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": "2020-10-20T20:36:36.523957Z",
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     "iopub.status.idle": "2020-10-20T20:36:39.015211Z",
     "shell.execute_reply": "2020-10-20T20:36:39.015793Z"
    }
   },
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "\n",
    "import numpy as np\n",
    "\n",
    "import mass.test\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": {
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     "shell.execute_reply": "2020-10-20T20:36:39.182886Z"
    }
   },
   "outputs": [],
   "source": [
    "# Load the JSON version of the textbook model\n",
    "model = mass.test.create_test_model(\"textbook\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2020-10-20T20:36:39.272365Z",
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     "shell.execute_reply": "2020-10-20T20:36:39.536607Z"
    }
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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>0x07fd129545a90</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 0x7fd129545a90>"
      ]
     },
     "execution_count": 1,
     "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": "2020-10-20T20:36:39.541082Z",
     "iopub.status.busy": "2020-10-20T20:36:39.540316Z",
     "iopub.status.idle": "2020-10-20T20:36:39.542961Z",
     "shell.execute_reply": "2020-10-20T20:36:39.543405Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<ConcSolver RBC_PFK at 0x7fd12953ef50>\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": "2020-10-20T20:36:39.547981Z",
     "iopub.status.busy": "2020-10-20T20:36:39.547181Z",
     "iopub.status.idle": "2020-10-20T20:36:39.549917Z",
     "shell.execute_reply": "2020-10-20T20:36:39.550404Z"
    }
   },
   "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": "2020-10-20T20:36:39.555846Z",
     "iopub.status.busy": "2020-10-20T20:36:39.555180Z",
     "iopub.status.idle": "2020-10-20T20:36:39.557576Z",
     "shell.execute_reply": "2020-10-20T20:36:39.558063Z"
    }
   },
   "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": "2020-10-20T20:36:39.565756Z",
     "iopub.status.busy": "2020-10-20T20:36:39.565070Z",
     "iopub.status.idle": "2020-10-20T20:36:39.567575Z",
     "shell.execute_reply": "2020-10-20T20:36:39.568063Z"
    }
   },
   "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": "2020-10-20T20:36:39.591342Z",
     "iopub.status.busy": "2020-10-20T20:36:39.590662Z",
     "iopub.status.idle": "2020-10-20T20:36:39.593212Z",
     "shell.execute_reply": "2020-10-20T20:36:39.593655Z"
    }
   },
   "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": "2020-10-20T20:36:39.597980Z",
     "iopub.status.busy": "2020-10-20T20:36:39.597334Z",
     "iopub.status.idle": "2020-10-20T20:36:39.599851Z",
     "shell.execute_reply": "2020-10-20T20:36:39.600297Z"
    }
   },
   "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": "2020-10-20T20:36:39.605231Z",
     "iopub.status.busy": "2020-10-20T20:36:39.604397Z",
     "iopub.status.idle": "2020-10-20T20:36:39.606993Z",
     "shell.execute_reply": "2020-10-20T20:36:39.607431Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<optlang.gurobi_interface.Model object at 0x7fd129542190>\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": "2020-10-20T20:36:39.703983Z",
     "iopub.status.busy": "2020-10-20T20:36:39.659685Z",
     "iopub.status.idle": "2020-10-20T20:36:40.400168Z",
     "shell.execute_reply": "2020-10-20T20:36:40.400904Z"
    }
   },
   "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": "2020-10-20T20:36:40.406028Z",
     "iopub.status.busy": "2020-10-20T20:36:40.405300Z",
     "iopub.status.idle": "2020-10-20T20:36:40.409761Z",
     "shell.execute_reply": "2020-10-20T20:36:40.410527Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "min\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<optlang.gurobi_interface.Objective at 0x7fd12841b110>"
      ]
     },
     "execution_count": 1,
     "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": "2020-10-20T20:36:40.415043Z",
     "iopub.status.busy": "2020-10-20T20:36:40.414249Z",
     "iopub.status.idle": "2020-10-20T20:36:40.416804Z",
     "shell.execute_reply": "2020-10-20T20:36:40.417239Z"
    }
   },
   "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": "2020-10-20T20:36:40.506080Z",
     "iopub.status.busy": "2020-10-20T20:36:40.462081Z",
     "iopub.status.idle": "2020-10-20T20:36:40.643272Z",
     "shell.execute_reply": "2020-10-20T20:36:40.643747Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<strong><em>Optimal</em> solution with objective value 0.000</strong><br><div>\n",
       "<style scoped>\n",
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       "        vertical-align: middle;\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 0x7fd1295a9ed0>"
      ]
     },
     "execution_count": 1,
     "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": "2020-10-20T20:36:40.648488Z",
     "iopub.status.busy": "2020-10-20T20:36:40.647638Z",
     "iopub.status.idle": "2020-10-20T20:36:40.651067Z",
     "shell.execute_reply": "2020-10-20T20:36:40.651528Z"
    }
   },
   "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": 1,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dir(conc_solution)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2020-10-20T20:36:40.655642Z",
     "iopub.status.busy": "2020-10-20T20:36:40.655029Z",
     "iopub.status.idle": "2020-10-20T20:36:40.657655Z",
     "shell.execute_reply": "2020-10-20T20:36:40.657113Z"
    }
   },
   "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": "2020-10-20T20:36:40.677467Z",
     "iopub.status.busy": "2020-10-20T20:36:40.676713Z",
     "iopub.status.idle": "2020-10-20T20:36:41.718297Z",
     "shell.execute_reply": "2020-10-20T20:36:41.718737Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x7fd129681310>"
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "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": "2020-10-20T20:36:41.728517Z",
     "iopub.status.busy": "2020-10-20T20:36:41.727884Z",
     "iopub.status.idle": "2020-10-20T20:36:41.842931Z",
     "shell.execute_reply": "2020-10-20T20:36:41.843520Z"
    }
   },
   "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": "2020-10-20T20:36:41.848905Z",
     "iopub.status.busy": "2020-10-20T20:36:41.848122Z",
     "iopub.status.idle": "2020-10-20T20:36:41.850000Z",
     "shell.execute_reply": "2020-10-20T20:36:41.850629Z"
    }
   },
   "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": "2020-10-20T20:36:41.862165Z",
     "iopub.status.busy": "2020-10-20T20:36:41.861505Z",
     "iopub.status.idle": "2020-10-20T20:36:41.864248Z",
     "shell.execute_reply": "2020-10-20T20:36:41.864766Z"
    }
   },
   "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": "2020-10-20T20:36:41.876271Z",
     "iopub.status.busy": "2020-10-20T20:36:41.875467Z",
     "iopub.status.idle": "2020-10-20T20:36:42.510286Z",
     "shell.execute_reply": "2020-10-20T20:36:42.510928Z"
    }
   },
   "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",
       "    .dataframe tbody tr th {\n",
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       "<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>0.573084</td>\n",
       "      <td>0.072931</td>\n",
       "      <td>0.029583</td>\n",
       "      <td>0.005041</td>\n",
       "      <td>0.072693</td>\n",
       "      <td>0.003611</td>\n",
       "      <td>0.000257</td>\n",
       "      <td>0.039993</td>\n",
       "      <td>0.005171</td>\n",
       "      <td>0.007705</td>\n",
       "      <td>...</td>\n",
       "      <td>0.000005</td>\n",
       "      <td>7.853042e-07</td>\n",
       "      <td>6.694715e-07</td>\n",
       "      <td>0.000002</td>\n",
       "      <td>3.965789e-07</td>\n",
       "      <td>9.650193e-11</td>\n",
       "      <td>1.505694e-09</td>\n",
       "      <td>2.101538e-08</td>\n",
       "      <td>1.328247e-07</td>\n",
       "      <td>3.876323e-07</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.856706</td>\n",
       "      <td>0.150834</td>\n",
       "      <td>0.060231</td>\n",
       "      <td>0.015956</td>\n",
       "      <td>0.159873</td>\n",
       "      <td>0.007932</td>\n",
       "      <td>0.000379</td>\n",
       "      <td>0.127215</td>\n",
       "      <td>0.018441</td>\n",
       "      <td>0.029765</td>\n",
       "      <td>...</td>\n",
       "      <td>0.000005</td>\n",
       "      <td>6.515172e-07</td>\n",
       "      <td>5.497481e-07</td>\n",
       "      <td>0.000002</td>\n",
       "      <td>3.517310e-07</td>\n",
       "      <td>5.981162e-11</td>\n",
       "      <td>9.459993e-10</td>\n",
       "      <td>1.811540e-08</td>\n",
       "      <td>1.543798e-07</td>\n",
       "      <td>3.845968e-07</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.998544</td>\n",
       "      <td>0.195311</td>\n",
       "      <td>0.063848</td>\n",
       "      <td>0.017021</td>\n",
       "      <td>0.163829</td>\n",
       "      <td>0.005826</td>\n",
       "      <td>0.000346</td>\n",
       "      <td>0.090935</td>\n",
       "      <td>0.011576</td>\n",
       "      <td>0.016030</td>\n",
       "      <td>...</td>\n",
       "      <td>0.000003</td>\n",
       "      <td>4.135990e-07</td>\n",
       "      <td>3.306412e-07</td>\n",
       "      <td>0.000002</td>\n",
       "      <td>3.379217e-07</td>\n",
       "      <td>1.277482e-10</td>\n",
       "      <td>1.890705e-09</td>\n",
       "      <td>2.948550e-08</td>\n",
       "      <td>2.131460e-07</td>\n",
       "      <td>4.545959e-07</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0.914117</td>\n",
       "      <td>0.167755</td>\n",
       "      <td>0.058189</td>\n",
       "      <td>0.017858</td>\n",
       "      <td>0.153780</td>\n",
       "      <td>0.005535</td>\n",
       "      <td>0.000390</td>\n",
       "      <td>0.067050</td>\n",
       "      <td>0.009733</td>\n",
       "      <td>0.014720</td>\n",
       "      <td>...</td>\n",
       "      <td>0.000004</td>\n",
       "      <td>6.057890e-07</td>\n",
       "      <td>3.992094e-07</td>\n",
       "      <td>0.000003</td>\n",
       "      <td>3.881900e-07</td>\n",
       "      <td>1.254980e-10</td>\n",
       "      <td>1.799046e-09</td>\n",
       "      <td>2.254959e-08</td>\n",
       "      <td>2.210896e-07</td>\n",
       "      <td>4.464778e-07</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>1.342935</td>\n",
       "      <td>0.239222</td>\n",
       "      <td>0.075899</td>\n",
       "      <td>0.019497</td>\n",
       "      <td>0.156620</td>\n",
       "      <td>0.006916</td>\n",
       "      <td>0.000357</td>\n",
       "      <td>0.122204</td>\n",
       "      <td>0.017919</td>\n",
       "      <td>0.027510</td>\n",
       "      <td>...</td>\n",
       "      <td>0.000005</td>\n",
       "      <td>7.079300e-07</td>\n",
       "      <td>4.701749e-07</td>\n",
       "      <td>0.000003</td>\n",
       "      <td>4.453493e-07</td>\n",
       "      <td>7.721228e-11</td>\n",
       "      <td>1.881876e-09</td>\n",
       "      <td>2.896366e-08</td>\n",
       "      <td>1.929782e-07</td>\n",
       "      <td>4.755604e-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  0.573084  0.072931  0.029583  0.005041  0.072693  0.003611  0.000257   \n",
       "1  0.856706  0.150834  0.060231  0.015956  0.159873  0.007932  0.000379   \n",
       "2  0.998544  0.195311  0.063848  0.017021  0.163829  0.005826  0.000346   \n",
       "3  0.914117  0.167755  0.058189  0.017858  0.153780  0.005535  0.000390   \n",
       "4  1.342935  0.239222  0.075899  0.019497  0.156620  0.006916  0.000357   \n",
       "\n",
       "     _3pg_c    _2pg_c     pep_c  ...  pfk_R3_A_c   pfk_R3_AF_c      pfk_R4_c  \\\n",
       "0  0.039993  0.005171  0.007705  ...    0.000005  7.853042e-07  6.694715e-07   \n",
       "1  0.127215  0.018441  0.029765  ...    0.000005  6.515172e-07  5.497481e-07   \n",
       "2  0.090935  0.011576  0.016030  ...    0.000003  4.135990e-07  3.306412e-07   \n",
       "3  0.067050  0.009733  0.014720  ...    0.000004  6.057890e-07  3.992094e-07   \n",
       "4  0.122204  0.017919  0.027510  ...    0.000005  7.079300e-07  4.701749e-07   \n",
       "\n",
       "   pfk_R4_A_c   pfk_R4_AF_c      pfk_T0_c      pfk_T1_c      pfk_T2_c  \\\n",
       "0    0.000002  3.965789e-07  9.650193e-11  1.505694e-09  2.101538e-08   \n",
       "1    0.000002  3.517310e-07  5.981162e-11  9.459993e-10  1.811540e-08   \n",
       "2    0.000002  3.379217e-07  1.277482e-10  1.890705e-09  2.948550e-08   \n",
       "3    0.000003  3.881900e-07  1.254980e-10  1.799046e-09  2.254959e-08   \n",
       "4    0.000003  4.453493e-07  7.721228e-11  1.881876e-09  2.896366e-08   \n",
       "\n",
       "       pfk_T3_c      pfk_T4_c  \n",
       "0  1.328247e-07  3.876323e-07  \n",
       "1  1.543798e-07  3.845968e-07  \n",
       "2  2.131460e-07  4.545959e-07  \n",
       "3  2.210896e-07  4.464778e-07  \n",
       "4  1.929782e-07  4.755604e-07  \n",
       "\n",
       "[5 rows x 66 columns]"
      ]
     },
     "execution_count": 1,
     "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": "2020-10-20T20:36:42.525724Z",
     "iopub.status.busy": "2020-10-20T20:36:42.524825Z",
     "iopub.status.idle": "2020-10-20T20:37:02.349030Z",
     "shell.execute_reply": "2020-10-20T20:37:02.349806Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "One process:\n",
      "CPU times: user 12.7 s, sys: 62 ms, total: 12.8 s\n",
      "Wall time: 12.7 s\n",
      "\n",
      "Two processes:\n",
      "CPU times: user 506 ms, sys: 35.4 ms, total: 541 ms\n",
      "Wall time: 7.08 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": "2020-10-20T20:37:02.368167Z",
     "iopub.status.busy": "2020-10-20T20:37:02.367288Z",
     "iopub.status.idle": "2020-10-20T20:37:03.920445Z",
     "shell.execute_reply": "2020-10-20T20:37:03.920897Z"
    }
   },
   "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": "2020-10-20T20:37:03.925571Z",
     "iopub.status.busy": "2020-10-20T20:37:03.924888Z",
     "iopub.status.idle": "2020-10-20T20:37:03.927112Z",
     "shell.execute_reply": "2020-10-20T20:37:03.927581Z"
    }
   },
   "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": "2020-10-20T20:37:03.939333Z",
     "iopub.status.busy": "2020-10-20T20:37:03.938621Z",
     "iopub.status.idle": "2020-10-20T20:37:04.259161Z",
     "shell.execute_reply": "2020-10-20T20:37:04.259599Z"
    }
   },
   "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",
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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": 1,
     "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": "2020-10-20T20:37:04.263804Z",
     "iopub.status.busy": "2020-10-20T20:37:04.263135Z",
     "iopub.status.idle": "2020-10-20T20:37:04.269147Z",
     "shell.execute_reply": "2020-10-20T20:37:04.269616Z"
    }
   },
   "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": "2020-10-20T20:37:04.282221Z",
     "iopub.status.busy": "2020-10-20T20:37:04.281526Z",
     "iopub.status.idle": "2020-10-20T20:37:04.597832Z",
     "shell.execute_reply": "2020-10-20T20:37:04.598286Z"
    }
   },
   "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": "2020-10-20T20:37:04.602866Z",
     "iopub.status.busy": "2020-10-20T20:37:04.602233Z",
     "iopub.status.idle": "2020-10-20T20:37:04.751726Z",
     "shell.execute_reply": "2020-10-20T20:37:04.752357Z"
    }
   },
   "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": "2020-10-20T20:37:04.779147Z",
     "iopub.status.busy": "2020-10-20T20:37:04.778316Z",
     "iopub.status.idle": "2020-10-20T20:37:17.719373Z",
     "shell.execute_reply": "2020-10-20T20:37:17.719795Z"
    },
    "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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