sp\n", "import matplotlib.pyplot as plt\n", "import IPython.display as disp\n", "\n", "## Stoichiometric analysis\n", "import stoich as st\n", "\n", "## SVG bg representation conversion\n", "import svgBondGraph as sbg\n", "\n", "## Modular bond graphs\n", "import modularBondGraph as mbg\n", "\n", "## Data structure copy\n", "import copy\n", "\n", "## Set quiet=False for verbose output\n", "quiet = True" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Enzyme-catalysed reaction\n", "The basic enzyme-catalysed reaction is given in this section. It is the basic building block of cooperative enzyme-catalysed reactions\n", "More details are given by (Gawthrop and Crampin, 2014).\n" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "'0.3.7'" ] }, "execution_count": 2, "metadata": {}, "output_type": "execute_result" } ], "source": [ "bgt.version" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "data": { "image/svg+xml": [ "\n", "\n", "\n", "\n", "Re:r1\n", "\n", "\n", "Re:r2\n", "\n", "Ce:A\n", "\n", "1\n", "\n", "0\n", "\n", "Ce:E\n", "\n", "0\n", "\n", "0\n", "\n", "Ce:C\n", "\n", "Ce:B\n", "\n", "0\n", "\n", "1\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "" ], "text/plain": [ "" ] }, "execution_count": 3, "metadata": {}, "output_type": "execute_result" } ], "source": [ "## Enzyme-catalysed reaction\n", "sbg.model('RE_abg.svg')\n", "import RE_abg\n", "disp.SVG('RE_abg.svg')" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "data": { "text/latex": [ "\\begin{align}\n", "\\ch{A + E &<>[ r1 ] C }\\\\\n", "\\ch{C &<>[ r2 ] B + E }\n", "\\end{align}\n" ], "text/plain": [ "" ] }, "execution_count": 4, "metadata": {}, "output_type": "execute_result" } ], "source": [ "s = st.stoich(RE_abg.model(),quiet=quiet)\n", "disp.Latex(st.sprintrl(s,chemformula=True))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Cooperative enzyme-catalysed reaction\n", "\n", "(Keener and Sneyd, 2009), Section 1.4.4, discusses cooperativity. This section gives a bond graph interpretation. This is done in two ways:\n", "\n", "1. As a graphical representation of a two-stage cooperative enzyme-catalysed reaction.\n", "2. As a generic representation of an N-stage cooperative enzyme-catalysed reaction using [bond-graph tools](https://pypi.org/project/BondGraphTools/)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Two-stage cooperative enzyme-catalysed reaction (N=2) \n" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "data": { "image/svg+xml": [ "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "0\n", "\n", "1\n", "\n", "0\n", "\n", "1\n", "\n", "0\n", "\n", "0\n", "\n", "0\n", "\n", "1\n", "\n", "0\n", "\n", "1\n", "\n", "0\n", "\n", "0\n", "\n", "0\n", "\n", "1\n", "\n", "0\n", "\n", "1\n", "\n", "0\n", "\n", "0\n", "\n", "Ce:A\n", "\n", "Ce:B\n", "\n", "Ce:E0\n", "\n", "Re:r01\n", "\n", "Re:r02\n", "\n", "Ce:E1\n", "\n", "Re:r11\n", "\n", "Ce:E2\n", "\n", "Re:r21\n", "\n", "Re:r22\n", "\n", "Ce:E3\n", "\n", "Re:r12\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "" ], "text/plain": [ "" ] }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" } ], "source": [ "## Two-stage cooperative enzyme-catalysed reaction (N=2)\n", "sbg.model('Coop_abg.svg',quiet=quiet)\n", "import Coop_abg\n", "disp.SVG('Coop_abg.svg')" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "data": { "text/latex": [ "\\begin{align}\n", "\\ch{A + E0 &<>[ r01 ] E1 }\\\\\n", "\\ch{E1 &<>[ r02 ] B + E0 }\\\\\n", "\\ch{A + E1 &<>[ r11 ] E2 }\\\\\n", "\\ch{E2 &<>[ r12 ] B + E1 }\\\\\n", "\\ch{A + E2 &<>[ r21 ] E3 }\\\\\n", "\\ch{E3 &<>[ r22 ] B + E2 }\n", "\\end{align}\n" ], "text/plain": [ "" ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" } ], "source": [ "ss = st.stoich(Coop_abg.model(),quiet=quiet)\n", "ssc = st.statify(ss,chemostats=['A','B'])\n", "disp.Latex(st.sprintrl(ss,chemformula=True))\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Create cooperative enzyme-catalysed reaction of any degree N\n", "The following code builds an N-stage cooperative enzyme-catalysed reaction using [bond-graph tools](https://pypi.org/project/BondGraphTools/).\n", "\n", "1. N+1 instances of the basic enzyme-catalysed reaction are created and the enzyme and complex renamed.\n", "2. The substrate A, product B and enzymes E1-EN are unified." ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [], "source": [ "## Create cooperative enzyme-catalysed reaction of any degree N\n", "## Optionally append a simple reaction\n", "## Optionally use feedback inhibition\n", "def makeCoop(N=3,quiet=True):\n", " Coop = bgt.new(name='Coop')\n", " for i in range(N+1):\n", " RE = RE_abg.model()\n", " RE.name = 'RE'+str(i)\n", " mbg.rename(RE,{\n", " 'E':'E'+str(i), \n", " 'C':'E'+str(i+1),\n", " 'r1':'r'+str(i)+'1',\n", " 'r2':'r'+str(i)+'2'\n", " },\n", " quiet=quiet)\n", " Coop.add(RE)\n", "\n", " ## Unify common components\n", " unified = ['A','B']\n", " for i in range(N): \n", " Ei = 'E'+str(i+1)\n", " unified.append(Ei)\n", " print('unified =',unified)\n", " mbg.unify(Coop,unified,quiet=quiet)\n", "\n", " \n", " ## Stoichiometry\n", " chemostats = ['A','B']\n", " s = st.stoich(Coop,quiet=quiet)\n", " sc = st.statify(s,chemostats=chemostats)\n", " if not quiet:\n", " print(st.sprint(sc,'species'))\n", " print(st.sprint(sc,'reaction'))\n", " return s,sc,Coop" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Generate equations for $N=2$\n", "Note that these equations are identical to those of the explicit bondgraph." ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "unified = ['A', 'B', 'E1', 'E2']\n" ] }, { "data": { "text/latex": [ "\\begin{align}\n", "\\ch{E0 + A &<>[ r01 ] E1 }\\\\\n", "\\ch{E1 &<>[ r02 ] E0 + B }\\\\\n", "\\ch{A + E1 &<>[ r11 ] E2 }\\\\\n", "\\ch{E2 &<>[ r12 ] B + E1 }\\\\\n", "\\ch{A + E2 &<>[ r21 ] E3 }\\\\\n", "\\ch{E3 &<>[ r22 ] B + E2 }\n", "\\end{align}\n" ], "text/plain": [ "" ] }, "execution_count": 8, "metadata": {}, "output_type": "execute_result" } ], "source": [ "### Generate equations for N=2\n", "s,sc,Coop = makeCoop(N=2,quiet=quiet)\n", "disp.Latex(st.sprintrl(s,chemformula=True))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Generate pathway equations for $N=2$\n", "Pathways are generated using the approach of Gawthrop and Crampin (2014)." ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "3 pathways\n", "0: + r01 + r02\n", "1: + r11 + r12\n", "2: + r21 + r22\n", "\n" ] }, { "data": { "text/latex": [ "\\begin{align}\n", "A &\\Leftrightarrow B \\\\\n", "A &\\Leftrightarrow B \\\\\n", "A &\\Leftrightarrow B \n", "\\end{align}\n" ], "text/plain": [ "" ] }, "execution_count": 9, "metadata": {}, "output_type": "execute_result" } ], "source": [ "sp = st.path(s,sc)\n", "print(st.sprintp(sc))\n", "disp.Latex(st.sprintrl(sp))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Steady-state properties\n", "\n", "The steady state properties are investigated using dynamic simulation where slowly varing exogenous quantities are used to induce quasi-steady-state behaviour. In each case, the variable is at a constant value to start with followed by a slowly increasing ramp. The response after the initial reponse is plotted to remove artefacts due to the initial transient.\n", "\n", "All parameters are unity except for $K_B=0.01$ (to approximate an irreversible reaction) and initial states are chosen so that the total enzyme is $e_0=1$." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Set up some parameters for simulation" ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [], "source": [ "## Set up some parameters for simulation\n", "def setParameter(s,N,e0):\n", " ## Set up the non-unit parameters and states\n", " \n", " K_E0 = 1\n", " K_EN = 1/K_E0\n", " K_m = K_EN/K_E0\n", " parameter = {}\n", "\n", " ## Set product constant to a small value\n", " ## to make the ECR approximately irreversible\n", " K_B = 0.01\n", " parameter['K_B'] = K_B\n", " \n", " ## Set up enzyme parameters and reaction constants\n", " parameter['K_E0'] = K_E0\n", " parameter['K_E'+str(N+1)] = K_EN\n", " \n", " ## States\n", " ## Set total enzyme to e0\n", " X0 = np.ones(s['n_X'])\n", " for i in range(N+2):\n", " Ei = 'E'+str(i)\n", " X0[s['spec_index'][Ei]] = (e0/(N+2)) \n", " \n", " return parameter,X0,K_EN,K_m" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [], "source": [ "## Compute the total enzyme\n", "def totalE(N,dat,Feedback=False):\n", " E_spec = []\n", " for i in range(N+2):\n", " Ei = 'E'+str(i)\n", " E_spec.append(Ei)\n", " \n", " for spec in E_spec:\n", " x = copy.copy(dat['X'][:,s['spec_index'][spec]])\n", " if spec is E_spec[0]:\n", " X = x\n", " else:\n", " X += x\n", " \n", " return X\n", " " ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [], "source": [ "## Compute the total flow\n", "def totalFlow(s,N,dat):\n", " for i in range(N+1):\n", " r = 'r'+str(i)+'2'\n", " Vi = copy.copy(dat['V'][:,s['reac_index'][r]])\n", " if i is 0:\n", " V = Vi\n", " else:\n", " V += Vi\n", " return V" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Vary substrate concentration $x_A$" ] }, { "cell_type": "code", "execution_count": 27, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "unified = ['A', 'B']\n", "unified = ['A', 'B', 'E1']\n", "unified = ['A', 'B', 'E1', 'E2', 'E3', 'E4', 'E5']\n" ] }, { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "## Simulation\n", "## Vary x_A\n", "\n", "##Time\n", "quiet = True\n", "t_max = int(1e4)\n", "t = np.linspace(0,t_max,10000)\n", "t_0 = 100\n", "t_1 = t_max-t_0\n", "i_max = len(t)\n", "i_0 = int(i_max*t_0/t_max)\n", "i_1 = i_max-i_0\n", "\n", "NN = [0,1,5]\n", "for N in NN:\n", " ## Create system stoichiometry\n", " s,sc,Coop = makeCoop(N=N,quiet=quiet)\n", " \n", " ## Non-unit parameters and states\n", " e0 = 1 # Total enzyme\n", " parameter,X0,K_EN,K_m = setParameter(s,N,e0)\n", " K_B = parameter['K_B']\n", "\n", " ## Chemostats: vary x_A\n", " x_max = 100\n", " x_A_max = 10\n", " x_min = K_B\n", " \n", " A_chemo = '{3} + ({0}-{3})*np.heaviside(t-{1},1)*((t-{1})/{2})'.format(x_max,t_0,t_1,x_min)\n", " X_chemo = {'A':A_chemo}\n", " \n", " ## Simulate\n", " dat = st.sim(s,sc=sc,t=t,parameter=parameter,X0=X0,X_chemo=X_chemo,quiet=quiet)\n", " V = totalFlow(s,N,dat)\n", " x_A = dat['X'][:,s['spec_index']['A']]\n", " \n", " ## Compute approx ECR flow (assumes K_B is small)\n", " V_ECR = e0*(x_A-K_B)/((2*K_m) + x_A)\n", " \n", " if N is NN[0]:\n", " VV = V\n", " VV_ECR = V_ECR\n", " else:\n", " VV = np.vstack((VV,V))\n", "\n", "\n", "## Plot flow v. x_A \n", "grey = '0.8'\n", "plt.clf()\n", "plt.plot(x_A,VV_ECR,color=grey,lw=10)\n", "if len(NN) is 1:\n", " plt.plot(x_A[-i_1:],VV[-i_1:])\n", "else:\n", " plt.plot(x_A[-i_1:],VV[:,-i_1:].T) \n", "plt.grid()\n", "plt.ylim((0,e0))\n", "plt.xlim((0,x_A_max))\n", "plt.legend(['N=0 (theory)']+['N='+str(i) for i in NN])\n", "plt.xlabel('$x_A$')\n", "plt.ylabel('$v$')\n", "plt.show()\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The effect of cooperativity is to give an approximation to a linear rise in $v$ as $x_A$ increases with a cut off at $v=e0=1$." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Replot against $\\phi_A$\n", "It is common to plot v against the logarithm of $x_A$. Here we use the potential $\\phi_A = \\ln K_A x_A$." ] }, { "cell_type": "code", "execution_count": 28, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "phi_A = dat['phi'][:,s['spec_index']['A']]\n", "plt.clf()\n", "plt.plot(phi_A,VV_ECR,color=grey,lw=10)\n", "if len(NN) is 1:\n", " plt.plot(phi_A[-i_1:],VV[-i_1:])\n", "else:\n", " plt.plot(phi_A[-i_1:],VV[:,-i_1:].T) \n", "plt.grid()\n", "plt.ylim((0,e0))\n", "#plt.xlim((0,x_max))\n", "plt.legend(['N=0 (theory)']+['N='+str(i) for i in NN])\n", "plt.xlabel('$\\phi_A$')\n", "plt.ylabel('$v$')\n", "plt.show()\n", "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## A closer look\n", "The following graphs look more closely at the behaviour of the system for N=5. \n", "\n", "1. The first graph shows the $N+1=6$ enzyme/complex states plotted against $x_A$. These states form a conserved moiety and the sum is $e_0$.\n", "2. The second graph shows the $N=5$ reaction flows plotted against $x_A$. In this particular case, $K_B\\approx0$ and so the flow though reaction $ri2$ is $v_i \\approx \\kappa_{ri2} K_{Ei+1} x_{Ei+1} = x_{Ei+1}$." ] }, { "cell_type": "code", "execution_count": 14, "metadata": { "scrolled": true }, "outputs": [ { "data": { "image/png": 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\n", 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\n", 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