docs/tutorials/thermo_concentrations.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
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   "source": [
    "# Thermodynamic Feasibility and Sampling of Metabolite Concentrations\n",
    "This notebook demonstrates how **MASSpy** is used to ensure thermodynamic feasibility in the metabolite concentrations of a model, and how samples of thermodynamically feasible metabolite concentrations are generated for a model."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2021-01-25T18:43:57.197702Z",
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     "shell.execute_reply": "2021-01-25T18:43:59.957408Z"
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   },
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "\n",
    "import numpy as np\n",
    "\n",
    "import mass.example_data\n",
    "\n",
    "from mass import MassConfiguration\n",
    "from mass.thermo import ConcSolver\n",
    "\n",
    "MASSCONFIGURATION = MassConfiguration()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Note**: Throughout this notebook, the term *thermodynamic feasibility constraint* for a reaction refers to the following:\n",
    "\n",
    "For a given reaction:\n",
    "\n",
    "$$\n",
    "\\textbf{S}^T \\ln{(\\textbf{x})} < \\ln{(\\text{Keq})}\\ - \\epsilon\\ \\text{if}\\ \\text{v}\\ > 0\\\\\n",
    "\\textbf{S}^T \\ln{(\\textbf{x})} > \\ln{(\\text{Keq})}\\ + \\epsilon\\ \\text{if}\\ \\text{v}\\ < 0\\\\\n",
    "$$\n",
    "\n",
    "where\n",
    "\n",
    "* $\\textbf{S}$ refers to the stoichiometry of the reaction\n",
    "* $\\textbf{x}$ refers to the vector of concentrations for the reaction metabolites\n",
    "* $\\text{Keq}$ refers to the equilibrium constant of the reaction\n",
    "* $\\text{v}$ refers to the reaction flux.\n",
    "* $\\epsilon$ refers to a buffer value for the constraint.\n",
    "\n",
    "Based on methods outlined in <cite data-cite=\"KummelPH06\">(Kummel et al., 2006)</cite> and <cite data-cite=\"HDR13\">(Hamilton, et al., 2013)</cite>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## The ConcSolver Object\n",
    "\n",
    "Upon initialization of the `ConcSolver` instance, the model becomes associated with the `ConcSolver` instance.\n",
    "Metabolite concentrations and reaction equilibrium constants are added as variables to the `ConcSolver`.Thermodynamic feasibility constraints, based on the reaction's flux direction and stoichiometry, are created and also added to the solver. **All solver variables and constraints exist in logarithmic space.**\n",
    "\n",
    "Metabolite concentrations that should be excluded from the solver can be defined using the `exclude_metabolites` argument (e.g., hydrogen and water). Reactions can also be excluded from the solver using the `exclude_reactions` argument.\n",
    "\n",
    "Reactions that should exist at equilibrium or equilibrate very quickly should be set using the `equilibrium_reactions` argument. These reactions, such as the hemoglobin binding reactions and the adenylate kinase (ADK1) reaction, typically have a steady state flux value of 0."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2021-01-25T18:43:59.965212Z",
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     "shell.execute_reply": "2021-01-25T18:44:00.191935Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Set parameter Username\n"
     ]
    }
   ],
   "source": [
    "# Load the JSON version of the textbook model\n",
    "model = mass.example_data.create_example_model(\"textbook\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2021-01-25T18:44:00.281721Z",
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     "iopub.status.idle": "2021-01-25T18:44:00.587384Z",
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   "outputs": [
    {
     "data": {
      "text/html": [
       "\n",
       "            <table>\n",
       "                <tr>\n",
       "                    <td><strong>Name</strong></td><td>RBC_PFK</td>\n",
       "                </tr><tr>\n",
       "                    <td><strong>Memory address</strong></td><td>0x07f7cf009bee0</td>\n",
       "                </tr><tr>\n",
       "                    <td><strong>Stoichiometric Matrix</strong></td>\n",
       "                    <td>68x76</td>\n",
       "                </tr><tr>\n",
       "                    <td><strong>Matrix Rank</strong></td>\n",
       "                    <td>63</td>\n",
       "                </tr><tr>\n",
       "                    <td><strong>Number of metabolites</strong></td>\n",
       "                    <td>68</td>\n",
       "                </tr><tr>\n",
       "                    <td><strong>Initial conditions defined</strong></td>\n",
       "                    <td>68/68</td>\n",
       "                </tr><tr>\n",
       "                    <td><strong>Number of reactions</strong></td>\n",
       "                    <td>76</td>\n",
       "                </tr><tr>\n",
       "                    <td><strong>Number of genes</strong></td>\n",
       "                    <td>0</td>\n",
       "                </tr><tr>\n",
       "                    <td><strong>Number of enzyme modules</strong></td>\n",
       "                    <td>1</td>\n",
       "                </tr><tr>\n",
       "                    <td><strong>Number of groups</strong></td>\n",
       "                    <td>16</td>\n",
       "                </tr><tr>\n",
       "                    <td><strong>Objective expression</strong></td>\n",
       "                    <td>0</td>\n",
       "                </tr><tr>\n",
       "                    <td><strong>Compartments</strong></td>\n",
       "                    <td>Cytosol</td>\n",
       "                </tr>\n",
       "            </table>\n",
       "        "
      ],
      "text/plain": [
       "<MassModel RBC_PFK at 0x7f7cf009bee0>"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "conc_solver = ConcSolver(\n",
    "    model,\n",
    "    excluded_metabolites=[\"h_c\", \"h2o_c\"],\n",
    "    excluded_reactions=None,\n",
    "    equilibrium_reactions=[\"HBDPG\", \"HBO1\", \"HBO2\", \"HBO3\", \"HBO4\", \"ADK1\",\n",
    "                           \"PFK_L\"])\n",
    "# View the model in the ConcSolver\n",
    "conc_solver.model"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The `ConcSolver` also becomes associated with the loaded model."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2021-01-25T18:44:00.593994Z",
     "iopub.status.busy": "2021-01-25T18:44:00.592838Z",
     "iopub.status.idle": "2021-01-25T18:44:00.596696Z",
     "shell.execute_reply": "2021-01-25T18:44:00.597169Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<ConcSolver RBC_PFK at 0x7f7d20c210d0>\n"
     ]
    }
   ],
   "source": [
    "print(model.conc_solver)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Concentrations and equilibrium constants cannot be negative numbers; therefore, the bounds for each variable are set to ensure such behavior. Because $\\ln(0)$ results in a domain error, the `ConcSolver` has the `zero_value_log_substitute` attribute. The value of the attribute is substituted for 0 to avoid any errors.\n",
    "\n",
    "For example, if `zero_value_log_substitute=1e-10`, then taking the logarithm of 0 is treated as $\\ln(0) \\approx \\ln(1*10^{-10}) = -23.026$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2021-01-25T18:44:00.602158Z",
     "iopub.status.busy": "2021-01-25T18:44:00.601538Z",
     "iopub.status.idle": "2021-01-25T18:44:00.603912Z",
     "shell.execute_reply": "2021-01-25T18:44:00.604393Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Substitute for ln(0): ln(1.0e-10)\n"
     ]
    }
   ],
   "source": [
    "print(\"Substitute for ln(0): ln({0:.1e})\".format(\n",
    "    conc_solver.zero_value_log_substitute))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Variables can be accessed through the `variables` attribute. The number of variables equals the combined total of  the number of included metabolites and the number of included reactions. Specific variables can be accessed using their identifiers as a key."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2021-01-25T18:44:00.610843Z",
     "iopub.status.busy": "2021-01-25T18:44:00.609795Z",
     "iopub.status.idle": "2021-01-25T18:44:00.613077Z",
     "shell.execute_reply": "2021-01-25T18:44:00.613769Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Number of included metabolites: 66 \n",
      "Number of included reactions: 48 \n",
      "Total number of variables: 114\n",
      "\n",
      "The glucose concentration variable \n",
      "----------------------------------\n",
      " -23.025850929940457 <= glc__D_c <= inf\n"
     ]
    }
   ],
   "source": [
    "print(\"Number of included metabolites: {0}\".format(len(conc_solver.included_metabolites)),\n",
    "      \"\\nNumber of included reactions: {0}\".format(len(conc_solver.included_reactions)),\n",
    "      \"\\nTotal number of variables: {0}\\n\".format(len(conc_solver.variables)))\n",
    "\n",
    "# Access the glucose concentration variable\n",
    "variable = conc_solver.variables[\"glc__D_c\"]\n",
    "print(\"The glucose concentration variable\",\n",
    "      \"\\n----------------------------------\\n\",\n",
    "      variable)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Constraints can be accessed through the `constraints` attribute. The number of constraints equals the number of included reactions. Just like variables, specific constraints can be accessed using reaction identifiers as a key."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2021-01-25T18:44:00.623235Z",
     "iopub.status.busy": "2021-01-25T18:44:00.621387Z",
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     "shell.execute_reply": "2021-01-25T18:44:00.627597Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Total number of constraints: 48\n",
      "\n",
      "Thermodynamic feasibility constraint for HEX1 \n",
      "-------------------------------------------\n",
      " HEX1: -1.0*Keq_HEX1 + 1.0*adp_c - 1.0*atp_c + 1.0*g6p_c - 1.0*glc__D_c <= 0\n"
     ]
    }
   ],
   "source": [
    "print(\"Total number of constraints: {0}\\n\".format(len(conc_solver.constraints)))\n",
    "# Access the hexokinase thermodynamic feasibility constraint\n",
    "print(\"Thermodynamic feasibility constraint for HEX1\",\n",
    "      \"\\n-------------------------------------------\\n\",\n",
    "      conc_solver.constraints[\"HEX1\"])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Currently, the constraints do not have an error buffer, which provides some flexibility when solving the underlying mathematical problem of the `ConcSolver`. The `constraint_buffer` attribute can be used to set the *epsilon* value of the constraint. The constraints must be reset in order for the changed buffer value to take effect."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2021-01-25T18:44:00.654519Z",
     "iopub.status.busy": "2021-01-25T18:44:00.653589Z",
     "iopub.status.idle": "2021-01-25T18:44:00.656275Z",
     "shell.execute_reply": "2021-01-25T18:44:00.656677Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Thermodynamic feasibility constraint for HEX1 \n",
      "-------------------------------------------\n",
      " HEX1: -1.0*Keq_HEX1 + 1.0*adp_c - 1.0*atp_c + 1.0*g6p_c - 1.0*glc__D_c <= -1e-07\n"
     ]
    }
   ],
   "source": [
    "conc_solver.constraint_buffer = 1e-7\n",
    "conc_solver.reset_constraints()\n",
    "print(\"Thermodynamic feasibility constraint for HEX1\",\n",
    "      \"\\n-------------------------------------------\\n\",\n",
    "      conc_solver.constraints[\"HEX1\"])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Upon initialization of the `ConcSolver`, the `ConcSolver.problem_type` is considered generic and no objective is set."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2021-01-25T18:44:00.662547Z",
     "iopub.status.busy": "2021-01-25T18:44:00.661729Z",
     "iopub.status.idle": "2021-01-25T18:44:00.664179Z",
     "shell.execute_reply": "2021-01-25T18:44:00.664575Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "generic\n",
      "Maximize\n",
      "0\n"
     ]
    }
   ],
   "source": [
    "print(conc_solver.problem_type)\n",
    "print(conc_solver.objective)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The following sections demonstrate different types of problems that can be solved using the `ConcSolver`."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Solving for Feasible Concentrations\n",
    "### Creating the QP problem\n",
    "\n",
    "In order to determine thermodynamically feasible concentrations, a quadratic programming (QP) problem can be set up as follows:\n",
    "\n",
    "Minimize\n",
    "$$\\ln( (\\textbf{x}/\\textbf{x}_0)^{2} )$$\n",
    "\n",
    "subject to\n",
    "\n",
    "$$\n",
    "\\textbf{S}^T \\ln{(\\textbf{x})} \\lt \\ln{(\\text{Keq}_i)}\\ - \\epsilon\\ \\text{if}\\ \\text{v}_i\\ \\gt 0 \\\\\n",
    "\\textbf{S}^T \\ln{(\\textbf{x})} \\gt \\ln{(\\text{Keq}_i)}\\ + \\epsilon\\ \\text{if}\\ \\text{v}_i\\ \\lt 0 \\\\\n",
    "\\ln(\\text{Keq}_{i,\\ lb}) \\leq \\ln(\\text{Keq}_i) \\leq \\ln(\\text{Keq}_{i,\\ ub}) \\\\\n",
    "\\ln(\\text{x}_{j,\\ lb}) \\leq \\ln(\\text{x}_j) \\leq \\ln(\\text{x}_{j,\\ ub}) \\\\\n",
    "$$\n",
    "\n",
    "where \n",
    "\n",
    "* $\\textbf{S}$ refers to the stoichiometric matrix.\n",
    "* $\\textbf{x}$ refers to the vector of metabolite concentrations.\n",
    "* $\\textbf{x}_0$ refers to the vector of initial metabolite concentrations.\n",
    "* $\\text{Keq}_i$ refers to the equilibrium constant of reaction $i$.\n",
    "* $\\text{v}_i$ refers to the flux for reaction $i$.\n",
    "* $\\text{x}_j$ refers to the concentration of metabolite $j$.\n",
    "* $\\epsilon$ refers to a buffer value for the constraint.\n",
    "\n",
    "Note that solving the QP problem requires a capable solver. Although **MASSpy** does not come with any QP solvers installed, it can interface with an installed version of [gurobi](https://www.gurobi.com/) through the **optlang** package."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The first step is to set the optimization solver to one that is capable of handling quadratic objectives. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2021-01-25T18:44:00.668808Z",
     "iopub.status.busy": "2021-01-25T18:44:00.668148Z",
     "iopub.status.idle": "2021-01-25T18:44:00.671460Z",
     "shell.execute_reply": "2021-01-25T18:44:00.671919Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<optlang.gurobi_interface.Model object at 0x7f7d20c211f0>\n"
     ]
    }
   ],
   "source": [
    "conc_solver.solver = conc_solver.choose_solver(qp=True)\n",
    "print(repr(conc_solver.solver))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To set up the underlying mathematical problem in the `ConcSolver`, the `setup_feasible_qp_problem()` method can be used. The `fixed_conc_bounds` and `fixed_Keq_bounds` arguments can be used to set the upper and lower bounds of the corresponding variables equal to one other, fixing the variable's value. In this example, the metabolite concentrations are allowed to change, while the equilibrium constants are fixed at their original value."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2021-01-25T18:44:00.765375Z",
     "iopub.status.busy": "2021-01-25T18:44:00.722754Z",
     "iopub.status.idle": "2021-01-25T18:44:01.359135Z",
     "shell.execute_reply": "2021-01-25T18:44:01.359581Z"
    }
   },
   "outputs": [],
   "source": [
    "conc_solver.setup_feasible_qp_problem(\n",
    "    fixed_Keq_bounds=conc_solver.model.reactions)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Using the `setup_feasible_qp_problem()` method also sets the objective for the optimization."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2021-01-25T18:44:01.364024Z",
     "iopub.status.busy": "2021-01-25T18:44:01.363297Z",
     "iopub.status.idle": "2021-01-25T18:44:01.366671Z",
     "shell.execute_reply": "2021-01-25T18:44:01.367067Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "min\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<optlang.gurobi_interface.Objective at 0x7f7d209065e0>"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "print(conc_solver.objective_direction)\n",
    "conc_solver.objective"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "After using the `setup_feasible_qp_problem()` method, the `ConcSolver` is ready for optimization. The `problem_type` is automatically changed to reflect the current problem setup."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2021-01-25T18:44:01.370906Z",
     "iopub.status.busy": "2021-01-25T18:44:01.370254Z",
     "iopub.status.idle": "2021-01-25T18:44:01.372535Z",
     "shell.execute_reply": "2021-01-25T18:44:01.373032Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "feasible_qp\n"
     ]
    }
   ],
   "source": [
    "print(conc_solver.problem_type)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### The ConcSolution Object\n",
    "Once the `ConcSolver` is set up to solve the QP, the next step is to use the `optimize()` method to solve the QP. A successful optimization returns a `ConcSolution` object. All values are transformed back into linear space upon being returned."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2021-01-25T18:44:01.377381Z",
     "iopub.status.busy": "2021-01-25T18:44:01.376338Z",
     "iopub.status.idle": "2021-01-25T18:44:01.651801Z",
     "shell.execute_reply": "2021-01-25T18:44:01.652220Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<strong><em>Optimal</em> solution with objective value 0.000</strong><br><div>\n",
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>variables</th>\n",
       "      <th>reduced_costs</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>glc__D_c</th>\n",
       "      <td>1.296763</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>g6p_c</th>\n",
       "      <td>0.165018</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>f6p_c</th>\n",
       "      <td>0.067532</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>fdp_c</th>\n",
       "      <td>0.016615</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>dhap_c</th>\n",
       "      <td>0.169711</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Keq_PFK_L</th>\n",
       "      <td>0.001100</td>\n",
       "      <td>-0.103955</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Keq_PFK_T1</th>\n",
       "      <td>10.000000</td>\n",
       "      <td>-1.097455</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Keq_PFK_T2</th>\n",
       "      <td>10.000000</td>\n",
       "      <td>-0.408917</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Keq_PFK_T3</th>\n",
       "      <td>10.000000</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Keq_PFK_T4</th>\n",
       "      <td>10.000000</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>114 rows × 2 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "<Solution 0.000 at 0x7f7d20c4ed30>"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "conc_solution = conc_solver.optimize()\n",
    "conc_solution"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The `ConcSolution` object has several methods for viewing the results of the optimization and returning `pandas` objects containing the numerical solutions."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2021-01-25T18:44:01.656553Z",
     "iopub.status.busy": "2021-01-25T18:44:01.655844Z",
     "iopub.status.idle": "2021-01-25T18:44:01.658943Z",
     "shell.execute_reply": "2021-01-25T18:44:01.659639Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "['Keq_reduced_costs',\n",
       " 'Keqs',\n",
       " 'Keqs_to_frame',\n",
       " 'concentration_reduced_costs',\n",
       " 'concentrations',\n",
       " 'concentrations_to_frame',\n",
       " 'get_primal_by_id',\n",
       " 'objective_value',\n",
       " 'shadow_prices',\n",
       " 'status',\n",
       " 'to_frame']"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dir(conc_solution)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2021-01-25T18:44:01.663706Z",
     "iopub.status.busy": "2021-01-25T18:44:01.662934Z",
     "iopub.status.idle": "2021-01-25T18:44:01.664940Z",
     "shell.execute_reply": "2021-01-25T18:44:01.665497Z"
    }
   },
   "outputs": [],
   "source": [
    "from mass.visualization import plot_comparison"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Through visualization features of **MASSPy**, the predicted values can be plotted against the original model values for comparison using the `plot_comparison()` function."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2021-01-25T18:44:01.686065Z",
     "iopub.status.busy": "2021-01-25T18:44:01.685447Z",
     "iopub.status.idle": "2021-01-25T18:44:03.432321Z",
     "shell.execute_reply": "2021-01-25T18:44:03.432731Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Create figure\n",
    "fig, ax = plt.subplots(figsize=(6, 6))\n",
    "\n",
    "# Compare values\n",
    "plot_comparison(\n",
    "    x=model, y=conc_solution, compare=\"concentrations\",\n",
    "    observable=conc_solver.included_metabolites, legend=\"right outside\",\n",
    "    xlabel=\"Current Concentrations [mM]\",\n",
    "    ylabel=\"Predicted Concentrations [mM]\",\n",
    "    plot_function=\"loglog\", xy_line=True, xy_legend=\"best\");"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The model in the `ConcSolver` can be updated with the results contained within the `ConcSolution` using the `update_model_with_solution()` method. Setting `inplace=True` updates the current model in the `ConcSolver`, while setting `inplace=False` replaces the model in the `ConcSolver` with an updated copy the model without modifying the original. Setting `inplace=False` also removes the previous model's association with the `ConcSolver`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2021-01-25T18:44:03.451986Z",
     "iopub.status.busy": "2021-01-25T18:44:03.451346Z",
     "iopub.status.idle": "2021-01-25T18:44:03.616432Z",
     "shell.execute_reply": "2021-01-25T18:44:03.616978Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Same model object? False\n",
      "None\n"
     ]
    }
   ],
   "source": [
    "conc_solver.update_model_with_solution(\n",
    "    conc_solution, concentrations=True, Keqs=False, inplace=False)\n",
    "print(\"Same model object? {0}\".format(conc_solver.model == model))\n",
    "print(model.conc_solver)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Concentration Sampling\n",
    "### Basic usage\n",
    "\n",
    "The easiest method of sampling concentrations is to use the `sample_concentrations()` function in the `conc_sampling` submodule."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2021-01-25T18:44:03.622171Z",
     "iopub.status.busy": "2021-01-25T18:44:03.621489Z",
     "iopub.status.idle": "2021-01-25T18:44:03.623563Z",
     "shell.execute_reply": "2021-01-25T18:44:03.624164Z"
    }
   },
   "outputs": [],
   "source": [
    "from mass.thermo.conc_sampling import sample_concentrations"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To set up the `ConcSolver` for sampling, the `setup_sampling_problem` method is used. The `conc_percent_deviation` and `Keq_percent_deviation` arguments can be used to set the variable bounds for sampling. For this example, the defined concentrations are allowed to deviate up to %75 from their baseline value, while the defined equilibrium constants remain fixed at their current values. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2021-01-25T18:44:03.637001Z",
     "iopub.status.busy": "2021-01-25T18:44:03.636291Z",
     "iopub.status.idle": "2021-01-25T18:44:03.638842Z",
     "shell.execute_reply": "2021-01-25T18:44:03.639247Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "sampling\n"
     ]
    }
   ],
   "source": [
    "conc_solver.setup_sampling_problem(\n",
    "    conc_percent_deviation=0.75,\n",
    "    Keq_percent_deviation=0)\n",
    "print(conc_solver.problem_type)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Using the `sample_concentrations()` function requires at least two arguments: a `ConcSolver` that has been set up for sampling, and the number of samples to generate."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2021-01-25T18:44:03.653867Z",
     "iopub.status.busy": "2021-01-25T18:44:03.653174Z",
     "iopub.status.idle": "2021-01-25T18:44:04.327896Z",
     "shell.execute_reply": "2021-01-25T18:44:04.328468Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>glc__D_c</th>\n",
       "      <th>g6p_c</th>\n",
       "      <th>f6p_c</th>\n",
       "      <th>fdp_c</th>\n",
       "      <th>dhap_c</th>\n",
       "      <th>g3p_c</th>\n",
       "      <th>_13dpg_c</th>\n",
       "      <th>_3pg_c</th>\n",
       "      <th>_2pg_c</th>\n",
       "      <th>pep_c</th>\n",
       "      <th>...</th>\n",
       "      <th>pfk_R3_A_c</th>\n",
       "      <th>pfk_R3_AF_c</th>\n",
       "      <th>pfk_R4_c</th>\n",
       "      <th>pfk_R4_A_c</th>\n",
       "      <th>pfk_R4_AF_c</th>\n",
       "      <th>pfk_T0_c</th>\n",
       "      <th>pfk_T1_c</th>\n",
       "      <th>pfk_T2_c</th>\n",
       "      <th>pfk_T3_c</th>\n",
       "      <th>pfk_T4_c</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1.776031</td>\n",
       "      <td>0.225999</td>\n",
       "      <td>0.089964</td>\n",
       "      <td>0.020589</td>\n",
       "      <td>0.154565</td>\n",
       "      <td>0.008504</td>\n",
       "      <td>0.000416</td>\n",
       "      <td>0.102543</td>\n",
       "      <td>0.011834</td>\n",
       "      <td>0.020057</td>\n",
       "      <td>...</td>\n",
       "      <td>0.000014</td>\n",
       "      <td>2.261391e-06</td>\n",
       "      <td>1.888078e-06</td>\n",
       "      <td>0.000007</td>\n",
       "      <td>3.013082e-07</td>\n",
       "      <td>4.227295e-11</td>\n",
       "      <td>9.171097e-10</td>\n",
       "      <td>1.284325e-08</td>\n",
       "      <td>1.304504e-07</td>\n",
       "      <td>3.808015e-07</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1.584736</td>\n",
       "      <td>0.219790</td>\n",
       "      <td>0.087706</td>\n",
       "      <td>0.018811</td>\n",
       "      <td>0.137524</td>\n",
       "      <td>0.006709</td>\n",
       "      <td>0.000414</td>\n",
       "      <td>0.082037</td>\n",
       "      <td>0.010206</td>\n",
       "      <td>0.014495</td>\n",
       "      <td>...</td>\n",
       "      <td>0.000006</td>\n",
       "      <td>9.566485e-07</td>\n",
       "      <td>7.988064e-07</td>\n",
       "      <td>0.000003</td>\n",
       "      <td>2.393127e-07</td>\n",
       "      <td>4.203981e-11</td>\n",
       "      <td>7.653907e-10</td>\n",
       "      <td>1.484397e-08</td>\n",
       "      <td>1.450826e-07</td>\n",
       "      <td>4.380999e-07</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1.476564</td>\n",
       "      <td>0.203249</td>\n",
       "      <td>0.075462</td>\n",
       "      <td>0.016502</td>\n",
       "      <td>0.122260</td>\n",
       "      <td>0.006041</td>\n",
       "      <td>0.000394</td>\n",
       "      <td>0.070950</td>\n",
       "      <td>0.009434</td>\n",
       "      <td>0.013528</td>\n",
       "      <td>...</td>\n",
       "      <td>0.000005</td>\n",
       "      <td>8.413586e-07</td>\n",
       "      <td>6.497424e-07</td>\n",
       "      <td>0.000002</td>\n",
       "      <td>2.212789e-07</td>\n",
       "      <td>3.343054e-11</td>\n",
       "      <td>6.646832e-10</td>\n",
       "      <td>1.393792e-08</td>\n",
       "      <td>1.401509e-07</td>\n",
       "      <td>4.242574e-07</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1.611821</td>\n",
       "      <td>0.218186</td>\n",
       "      <td>0.078626</td>\n",
       "      <td>0.015716</td>\n",
       "      <td>0.117922</td>\n",
       "      <td>0.006131</td>\n",
       "      <td>0.000429</td>\n",
       "      <td>0.045345</td>\n",
       "      <td>0.006051</td>\n",
       "      <td>0.008962</td>\n",
       "      <td>...</td>\n",
       "      <td>0.000005</td>\n",
       "      <td>1.109585e-06</td>\n",
       "      <td>8.686517e-07</td>\n",
       "      <td>0.000003</td>\n",
       "      <td>3.090001e-07</td>\n",
       "      <td>4.128989e-11</td>\n",
       "      <td>7.914225e-10</td>\n",
       "      <td>1.757626e-08</td>\n",
       "      <td>1.561635e-07</td>\n",
       "      <td>4.600968e-07</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>2.148799</td>\n",
       "      <td>0.261852</td>\n",
       "      <td>0.100766</td>\n",
       "      <td>0.008254</td>\n",
       "      <td>0.068786</td>\n",
       "      <td>0.003777</td>\n",
       "      <td>0.000408</td>\n",
       "      <td>0.029591</td>\n",
       "      <td>0.004135</td>\n",
       "      <td>0.006085</td>\n",
       "      <td>...</td>\n",
       "      <td>0.000006</td>\n",
       "      <td>1.097732e-06</td>\n",
       "      <td>1.088903e-06</td>\n",
       "      <td>0.000003</td>\n",
       "      <td>5.549445e-07</td>\n",
       "      <td>6.531665e-11</td>\n",
       "      <td>1.573526e-09</td>\n",
       "      <td>4.263682e-08</td>\n",
       "      <td>2.259306e-07</td>\n",
       "      <td>6.118950e-07</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>5 rows × 66 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "   glc__D_c     g6p_c     f6p_c     fdp_c    dhap_c     g3p_c  _13dpg_c  \\\n",
       "0  1.776031  0.225999  0.089964  0.020589  0.154565  0.008504  0.000416   \n",
       "1  1.584736  0.219790  0.087706  0.018811  0.137524  0.006709  0.000414   \n",
       "2  1.476564  0.203249  0.075462  0.016502  0.122260  0.006041  0.000394   \n",
       "3  1.611821  0.218186  0.078626  0.015716  0.117922  0.006131  0.000429   \n",
       "4  2.148799  0.261852  0.100766  0.008254  0.068786  0.003777  0.000408   \n",
       "\n",
       "     _3pg_c    _2pg_c     pep_c  ...  pfk_R3_A_c   pfk_R3_AF_c      pfk_R4_c  \\\n",
       "0  0.102543  0.011834  0.020057  ...    0.000014  2.261391e-06  1.888078e-06   \n",
       "1  0.082037  0.010206  0.014495  ...    0.000006  9.566485e-07  7.988064e-07   \n",
       "2  0.070950  0.009434  0.013528  ...    0.000005  8.413586e-07  6.497424e-07   \n",
       "3  0.045345  0.006051  0.008962  ...    0.000005  1.109585e-06  8.686517e-07   \n",
       "4  0.029591  0.004135  0.006085  ...    0.000006  1.097732e-06  1.088903e-06   \n",
       "\n",
       "   pfk_R4_A_c   pfk_R4_AF_c      pfk_T0_c      pfk_T1_c      pfk_T2_c  \\\n",
       "0    0.000007  3.013082e-07  4.227295e-11  9.171097e-10  1.284325e-08   \n",
       "1    0.000003  2.393127e-07  4.203981e-11  7.653907e-10  1.484397e-08   \n",
       "2    0.000002  2.212789e-07  3.343054e-11  6.646832e-10  1.393792e-08   \n",
       "3    0.000003  3.090001e-07  4.128989e-11  7.914225e-10  1.757626e-08   \n",
       "4    0.000003  5.549445e-07  6.531665e-11  1.573526e-09  4.263682e-08   \n",
       "\n",
       "       pfk_T3_c      pfk_T4_c  \n",
       "0  1.304504e-07  3.808015e-07  \n",
       "1  1.450826e-07  4.380999e-07  \n",
       "2  1.401509e-07  4.242574e-07  \n",
       "3  1.561635e-07  4.600968e-07  \n",
       "4  2.259306e-07  6.118950e-07  \n",
       "\n",
       "[5 rows x 66 columns]"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "samples = sample_concentrations(conc_solver, n=20)\n",
    "samples.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "By default `sample_concentrations` uses the `optgp` method <cite data-cite=\"MHM14\">\n",
    "(Megchelenbrink, Huynen, and Marchiori, 2014)</cite>, as it is suited for larger models and can run in parallel. The number of processes can be changed by using the `processes` argument."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2021-01-25T18:44:04.344046Z",
     "iopub.status.busy": "2021-01-25T18:44:04.343294Z",
     "iopub.status.idle": "2021-01-25T18:44:36.177838Z",
     "shell.execute_reply": "2021-01-25T18:44:36.178602Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "One process:\n",
      "CPU times: user 12.7 s, sys: 357 ms, total: 13.1 s\n",
      "Wall time: 11.7 s\n",
      "\n",
      "Two processes:\n",
      "CPU times: user 695 ms, sys: 199 ms, total: 895 ms\n",
      "Wall time: 9.44 s\n"
     ]
    }
   ],
   "source": [
    "print(\"One process:\")\n",
    "%time samples = sample_concentrations(conc_solver, n=1000, processes=1)\n",
    "print(\"\\nTwo processes:\")\n",
    "%time samples = sample_concentrations(conc_solver, n=1000, processes=2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Alternatively, the Artificial Centering Hit-and-Run for sampling <cite data-cite=\"KS98\">\n",
    "(Kaufman and Smith, 1998)</cite> can be utilized by setting the method to `achr`. The `achr` method does not support parallel execution, but it has good convergence and is almost Markovian."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2021-01-25T18:44:36.200562Z",
     "iopub.status.busy": "2021-01-25T18:44:36.199618Z",
     "iopub.status.idle": "2021-01-25T18:44:38.163260Z",
     "shell.execute_reply": "2021-01-25T18:44:38.163712Z"
    }
   },
   "outputs": [],
   "source": [
    "samples = sample_concentrations(conc_solver, n=100, method=\"achr\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In general, setting up the sampler is expensive since initial search directions are generated by solving many linear programming problems. Thus, it is recommended to generate as many samples as possible in one go. However, generating large numbers of samples might require finer control over the sampling procedure, as described in the following section."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Advance usage\n",
    "#### Sampler objects\n",
    "\n",
    "The concentration sampling process can be controlled on a lower level by using the sampler classes directly, found in the `conc_sampling` submodule."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2021-01-25T18:44:38.168002Z",
     "iopub.status.busy": "2021-01-25T18:44:38.167228Z",
     "iopub.status.idle": "2021-01-25T18:44:38.169256Z",
     "shell.execute_reply": "2021-01-25T18:44:38.169705Z"
    }
   },
   "outputs": [],
   "source": [
    "from mass.thermo.conc_sampling import ConcACHRSampler, ConcOptGPSampler"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Both concentration sampler classes have standardized interfaces and take some additional arguments. \n",
    "\n",
    "For example, one such argument is the thinning factor, where “thinning” means only recording samples every `x` iterations where `x` is the thinning factor. Higher thinning factors mean less correlated samples but also larger computation times.\n",
    "\n",
    "By default, the samplers use a thinning factor of 100, which creates roughly uncorrelated samples. Increasing the thinning factor leads to better mixing of samples, while lowering the thinning factor leads to more correlated samples. For example, it may be desirable to set a thinning factor of 1 to obtain all iterates when studying convergence for a model.\n",
    "\n",
    "Samplers can be seeded so that they produce the same results each time they are run."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2021-01-25T18:44:38.181186Z",
     "iopub.status.busy": "2021-01-25T18:44:38.180443Z",
     "iopub.status.idle": "2021-01-25T18:44:38.509984Z",
     "shell.execute_reply": "2021-01-25T18:44:38.510444Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
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       "\n",
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       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
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       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>glc__D_c</th>\n",
       "      <th>g6p_c</th>\n",
       "      <th>f6p_c</th>\n",
       "      <th>fdp_c</th>\n",
       "      <th>dhap_c</th>\n",
       "      <th>g3p_c</th>\n",
       "      <th>_13dpg_c</th>\n",
       "      <th>_3pg_c</th>\n",
       "      <th>_2pg_c</th>\n",
       "      <th>pep_c</th>\n",
       "      <th>...</th>\n",
       "      <th>pfk_R3_A_c</th>\n",
       "      <th>pfk_R3_AF_c</th>\n",
       "      <th>pfk_R4_c</th>\n",
       "      <th>pfk_R4_A_c</th>\n",
       "      <th>pfk_R4_AF_c</th>\n",
       "      <th>pfk_T0_c</th>\n",
       "      <th>pfk_T1_c</th>\n",
       "      <th>pfk_T2_c</th>\n",
       "      <th>pfk_T3_c</th>\n",
       "      <th>pfk_T4_c</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1.592336</td>\n",
       "      <td>0.197568</td>\n",
       "      <td>0.078832</td>\n",
       "      <td>0.018910</td>\n",
       "      <td>0.142081</td>\n",
       "      <td>0.007510</td>\n",
       "      <td>0.000472</td>\n",
       "      <td>0.090709</td>\n",
       "      <td>0.013006</td>\n",
       "      <td>0.021494</td>\n",
       "      <td>...</td>\n",
       "      <td>0.000003</td>\n",
       "      <td>4.536657e-07</td>\n",
       "      <td>3.693232e-07</td>\n",
       "      <td>0.000001</td>\n",
       "      <td>2.228541e-07</td>\n",
       "      <td>3.305772e-11</td>\n",
       "      <td>6.624519e-10</td>\n",
       "      <td>1.327504e-08</td>\n",
       "      <td>1.311206e-07</td>\n",
       "      <td>3.905462e-07</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>2.248172</td>\n",
       "      <td>0.285898</td>\n",
       "      <td>0.116922</td>\n",
       "      <td>0.004324</td>\n",
       "      <td>0.043806</td>\n",
       "      <td>0.002030</td>\n",
       "      <td>0.000364</td>\n",
       "      <td>0.022330</td>\n",
       "      <td>0.003282</td>\n",
       "      <td>0.005558</td>\n",
       "      <td>...</td>\n",
       "      <td>0.000002</td>\n",
       "      <td>3.634455e-07</td>\n",
       "      <td>3.032560e-07</td>\n",
       "      <td>0.000001</td>\n",
       "      <td>1.922307e-07</td>\n",
       "      <td>2.714412e-11</td>\n",
       "      <td>5.768461e-10</td>\n",
       "      <td>1.225869e-08</td>\n",
       "      <td>1.236426e-07</td>\n",
       "      <td>3.810419e-07</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>2.263896</td>\n",
       "      <td>0.288041</td>\n",
       "      <td>0.117857</td>\n",
       "      <td>0.004522</td>\n",
       "      <td>0.045433</td>\n",
       "      <td>0.002117</td>\n",
       "      <td>0.000370</td>\n",
       "      <td>0.023388</td>\n",
       "      <td>0.003439</td>\n",
       "      <td>0.005827</td>\n",
       "      <td>...</td>\n",
       "      <td>0.000002</td>\n",
       "      <td>3.618207e-07</td>\n",
       "      <td>3.020507e-07</td>\n",
       "      <td>0.000001</td>\n",
       "      <td>1.916574e-07</td>\n",
       "      <td>2.703623e-11</td>\n",
       "      <td>5.752355e-10</td>\n",
       "      <td>1.223898e-08</td>\n",
       "      <td>1.234960e-07</td>\n",
       "      <td>3.808523e-07</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>2.258775</td>\n",
       "      <td>0.287343</td>\n",
       "      <td>0.117552</td>\n",
       "      <td>0.004406</td>\n",
       "      <td>0.044485</td>\n",
       "      <td>0.002067</td>\n",
       "      <td>0.000366</td>\n",
       "      <td>0.022777</td>\n",
       "      <td>0.003348</td>\n",
       "      <td>0.005673</td>\n",
       "      <td>...</td>\n",
       "      <td>0.000002</td>\n",
       "      <td>3.623478e-07</td>\n",
       "      <td>3.024418e-07</td>\n",
       "      <td>0.000001</td>\n",
       "      <td>1.918435e-07</td>\n",
       "      <td>2.707124e-11</td>\n",
       "      <td>5.757583e-10</td>\n",
       "      <td>1.224538e-08</td>\n",
       "      <td>1.235436e-07</td>\n",
       "      <td>3.809139e-07</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>2.267224</td>\n",
       "      <td>0.288494</td>\n",
       "      <td>0.109154</td>\n",
       "      <td>0.004331</td>\n",
       "      <td>0.043882</td>\n",
       "      <td>0.002036</td>\n",
       "      <td>0.000365</td>\n",
       "      <td>0.022409</td>\n",
       "      <td>0.003295</td>\n",
       "      <td>0.005585</td>\n",
       "      <td>...</td>\n",
       "      <td>0.000002</td>\n",
       "      <td>3.614792e-07</td>\n",
       "      <td>3.017973e-07</td>\n",
       "      <td>0.000001</td>\n",
       "      <td>1.915368e-07</td>\n",
       "      <td>2.701355e-11</td>\n",
       "      <td>5.748966e-10</td>\n",
       "      <td>1.223483e-08</td>\n",
       "      <td>1.234651e-07</td>\n",
       "      <td>3.808123e-07</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>5 rows × 66 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "   glc__D_c     g6p_c     f6p_c     fdp_c    dhap_c     g3p_c  _13dpg_c  \\\n",
       "0  1.592336  0.197568  0.078832  0.018910  0.142081  0.007510  0.000472   \n",
       "1  2.248172  0.285898  0.116922  0.004324  0.043806  0.002030  0.000364   \n",
       "2  2.263896  0.288041  0.117857  0.004522  0.045433  0.002117  0.000370   \n",
       "3  2.258775  0.287343  0.117552  0.004406  0.044485  0.002067  0.000366   \n",
       "4  2.267224  0.288494  0.109154  0.004331  0.043882  0.002036  0.000365   \n",
       "\n",
       "     _3pg_c    _2pg_c     pep_c  ...  pfk_R3_A_c   pfk_R3_AF_c      pfk_R4_c  \\\n",
       "0  0.090709  0.013006  0.021494  ...    0.000003  4.536657e-07  3.693232e-07   \n",
       "1  0.022330  0.003282  0.005558  ...    0.000002  3.634455e-07  3.032560e-07   \n",
       "2  0.023388  0.003439  0.005827  ...    0.000002  3.618207e-07  3.020507e-07   \n",
       "3  0.022777  0.003348  0.005673  ...    0.000002  3.623478e-07  3.024418e-07   \n",
       "4  0.022409  0.003295  0.005585  ...    0.000002  3.614792e-07  3.017973e-07   \n",
       "\n",
       "   pfk_R4_A_c   pfk_R4_AF_c      pfk_T0_c      pfk_T1_c      pfk_T2_c  \\\n",
       "0    0.000001  2.228541e-07  3.305772e-11  6.624519e-10  1.327504e-08   \n",
       "1    0.000001  1.922307e-07  2.714412e-11  5.768461e-10  1.225869e-08   \n",
       "2    0.000001  1.916574e-07  2.703623e-11  5.752355e-10  1.223898e-08   \n",
       "3    0.000001  1.918435e-07  2.707124e-11  5.757583e-10  1.224538e-08   \n",
       "4    0.000001  1.915368e-07  2.701355e-11  5.748966e-10  1.223483e-08   \n",
       "\n",
       "       pfk_T3_c      pfk_T4_c  \n",
       "0  1.311206e-07  3.905462e-07  \n",
       "1  1.236426e-07  3.810419e-07  \n",
       "2  1.234960e-07  3.808523e-07  \n",
       "3  1.235436e-07  3.809139e-07  \n",
       "4  1.234651e-07  3.808123e-07  \n",
       "\n",
       "[5 rows x 66 columns]"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "conc_achr = ConcACHRSampler(conc_solver, thinning=1, seed=5)\n",
    "samples = conc_achr.sample(10, concs=True)\n",
    "# Display only the first 5 samples\n",
    "samples.head(5)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The `sample()` method also comes with the `concs` argument that controls the sample output. Setting `concs=True` returns only concentration variables, while setting `concs=False` returns the equilibrium constant variables and any additional variables."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2021-01-25T18:44:38.514970Z",
     "iopub.status.busy": "2021-01-25T18:44:38.514104Z",
     "iopub.status.idle": "2021-01-25T18:44:38.520460Z",
     "shell.execute_reply": "2021-01-25T18:44:38.521053Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Index(['ade_c', 'adn_c', 'imp_c', 'prpp_c', 'nh3_c', 'glc__D_c', 'g6p_c',\n",
      "       'adp_c', 'atp_c', 'Keq_HEX1',\n",
      "       ...\n",
      "       'pfk_T0_c', 'Keq_PFK_L', 'pfk_T1_c', 'Keq_PFK_T1', 'pfk_T2_c',\n",
      "       'Keq_PFK_T2', 'pfk_T3_c', 'Keq_PFK_T3', 'pfk_T4_c', 'Keq_PFK_T4'],\n",
      "      dtype='object', length=114)\n"
     ]
    }
   ],
   "source": [
    "samples = conc_achr.sample(10, concs=False)\n",
    "print(samples.columns)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The `ConcOptGPSampler` has an additional `processes` argument that specifies how many processes are used to create parallel sampling chains. The number of processes should be in the order of available CPU cores for maximum efficiency. As noted before, the class initialization can take up to a few minutes due to generation of initial search directions. On the other hand, sampling is quicker."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2021-01-25T18:44:38.532444Z",
     "iopub.status.busy": "2021-01-25T18:44:38.531695Z",
     "iopub.status.idle": "2021-01-25T18:44:39.131219Z",
     "shell.execute_reply": "2021-01-25T18:44:39.132008Z"
    }
   },
   "outputs": [],
   "source": [
    "conc_optgp = ConcOptGPSampler(conc_solver, processes=4, seed=5)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For the `ConcOptGPSampler`, the number of samples should be a multiple of the number of processes. Otherwise, the number is increased automatically to the nearest multiple."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2021-01-25T18:44:39.137360Z",
     "iopub.status.busy": "2021-01-25T18:44:39.136268Z",
     "iopub.status.idle": "2021-01-25T18:44:39.288403Z",
     "shell.execute_reply": "2021-01-25T18:44:39.289349Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Number of samples generated: 12\n"
     ]
    }
   ],
   "source": [
    "samples = conc_optgp.sample(10)\n",
    "print(\"Number of samples generated: {0}\".format(len(samples)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Batch sampling\n",
    "\n",
    "Sampler objects are made for generating billions of samples, however using the sampling functions might quickly fill up the computer RAM when working with genome-scale models. \n",
    "\n",
    "In this scenario, the batch method of the sampler objects might be useful. The `batch` method takes two arguments: the number of samples in each batch and the number of batches.\n",
    "\n",
    "Suppose the concentration of ATP, ADP and AMP are unknown. The batch sampler could be used to generate 10 batches of feasible concentrations with 100 samples each. The samples could be averaged to get the mean metabolite concentrations per batch. Finally, the mean metabolite concentrations and standard deviation could be calculated."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2021-01-25T18:44:39.314551Z",
     "iopub.status.busy": "2021-01-25T18:44:39.313598Z",
     "iopub.status.idle": "2021-01-25T18:44:59.115736Z",
     "shell.execute_reply": "2021-01-25T18:44:59.116202Z"
    },
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Ave. atp_c concentration: 2.17516 +- 0.10551\n",
      "Ave. adp_c concentration: 0.24789 +- 0.01742\n",
      "Ave. amp_c concentration: 0.12479 +- 0.00738\n"
     ]
    }
   ],
   "source": [
    "# Remove current initial conditions for example\n",
    "conc_solver.model.metabolites.atp_c.ic = None\n",
    "conc_solver.model.metabolites.adp_c.ic = None\n",
    "conc_solver.model.metabolites.amp_c.ic = None\n",
    "# Set up concentration sampling problem\n",
    "conc_solver.setup_sampling_problem(\n",
    "    conc_percent_deviation=0.5,\n",
    "    Keq_percent_deviation=0)\n",
    "\n",
    "# Get batch samples\n",
    "conc_optgp = ConcOptGPSampler(conc_solver, processes=1, seed=5)\n",
    "batch_samples = [sample for sample in conc_optgp.batch(100, 10)]\n",
    "\n",
    "# Determine average metabolite concentrations per batch\n",
    "for met in [\"atp_c\", \"adp_c\", \"amp_c\"]:\n",
    "    met = conc_solver.model.metabolites.get_by_id(met)\n",
    "    per_batch_axp_ave = [\n",
    "        np.mean(sample[met.id])\n",
    "        for sample in batch_samples]\n",
    "    print(\"Ave. {2} concentration: {0:.5f} +- {1:.5f}\".format(\n",
    "        np.mean(per_batch_axp_ave), np.std(per_batch_axp_ave), met.id))\n",
    "    met.ic = np.mean(per_batch_axp_ave)"
   ]
  }
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