{
"cells": [
{
"cell_type": "code",
"execution_count": 2,
"id": "8cbcb4cc-b643-4f0e-9d49-e4096ab89477",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Matplotlib backend set to: \"module://ipympl.backend_nbagg\"\n",
"Matplotlib interface loaded (pysces.plt.m)\n",
"Continuation routines available\n",
"NLEQ2 routines available\n",
"SBML support available\n",
"You are using NumPy (2.4.2) with SciPy (1.17.0)\n",
"Assimulo CVode available\n",
"RateChar is available\n",
"Parallel scanner is available\n",
"\n",
"PySCeS environment\n",
"******************\n",
"pysces.model_dir = C:\\Users\\27646\\Pysces\\psc\n",
"pysces.output_dir = C:\\Users\\27646\\Pysces\n",
"\n",
"\n",
"***********************************************************************\n",
"* Welcome to PySCeS (1.2.3) - Python Simulator for Cellular Systems *\n",
"* http://pysces.sourceforge.net *\n",
"* Copyright(C) B.G. Olivier, J.M. Rohwer, J.-H.S. Hofmeyr, 2004-2025 *\n",
"* Triple-J Group for Molecular Cell Physiology *\n",
"* Stellenbosch University, ZA and VU University Amsterdam, NL *\n",
"* PySCeS is distributed under the PySCeS (BSD style) licence, see *\n",
"* LICENCE.txt (supplied with this release) for details *\n",
"* Please cite PySCeS with: doi:10.1093/bioinformatics/bti046 *\n",
"***********************************************************************\n"
]
}
],
"source": [
"%matplotlib widget\n",
"import numpy as np\n",
"import scipy as sp\n",
"import pandas as pd\n",
"import scipy.optimize\n",
"import pysces\n",
"from matplotlib import pyplot as plt\n",
"import os\n",
"import copy\n",
"from lmfit import Model\n",
"backupdir = os.getcwd()\n",
"import scipy.stats\n",
"from numdifftools import Derivative"
]
},
{
"cell_type": "markdown",
"id": "89f001b8-01ed-41d3-ad9b-7683f1220b56",
"metadata": {},
"source": [
"## Question 1"
]
},
{
"cell_type": "code",
"execution_count": 17,
"id": "c128095e-b89c-4eb4-b45e-41bb817ffa3b",
"metadata": {},
"outputs": [],
"source": [
"dfA2B24 = pd.read_csv('A2B24.csv', names=['Time', 'NADH'])\n",
"dfA0B0 = pd.read_csv('A0B0.csv', names=['Time', 'NADH'])\n",
"dfA1B24 = pd.read_csv('A1B24.csv', names=['Time', 'NADH'])\n",
"dfA8B15 = pd.read_csv('A8B1.5.csv', names=['Time', 'NADH'])\n",
"dfA05B24 = pd.read_csv('A0.5B24.csv', names=['Time', 'NADH'])\n",
"dfA8B6 = pd.read_csv('A8B6.csv', names=['Time', 'NADH'])\n",
"dfA4B24 = pd.read_csv('A4B24.csv', names=['Time', 'NADH'])\n",
"dfA8B3 = pd.read_csv('A8B3.csv', names=['Time', 'NADH'])\n",
"dfA8B24 = pd.read_csv('A8B24.csv', names=['Time', 'NADH'])\n",
"dfA8B12 = pd.read_csv('A8B12.csv', names=['Time', 'NADH'])"
]
},
{
"cell_type": "code",
"execution_count": 18,
"id": "f76f2bd4-70f2-4c1d-96de-e89e6ab7d43b",
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"\n",
"\n",
"
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" \n",
" \n",
" | \n",
" Time | \n",
" NADH | \n",
"
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" \n",
" \n",
" \n",
" | 0 | \n",
" 0.00 | \n",
" -0.001955 | \n",
"
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" \n",
" | 1 | \n",
" 0.01 | \n",
" 0.006906 | \n",
"
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" \n",
" | 2 | \n",
" 0.02 | \n",
" 0.013118 | \n",
"
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" \n",
" | 3 | \n",
" 0.03 | \n",
" 0.017290 | \n",
"
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" \n",
" | 4 | \n",
" 0.04 | \n",
" 0.018607 | \n",
"
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" | 5 | \n",
" 0.05 | \n",
" 0.024646 | \n",
"
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" | 6 | \n",
" 0.06 | \n",
" 0.034201 | \n",
"
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" | 7 | \n",
" 0.07 | \n",
" 0.039882 | \n",
"
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" \n",
" | 8 | \n",
" 0.08 | \n",
" 0.046188 | \n",
"
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" \n",
" | 9 | \n",
" 0.09 | \n",
" 0.052640 | \n",
"
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" \n",
" | 10 | \n",
" 0.10 | \n",
" 0.055883 | \n",
"
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" \n",
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"
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" Figure\n",
"
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" Figure\n",
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" rate | \n",
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" \n",
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" \n",
" | 0 | \n",
" 0.0 | \n",
" 0.0 | \n",
" 0.004955 | \n",
"
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" \n",
" | 1 | \n",
" 0.5 | \n",
" 24.0 | \n",
" 0.241187 | \n",
"
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" | 2 | \n",
" 1.0 | \n",
" 24.0 | \n",
" 0.352630 | \n",
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" 2.0 | \n",
" 24.0 | \n",
" 0.574650 | \n",
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" \n",
" | 4 | \n",
" 4.0 | \n",
" 24.0 | \n",
" 0.732286 | \n",
"
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" \n",
" | 5 | \n",
" 8.0 | \n",
" 1.5 | \n",
" 0.254221 | \n",
"
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" \n",
" | 6 | \n",
" 8.0 | \n",
" 3.0 | \n",
" 0.367954 | \n",
"
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" | 7 | \n",
" 8.0 | \n",
" 6.0 | \n",
" 0.556409 | \n",
"
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" | 8 | \n",
" 8.0 | \n",
" 12.0 | \n",
" 0.701204 | \n",
"
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" 8.0 | \n",
" 24.0 | \n",
" 0.825079 | \n",
"
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" \n",
"
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"
Parameters| name | value | initial value | min | max | vary |
|---|
| Vf | 1.00000000 | 1.0 | -inf | inf | True |
| Ka | 1.00000000 | 1.0 | -inf | inf | True |
| Kb | 1.00000000 | 1.0 | -inf | inf | True |
"
],
"text/plain": [
"Parameters([('Vf', ), ('Ka', ), ('Kb', )])"
]
},
"execution_count": 59,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"mymod = Model(v, independent_vars=['A', 'B'])\n",
"mypar = mymod.make_params(Vf=1, Ka=1,Kb=1)\n",
"mypar"
]
},
{
"cell_type": "markdown",
"id": "8078d042-6d44-4438-98ab-6635cc05cad5",
"metadata": {},
"source": [
"Ka = mM\n",
"Kb = mM\n",
"Vf = mM.s^-1"
]
},
{
"cell_type": "code",
"execution_count": 61,
"id": "ab473c15-3507-4282-9594-70ce200d2c91",
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"Fit Result
Model: Model(v)
Fit Statistics| fitting method | leastsq |
| # function evals | 25 |
| # data points | 10 |
| # variables | 3 |
| chi-square | 0.00248796 |
| reduced chi-square | 3.5542e-04 |
| Akaike info crit. | -76.9887719 |
| Bayesian info crit. | -76.0810166 |
| R-squared | 0.99588985 |
Parameters| name | value | standard error | relative error | initial value | min | max | vary |
|---|
| Vf | 1.20594964 | 0.04570438 | (3.79%) | 1.0 | -inf | inf | True |
| Ka | 1.61269234 | 0.13567971 | (8.41%) | 1.0 | -inf | inf | True |
| Kb | 4.89874506 | 0.41256005 | (8.42%) | 1.0 | -inf | inf | True |
Correlations (unreported values are < 0.100)| Parameter1 | Parameter 2 | Correlation |
|---|
| Vf | Kb | +0.7926 |
| Vf | Ka | +0.7903 |
| Ka | Kb | +0.3778 |
"
],
"text/plain": [
""
]
},
"execution_count": 61,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"myfit = mymod.fit(dfabrate.rate, mypar, A=dfabrate.A, B=dfabrate.B)\n",
"myfit"
]
},
{
"cell_type": "markdown",
"id": "d736ad77-0b00-4bad-9a22-6236b050b499",
"metadata": {},
"source": [
"## Question 5"
]
},
{
"cell_type": "code",
"execution_count": 67,
"id": "7d77bdce-7fa4-4a79-bf55-020fff1509a0",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"[0.24118661 0.35263044 0.57465007 0.73228566]\n"
]
},
{
"data": {
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