{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"***Note: this is the modulatedCooperative.ipynb notebook. The\n",
"PDF version \"Modulated Cooperative Enzyme-catalysed Reactions\"\n",
"is available [here](modulatedCooperative.pdf).***"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Introduction\n",
"*\"the ordinary laws [Michaelis-Menten] are inadequate for supplying the degree of control needed for metabolism\"* (Cornish-Bowden, 2012). In fact, key metabolic enzymes display *cooperativity* which *\"display the property of responding with exceptional sensitivity to changes in metabolite concentrations\"*\n",
"(Cornish-Bowden, 2012).\n",
"\n",
"Cooperativity is discussed in the notebook [Cooperativity](Cooperativity.ipynb). Here, the cooperativity is augmented by *competitive activation and inhibition* to provide a mechanism for modulation and hence feedback control.\n",
"\n",
"This note gives a bond graph (Gawthrop and Crampin, 2014) interpretation of such modulated cooperativity and uses the iterative properties of [BondGraphTools](https://pypi.org/project/BondGraphTools/) (Cudmore et. al., 2019) to build high-order modulated cooperative systems.\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": [
"# Modulated 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": [
"## 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": {
"image/svg+xml": [
""
],
"text/plain": [
""
]
},
"execution_count": 2,
"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": 3,
"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": 3,
"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": [
"## Modulation\n",
"Competitive inhibition and activation are discussed in chapter 6 of (Cornish-Bowden, 2012)."
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [
{
"data": {
"image/svg+xml": [
""
],
"text/plain": [
""
]
},
"execution_count": 4,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"## Modulation\n",
"sbg.model('Mod_abg.svg')\n",
"import Mod_abg\n",
"disp.SVG('Mod_abg.svg')"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [
{
"data": {
"text/latex": [
"\\begin{align}\n",
"\\ch{E0 + Inh &<>[ rm ] Act + E00 }\n",
"\\end{align}\n"
],
"text/plain": [
""
]
},
"execution_count": 5,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"s = st.stoich(Mod_abg.model(),quiet=quiet)\n",
"disp.Latex(st.sprintrl(s,chemformula=True))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Two-stage cooperative enzyme-catalysed reaction (N=2) with modulation\n",
"The cooperative enzyme-catalysed reaction is modulated by the activation species (Act) and the inhibition species (Inh)."
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {},
"outputs": [
{
"data": {
"image/svg+xml": [
""
],
"text/plain": [
""
]
},
"execution_count": 6,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"## Two-stage cooperative enzyme-catalysed reaction (N=2)\n",
"sbg.model('mCoop_abg.svg',quiet=quiet)\n",
"import mCoop_abg\n",
"disp.SVG('mCoop_abg.svg')"
]
},
{
"cell_type": "code",
"execution_count": 7,
"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",
"\\ch{E0 + Inh &<>[ rm ] Act + E00 }\n",
"\\end{align}\n"
],
"text/plain": [
""
]
},
"execution_count": 7,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"s = st.stoich(mCoop_abg.model(),quiet=quiet)\n",
"sc = st.statify(s,chemostats=['A','B','Act','Inh'])\n",
"disp.Latex(st.sprintrl(s,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": 8,
"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",
" Mod = Mod_abg.model()\n",
" Coop.add(Mod)\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','E0']\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','Act','Inh']\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": 9,
"metadata": {},
"outputs": [
{
"data": {
"text/latex": [
"\\begin{align}\n",
"\\ch{Inh + E0 &<>[ rm ] Act + E00 }\\\\\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": 9,
"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": 10,
"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": 10,
"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": [
"# Simulation of 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 $K_B=10^{-6}$ (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": 11,
"metadata": {},
"outputs": [],
"source": [
"## Set up some parameters for simulation\n",
"def setParameter(s,N,e0,K_B=1e-6,modulate=True):\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",
" 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",
" ## Modulation \n",
" parameter['kappa_rm'] = 1e3\n",
" parameter['K_E00'] = 1e-1\n",
" \n",
" ## States\n",
" ## Set total enzyme to e0\n",
" X0 = np.ones(s['n_X'])\n",
" if modulate:\n",
" X0[s['spec_index']['Act']] = 100\n",
" X0[s['spec_index']['E00']] = (e0/(N+3))\n",
" for i in range(N+2):\n",
" Ei = 'E'+str(i)\n",
" X0[s['spec_index'][Ei]] = (e0/(N+3))\n",
" else:\n",
" for i in range(N+2):\n",
" Ei = 'E'+str(i)\n",
" X0[s['spec_index'][Ei]] = (e0/(N+2))\n",
" \n",
"\n",
" \n",
" return parameter,X0,K_EN,K_m"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Simulation code\n",
"The flow $v$ is a dynamical function of substrate $x_A$, activation $x_{Act}$, inhibition $x_{Inh}$ and cooperativity index $N$. An approximate steady-state is acjieved by varying one of the three concentrations slowly whilst fixing the other two. The following function does this by declaring the varying function species by the string sX, a fixed species with a number of discrete values as sX1 with values XX1 and the other species as sX2 with value X2.\n",
"N can take on a range of values.\n",
"\n",
"deriv=True gives a plot of the derivative of the flow with respect to $\\log_{10} X$."
]
},
{
"cell_type": "code",
"execution_count": 12,
"metadata": {},
"outputs": [],
"source": [
"def label(sX1,sX2,X1,X2,N):\n",
" if N<0:\n",
" return f'{sX1}={X1}, N={-N} (graphical)'\n",
" else:\n",
" return f'{sX1}={X1}, N={N}'\n",
"\n",
"def VaryX(sX='A',sX1='Act',sX2='Inh',XX1=[0.1,1,10],X2=1,NN=[2],K_B=1e-6,deriv=False):\n",
"\n",
" ## Time\n",
" t_max = int(1e4)\n",
" t = np.linspace(0,t_max,100000)\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",
" \n",
" ## Set up the chemostats: vary X\n",
" x_max = 1e2\n",
" x_min = 1e-2\n",
" chemo = '{3} + ({0}-{3})*np.heaviside(t-{1},1)*((t-{1})/{2})'.format(x_max,t_0,t_1,x_min)\n",
" X_chemo = {sX:chemo}\n",
" \n",
" for N in NN:\n",
" for X1 in XX1:\n",
" \n",
" if N<0:\n",
" ## Use graphical version\n",
" s = st.stoich(mCoop_abg.model(),quiet=quiet)\n",
" sc = st.statify(s,chemostats=['A','B','Act','Inh'])\n",
" lw = 6\n",
" ls = 'dashed'\n",
" else:\n",
" ## Use computational version \n",
" s,sc,Coop = makeCoop(N=N,quiet=quiet)\n",
" lw = 4\n",
" ls = None\n",
"\n",
" ## Non-unit parameters and states\n",
" e0 = 1 # Total enzyme\n",
" parameter,X0,K_EN,K_m = setParameter(s,abs(N),e0,K_B=K_B)\n",
" X0[s['spec_index'][sX1]] = X1\n",
" X0[s['spec_index'][sX2]] = X2\n",
" dat = st.sim(s,sc=sc,t=t,parameter=parameter,X0=X0,X_chemo=X_chemo,quiet=quiet)\n",
" dX = s['N']@(dat['V'].T)\n",
" dX_B = dX[s['spec_index']['B'],:]\n",
" V = dX_B\n",
" X = dat['X'][:,s['spec_index'][sX]]\n",
" \n",
" if deriv:\n",
" slope = np.gradient(V[-i_1:],np.log10(X[-i_1:]))\n",
" plt.semilogx(X[-i_1:],slope,lw=lw,label=label(sX1,sX2,X1,X2,N),linestyle=ls)\n",
" ylabel = '$dv/d \\log_{10}{x}$'\n",
" \n",
" else:\n",
" plt.semilogx(X[-i_1:],V[-i_1:],lw=lw,label=label(sX1,sX2,X1,X2,N),linestyle=ls)\n",
" ylabel = '$v$'\n",
" \n",
"\n",
" \n",
" plt.xlabel('$x_{'+sX+'}$')\n",
" plt.ylabel(ylabel)\n",
" plt.legend()\n",
" plt.grid()\n",
" #plt.title('N = '+str(N))\n",
" plt.show()\n",
" "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Vary the substrate concentration.\n",
"\n",
" The substrate concentration $x_A$ is varied for two values of activation $x_{Act}$ and two values of $N$.\n",
" The derivative is also plotted."
]
},
{
"cell_type": "code",
"execution_count": 13,
"metadata": {
"scrolled": false
},
"outputs": [
{
"data": {
"image/png": 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\n",
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