{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Optimal resource allocation in microbial growth\n",
"Sacha PSALMON, Baptiste SCHALL, Enzo ISNARD and Guillaume GROS\n",
"\n",
"![](\"maintenance.png\")
\n",
"\n",
"[Thumbnail](maintenance.png)\n",
"\n",
"Microorganisms must assign the resources available in the environment to different cellular functions. In nature, it is assumed that bacteria have evolved in a way that their resource allocation strategies maximize their biomass. Consider the simple resource allocation mathematical model\n",
"\n",
"$$ \\begin{array}{rcl}\n",
"\\dot{p} &=& E_m m - (p+1) v_R(p,r), \\\\\n",
"\\dot{r} &=& (\\alpha r_{max}-r) v_R(p,r), \\\\\n",
"\\dot{m} &=& ((1-\\alpha) r_{max}-m) v_R(p,r),\n",
"\\end{array} $$\n",
"\n",
"where $p$, $r$, $m$ and $q$ are the mass fractions of: precursor metabolites, the gene expression machinery (ribosomes, RNA polymerase...), the metabolic machinery (enzymes, transporters...) and the housekeeping machinery respectively. The microbial growth rate is defined as $v_R(p,r) = \\frac{p(r-r_{min})}{K+p}$. Constants $E_M$, $r_{max}$, $r_{min}$ and $K$ are positive. Maximizing the bacterial biomass is equivalent to maximizing the integral of the growth rate over a fixed time window $[0,T]$. Thus, the cost function of the optimal control problem can be written as\n",
"\n",
"$$J(\\alpha) = \\int_0^T v_R(p,r) \\, \\mathrm{d}t \\to \\max $$\n",
"\n",
"with the resource allocation parameter (i.e. the control) constrained to $\\alpha(t) \\in [0,1]$."
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"\u001b[37m// +++DRAFT+++ This class implements the OCP functions\u001b[39;49;00m\n",
"\u001b[37m// It derives from the generic class bocop3OCPBase\u001b[39;49;00m\n",
"\u001b[37m// OCP functions are defined with templates since they will be called\u001b[39;49;00m\n",
"\u001b[37m// from both the NLP solver (double arguments) and AD tool (ad_double arguments)\u001b[39;49;00m\n",
"\u001b[37m//#pragma once\u001b[39;49;00m\n",
"\n",
"\u001b[36m#\u001b[39;49;00m\u001b[36minclude\u001b[39;49;00m \u001b[37m\u001b[39;49;00m\u001b[36m\u001b[39;49;00m\n",
"\u001b[37m// ///////////////////////////////////////////////////////////////////\u001b[39;49;00m\n",
"\n",
"\n",
"\u001b[34mtemplate\u001b[39;49;00m <\u001b[34mtypename\u001b[39;49;00m \u001b[04m\u001b[32mVariable\u001b[39;49;00m>\n",
"\u001b[36mvoid\u001b[39;49;00m OCP::finalCost(\u001b[36mdouble\u001b[39;49;00m initial_time, \u001b[36mdouble\u001b[39;49;00m final_time, \u001b[34mconst\u001b[39;49;00m Variable *initial_state, \u001b[34mconst\u001b[39;49;00m Variable *final_state, \u001b[34mconst\u001b[39;49;00m Variable *parameters, \u001b[34mconst\u001b[39;49;00m \u001b[36mdouble\u001b[39;49;00m *constants, Variable &final_cost)\n",
"{\n",
" \u001b[37m// maximize the volume of the bacteria\u001b[39;49;00m\n",
" final_cost = -final_state[\u001b[34m3\u001b[39;49;00m];\n",
"}\n",
"\n",
"\n",
"\u001b[34mtemplate\u001b[39;49;00m <\u001b[34mtypename\u001b[39;49;00m \u001b[04m\u001b[32mVariable\u001b[39;49;00m>\n",
"\u001b[36mvoid\u001b[39;49;00m OCP::dynamics(\u001b[36mdouble\u001b[39;49;00m time, \u001b[34mconst\u001b[39;49;00m Variable *state, \u001b[34mconst\u001b[39;49;00m Variable *control, \u001b[34mconst\u001b[39;49;00m Variable *parameters, \u001b[34mconst\u001b[39;49;00m \u001b[36mdouble\u001b[39;49;00m *constants, Variable *state_dynamics)\n",
"{\n",
" \n",
" Variable p = state[\u001b[34m0\u001b[39;49;00m];\n",
" Variable r = state[\u001b[34m1\u001b[39;49;00m];\n",
" Variable m = state[\u001b[34m2\u001b[39;49;00m];\n",
" Variable V = state[\u001b[34m3\u001b[39;49;00m];\n",
" Variable u = control[\u001b[34m0\u001b[39;49;00m];\n",
" \n",
" \n",
" \n",
" \u001b[36mdouble\u001b[39;49;00m Em = constants[\u001b[34m0\u001b[39;49;00m];\n",
" \u001b[36mdouble\u001b[39;49;00m K = constants[\u001b[34m1\u001b[39;49;00m];\n",
" \u001b[36mdouble\u001b[39;49;00m rmax = constants[\u001b[34m2\u001b[39;49;00m];\n",
" \u001b[36mdouble\u001b[39;49;00m rmin = constants[\u001b[34m3\u001b[39;49;00m];\n",
" \n",
" Variable vR = (r-rmin)*p/(K+p);\n",
" \n",
" state_dynamics[\u001b[34m0\u001b[39;49;00m] = Em*m - (p+\u001b[34m1\u001b[39;49;00m)*vR;\n",
" state_dynamics[\u001b[34m1\u001b[39;49;00m] = (u*rmax-r)*vR;\n",
" state_dynamics[\u001b[34m2\u001b[39;49;00m] = ((\u001b[34m1\u001b[39;49;00m-u)*rmax-m)*vR;\n",
" state_dynamics[\u001b[34m3\u001b[39;49;00m] = vR*V;\n",
" \n",
"}\n",
"\n",
"\u001b[34mtemplate\u001b[39;49;00m <\u001b[34mtypename\u001b[39;49;00m \u001b[04m\u001b[32mVariable\u001b[39;49;00m>\n",
"\u001b[36mvoid\u001b[39;49;00m OCP::boundaryConditions(\u001b[36mdouble\u001b[39;49;00m initial_time, \u001b[36mdouble\u001b[39;49;00m final_time, \u001b[34mconst\u001b[39;49;00m Variable *initial_state, \u001b[34mconst\u001b[39;49;00m Variable *final_state, \u001b[34mconst\u001b[39;49;00m Variable *parameters, \u001b[34mconst\u001b[39;49;00m \u001b[36mdouble\u001b[39;49;00m *constants, Variable *boundary_conditions)\n",
"{\n",
" boundary_conditions[\u001b[34m0\u001b[39;49;00m] = initial_state[\u001b[34m0\u001b[39;49;00m];\n",
" boundary_conditions[\u001b[34m1\u001b[39;49;00m] = initial_state[\u001b[34m1\u001b[39;49;00m];\n",
" boundary_conditions[\u001b[34m2\u001b[39;49;00m] = initial_state[\u001b[34m2\u001b[39;49;00m];\n",
" boundary_conditions[\u001b[34m3\u001b[39;49;00m] = initial_state[\u001b[34m3\u001b[39;49;00m];\n",
"}\n",
"\n",
"\u001b[34mtemplate\u001b[39;49;00m <\u001b[34mtypename\u001b[39;49;00m \u001b[04m\u001b[32mVariable\u001b[39;49;00m>\n",
"\u001b[36mvoid\u001b[39;49;00m OCP::pathConstraints(\u001b[36mdouble\u001b[39;49;00m time, \u001b[34mconst\u001b[39;49;00m Variable *state, \u001b[34mconst\u001b[39;49;00m Variable *control, \u001b[34mconst\u001b[39;49;00m Variable *parameters, \u001b[34mconst\u001b[39;49;00m \u001b[36mdouble\u001b[39;49;00m *constants, Variable *path_constraints)\n",
"{}\n",
"\n",
"\u001b[36mvoid\u001b[39;49;00m OCP::preProcessing()\n",
"{}\n",
"\n",
"\u001b[37m// ///////////////////////////////////////////////////////////////////\u001b[39;49;00m\n",
"\u001b[37m// explicit template instanciation for template functions, with double and double_ad \u001b[39;49;00m\n",
"\u001b[37m// +++ could be in an included separate file ? \u001b[39;49;00m\n",
"\u001b[37m// but needs to be done for aux functions too ? APPARENTLY NOT !\u001b[39;49;00m\n",
"\u001b[34mtemplate\u001b[39;49;00m \u001b[36mvoid\u001b[39;49;00m OCP::finalCost<\u001b[36mdouble\u001b[39;49;00m>(\u001b[36mdouble\u001b[39;49;00m initial_time, \u001b[36mdouble\u001b[39;49;00m final_time, \u001b[34mconst\u001b[39;49;00m \u001b[36mdouble\u001b[39;49;00m *initial_state, \u001b[34mconst\u001b[39;49;00m \u001b[36mdouble\u001b[39;49;00m *final_state, \u001b[34mconst\u001b[39;49;00m \u001b[36mdouble\u001b[39;49;00m *parameters, \u001b[34mconst\u001b[39;49;00m \u001b[36mdouble\u001b[39;49;00m *constants, \u001b[36mdouble\u001b[39;49;00m &final_cost);\n",
"\u001b[34mtemplate\u001b[39;49;00m \u001b[36mvoid\u001b[39;49;00m OCP::dynamics<\u001b[36mdouble\u001b[39;49;00m>(\u001b[36mdouble\u001b[39;49;00m time, \u001b[34mconst\u001b[39;49;00m \u001b[36mdouble\u001b[39;49;00m *state, \u001b[34mconst\u001b[39;49;00m \u001b[36mdouble\u001b[39;49;00m *control, \u001b[34mconst\u001b[39;49;00m \u001b[36mdouble\u001b[39;49;00m *parameters, \u001b[34mconst\u001b[39;49;00m \u001b[36mdouble\u001b[39;49;00m *constants, \u001b[36mdouble\u001b[39;49;00m *state_dynamics);\n",
"\u001b[34mtemplate\u001b[39;49;00m \u001b[36mvoid\u001b[39;49;00m OCP::boundaryConditions<\u001b[36mdouble\u001b[39;49;00m>(\u001b[36mdouble\u001b[39;49;00m initial_time, \u001b[36mdouble\u001b[39;49;00m final_time, \u001b[34mconst\u001b[39;49;00m \u001b[36mdouble\u001b[39;49;00m *initial_state, \u001b[34mconst\u001b[39;49;00m \u001b[36mdouble\u001b[39;49;00m *final_state, \u001b[34mconst\u001b[39;49;00m \u001b[36mdouble\u001b[39;49;00m *parameters, \u001b[34mconst\u001b[39;49;00m \u001b[36mdouble\u001b[39;49;00m *constants, \u001b[36mdouble\u001b[39;49;00m *boundary_conditions);\n",
"\u001b[34mtemplate\u001b[39;49;00m \u001b[36mvoid\u001b[39;49;00m OCP::pathConstraints<\u001b[36mdouble\u001b[39;49;00m>(\u001b[36mdouble\u001b[39;49;00m time, \u001b[34mconst\u001b[39;49;00m \u001b[36mdouble\u001b[39;49;00m *state, \u001b[34mconst\u001b[39;49;00m \u001b[36mdouble\u001b[39;49;00m *control, \u001b[34mconst\u001b[39;49;00m \u001b[36mdouble\u001b[39;49;00m *parameters, \u001b[34mconst\u001b[39;49;00m \u001b[36mdouble\u001b[39;49;00m *constants, \u001b[36mdouble\u001b[39;49;00m *path_constraints);\n",
"\n",
"\u001b[34mtemplate\u001b[39;49;00m \u001b[36mvoid\u001b[39;49;00m OCP::finalCost(\u001b[36mdouble\u001b[39;49;00m initial_time, \u001b[36mdouble\u001b[39;49;00m final_time, \u001b[34mconst\u001b[39;49;00m double_ad *initial_state, \u001b[34mconst\u001b[39;49;00m double_ad *final_state, \u001b[34mconst\u001b[39;49;00m double_ad *parameters, \u001b[34mconst\u001b[39;49;00m \u001b[36mdouble\u001b[39;49;00m *constants, double_ad &final_cost);\n",
"\u001b[34mtemplate\u001b[39;49;00m \u001b[36mvoid\u001b[39;49;00m OCP::dynamics(\u001b[36mdouble\u001b[39;49;00m time, \u001b[34mconst\u001b[39;49;00m double_ad *state, \u001b[34mconst\u001b[39;49;00m double_ad *control, \u001b[34mconst\u001b[39;49;00m double_ad *parameters, \u001b[34mconst\u001b[39;49;00m \u001b[36mdouble\u001b[39;49;00m *constants, double_ad *state_dynamics);\n",
"\u001b[34mtemplate\u001b[39;49;00m \u001b[36mvoid\u001b[39;49;00m OCP::boundaryConditions(\u001b[36mdouble\u001b[39;49;00m initial_time, \u001b[36mdouble\u001b[39;49;00m final_time, \u001b[34mconst\u001b[39;49;00m double_ad *initial_state, \u001b[34mconst\u001b[39;49;00m double_ad *final_state, \u001b[34mconst\u001b[39;49;00m double_ad *parameters, \u001b[34mconst\u001b[39;49;00m \u001b[36mdouble\u001b[39;49;00m *constants, double_ad *boundary_conditions);\n",
"\u001b[34mtemplate\u001b[39;49;00m \u001b[36mvoid\u001b[39;49;00m OCP::pathConstraints(\u001b[36mdouble\u001b[39;49;00m time, \u001b[34mconst\u001b[39;49;00m double_ad *state, \u001b[34mconst\u001b[39;49;00m double_ad *control, \u001b[34mconst\u001b[39;49;00m double_ad *parameters, \u001b[34mconst\u001b[39;49;00m \u001b[36mdouble\u001b[39;49;00m *constants, double_ad *path_constraints);\n"
]
}
],
"source": [
"import matplotlib.pyplot as plt\n",
"from matplotlib.animation import FuncAnimation\n",
"import matplotlib.animation as animation\n",
"from IPython.display import HTML\n",
"%matplotlib inline\n",
"\n",
"import numpy as np\n",
"import math\n",
"import os,shutil\n",
"!pygmentize ./problem.cpp"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"[EXEC] > ['cmake -DCMAKE_BUILD_TYPE=Debug -DPROBLEM_DIR=/home/caillau/gallery/examples/bacteria -DCPP_FILE=problem.cpp -DCMAKE_CXX_COMPILER=g++ /home/caillau/.conda/envs/ct-gallery/lib/python3.7/site-packages/bocop']\n",
">\t-- The C compiler identification is GNU 7.5.0\n",
">\t-- The CXX compiler identification is GNU 9.3.0\n",
">\t-- Detecting C compiler ABI info\n",
">\t-- Detecting C compiler ABI info - done\n",
">\t-- Check for working C compiler: /home/caillau/.conda/envs/ct-gallery/bin/x86_64-conda-linux-gnu-cc - skipped\n",
">\t-- Detecting C compile features\n",
">\t-- Detecting C compile features - done\n",
">\t-- Detecting CXX compiler ABI info\n",
">\t-- Detecting CXX compiler ABI info - done\n",
">\t-- Check for working CXX compiler: /usr/bin/g++ - skipped\n",
">\t-- Detecting CXX compile features\n",
">\t-- Detecting CXX compile features - done\n",
">\t-- Problem path: /home/caillau/gallery/examples/bacteria\n",
">\t-- Using CPPAD found at /home/caillau/.conda/envs/ct-gallery/include/cppad/..\n",
">\t-- Using IPOPT found at /home/caillau/.conda/envs/ct-gallery/lib/libipopt.so\n",
">\t-- Found Python3: /home/caillau/.conda/envs/ct-gallery/bin/python3.7 (found version \"3.7.10\") found components: Interpreter Development Development.Module Development.Embed \n",
">\t-- Found SWIG: /home/caillau/.conda/envs/ct-gallery/bin/swig (found suitable version \"4.0.2\", minimum required is \"4\") \n",
">\t-- Build type: Debug\n",
">\t-- Configuring done\n",
">\t-- Generating done\n",
">\t-- Build files have been written to: /home/caillau/gallery/examples/bacteria/build\n",
"[DONE] > ['cmake -DCMAKE_BUILD_TYPE=Debug -DPROBLEM_DIR=/home/caillau/gallery/examples/bacteria -DCPP_FILE=problem.cpp -DCMAKE_CXX_COMPILER=g++ /home/caillau/.conda/envs/ct-gallery/lib/python3.7/site-packages/bocop']\n",
"[EXEC] > make\n",
">\tmake: Warning: File 'Makefile' has modification time 10 s in the future\n",
">\tmake[1]: Warning: File 'CMakeFiles/Makefile2' has modification time 10 s in the future\n",
">\tmake[2]: Warning: File 'src/CMakeFiles/bocop.dir/flags.make' has modification time 10 s in the future\n",
">\tmake[2]: warning: Clock skew detected. Your build may be incomplete.\n",
">\tmake[2]: Warning: File 'src/CMakeFiles/bocop.dir/flags.make' has modification time 10 s in the future\n",
">\t[ 3%] Building CXX object src/CMakeFiles/bocop.dir/AD/dOCPCppAD.cpp.o\n",
">\t[ 7%] Building CXX object src/CMakeFiles/bocop.dir/DOCP/dOCP.cpp.o\n",
">\t[ 10%] Building CXX object src/CMakeFiles/bocop.dir/DOCP/dODE.cpp.o\n",
">\t[ 14%] Building CXX object src/CMakeFiles/bocop.dir/DOCP/dControl.cpp.o\n",
">\t[ 17%] Building CXX object src/CMakeFiles/bocop.dir/DOCP/dState.cpp.o\n",
">\t[ 21%] Building CXX object src/CMakeFiles/bocop.dir/DOCP/solution.cpp.o\n",
">\t[ 25%] Building CXX object src/CMakeFiles/bocop.dir/NLP/NLPSolverIpopt.cpp.o\n",
">\t[ 28%] Building CXX object src/CMakeFiles/bocop.dir/OCP/OCP.cpp.o\n",
">\t[ 32%] Building CXX object src/CMakeFiles/bocop.dir/tools/tools.cpp.o\n",
">\t[ 35%] Building CXX object src/CMakeFiles/bocop.dir/tools/tools_interpolation.cpp.o\n",
">\t[ 39%] Building CXX object src/CMakeFiles/bocop.dir/home/caillau/gallery/examples/bacteria/problem.cpp.o\n",
">\t[ 42%] Linking CXX shared library /home/caillau/gallery/examples/bacteria/libbocop.so\n",
">\tmake[2]: warning: Clock skew detected. Your build may be incomplete.\n",
">\t[ 42%] Built target bocop\n",
">\tScanning dependencies of target bocopwrapper_swig_compilation\n",
">\t[ 46%] Swig compile /home/caillau/.conda/envs/ct-gallery/lib/python3.7/site-packages/bocop/src/bocopwrapper.i for python\n",
">\tLanguage subdirectory: python\n",
">\tSearch paths:\n",
">\t ./\n",
">\t /home/caillau/.conda/envs/ct-gallery/include/python3.7m/\n",
">\t AD/\n",
">\t DOCP/\n",
">\t NLP/\n",
">\t OCP/\n",
">\t tools/\n",
">\t /home/caillau/.conda/envs/ct-gallery/include/cppad/../\n",
">\t /home/caillau/.conda/envs/ct-gallery/include/coin/\n",
">\t /home/caillau/.conda/envs/ct-gallery/include/python3.7m/\n",
">\t /home/caillau/.conda/envs/ct-gallery/lib/python3.7/site-packages/bocop/src/AD/\n",
">\t /home/caillau/.conda/envs/ct-gallery/lib/python3.7/site-packages/bocop/src/DOCP/\n",
">\t /home/caillau/.conda/envs/ct-gallery/lib/python3.7/site-packages/bocop/src/NLP/\n",
">\t /home/caillau/.conda/envs/ct-gallery/lib/python3.7/site-packages/bocop/src/OCP/\n",
">\t /home/caillau/.conda/envs/ct-gallery/lib/python3.7/site-packages/bocop/src/tools/\n",
">\t ./swig_lib/python/\n",
">\t /home/caillau/.conda/envs/ct-gallery/share/swig/4.0.2/python/\n",
">\t ./swig_lib/\n",
">\t /home/caillau/.conda/envs/ct-gallery/share/swig/4.0.2/\n",
">\tPreprocessing...\n",
">\tStarting language-specific parse...\n",
">\tProcessing types...\n",
">\tC++ analysis...\n",
">\tProcessing nested classes...\n",
">\tGenerating wrappers...\n",
">\t[ 46%] Built target bocopwrapper_swig_compilation\n",
">\tmake[2]: Warning: File 'src/CMakeFiles/bocopwrapper.dir/bocopwrapperPYTHON_wrap.cxx' has modification time 10 s in the future\n",
">\t[ 50%] Building CXX object src/CMakeFiles/bocopwrapper.dir/CMakeFiles/bocopwrapper.dir/bocopwrapperPYTHON_wrap.cxx.o\n",
">\t[ 53%] Linking CXX shared module /home/caillau/gallery/examples/bacteria/_bocopwrapper.so\n",
">\t-- Moving python modules to /home/caillau/gallery/examples/bacteria\n",
">\tmake[2]: warning: Clock skew detected. Your build may be incomplete.\n",
">\t[ 53%] Built target bocopwrapper\n",
">\t[ 57%] Building CXX object src/CMakeFiles/bocopApp.dir/AD/dOCPCppAD.cpp.o\n",
">\t[ 60%] Building CXX object src/CMakeFiles/bocopApp.dir/DOCP/dOCP.cpp.o\n",
">\t[ 64%] Building CXX object src/CMakeFiles/bocopApp.dir/DOCP/dODE.cpp.o\n",
">\t[ 67%] Building CXX object src/CMakeFiles/bocopApp.dir/DOCP/dControl.cpp.o\n",
">\t[ 71%] Building CXX object src/CMakeFiles/bocopApp.dir/DOCP/dState.cpp.o\n",
">\t[ 75%] Building CXX object src/CMakeFiles/bocopApp.dir/DOCP/solution.cpp.o\n",
">\t[ 78%] Building CXX object src/CMakeFiles/bocopApp.dir/NLP/NLPSolverIpopt.cpp.o\n",
">\t[ 82%] Building CXX object src/CMakeFiles/bocopApp.dir/OCP/OCP.cpp.o\n",
">\t[ 85%] Building CXX object src/CMakeFiles/bocopApp.dir/tools/tools.cpp.o\n",
">\t[ 89%] Building CXX object src/CMakeFiles/bocopApp.dir/tools/tools_interpolation.cpp.o\n",
">\t[ 92%] Building CXX object src/CMakeFiles/bocopApp.dir/home/caillau/gallery/examples/bacteria/problem.cpp.o\n",
">\t[ 96%] Building CXX object src/CMakeFiles/bocopApp.dir/main.cpp.o\n",
">\t[100%] Linking CXX executable /home/caillau/gallery/examples/bacteria/bocopApp\n",
">\t[100%] Built target bocopApp\n",
">\tmake[1]: warning: Clock skew detected. Your build may be incomplete.\n",
">\tmake: warning: Clock skew detected. Your build may be incomplete.\n",
"[DONE] > make\n",
"Done\n"
]
},
{
"data": {
"text/plain": [
"0"
]
},
"execution_count": 2,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"import bocop\n",
"problem1_path = \".\" # using local problem definition\n",
"bocop.build(problem1_path, cmake_options = '-DCMAKE_CXX_COMPILER=g++')"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Executing bocop ... \n",
"Done\n",
"Executing bocop ... \n",
"Done\n",
"Executing bocop ... \n",
"Done\n",
"Executing bocop ... \n",
"Done\n"
]
}
],
"source": [
"path_def = './def'\n",
"fileList = os.listdir(path_def)\n",
"for file in os.listdir(path_def):\n",
" if file.endswith('.def'):\n",
" shutil.copyfile(os.path.join(path_def,file), os.path.join(problem1_path,'problem.def'))\n",
" sol_name = file.replace('.def','.sol')\n",
" bocop.run(problem1_path, graph=0)\n",
" os.rename(\"problem.sol\",sol_name)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Optimal resource allocation"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Loading solution: ./problem1.sol\n"
]
},
{
"data": {
"image/png": 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\n",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"rmin = 0.07\n",
"rmax = 0.5\n",
"umin = rmin/rmax\n",
"Em = 0.6; K = 0.003\n",
"param = [Em,K,rmax,rmin]\n",
"\n",
"popt = np.sqrt(K*Em)\n",
"f = popt/(K + popt)*(popt+1)\n",
"uopt = (Em + f*rmin/rmax)/(Em + f)\n",
"ropt = uopt*rmax\n",
"mopt = (1-uopt)*rmax\n",
"muopt = popt/(K + popt)*(ropt-rmin)\n",
"\n",
"solution = bocop.readSolution(\"./problem1.sol\")\n",
"t = solution.time_steps\n",
"p = solution.state[0]\n",
"r = solution.state[1]\n",
"m = solution.state[2]\n",
"V = solution.state[3]\n",
"u = solution.control[0]\n",
"q = 1 - r - m\n",
"mu = p*(r-rmin)/(K + p)\n",
"\n",
"t0 = t[0]; t1 = t[-1]\n",
"\n",
"plt.figure(0, figsize=(10,5))\n",
"plt.subplot(221)\n",
"plt.subplots_adjust(hspace=0.3, wspace=0.5)\n",
"\n",
"plt.grid(linestyle='dotted')\n",
"ax = plt.gca()\n",
"plt.xlabel('t')\n",
"plt.ylabel('Allocation $\\\\alpha$')\n",
"plt.plot([t0,t1],[0,0],linewidth=1,color='grey',linestyle='--')\n",
"plt.plot([t0,t1],[1,1],linewidth=1,color='grey',linestyle='--')\n",
"plt.plot([t0,t1],[uopt,uopt],linewidth=1, linestyle='dotted', color='black',label='$\\\\alpha^*_{opt}$')\n",
"plt.plot(t[1:],u,linewidth=1,label='$\\\\alpha$')\n",
"ax.set_xlim(t0,t1)\n",
"plt.tick_params(axis='x', which='both', bottom=False, top=False, labelbottom=False)\n",
"ax2 = ax.twinx()\n",
"ax2.set_ylim(ax.get_ylim())\n",
"plt.tick_params(axis='y', which='minor', labelleft='off', labelright='on')\n",
"plt.yticks([uopt], ['$\\\\alpha^*_{opt}$'])\n",
"\n",
"plt.subplot(222)\n",
"plt.grid(linestyle='dotted')\n",
"ax = plt.gca()\n",
"plt.plot([t0,t1],[popt,popt],linewidth=1, linestyle='dotted', color='black',label='$\\hat p^*_{opt}$')\n",
"plt.plot(t, p, linewidth=1, label='$p$')\n",
"plt.legend()\n",
"ax.set_xlim(t0,t1)\n",
"plt.xlabel('t')\n",
"plt.ylabel('$p$')\n",
"ax2 = ax.twinx()\n",
"ax2.set_ylim(ax.get_ylim())\n",
"plt.tick_params(axis='y', which='minor', labelleft='off', labelright='on')\n",
"plt.yticks([popt], ['$p^*_{opt}$'])\n",
"\n",
"plt.subplot(223)\n",
"plt.grid(linestyle='dotted')\n",
"plt.xlabel('t')\n",
"plt.ylabel('Mass fractions')\n",
"ax = plt.gca()\n",
"ax2 = ax.twinx()\n",
"ax2.set_ylim(ax.get_ylim())\n",
"plt.tick_params(axis='y', which='minor', labelleft='off', labelright='on')\n",
"plt.yticks([rmin,ropt,rmax], ['$r_{min}$','$r^*_{opt}$','$r_{max}$'])\n",
"ax.set_xlim(t[0],t[-1])\n",
"plt.fill_between(t, r, color='#374e55', label='$r$', alpha=0.7)\n",
"plt.fill_between(t, r, r+m, color='#b24746', label='$m$', alpha=0.8)\n",
"plt.fill_between(t, r+m, 1, color='#79af97', label='$q$', alpha=0.9)\n",
"plt.plot(t, r, color='#374e55',linewidth=0.5)\n",
"plt.plot(t, r+m, color='#b24746',linewidth=0.5)\n",
"plt.grid(linestyle='dotted',color='black')\n",
"plt.legend(ncol = 2)\n",
"\n",
"plt.subplot(224)\n",
"plt.grid(linestyle='dotted')\n",
"plt.xlabel('t')\n",
"plt.ylabel('Growth rate $\\mu$')\n",
"ax = plt.gca()\n",
"plt.plot([t0,t1],[muopt,muopt],linewidth=1, linestyle='dotted', color='black',label='$\\mu^*_{opt}$')\n",
"plt.plot(t,mu,linewidth=1,label='$\\mu(p,r)$')\n",
"ax.set_xlim(t0,t1)\n",
"ax2 = ax.twinx()\n",
"ax2.set_ylim(ax.get_ylim())\n",
"plt.tick_params(axis='y', which='minor', labelleft='off', labelright='on')\n",
"plt.yticks([muopt], ['$\\mu^*_{opt}$'])\n",
"\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Comparison between the optimal and naive method\n",
"\n",
"(Naive method: $\\alpha(t)$ constant for the interval $[0,T]$)"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Loading solution: ./naiveproblem.sol\n"
]
},
{
"data": {
"text/html": [
""
],
"text/plain": [
""
]
},
"execution_count": 5,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
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\n",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"naivesol = bocop.readSolution(\"./naiveproblem.sol\")\n",
"\n",
"length=len(solution.state[1])\n",
"\n",
"langs=['r','m','q']\n",
"colors = [\"#374e55\",\"#b24746\", \"#79af97\"]\n",
"\n",
"fig = plt.figure(figsize=(12,6))\n",
"ax1 = plt.subplot(1,2,1) \n",
"ax2 = plt.subplot(1,2,2)\n",
"\n",
"def update(frame):\n",
" ax1.clear()\n",
" ax2.clear()\n",
" r=solution.state[1][frame]\n",
" m=solution.state[2][frame]\n",
" q=1-r-m\n",
" \n",
" rn=naivesol.state[1][frame]\n",
" mn=naivesol.state[2][frame]\n",
" qn=1-rn-mn\n",
" \n",
" ax1.pie([r,m,q], colors=colors, labels=langs, autopct='%1.2f%%',startangle=90,radius=math.sqrt(solution.state[3][frame])*3+0.7)\n",
" title1='(Optimal Method) Volume = '+str(solution.state[3][frame])\n",
" ax1.set_title(title1)\n",
" \n",
" ax2.pie([rn,mn,qn], colors=colors, labels=langs, autopct='%1.2f%%',startangle=90,radius=math.sqrt(naivesol.state[3][frame])*3+0.7)\n",
" title2='(Naive Method) Volume = '+str(naivesol.state[3][frame])\n",
" ax2.set_title(title2)\n",
"\n",
"ani = FuncAnimation(fig, update, frames=range(length),interval=10, repeat=False)\n",
"\n",
"FFwriter= animation.FFMpegWriter(fps=120)\n",
"\n",
"ani.save('./images/comparison.mp4',writer=FFwriter)\n",
"HTML(ani.to_html5_video())"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Optimal resource allocation during a nutrient shift"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Loading solution: ./problem2.sol\n"
]
},
{
"data": {
"image/png": 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\n",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"rmin = 0.07\n",
"rmax = 0.5\n",
"umin = rmin/rmax\n",
"Em = 0.7; K = 0.003\n",
"param = [Em,K,rmax,rmin]\n",
"\n",
"popt = np.sqrt(K*Em)\n",
"f = popt/(K + popt)*(popt+1)\n",
"uopt = (Em + f*rmin/rmax)/(Em + f)\n",
"ropt = uopt*rmax\n",
"mopt = (1-uopt)*rmax\n",
"muopt = popt/(K + popt)*(ropt-rmin)\n",
"\n",
"solution = bocop.readSolution(\"./problem2.sol\")\n",
"t = solution.time_steps\n",
"p = solution.state[0]\n",
"r = solution.state[1]\n",
"m = solution.state[2]\n",
"V = solution.state[3]\n",
"u = solution.control[0]\n",
"q = 1 - r - m\n",
"mu = p*(r-rmin)/(K + p)\n",
" \n",
"t0 = t[0]; t1 = t[-1]\n",
"\n",
"plt.figure(0, figsize=(10,5))\n",
"plt.subplot(221)\n",
"plt.subplots_adjust(hspace=0.3, wspace=0.5)\n",
"\n",
"plt.grid(linestyle='dotted')\n",
"ax = plt.gca()\n",
"plt.xlabel('t')\n",
"plt.ylabel('Allocation $\\\\alpha$')\n",
"plt.plot([t0,t1],[0,0],linewidth=1,color='grey',linestyle='--')\n",
"plt.plot([t0,t1],[1,1],linewidth=1,color='grey',linestyle='--')\n",
"plt.plot([t0,t1],[uopt,uopt],linewidth=1, linestyle='dotted', color='black',label='$\\\\alpha^*_{opt}$')\n",
"plt.plot(t[1:],u,linewidth=1,label='$\\\\alpha$')\n",
"ax.set_xlim(t0,t1)\n",
"ax2 = ax.twinx()\n",
"ax2.set_ylim(ax.get_ylim())\n",
"plt.tick_params(axis='y', which='minor', labelleft='off', labelright='on')\n",
"plt.yticks([uopt], ['$\\\\alpha^*_{opt}$'])\n",
"\n",
"plt.subplot(222)\n",
"plt.grid(linestyle='dotted')\n",
"ax = plt.gca()\n",
"plt.plot([t0,t1],[popt,popt],linewidth=1, linestyle='dotted', color='black',label='$\\hat p^*_{opt}$')\n",
"plt.plot(t, p, linewidth=1, label='$p$')\n",
"plt.legend()\n",
"ax.set_xlim(t0,t1)\n",
"plt.xlabel('t')\n",
"plt.ylabel('$p$')\n",
"ax2 = ax.twinx()\n",
"ax2.set_ylim(ax.get_ylim())\n",
"plt.tick_params(axis='y', which='minor', labelleft='off', labelright='on')\n",
"plt.yticks([popt], ['$p^*_{opt}$'])\n",
"\n",
"plt.subplot(223)\n",
"plt.grid(linestyle='dotted')\n",
"plt.xlabel('t')\n",
"plt.ylabel('Mass fractions')\n",
"ax = plt.gca()\n",
"ax2 = ax.twinx()\n",
"ax2.set_ylim(ax.get_ylim())\n",
"plt.tick_params(axis='y', which='minor', labelleft='off', labelright='on')\n",
"plt.yticks([rmin,ropt,rmax], ['$r_{min}$','$r^*_{opt}$','$r_{max}$'])\n",
"ax.set_xlim(t[0],t[-1])\n",
"plt.fill_between(t, r, color='#374e55', label='$r$', alpha=0.7)\n",
"plt.fill_between(t, r, r+m, color='#b24746', label='$m$', alpha=0.8)\n",
"plt.fill_between(t, r+m, 1, color='#79af97', label='$q$', alpha=0.9)\n",
"plt.plot(t, r, color='#374e55',linewidth=0.5)\n",
"plt.plot(t, r+m, color='#b24746',linewidth=0.5)\n",
"plt.grid(linestyle='dotted',color='black')\n",
"plt.legend(ncol = 2)\n",
"\n",
"plt.subplot(224)\n",
"plt.grid(linestyle='dotted')\n",
"plt.xlabel('t')\n",
"plt.ylabel('Growth rate $\\mu$')\n",
"ax = plt.gca()\n",
"plt.plot([t0,t1],[muopt,muopt],linewidth=1, linestyle='dotted', color='black',label='$\\mu^*_{opt}$')\n",
"plt.plot(t,mu,linewidth=1,label='$\\mu(p,r)$')\n",
"ax.set_xlim(t0,t1)\n",
"ax2 = ax.twinx()\n",
"ax2.set_ylim(ax.get_ylim())\n",
"plt.tick_params(axis='y', which='minor', labelleft='off', labelright='on')\n",
"plt.yticks([muopt], ['$\\mu^*_{opt}$'])\n",
"\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Optimal resource allocation when synthesizing an anti-stress protein $w$"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Loading solution: ./problem3.sol\n"
]
},
{
"data": {
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\n",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"rmax = 0.3\n",
"rmax_old = 0.5\n",
"rmin = 0.07\n",
"umin = rmin/rmax\n",
"Em = 0.7; K = 0.003\n",
"param = [Em,K,rmax,rmin]\n",
"\n",
"popt = np.sqrt(K*Em)\n",
"f = popt/(K + popt)*(popt+1)\n",
"uopt = (Em + f*rmin/rmax)/(Em + f)\n",
"ropt = uopt*rmax\n",
"mopt = (1-uopt)*rmax\n",
"muopt = popt/(K + popt)*(ropt-rmin)\n",
"\n",
"solution = bocop.readSolution(\"./problem3.sol\")\n",
"t = solution.time_steps\n",
"p = solution.state[0]\n",
"r = solution.state[1]\n",
"m = solution.state[2]\n",
"V = solution.state[3]\n",
"u = solution.control[0]\n",
"q = 1 - r - m\n",
"mu = p*(r-rmin)/(K + p)\n",
" \n",
"t0 = t[0]; t1 = t[-1]\n",
"\n",
"names = ['p','r','m','\\\\alpha']\n",
"\n",
"plt.figure(0, figsize=(10,5))\n",
"plt.subplot(221)\n",
"plt.subplots_adjust(hspace=0.3, wspace=0.5)\n",
"\n",
"plt.grid(linestyle='dotted')\n",
"ax = plt.gca()\n",
"plt.xlabel('t')\n",
"plt.ylabel('Allocation $\\\\alpha$')\n",
"plt.plot([t0,t1],[0,0],linewidth=1,color='grey',linestyle='--')\n",
"plt.plot([t0,t1],[1,1],linewidth=1,color='grey',linestyle='--')\n",
"plt.plot([t0,t1],[uopt,uopt],linewidth=1, linestyle='dotted', color='black',label='$\\\\alpha^*_{opt}$')\n",
"plt.plot(t[1:],u,linewidth=1,label='$\\\\alpha$')\n",
"ax.set_xlim(t0,t1)\n",
"ax2 = ax.twinx()\n",
"ax2.set_ylim(ax.get_ylim())\n",
"plt.tick_params(axis='y', which='minor', labelleft='off', labelright='on')\n",
"plt.yticks([uopt], ['$\\\\alpha^*_{opt}$'])\n",
"\n",
"plt.subplot(222)\n",
"plt.grid(linestyle='dotted')\n",
"ax = plt.gca()\n",
"plt.plot([t0,t1],[popt,popt],linewidth=1, linestyle='dotted', color='black',label='$\\hat p^*_{opt}$')\n",
"plt.plot(t, p, linewidth=1, label='$p$')\n",
"plt.legend()\n",
"ax.set_xlim(t0,t1)\n",
"plt.xlabel('t')\n",
"plt.ylabel('$p$')\n",
"ax2 = ax.twinx()\n",
"ax2.set_ylim(ax.get_ylim())\n",
"plt.tick_params(axis='y', which='minor', labelleft='off', labelright='on')\n",
"plt.yticks([popt], ['$p^*_{opt}$'])\n",
"\n",
"plt.subplot(223)\n",
"plt.grid(linestyle='dotted')\n",
"plt.xlabel('t')\n",
"plt.ylabel('Mass fractions')\n",
"ax = plt.gca()\n",
"ax2 = ax.twinx()\n",
"ax2.set_ylim(ax.get_ylim())\n",
"plt.tick_params(axis='y', which='minor', labelleft='off', labelright='on')\n",
"plt.yticks([rmin,ropt,rmax_old,rmax], ['$r_{min}$','$r^*_{opt}$','$r_{max}$','$r^w_{max}$'])\n",
"ax.set_xlim(t[0],t[-1])\n",
"plt.fill_between(t, r, color='#374e55', label='$r$', alpha=0.7)\n",
"plt.fill_between(t, r, r+m, color='#b24746', label='$m$', alpha=0.8)\n",
"plt.fill_between(t, r+m, rmax_old, color='#df8f44', label='$w$', alpha=0.9)\n",
"plt.fill_between(t, rmax_old, 1, color='#79af97', label='$q$', alpha=0.9)\n",
"plt.plot(t, r, color='#374e55',linewidth=0.5)\n",
"plt.plot(t, r+m, color='#b24746',linewidth=0.5)\n",
"plt.grid(linestyle='dotted',color='black')\n",
"plt.legend(ncol = 2)\n",
"\n",
"plt.subplot(224)\n",
"plt.grid(linestyle='dotted')\n",
"plt.xlabel('t')\n",
"plt.ylabel('Growth rate $\\mu$')\n",
"ax = plt.gca()\n",
"plt.plot([t0,t1],[muopt,muopt],linewidth=1, linestyle='dotted', color='black',label='$\\mu^*_{opt}$')\n",
"plt.plot(t,mu,linewidth=1,label='$\\mu(p,r)$')\n",
"ax.set_xlim(t0,t1)\n",
"ax2 = ax.twinx()\n",
"ax2.set_ylim(ax.get_ylim())\n",
"plt.tick_params(axis='y', which='minor', labelleft='off', labelright='on')\n",
"plt.yticks([muopt], ['$\\mu^*_{opt}$'])\n",
"\n",
"plt.show()"
]
}
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