docs/education/sb2/chapters/sb2_chapter6.ipynb

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    "# Open Systems\n",
    "All of the examples in the previous two chapters were closed systems. The ultimate state of closed, chemically reacting systems is chemical equilibrium. Living systems are characterized by mass and energy flow across their boundaries that keep them away from equilibrium. We now discuss open systems, which allow molecules to enter and leave. Open systems ultimately reach a steady state that is often close to a homeostatic state of interest. \n",
    "\n",
    "**MASSpy** will be used to demonstrate some of the topics in this chapter. "
   ]
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   "source": [
    "from mass import (\n",
    "    MassModel, MassMetabolite, MassReaction, Simulation, MassSolution)\n",
    "from mass.visualization import plot_time_profile, plot_phase_portrait"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Other useful packages are also imported at this time."
   ]
  },
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   "source": [
    "import matplotlib.pyplot as plt"
   ]
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    "## Basic Concepts\n",
    "There are several fundamental concepts that need to be understood when one considers open systems. We discuss the more significant ones in this section. \n",
    "\n",
    "### The system boundary  \n",
    "Implicit in the term 'open system' is the notion of an inside and an outside, the division of the world into two domains. The separation between the two is the _system boundary,_ which thus defines what is inside a system and belongs to it, and what is outside. \n",
    "\n",
    "The definition of a boundary can be physical. An example of a physical boundary may be the cell wall, that clearly defines what is inside and what is outside. Similarly, the outer membrane of the mitochondria can serve as a clearly defined physical system boundary. Thus, systems can have hard, immovable boundaries or soft, flexible ones. In the latter case, the volume of the system may be changing. \n",
    "\n",
    "The definition of a boundary can also be virtual. For instance, we can define a pathway, such as the TCA cycle, as a system, or the amino acid biosynthetic pathways in a cell as a system. In both cases we might draw dashed lines around it on the metabolic map to indicate the system boundary. \n",
    "\n",
    "### Crossing the boundary: inputs and outputs  \n",
    "Once a system boundary has been established, we can identify and define interactions across it. They are the _inputs_ and _outputs_ of the system. In most cases, we will be considering mass flows in and out of a system; molecules coming and going. Such flows are normally amenable to experimental determination. \n",
    "\n",
    "There may be other quantities crossing the system boundary. For instance, if we are considering photosynthesis, photons are crossing the system boundary providing a net influx of energy. Forces can also act on the system boundary. For instance, if the number of molecules coming into and leaving a system through a coupled transport mechanism is not balanced, then osmotic pressure may be generated across the system boundary. Cells have sodium-potassium pumps that displace an uneven number of two types of cations to deal with osmotic imbalances. \n",
    "\n",
    "### Perturbations and boundaries  \n",
    "In most analyses of living systems, we are concerned about changes in the environment. The temperature may change, substrate availability may change, and so on. Such changes in the environment can be thought of as forcing functions to which the living system responds. These are one-way interactions, from the environment to the system. In most cases, we consider the system to be small (relative to the environment) and that the environment buffers the activities of the system. For instance, the environment may provide an infinite sink for cellular waste products. \n",
    "\n",
    "In other cases, the activities of the system influence the state of the environment. In batch fermentation, for example, the metabolic activities will substantially change the chemical composition of the medium during the course of the fermentation. On a global scale, we are now becoming more concerned about the impact that human activities have on the climate and the larger environment of human socio-economic activities. In such cases, there are two-way interactions between the system and the environment that need to be described. \n",
    "\n",
    "### Inside the boundary: the internal network  \n",
    "The definition of a system boundary determines what is inside. Once we know what is inside the system, we can determine the network of chemical transformations that takes place. This network has topology and its links have kinetic properties. \n",
    "\n",
    "In most cases, it is hard to measure the internal state of a system. There typically are only a few non-invasive measurements available. Occasionally, there are probes that we can use to observe the internal activities. Tracers, such as $^{13}C$ atoms strategically placed in substrates, can be used to trace input to output and allow us to determine pieces of the internal state of a system. Tearing a system apart to enumerate its components is of course possible, but the system is destroyed in the process. Thus, we are most often in the situation where we cannot fully experimentally determine the internal state of a system, and may have to be satisfied with only partial knowledge. \n",
    "\n",
    "### From networks to system models  \n",
    "Mathematical models may help us to simulate or estimate the internal state of the system. Sometimes we are able to bracket its state based on the inputs and outputs and our knowledge of the internal network. \n",
    "\n",
    "Full dynamic simulation requires extensive knowledge about the internal properties of a system. Detailed models that describe the dynamic state of a system require the definition of the system boundary, the inputs and outputs, the structure of the internal network, and the kinetic properties of the links in the network. We can then simulate the response of the system to various perturbations, such as changes in the environmental conditions. \n",
    "\n",
    "### The functional state  \n",
    "Once a system model has been formulated, it can be used to compute the functional state of the system for a given set of conditions. Closed systems will eventually go to chemical equilibrium. However, open systems are fundamentally different. Due to continuous interactions with the environment, they have internal states that are either dynamic or steady. A system that has fast internal time constants relative to changes in the environment will reach a steady state, or a quasi-steady state. For a biological system, such functional states are called _homeostatic states_. Such states are maintained through energy dissipation. The flow of energy in has to exceed the energy leaving the system. This difference allows living systems to reach a functional homeostatic state. \n",
    "\n",
    "![Figure-6-1](../images/Ch6/Figure-6-1.png)\n",
    "\n",
    "**Figure 6.1:** Open systems. (a) example production of ATP from pyruvate by mitochondria (Prepared by Nathan Lewis). (b) Basic definitions associated with an open system."
   ]
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    "## Reversible reaction in an Open Environment\n",
    "In an open environment, the simple reaction of Eq. (4.1)  has an inflow $(b_1)$ of $x_1$ and an outflow $(b_2)$ of $x_2$: \n",
    "\n",
    "$$\\begin{equation} \\stackrel{b_1}{\\rightarrow} x_1 \\underset{v_{-1}}{\\stackrel{v_1}{\\rightleftharpoons}} x_2 \\stackrel{b_2}{\\rightarrow} \\tag{6.1} \\end{equation}$$\n",
    "\n",
    "The input is fixed by the environment and there is a first-order rate for the product to leave the system and thus we have \n",
    "\n",
    "$$\\begin{equation} b_1 = \\text{constant and}\\ b_2 = k_2x_2 \\end{equation}$$\n",
    "\n",
    "This defines the system boundary, and the inputs and outputs. \n",
    "\n",
    "The stoichiometric matrix is \n",
    "\n",
    "$$\\begin{equation} \\textbf{S} = \\begin{pmatrix} {1} & {-1} & {1} & {0} \\\\ {0} & {1} & {-1} & {-1} \\\\ \\end{pmatrix} \\end{equation}$$\n",
    "$$\\tag{6.2}$$\n",
    "\n",
    "where $\\textbf{x} = (x_1,\\  x_2)$ and $\\textbf{v} = (b_1, \\ k_1x_1, \\  k_{-1}x_2, \\  k_2x_2)$ The stoichiometric matrix has a rank of 2 and is thus a two-dimensional dynamic system. The differential equations that will need to be solved are: \n",
    "\n",
    "$$\\begin{equation} \\frac{dx_1}{dt} = b_1 - k_1x_1 + k_{-1}x_2, \\ \\frac{dx_2}{dt} = k_1x_1 - k_{-1}x_2 - k_2x_2 \\tag{6.3} \\end{equation}$$\n",
    "\n",
    "There are no conservation quantities. \n",
    "\n",
    "### The steady states  \n",
    "There are three properties of the steady state of interest. We can find first the steady state fluxes and second the steady state concentrations. Third, we can determine the difference between the steady state and the equilibrium state of this open system. \n",
    "\n",
    "#### Steady state fluxes:  \n",
    "The steady state of the fluxes is given by \n",
    "\n",
    "$$\\begin{equation} \\textbf{Sv}_{ss} = 0 \\tag{6.4} \\end{equation}$$\n",
    "\n",
    "and thus $\\textbf{v}_{ss}$ resides in the null space of $\\textbf{S}$. For this matrix, the null space is two dimensional; $\\text{Dim}(\\text{Null}(\\textbf{S}))=n-r=4-2=2$, where $n=4$ is the number of fluxes and the rank is $r=2$. The null space is spanned by two pathway vectors: (1,1,0,1) and (0,1,1,0). The former is the path through the system while the latter corresponds to the reversible reaction. These are known as type 1 and type 3 extreme pathways, respectively (_Systems Biology: Properties of Reconstructed Networks_). All steady state flux states of the system are a non-negative combination of these two vectors. \n",
    "\n",
    "$$\\begin{align} \\textbf{v}_{ss} &= (b_1, \\ k_1x_{1, ss}, \\ k_{-1}x_{2, ss}, \\ k_2x_{2, ss})  \\tag{6.5} \\\\ &= a(1, 1, 0, 1) + b(0, 1, 1, 0), \\ a \\geq 0, \\ b \\geq 0 \\tag{6.6} \\end{align}$$\n",
    "\n",
    "#### Steady state concentrations:  \n",
    "The concentrations in the steady state can be evaluated from \n",
    "\n",
    "$$\\begin{equation} 0 = b_1 - k_1x_1 + k_{-1}x_2, \\ 0 = k_1x_1 - k_{-1}x_2 - k_2x_2 \\end{equation}$$ $$\\tag{6.7}$$\n",
    "\n",
    "If we add these equations we find that $x_{2, ss} = b_1 / k_2$. This concentration can then be substituted into either of the two equations to show that $x_{1, ss} = (1 + k_{-1}/k_2)(b_1/k_1)$. Thus, the steady state concentration vector is \n",
    "\n",
    "$$\\begin{equation} \\textbf{x}_{ss} = \\begin{pmatrix} {x_{1, ss}} \\\\ {x_{2, ss}} \\end{pmatrix} = (\\frac{b_1}{k_2})\\begin{pmatrix} {\\frac{k_2 + k_{-1}}{k_1}} \\\\ {1} \\end{pmatrix} \\end{equation}$$ $$\\tag{6.8}$$\n",
    "\n",
    "These steady state concentrations can be substituted into the steady state flux vector to get \n",
    "\n",
    "$$\\begin{align} \\textbf{v}_{ss} &= b_1(1, 1+(\\frac{k_{-1}}{k_2}), \\ (\\frac{k_{-1}}{k_2}), \\ 1)  \\tag{6.9} \\\\ &= a(1, 1, 0, 1) + b(0, 1, 1, 0), \\ a = b_1, \\ b = (\\frac{b_1k_{-1}}{k_2}) \\end{align}$$\n",
    "\n",
    "Therefore, the steady state flux distribution is a summation of the straight through pathway and the discounted flux through the reversible reaction. The key quantity is $k_{-1} / k_2$ that measures the relative rate of $x_2$ reacting back to form $x_1$ versus the rate at which it leaves the system. \n",
    "\n",
    "#### The distance from the equilibrium state:  \n",
    "The difference between the steady state and the equilibrium state can be measured by: \n",
    "\n",
    "$$\\begin{equation} \\frac{x_{2, ss}/x_{1, ss}}{x_{2, eq}/x_{1, eq}} = \\frac{1}{1 + k_2/k_{-1}} \\stackrel{k_2 << k_{-1}}{\\longrightarrow} 1 \\tag{6.11} \\end{equation}$$\n",
    "\n",
    "Thus, when $k_2 << k_{-1}$, the steady state approaches the equilibrium state (recall that $(x_{2, ss}/x_{1, ss})/(x_{2, eq}/x_{1, eq}) = \\Gamma/K_{eq}$ Section 2.2). If the exchange with the environment is slow relative to the internal reaction rates, the internal system approaches that of an equilibrium state. \n",
    "\n",
    "### Dynamic states for reversible reactions\n",
    "The dynamic states are computed from the dynamic mass balances for a given condition. We are interested in two dynamic states: the approach to the steady state, and the response to a change in the input flux, $b_1$\n",
    "\n",
    "#### A two-phase transient response:  \n",
    "Simulation of this system with an input rate of $b_1 = 0.01$ and a slow removal rate, $k_2 = 0.1$, from an initial state of $x_1(0) = 1.0$ and $x_2(0) = 0$ is shown in Figure 6.2. There are two discernible time scales: a rapid motion of the equilibrating reaction, and a slow removal of $x_2$ from the system, Figure 6.2b. A phase portrait shows a rapid movement along a line with a negative slope of 1, showing the existence of a conservation quantity $(x_1 + x_2)$ on a fast time scale, followed by a slow motion down a quasi-equilibrium line with a slope of 1/2 to a steady state point. Note the difference from Figure 4.4c. "
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     "text": [
      "Set parameter Username\n"
     ]
    }
   ],
   "source": [
    "# Create MassModel\n",
    "model = MassModel('Linear_Reversible_Open')\n",
    "# Generate the MassMetabolites \n",
    "x1 = MassMetabolite(\"x1\")\n",
    "x2 = MassMetabolite(\"x2\")\n",
    "\n",
    "# Generate the MassReactions \n",
    "b1 = MassReaction(\"b1\", reversible=False)\n",
    "v1 = MassReaction(\"v1\")\n",
    "b2 = MassReaction(\"b2\", reversible=False)\n",
    "# Add metabolites to the reaction, add reaction to the model\n",
    "b1.add_metabolites({x1: 1})\n",
    "v1.add_metabolites({x1: -1, x2: 1})\n",
    "b2.add_metabolites({x2: -1})\n",
    "model.add_reactions([b1, v1, b2])\n",
    "# Set parameters\n",
    "b1.kf = 0.01\n",
    "v1.kf, v1.kr = (1, 2)\n",
    "b2.kf = 0.1\n",
    "\n",
    "# Set initial conditions for model\n",
    "x1.ic = 1\n",
    "x2.ic = 0\n",
    "# Utilize type 2 rate law for kf and kr parameters defined\n",
    "model.get_rate_expressions(rate_type=2, update_reactions=True)\n",
    "\n",
    "# Set a custom rate for b1 to remove substrate concentration dependence\n",
    "model.add_custom_rate(reaction=b1, custom_rate=b1.kf_str)"
   ]
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    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\u001b[93mWARNING:\u001b[0m \u001b[93mNo compartments found in model. Therefore creating compartment 'compartment' for entire model.\u001b[0m\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Successfully loaded MassModel 'Linear_Reversible_Open' into RoadRunner.\n",
      "Getting time points\n",
      "Setting output selections\n",
      "Setting simulation values for 'Linear_Reversible_Open'\n",
      "Simulating 'Linear_Reversible_Open'\n",
      "Simulation for 'Linear_Reversible_Open' successful\n",
      "Adding 'Linear_Reversible_Open' simulation solutions to output\n",
      "Updating stored solutions\n"
     ]
    }
   ],
   "source": [
    "t0 = 0\n",
    "tf = 150\n",
    "\n",
    "sim = Simulation(model, verbose=True)\n",
    "conc_sol, flux_sol = sim.simulate(model, time=(t0, tf),\n",
    "                                  interpolate=True,\n",
    "                                  verbose=True)"
   ]
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\n",
      "text/plain": [
       "<Figure size 1300x500 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig_6_2 = plt.figure(figsize=(13, 5))\n",
    "gs = fig_6_2.add_gridspec(nrows=1, ncols=2, width_ratios=[1, 1.5])\n",
    "\n",
    "ax1 = fig_6_2.add_subplot(gs[0, 0])\n",
    "ax2 = fig_6_2.add_subplot(gs[0, 1])\n",
    "\n",
    "plot_phase_portrait(\n",
    "    conc_sol, x=x1, y=x2, ax=ax1,\n",
    "    xlabel=x1.id, ylabel=x2.id, xlim=(-.05, 1.2), ylim=(-.05, 0.5),\n",
    "    title=(\"(a) Phase portrait of x1 vs. x2\", {\"size\": \"large\"}),\n",
    "    annotate_time_points=[t0, 1e0, 1e1, tf],\n",
    "    annotate_time_points_color=[\"red\"],\n",
    "    annotate_time_points_labels=True);\n",
    "\n",
    "ax1.annotate(\n",
    "    'motion towards\\n  a qe state', \n",
    "    xy=(conc_sol[x1.id](0.5), conc_sol[x2.id](0.5)), \n",
    "    xytext=(conc_sol[x1.id](0.3), conc_sol[x2.id](0.3)));\n",
    "\n",
    "ax1.annotate(\n",
    "    'motion of a\\n  qe state', \n",
    "    xy=(conc_sol[x1.id](tf), conc_sol[x2.id](tf)), \n",
    "    xytext=(conc_sol[x1.id](tf) + 0.05, conc_sol[x2.id](tf) + 0.15));\n",
    "\n",
    "plot_time_profile(\n",
    "    conc_sol, ax=ax2, legend=\"right outside\", \n",
    "    xlabel=\"Time\", ylabel=\"Concentrations\",\n",
    "    title=(\"(b) Concentration Profiles\", {\"size\": \"large\"}));\n",
    "fig_6_2.tight_layout()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Figure 6.2:** The concentration time profiles for the reaction system $\\rightarrow x_1 \\rightleftharpoons x_2 \\rightarrow$ for $k_1 = 1$, $k_{-1} = 2$, $x_1(0) = 0$, and $b_1 = 0.01$. (a) The phase portrait of $x_1$ and $x_2$ (b) The concentrations as a function of time.\n",
    "\n",
    "The same pools can be formed as defined in Eq. (4.9):\n",
    "\n",
    "$$\\begin{equation}\\begin{pmatrix} {p_1} \\\\ {p_2} \\end{pmatrix} = \\begin{pmatrix} {1} & {-1/K_1} \\\\ {1} & {1} \\end{pmatrix} = \\begin{pmatrix} {x_1} \\\\ {x_2} \\end{pmatrix} \\end{equation}$$\n",
    "$$\\tag{6.12}$$\n",
    "\n",
    "This matrix can be used to post-process the concentrations and the results can be graphed, Figure 6.3. The pool transformation leads to dynamic decoupling and is clearly illustrated in this figure. The disequilibrium pool relaxes very quickly, while the conservation pool moves slowly, Figure 6.3b. The phase portrait formed by the pools thus has an L shape (Figure 6.3a), illustrating the dynamic decoupling. Note that: \n",
    "\n",
    "* There is first a vertical motion where $x_1 + x_2$ is essentially a constant, followed by a slow horizontal motion where the disequilibrium variable $x_1 - x_2 /K_1$ is a constant. \n",
    "\n",
    "* These two separate motions correspond to forming the pathways found in the steady state. \n",
    "\n",
    "* The disequilibrium aggregate is not zero, as it is forced away from equilibrium by the input and settling in a steady state. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2021-01-25T17:56:59.329920Z",
     "iopub.status.busy": "2021-01-25T17:56:59.329181Z",
     "iopub.status.idle": "2021-01-25T17:56:59.848270Z",
     "shell.execute_reply": "2021-01-25T17:56:59.849019Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1100x400 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Define pools\n",
    "pools = [\"x1 - x2 / Keq_v1\", \"x1 + x2\"]\n",
    "for i, equation_str in enumerate(pools):\n",
    "    pool_id = \"p\" + str(i + 1)\n",
    "    conc_sol.make_aggregate_solution(\n",
    "        pool_id, equation=equation_str, \n",
    "        parameters={v1.Keq_str: v1.kf/v1.kr}, update=True)\n",
    "\n",
    "fig_6_3 = plt.figure(figsize=(11, 4))\n",
    "gs = fig_6_3.add_gridspec(nrows=1, ncols=2, width_ratios=[1, 1.5])\n",
    "\n",
    "ax1 = fig_6_3.add_subplot(gs[0, 0])\n",
    "ax2 = fig_6_3.add_subplot(gs[0, 1])\n",
    "\n",
    "plot_phase_portrait(\n",
    "    conc_sol, x=\"p2\", y=\"p1\", ax=ax1,\n",
    "    xlabel=\"p2 (inventory)\", ylabel=\"p1 (distance from equilibrium)\",\n",
    "    xlim=(-.05, 2.1), ylim=(-.05, 1.05),\n",
    "    title=(\"(a) Phase portrait of p2 vs. p1\", {\"size\": \"large\"}),\n",
    "    annotate_time_points=[t0, 1e0, 1e1, tf],\n",
    "    annotate_time_points_color=[\"red\"],\n",
    "    annotate_time_points_labels=True);\n",
    "\n",
    "ax1.annotate(\n",
    "    'motion towards\\n  a qe state', \n",
    "    xy=(conc_sol[\"p2\"](0.5), conc_sol[\"p1\"](0.5)), \n",
    "    xytext=(conc_sol[\"p2\"](0.3), conc_sol[\"p1\"](0.3)));\n",
    "\n",
    "ax1.annotate(\n",
    "    'motion of a\\n  qe state', \n",
    "    xy=(conc_sol[\"p2\"](tf), conc_sol[\"p1\"](tf)), \n",
    "    xytext=(conc_sol[\"p2\"](tf) + 0.05, conc_sol[\"p1\"](tf) + 0.1));\n",
    "\n",
    "plot_time_profile(\n",
    "    conc_sol, observable=[\"p1\", \"p2\"], ax=ax2, legend=\"right outside\", \n",
    "    xlabel=\"Time\", ylabel=\"Concentrations\",\n",
    "    title=(\"(b) Pool Profiles\", {\"size\": \"large\"}));\n",
    "fig_6_3.tight_layout()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Figure 6.3:** The time profiles of the pools involved in reaction system $\\rightarrow x_1 \\rightleftharpoons x_2 \\rightarrow$ for the same conditions as in Figure 6.2. (a) The phase portrait of $p_2$ and $p_1$. (b) The pools as a function of time.\n",
    "\n",
    "#### External disturbance:  \n",
    "The previous simulation represents a biologically unrealistic situation. An internal concentration cannot suddenly deviate from its value independent of what else happens in the system. A much more realistic situation is one where we start out at a steady state and an environmental change is observed. In our case, the only environmental parameter is $b_1$. \n",
    "\n",
    "In Figure 6.4 we change the input flux, $b_1$, from 0.01 to 0.02 at time zero, when the system is initially in a steady state (the endpoint in Figure 6.4). We make three observations:  \n",
    "\n",
    "* We see that the fast motion is not activated. \n",
    "\n",
    "* The 'inventory' or the pool of $x_1 + x_2$ moves from one steady state to another. It increases, as the forcing function was stepped up. \n",
    "\n",
    "* The 'distance from equilibrium' \n",
    "\n",
    "$$\\begin{equation} x_{1, ss} - \\frac{x_{2, ss}}{K_1} = x_{1, ss} - \\frac{x_{2, ss}}{x_{2, eq}/x_{1, eq}} = x_{1, ss}(1 - \\frac{\\Gamma}{K_1}) \\tag{6.13} \\end{equation}$$\n",
    "\n",
    "is close to zero in both steady states. The higher throughput, however, does push the system farther from equilibrium. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2021-01-25T17:56:59.856607Z",
     "iopub.status.busy": "2021-01-25T17:56:59.855264Z",
     "iopub.status.idle": "2021-01-25T17:57:00.357807Z",
     "shell.execute_reply": "2021-01-25T17:57:00.358840Z"
    }
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\u001b[93mWARNING:\u001b[0m \u001b[93mNo compartments found in model. Therefore creating compartment 'compartment' for entire model.\u001b[0m\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Setting output selections\n",
      "Setting simulation values for 'Linear_Reversible_Open'\n",
      "Setting output selections\n",
      "Getting time points\n",
      "Simulating 'Linear_Reversible_Open'\n",
      "Found steady state for 'Linear_Reversible_Open'.\n",
      "Updating 'Linear_Reversible_Open' values\n",
      "Adding 'Linear_Reversible_Open' simulation solutions to output\n",
      "Getting time points\n",
      "Parsing perturbations\n",
      "Setting output selections\n",
      "Setting simulation values for 'Linear_Reversible_Open'\n",
      "Simulating 'Linear_Reversible_Open'\n",
      "Simulation for 'Linear_Reversible_Open' successful\n",
      "Adding 'Linear_Reversible_Open' simulation solutions to output\n",
      "Updating stored solutions\n"
     ]
    }
   ],
   "source": [
    "# Ensure model starts simulation at a steady state.\n",
    "sim.find_steady_state(model, strategy=\"simulate\", update_values=True, verbose=True);\n",
    "\n",
    "# Simulate model with disturbance from steady state\n",
    "conc_sol, flux_sol = sim.simulate(\n",
    "    model, time=(t0, tf), perturbations={\"kf_b1\": 0.02},\n",
    "    interpolate=True, verbose=True)\n",
    "\n",
    "# Determine pools\n",
    "for i, equation_str in enumerate(pools):\n",
    "    pool_id = \"p\" + str(i + 1)\n",
    "    conc_sol.make_aggregate_solution(\n",
    "        pool_id, equation=equation_str, \n",
    "        parameters={v1.Keq_str: v1.kf/v1.kr}, update=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2021-01-25T17:57:00.427493Z",
     "iopub.status.busy": "2021-01-25T17:57:00.403970Z",
     "iopub.status.idle": "2021-01-25T17:57:00.950166Z",
     "shell.execute_reply": "2021-01-25T17:57:00.950828Z"
    },
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1100x400 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig_6_4 = plt.figure(figsize=(11, 4))\n",
    "gs = fig_6_4.add_gridspec(nrows=1, ncols=2, width_ratios=[1, 1.5])\n",
    "\n",
    "ax1 = fig_6_4.add_subplot(gs[0, 0])\n",
    "ax2 = fig_6_4.add_subplot(gs[0, 1])\n",
    "\n",
    "plot_phase_portrait(\n",
    "    conc_sol, x=\"p2\", y=\"p1\", ax=ax1,\n",
    "    xlabel=\"p2 (inventory)\", ylabel=\"p1 (distance from equilibrium)\",\n",
    "    xlim=(0, 1), ylim=(0, 0.03),\n",
    "    title=(\"(a) Phase portrait of p2 vs. p1\", {\"size\": \"large\"}),\n",
    "    annotate_time_points=[t0, 1e0, 1e1, tf],\n",
    "    annotate_time_points_color=[\"red\"],\n",
    "    annotate_time_points_labels=True);\n",
    "\n",
    "plot_time_profile(\n",
    "    conc_sol,  observable=[\"p1\", \"p2\"], ax=ax2, legend=\"right outside\", \n",
    "    xlabel=\"Time\", ylabel=\"Concentrations\",\n",
    "    title=(\"(b) Pool Profiles\", {\"size\": \"large\"}));\n",
    "fig_6_4.tight_layout()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Figure 6.4:** The time profiles of the pools involved in reaction system $\\rightarrow x_1 \\rightleftharpoons x_2 \\rightarrow$ where the system starts out at equilibrium and the input rate, $b_1$, is changed from 0.01 to 0.02 at time zero. (a) The phase portrait of $p_2$ and $p_1$; (b) The pools as a function of time. Note the small numerical change in $p_1$ relative to $p_2$. Parameter values as in Figures 6.2 and Figure 6.3."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Michaelis-Menten Kinetics in an Open Environment\n",
    "We now consider the case when the Michaelis-Menten reaction mechanism operates in an open environment (Figure 6.5). The substrate enters the system and the product leaves. The enzyme stays internal to the system. \n",
    "\n",
    "![Figure-6-5](../images/Ch6/Figure-6-5.png)\n",
    "\n",
    "**Figure 6.5:** The Michaelis-Menten reaction mechanisms in an open setting. The substrate and the product enter and leave the system, while the enzyme stays inside.\n",
    "\n",
    "### Dynamic description  \n",
    "The mass action kinetic model is \n",
    "\n",
    "$$\\begin{align} \\frac{ds}{dt} &= b_1 - k_1es + k_{-1}x, \\ &s(t=0) &= s_0 &\\tag{6.14a} \\\\ \\frac{dx}{dt} &= k_1es - (k_{-1} + k_2)x, \\ &x(t=0) &= x_0 &\\tag{6.14b}\\\\ \\frac{de}{dt} &= -k_1es + (k_{-1} + k_2)x, \\ &e(t=0) &= e_0 &\\tag{6.14c} \\\\ \\frac{dp}{dt} &= k_2x + k_3p, \\ &p(t=0) &= p_0 &\\tag{6.14d} \\\\ \\end{align}$$\n",
    "\n",
    "The initial conditions would normally be the steady state conditions. The stoichiometric matrix is \n",
    "\n",
    "$$\\begin{equation} \\textbf{S} = \\begin{pmatrix} {1} & {-1} & {1} & {0} & {0} \\\\ {0} & {-1} & {1} & {1} & {0} \\\\ {0} & {1} & {-1} & {-1} & {0} \\\\ {0} & {0} & {0} & {1} & {-1} \\\\ \\end{pmatrix} \\end{equation}$$\n",
    "$$\\tag{6.15}$$\n",
    "\n",
    "where $\\textbf{x}=(s,\\ e, \\ x, \\ p)$ and $\\textbf{v} = (b_1, \\ k_1es, \\ k_{-1}x, \\ k_2x, \\ k_3p)$\n",
    "\n",
    "### The steady state  \n",
    "As in the previous section, we can compute the steady state fluxes and concentrations. We can also compute how the parameters determine the distance from equilibrium, and here we also run into an additional issue: capacity constraints that result from a conservation quantity. \n",
    "\n",
    "#### The steady state fluxes:  \n",
    "The rank of $\\textbf{S}$ is 3, thus the dimension of the null space is 5-3=2. The null space of $\\textbf{S}$ is spanned by two vectors, (1,1,0,1,1) and (0,1,1,0,0), that correspond to a pathway through the system and an internal reversible reaction. The steady state fluxes are given by \n",
    "\n",
    "$$\\begin{align} \\textbf{v}_{ss} &= (b_1, \\ k_1e_{ss}s_{ss}, \\ k_{-1}x_{ss}, \\ k_2x_{ss}, \\ k_3p_{ss}) \\tag{6.16} \\\\ &= a(1, \\ 1, \\ 0, \\ 1, \\ 1) + b(0, 1, 1, 0, 0), \\ a \\geq 0, \\ b \\geq 0 \\tag{6.17} \\\\ \\end{align}$$\n",
    "\n",
    "\n",
    "#### The steady state concentrations:  \n",
    "The dimension of the left null space is 4-3=1. The left null space has one conservation quantity ($e+x$), which can readily be seen from the fact that the second and third row of $\\textbf{S}$ add up to zero. The steady state flux balances for this system are \n",
    "\n",
    "$$\\begin{equation} b_1 = v_1 - v_{-1} = v_2 = v_3 \\tag{6.18} \\end{equation}$$\n",
    "\n",
    "Thus, the incoming flux and the kinetic parameters immediately set the concentrations for $X$, $P$, and $E$ as \n",
    "\n",
    "$$\\begin{equation} x_{ss} = b_1/k_2, \\ p_{ss} = b_1/k_3, \\ \\text{and} \\ e_{ss} = e_t - x_{ss} = e_t -  b_1/k_2 \\tag{6.19} \\end{equation}$$\n",
    "\n",
    "and the steady state substrate concentration can be determined. The steady state concentration of the substrate is given by $k_1s_{ss}e_{ss} = b_1 + k_{-1}x_{ss}$ that can be solved to give \n",
    "\n",
    "$$\\begin{equation} s_{ss} = (\\frac{k_2}{k_1})(\\frac{k_{-1}/k_2 + 1}{e_tk_2/b_1 - 1}) \\tag{6.20} \\end{equation}$$\n",
    "\n",
    "The steady state flux vector can now be computed \n",
    "\n",
    "$$\\begin{align} \\textbf{v}_{ss} &= (b_1, \\ b_1(k_{-1}/k_2 + 1), \\ b_1k_{-1}/k_2, \\ b_1, \\ b_1) \\tag{6.21} \\\\ &= a(1, \\ 1, \\ 0, \\ 1, \\ 1) + b(0, 1, 1, 0, 0), \\ a=b_1, \\ b=b_1k_{-1}/k_2 \\tag{6.22} \\\\ \\end{align}$$\n",
    "\n",
    "The distance from equilibrium can now be computed as in the previous section. \n",
    "\n",
    "#### Internal capacity constraints:  \n",
    "Since $e_{ss} \\geq 0$, the maximum input is \n",
    "\n",
    "$$\\begin{equation} b_1 \\leq b_{1, max} = k_2e_t = v_m \\tag{6.23} \\end{equation}$$\n",
    "\n",
    "which is the maximum reaction rate for the Michaelis-Menten mechanism. The total amount of the enzyme and the turnover rate set this flux constraint. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2021-01-25T17:57:00.972980Z",
     "iopub.status.busy": "2021-01-25T17:57:00.954076Z",
     "iopub.status.idle": "2021-01-25T17:57:00.980456Z",
     "shell.execute_reply": "2021-01-25T17:57:00.981026Z"
    }
   },
   "outputs": [],
   "source": [
    "model = MassModel('Michaelis_Menten_Open')\n",
    "## Define metabolites\n",
    "s = MassMetabolite(\"s\")\n",
    "e = MassMetabolite(\"e\")\n",
    "x = MassMetabolite(\"x\")\n",
    "p = MassMetabolite(\"p\")\n",
    "\n",
    "# Define reactions\n",
    "b1 = MassReaction(\"b1\", reversible=False)\n",
    "v1 = MassReaction(\"v1\")\n",
    "v2 = MassReaction(\"v2\", reversible=False)\n",
    "v3 = MassReaction(\"v3\", reversible=False)\n",
    "\n",
    "b1.add_metabolites({s: 1})\n",
    "v1.add_metabolites({s: -1, e: -1, x: 1})\n",
    "v2.add_metabolites({x: -1, e: 1, p: 1})\n",
    "v3.add_metabolites({p: -1})\n",
    "model.add_reactions([b1, v1, v2, v3])\n",
    "\n",
    "## Define parameters\n",
    "b1.kf = 0.025\n",
    "v1.kf, v1.kr = (1, 0.5)\n",
    "v2.kf = 0.5\n",
    "v3.kf = 1\n",
    "\n",
    "# Set initial conditions for model\n",
    "s.ic = 1\n",
    "e.ic = 0.05\n",
    "x.ic = 0.05\n",
    "p.ic = 0\n",
    "\n",
    "# Utilize type 2 rate law for kf and kr parameters defined\n",
    "model.get_rate_expressions(rate_type=2, update_reactions=True)\n",
    "\n",
    "# Set a custom rate for b1 to remove substrate concentration dependence\n",
    "model.add_custom_rate(reaction=b1, custom_rate=b1.kf_str)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2021-01-25T17:57:01.001989Z",
     "iopub.status.busy": "2021-01-25T17:57:00.995047Z",
     "iopub.status.idle": "2021-01-25T17:57:01.110517Z",
     "shell.execute_reply": "2021-01-25T17:57:01.111174Z"
    }
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\u001b[93mWARNING:\u001b[0m \u001b[93mNo compartments found in model. Therefore creating compartment 'compartment' for entire model.\u001b[0m\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Successfully loaded MassModel 'Michaelis_Menten_Open' into RoadRunner.\n",
      "Getting time points\n",
      "Parsing perturbations\n",
      "Setting output selections\n",
      "Setting simulation values for 'Michaelis_Menten_Open'\n",
      "Simulating 'Michaelis_Menten_Open'\n",
      "Simulation for 'Michaelis_Menten_Open' successful\n",
      "Adding 'Michaelis_Menten_Open' simulation solutions to output\n",
      "Updating stored solutions\n"
     ]
    }
   ],
   "source": [
    "t0 = 0\n",
    "tf = 2e3\n",
    "\n",
    "sim = Simulation(model, verbose=True)\n",
    "# Simulate model with disturbance from steady state\n",
    "conc_sol, flux_sol = sim.simulate(\n",
    "    model, time=(t0, tf), perturbations={\"kf_b1\": 0.04},\n",
    "    interpolate=True, verbose=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2021-01-25T17:57:01.124045Z",
     "iopub.status.busy": "2021-01-25T17:57:01.114112Z",
     "iopub.status.idle": "2021-01-25T17:57:01.898446Z",
     "shell.execute_reply": "2021-01-25T17:57:01.899862Z"
    }
   },
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 800x600 with 3 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig_6_6 = plt.figure(figsize=(8, 6))\n",
    "gs = fig_6_6.add_gridspec(nrows=2, ncols=2, width_ratios=[1, 1.5],\n",
    "                          height_ratios=[1, 1])\n",
    "\n",
    "ax1 = fig_6_6.add_subplot(gs[0, 0])\n",
    "ax2 = fig_6_6.add_subplot(gs[0, 1])\n",
    "ax3 = fig_6_6.add_subplot(gs[1, 1])\n",
    "\n",
    "plot_phase_portrait(\n",
    "    conc_sol, x=s, y=x, ax=ax1,\n",
    "    xlabel=s.id, ylabel=x.id,\n",
    "    xlim=(-0.1, 6), ylim=(0, 0.105),\n",
    "    title=(\"(a) Phase Portrait of s vs. x\", {\"size\":\"large\"}),\n",
    "    annotate_time_points=\"endpoints\",\n",
    "    annotate_time_points_labels=True)\n",
    "\n",
    "plot_time_profile(\n",
    "    conc_sol, observable=x, ax=ax2, legend=\"best\",\n",
    "    ylim=(0.03, 0.09), xlabel=\"Time\", ylabel=\"Concentration\",\n",
    "    title=(\"(b) Time Response of x\", {\"size\": \"large\"}));\n",
    "\n",
    "plot_time_profile(\n",
    "    conc_sol, observable=s, ax=ax3, legend=\"best\",\n",
    "    ylim=(0, 6), xlabel=\"Time\", ylabel=\"Concentration\",\n",
    "    title=(\"(c) Time Response of s\", {\"size\": \"large\"}));\n",
    "fig_6_6.tight_layout()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Figure 6.6:** The time profiles for the transient response of the Michaelis-Menten mechanisms for $b_1 = 0.025$ changed to 0.04 at time zero. The kinetic parameters are; $e_t = 0.1$,  $k_1 = 1$, $k_{-1} = 0.5$, $k_2 = 0.5$, $k_3 = 0.1$. (a) The phase portrait of $s$ vs. $x$. (b) The time response of $x$. (c) The time response of $s$.\n",
    "\n",
    "### Dynamic states for Michaelis-Menten kinetics\n",
    "The response of this system to a change in the input rate starting from a steady state is of greatest interest, see Figure 6.6. For the kinetic parameters given in the figure, the steady state concentrations of $s$ and $x$ are 1.0 and 0.5 respectively. The input rate is changed from 0.025 to 0.04 at time zero and the concentrations of $s$ and $x$ go to 4.0 and 0.8, respectively, as time goes to infinity. The maximum flux rate is 0.05. \n",
    "\n",
    "The change in the input rate triggers an internal motion that basically follows the quasi-steady state line (Figure 6.6c). Figure 6.6b and Figure 6.6c shows that since the internal steps are rapid relative to the exchange rates, there are no rapid transients produced by a perturbation in the input rate. \n",
    "\n",
    "If the input is increased towards $v_m$, the substrate concentration builds up to a very high value and most of the enzyme is found in the intermediate state. If the input rate exceeds $v_m$ there will be no steady state as the enzyme cannot convert the substrate to the product at the same rate as it is entering the system. \n",
    "\n",
    "The dynamic properties of this open system can be analyzed using pool formation."
   ]
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    "## Summary  \n",
    "* Open systems eventually reach a steady state, which is different from the equilibrium state of a closed system. Such steady states can be thought of as homeostatic, living states. \n",
    "\n",
    "* Living cells are open systems that continually exchange mass and energy with their environment. The continual net throughput of mass and concomitant energy dissipation is what allows steady states to form and differentiates them from equilibrium states. \n",
    "\n",
    "* The relative rates of the internal network to that of the exchanges across the system boundary are important. Time scale separation between internal and exchange processes can form. Rapid internal transients lead to pool formation. \n",
    "\n",
    "* Open systems are most naturally in a steady state and respond to external stimuli. It is normally not possible to suddenly change the internal state of the system since it is in balance with the environment. \n",
    "\n",
    "* If the internal dynamics are fast, they do not excite when external stimuli are experienced, and thus accurate information about the fast kinetics may not be needed. It may be enough to know that they are \"fast.\" \n",
    "\n",
    "* Non-exchanged moieties form dynamic invariants. They can set internal capacity constraints. "
   ]
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   "source": [
    "$\\tiny{\\text{© B. Ø. Palsson 2011;}\\ \\text{This publication is in copyright.}\\\\ \\text{Subject to statutory exception and to the provisions of relevant collective licensing agreements,}\\\\ \\text{no reproduction of any part may take place without the written permission of Cambridge University Press.}}$"
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