4_activation_cascade_simulation.ipynb

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    "# Activation Cascade Simulation\n",
    "To highlight the difference between a simulation without resource coupling and with resource coupling, an activation cascade from the paper: [Resource Competition Shapes the Response of Genetic Circuits](https://pubs.acs.org/doi/10.1021/acssynbio.6b00361) by Qian. *et al* is used. \n",
    "\n",
    "## Activation Cascade Description\n",
    "- A two-stage activation cascade was built by connecting three nodes in a cascade topology.\n",
    "- The first node produces the TF LuxR which is activated by AHL.\n",
    "- The second node is activated by active LuxR and produces NahR which is activated by SAL.\n",
    "- The third node is activated by activate NahR and produces GFP\n",
    "\n",
    "## Biologically Relevant Parameters\n",
    "First, here is a list of biologically relevant parameters sourced from the same paper to give a range of simulation values. The original values are under the \"Characteristic Values\" column. These values were converted to standard units of $\\mu M$ and $min^{-1}$.\n",
    "\n",
    "|          **Parameter**           |           **Physical Interpretation**           | **Converted Values** |   **Units**  | **Characteristic Values** | **Units**   |\n",
    "|----------------------------------|-------------------------------------------------|----------------------|--------------|---------------------------|-------------|\n",
    "|              $g_T$               | Total DNA/Promoter Concentration                | 0.001 per copy       | $\\mu M$      | 1 per copy                | $nM$        |\n",
    "|             $\\pi_T$              | Total RNAP Concentration                        | $\\lesssim 1$         | $\\mu M$      | $\\lesssim 1000$           | $nM$        |\n",
    "|            $\\rho_T$              | Total Ribosome Concentration                    | $\\lesssim 1$         | $\\mu M$      | $\\lesssim 1000$           | $nM$        |\n",
    "|    $\\kappa_i^- / \\kappa_i^+$     | Dissociation Constant Between TF and DNA        | $1^{-5} - 1$         | $\\mu M$      | 0.01  - 1000              | $nM$        |\n",
    "|    $\\kappa_i^+ / \\kappa_i^-$     | Binding Constant Between TF and DNA             | $1 - 10^5$           | $\\mu M^{-1}$ |                           |             |\n",
    "|    $ k_{1;i}^- / k_{1;i}^+ $     | Dissociation Constant between RNAP and DNA      | $0.5$                | $\\mu M$      | $\\gtrsim  500$            | $nM$        |\n",
    "|    $ k_{1;i}^+ / k_{1;i}^-$      | Binding Constant between RNAP and DNA           | $\\lesssim 2$         | $\\mu M^{-1}$ |                           |             |\n",
    "|    $ k_{2;i}^- /k_{2;i}^+ $      | Dissociation Constant Between Ribosomes and RBS | $\\gtrsim 5$          | $\\mu M$      | $\\gtrsim 5$               | $\\mu M$     |\n",
    "|    $ k_{2;i}^+ /k_{2;i}^- $      | Binding Constant Between Ribosomes and RBS      | $\\gtrsim 0.2$        | $\\mu M^{-1}$ |                           |             |\n",
    "|       $ k_{1;i}^\\theta $         | Transcription Elongation Rate Constant          | $\\approx 1.67$       | $min^{-1}$   | $\\approx 100$             | $hr^{-1}$   |\n",
    "|       $ k_{2;i}^\\theta $         | Translation Elongation Rate Constant            | $\\approx 1.67$       | $min^{-1}$   | $\\approx 100$             | $hr^{-1}$   |\n",
    "|               –                  | Number of RNAPs per DNA                         | $\\lesssim 20$        |              | $\\lesssim 20$             |             |\n",
    "|               –                  | Number of Ribosomes per mRNA                    | $\\lesssim 30$        |              | $\\lesssim 30$             |             |\n",
    "|          $ \\delta_i $            | mRNA Decay Rate Constant                        | 0.0667 - 0.25        | $min^{-1}$   | 4 - 15                    | $hr^{-1}$   |\n",
    "|           $ \\lambda $            | Protein Dilution Rate Constant                  | 0.005 - 0.006667     | $min^{-1}$   | 0.3 - 0.4                 |             |\n",
    "\n",
    "## Simulation Parameters\n",
    "| **Parameter**                     | **Physical Interpretation**                                                               | **Value** | **Units**    |\n",
    "|-----------------------------------|-------------------------------------------------------------------------------------------|-----------|--------------|\n",
    "| $\\pi_T$                           | Total RNAP Concentration                                                                  | $1$       | $\\mu M$      |\n",
    "| $\\rho_T$                          | Total Ribosome Concentration                                                              | $1$       | $\\mu M$      |\n",
    "| $g^1_T = g^2_T = g^3_T$           | Total DNA/Promoter Concentration = 60 copies                                              | $0.06$    | $\\mu M$      |\n",
    "| $\\hat{\\kappa}_1$                  | Binding Constant Between AHL and $g_1$                                                    | $1/252$   | $\\mu M^{-1}$ |\n",
    "| $\\hat{\\kappa}_2$                  | Binding Constant Between SAL and $g_2$                                                    | $1/1000$  | $\\mu M^{-1}$ |\n",
    "| $\\hat{k}^{m}_{a;1}$               | Binding Constant Between Activated LuxR and $g_2$                                         | 10        |              |\n",
    "| $\\hat{k}^{m}_{a;2}$               | Binding Constant Between Activated NahR and $g_3$                                         | 100       |              |\n",
    "| $ k_{1;1}^m$                      | Binding Constant between RNAP and DNA 1 (augmented by translation elongation rate)        | $1$       | $\\mu M^{-1}$ |\n",
    "| $ k_{1;2}^m$                      | Binding Constant between RNAP and DNA 2 (augmented by translation elongation rate)        | $1/6$     | $\\mu M^{-1}$ |\n",
    "| $ k_{1;3}^m$                      | Binding Constant between RNAP and DNA 3 (augmented by translation elongation rate)        | $1$       | $\\mu M^{-1}$ |\n",
    "| $ k_{2;1}^m$                      | Binding Constant Between Ribosomes and RBS 1 (augmented by transcription elongation rate) | $1/15$    | $\\mu M^{-1}$ |\n",
    "| $ k_{2;2}^m$                      | Binding Constant Between Ribosomes and RBS 2 (augmented by transcription elongation rate) | $1/15$    | $\\mu M^{-1}$ |\n",
    "| $ k_{2;3}^m$                      | Binding Constant Between Ribosomes and RBS 3 (augmented by transcription elongation rate) | $1/15$    | $\\mu M^{-1}$ |\n",
    "| $n_1$                             | Cooperativity of Activated LuxR                                                           | 1         | –            |\n",
    "| $n_2$                             | Cooperativity of Activated NahR                                                           | 1         | –            |\n",
    "| $n'_1$                            | Cooperativity of AHL binding to LuxR                                                      | 1.4       | –            |\n",
    "| $n'_1$                            | Cooperativity of SAL binding to NahR                                                      | 4         | –            |\n",
    "| $ \\delta_1 = \\delta_2 = \\delta_3$ | mRNA Decay Rate Constant                                                                  | 0.0833    | $min^{-1}$   |\n",
    "| $ \\lambda $                       | Protein Dilution Rate Constant                                                            | 0.006667  | $min^{-1}$   |\n",
    "| $I_1$                             | Concentration of AHL                                                                      | Range*    | $\\mu M^{-1}$ |\n",
    "| $I_2$                             | Concentration of SAL                                                                      | 100       | $\\mu M^{-1}$ |\n",
    "\n",
    "*Range of $I_2$ (AHL) Concentrations: $0.01, 0.02, 0.05, 0.08, 0.1, 0.5,1, 5, 10 uM^{-1}$"
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    "## Specification of Activation Cascade without DSL\n",
    "Here we use the original functions I coded to create the system. This is the original code and graph from my thesis. The activation cascade is now simulated with resource conservation. The simulation is to determine the dose response of the circuit to AHL ($I_2$).\n",
    "\n",
    "Computer specs:\n",
    "- Processor: 2 GHz Quad-Core Intel Core i5\n",
    "- RAM: 16 GB 3733 MHz LPDDR4X\n",
    "\n",
    "## Activation Cascade with Resource Convservation\n",
    "To simulate the model with resource conservation, we need to calculate the resource demand coefficients ($J = \\sum_j k^{m}_{j} \\cdot A_j$) and subsequently calculated $k_{eff}$.\n",
    "\n",
    "We now define the new rate (derived with QSS approximation), $k_{eff;i}$, as\n",
    "\n",
    "\\begin{align*}\n",
    "    k_{eff;i} = \\frac{k_{i}^{\\theta} \\cdot k^{m}_{i} \\cdot R_T}{{1 + \\sum_j k^{m}_{j} \\cdot A_j}}\n",
    "\\end{align*}\n",
    "\n",
    "The reaction equations are:\n",
    "\n",
    "#### Node 1\n",
    "\n",
    "\\begin{align*}\n",
    "    \\varnothing &\\xrightarrow{k_{eff,1;1} \\cdot g^T_1} m_1 \\\\\n",
    "    m_1 &\\xrightarrow{k_{eff,2;1}} x^0_1 \\\\\n",
    "    m_1 &\\xrightarrow{\\delta_1} \\varnothing \\\\\n",
    "    x^0_1 &\\xrightarrow{\\lambda} \\varnothing\n",
    "\\end{align*}\n",
    "\n",
    "#### Edge 1\n",
    "\n",
    "\\begin{align*}\n",
    "    x^0_1 + n'_1 \\cdot I_1 &\\xleftrightharpoons[\\kappa_1^-]{\\kappa_1^+} x^+_1 \\\\\n",
    "    x^+_1 &\\xrightarrow{\\lambda} \\varnothing\n",
    "\\end{align*}\n",
    "\n",
    "#### Node 2\n",
    "\n",
    "\\begin{align*}\n",
    "    \\varnothing &\\xrightarrow{k_{eff,1;2} \\cdot g^T_2 \\cdot \\alpha(x_1, n_1)} m_2 \\\\\n",
    "    m_2 &\\xrightarrow{k_{eff,2;2}} x^0_2 \\\\\n",
    "    m_2 &\\xrightarrow{\\delta_2} \\varnothing \\\\\n",
    "    x^0_2 &\\xrightarrow{\\lambda} \\varnothing\n",
    "\\end{align*}\n",
    "\n",
    "#### Edge 2\n",
    "\n",
    "\\begin{align*}\n",
    "    x^0_2 + n'_2 \\cdot I_2 &\\xleftrightharpoons[\\kappa_2^-]{\\kappa_2^+} x^+_2 \\\\\n",
    "    x^+_2 &\\xrightarrow{\\lambda} \\varnothing\n",
    "\\end{align*}\n",
    "\n",
    "#### Node 3\n",
    "\n",
    "\\begin{align*}\n",
    "    \\varnothing &\\xrightarrow{k_{eff,1;3} \\cdot g^T_3 \\cdot \\alpha(x_2, n_2)} m_3 \\\\\n",
    "    m_3 &\\xrightarrow{k_{eff,2;3}} x_3 \\\\\n",
    "    m_3 &\\xrightarrow{\\delta_3} \\varnothing \\\\\n",
    "    x_3 &\\xrightarrow{\\lambda} \\varnothing\n",
    "\\end{align*}\n",
    "\n",
    "Where the activation Hill function is:\n",
    "\\begin{align*}\n",
    "    \\alpha(x^+_j, n_j) = \\frac{\\hat{k}^m_{a;i} \\cdot (x^+_j)^{n_j}}{1 + \\hat{k}^m_{a;i} \\cdot (x^+_j)^{n_j}}\n",
    "\\end{align*}"
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       "\"/Users/alexandersim/Documents/Code/Y4_FYP/resource-conservation-simulation.png\""
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    "include(\"DSL_backend/ode_system.jl\")\n",
    "\n",
    "# Units = uM\n",
    "tx1 = [100,5,95] # km = 1\n",
    "tx2 = [17,2,100] # km = 1/6\n",
    "tx3 = [100,5,95] # km = 1\n",
    "tl1 = [7,1,104] # km = 1/15\n",
    "tl2 = [7,1,104] # km = 1/15\n",
    "tl3 = [7,1,104] # km = 1/15\n",
    "\n",
    "act1 = [10,1] # k =  10 uM\n",
    "act2 = [100,1] # k = 100 uM\n",
    "# act3 = [10,1] # k = 10 uM\n",
    "\n",
    "ind1 = [1,252] # k_hat = 1/252\n",
    "ind2 = [1,1000] # k_hat = 1/1000\n",
    "\n",
    "dg = 0.0833 # degradation rate δ\n",
    "\n",
    "vect = []\n",
    "conc = [0.01, 0.02, 0.05, 0.08, 0.1, 0.5,1, 5, 10] # AHL concentrations\n",
    "\n",
    "for i=1:length(conc)\n",
    "node_1 = createnode(:A, tx1, tl1, dg, 0.06) # Gene concentration = 0.06uM \n",
    "link_1 = tfactivation(:I1, node_1, ind1, 1.4, conc[i])\n",
    "\n",
    "node_2 = createnode(:B, tx2, tl2, dg, 0.06)\n",
    "link_2 = activate(node_1, node_2, act1, 1) # cooperativity = 1\n",
    "link_3 = tfactivation(:I2, node_2, ind2, 4, 100) # SAL conc. = 100uM\n",
    "\n",
    "node_3 = createnode(:C, tx3, tl3, dg, 0.06)\n",
    "link_4 = activate(node_2, node_3, act2, 1)\n",
    "\n",
    "compiled_links = compilelinks(link_1, link_2, link_3, link_4)\n",
    "compiled_nodes = compilenodes(node_1, node_2, node_3)\n",
    "\n",
    "node_sys = createnodesystem(compiled_nodes, compiled_links)\n",
    "\n",
    "res = runsystem(node_sys, 1, 1, 0.0067, (0,150)) # ribosome = rnap concentration = 1, λ = 0.0067\n",
    "\n",
    "push!(vect, maximum(res[10,:]))\n",
    "end\n",
    "plot(conc, vect,\n",
    "    xlabel = \"AHL Concentration (uM)\",\n",
    "    ylabel = \"GFP Concentration (uM)\",\n",
    "    label = \"GFP\", fmt = :png, title = \"Dose Response With Resource Conservation\"\n",
    ")\n",
    "# savefig(\"resource-conservation-simulation\")"
   ]
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    "## Simulation of Activation Cascade without Resource Conservation:\n",
    "To simulate the model without resource conservation, we simply need to remove the resource demand coefficient ($J = \\sum_j k^{m}_{j} \\cdot A_j$) from $k_{\\text{eff}} = \\frac{k_{i}^{\\theta} \\cdot k^{m}_{i} \\cdot R_T}{{1 + \\sum_j k^{m}_{j} \\cdot A_j}}$.\n",
    "\n",
    "We now define the new rate (derived with QSS approximation), $k_{old;i}$, as\n",
    "\n",
    "\\begin{align*}\n",
    "    k_{old;i} = k_{i}^{\\theta} \\cdot k^{m}_{i} \\cdot R_T\n",
    "\\end{align*}\n",
    "\n",
    "The reaction equations are now:\n",
    "\n",
    "#### Node 1\n",
    "\n",
    "\\begin{align*}\n",
    "    \\varnothing &\\xrightarrow{k_{old,1;1} \\cdot g^T_1} m_1 \\\\\n",
    "    m_1 &\\xrightarrow{k_{old,2;1}} x^0_1 \\\\\n",
    "    m_1 &\\xrightarrow{\\delta_1} \\varnothing \\\\\n",
    "    x^0_1 &\\xrightarrow{\\lambda} \\varnothing\n",
    "\\end{align*}\n",
    "\n",
    "#### Edge 1\n",
    "\n",
    "\\begin{align*}\n",
    "    x^0_1 + n'_1 \\cdot I_1 &\\xleftrightharpoons[\\kappa_1^-]{\\kappa_1^+} x^+_1 \\\\\n",
    "    x^+_1 &\\xrightarrow{\\lambda} \\varnothing\n",
    "\\end{align*}\n",
    "\n",
    "#### Node 2\n",
    "\n",
    "\\begin{align*}\n",
    "    \\varnothing &\\xrightarrow{k_{old,1;2} \\cdot g^T_2 \\cdot \\alpha(x_1, n_1)} m_2 \\\\\n",
    "    m_2 &\\xrightarrow{k_{old,2;2}} x^0_2 \\\\\n",
    "    m_2 &\\xrightarrow{\\delta_2} \\varnothing \\\\\n",
    "    x^0_2 &\\xrightarrow{\\lambda} \\varnothing\n",
    "\\end{align*}\n",
    "\n",
    "#### Edge 2\n",
    "\n",
    "\\begin{align*}\n",
    "    x^0_2 + n'_2 \\cdot I_2 &\\xleftrightharpoons[\\kappa_2^-]{\\kappa_2^+} x^+_2 \\\\\n",
    "    x^+_2 &\\xrightarrow{\\lambda} \\varnothing\n",
    "\\end{align*}\n",
    "\n",
    "#### Node 3\n",
    "\n",
    "\\begin{align*}\n",
    "    \\varnothing &\\xrightarrow{k_{old,1;3} \\cdot g^T_3 \\cdot \\alpha(x_2, n_2)} m_3 \\\\\n",
    "    m_3 &\\xrightarrow{k_{old,2;3}} x_3 \\\\\n",
    "    m_3 &\\xrightarrow{\\delta_3} \\varnothing \\\\\n",
    "    x_3 &\\xrightarrow{\\lambda} \\varnothing\n",
    "\\end{align*}\n",
    "\n",
    "Where the activation Hill function is:\n",
    "\\begin{align*}\n",
    "    \\alpha(x^+_j, n_j) = \\frac{\\hat{k}^m_{a;i} \\cdot (x^+_j)^{n_j}}{1 + \\hat{k}^m_{a;i} \\cdot (x^+_j)^{n_j}}\n",
    "\\end{align*}"
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R4+Sl8LOwAcOHBAtJhAIzM3N2Wy26NmNMe7duzdFUS9fvmxmM8mV8O7du2LBizUCYYlESO50EUKid3v19fXkaYvw6kcSIUJINOtjjJ2cnBBCjx8/bia2VtS1eo02g7ReVlRUIIT4fL6Pjw9N06QaIbRq1Sqapm/evNnY2IgQIs0UUVFRfD5f6jovXbrE4/EWLlzI5XJFl5PD986dO2+N6tSpUzo6Ojo6OioqKnZ2diEhIZMnT7548aKwwLlz50hgioqKwoUsFotkLHJNp2laTU0tPz+fPMhsxuzZs42MjIQvLS0tp06dWldXR24jEELXrl1DCK1Zs0b0U8uXL1dRUXnw4EFVVZXo8hUrVog+L3F3d0cICQchkL2XlJQk9imhyMjIZ8+eubq6DhkyRHT5okWL2Gw22bSmcDicQYMG4X9rP1VVVU+ePCG9SSmKGjJkSGhoKPkSyQPCESNGvMdTW2LmzJmmpqbCl46Ojvr6+qJjLaTutIULFxoaGsbExLz1S/lw69evFx5FLi4uL168WLRo0d69e4UFyFH0/fffi+4ENTW1efPm8Xg80nWIfF+pqamvX7+W+leio6NzcnL69Onj4eEhXEjT9HfffYcQunLlyvsF/91334lG9fDhw4KCAldXV1K3kOr8+fNkq0UXmpqaTpw4saCg4MmTJ019kJz+Yk27UpWUlAQHB2tpaZETTYh8y1evXhUrv2rVKtGXUs+FmJgYckxKunbtWnV19bx588SaLpcuXYokriTa2trkBkiIxWLNmzePz+eLjo6NjIxMTU11dXXt3r17M1tKbg4eP37cTBmpgoODi4uLXVxcRJ+2KCgokNtKsV2kqKi4fPly0SXk+5Ucs9RGunRnGVFkwCxJh9nZ2dXV1WZmZqJZASFkZGRkYmKSnZ2dmZnZo0ePsWPHGhsbnz9/Pjg4eMKECa6uru7u7qKN+OSUS05OFrsIkoc0LbkC6uvr29jYYIwLCgrS0tIUFRVdXV2FvQmEfyIgIEBsZBhZeWZmJkKIoqgFCxbs27fPxsZm9OjRo0aNcnd3l+y3ghDq16+f2BIHB4e//vorJSUFIVRaWlpYWKihoSH6tAMhpKWlZWVllZiY+PTpU9GeEWKPEsnTlFevXpGXVlZWw4cPDwwM7Nat24QJE0aMGDFmzBjRR1Bk0yoqKsT2HkJIRUWFbFozhg8f/uDBg8DAwKlTpwYHB/P5fNI+jBAaOnQoabB1cXER9pRpfm3NEB1oQRgaGiYlJdXW1qqoqGCMU1NTKYpydHQULaOgoNCnT5/CwsLk5GTJBzOty8zMzNzcnM/n5+XlkTZ/d3d30TsnsqsvXbp048YN0Q/GxcWhf48iQ0PDCRMm3L5928LCYty4cSNHjhw9erRo5OQgcXR0FLulILf27z1yUay7FunpKvbAVVRFRcXLly+VlZX37dsn9ha5qmZmZpL2Ekmk+1Jtbe1bo0pNTcUY29jYiD0As7e3V1BQyMjIqKmpUVVVFS5v/lwYOXKkhYXF5cuXIyIiyJVk9OjRkqf58+fPxc6FhoYGJHElsba2lnyS5+3t/eOPP54+fZrkIYQQqYaS1imhuLi4Xbt2kQcowmfJCCHSQeadkG9c8qm21OPB0tJSLGayi0g/NRmARIgQQhjjly9fIoTIE3iSFCX7cSCEDA0Ns7OzSSVGS0srIiJi/fr1N2/ePHz48OHDhzkczsyZM/fs2UM645WXlyOEAgMDJUdwa2trs9lv3/miwyeSkpLGjh379ddfW1lZCW+6ye359evXJSs02trawu5ee/bs6d69+9GjR2/evEl6BNjZ2R04cED0Zg0hJNkxhOwEsr3N75bExESxup3YNYIEg/8dj0xR1K1bt7Zu3frnn3+eP3/+/PnzFEWNGDHi0KFDNjY2wk1LTk4mX40omqZVVVX5fH4z+5DkNpLnyL/CREgatR49euTi4kJGEH5IIpTs4yC6pTwej8/na2hoKCsrixUjp3pTFeJWJDp8wt/ff/LkybNmzbKxsenTpw+Js6KigqKo33//XfKz2trawq/s0qVLO3bsOHv27F9//fXXX38hhIYMGXLo0CF7e3vU9OEhegi9B7F+rZWVlejf81QqUqtraGg4duyY1M0RCARNfZbU7NPT098aVVMby2KxyKOQqqoq0UTY/LmgpqYWFhb2ww8/XLt27ejRo0ePHmWz2Z988snevXvJQULOhZCQkMjISMktEjsLxPYYYW1tPXjwYNIh3NHRsaGh4eLFi6qqqsJeuAihgICA8ePHY4xHjhw5ceJE0nXl6dOnp0+fbmanNaWpXST1sJc8icgFjWGYd/277wcSIUIIRURElJaWcjgccqtI2kaKiookS5KbOGEvUDMzszNnzvD5/KioKH9//1OnTp09e/bVq1f37t0Trufw4cOk19YH6tOnz9mzZ0eNGrVs2TJXV1dy90r+9ff3l9qfUIim6eXLly9fvjwrK+vhw4dXrly5ffv2+PHj4+LiRO9VJTeZ3JGRDWn5bmkhNTW1n376aefOnSkpKf7+/n/88UdAQMCYMWOSk5PV1NTInxNrxGs5MpowMTGxpKQkMDCQy+UKK7KOjo6ampqBgYHTpk3Lzs42MDCQ7KfeWpSUlDgcTlVVVV1dnVguFNtpUs980bvyVjFq1Khdu3YtWbLks88+CwsLY7FYFEWpq6tXVVVlZmY2/w0qKytv2bJly5YtqampDx8+vHDhAun+kJKSoqOj09ThQQ4h4ZpJDpC8sLZwDjNNTU2EkOS0JkIkDC0treLi4ndt7h4yZMiRI0fI06/mP9vUxgoEguLiYvTu5wKXyz1x4sSRI0diY2P9/f1Pnz79119/5ebmkrZ98uf27Nkj1uYpVVORe3t7h4SEnDlzxtHR8caNG6WlpQsWLBAdw7Nu3ToyUoW03BJnzpwhj5DfVVO76P2uFW0NnhEiPp+/du1ahND06dPJYWFubq6urp6fn5+fny9aMi8vLz8/X01NTWx8FZvNHjhw4Pr16+Pj4/X19R88eEDuW0lrmOhkXR9o5MiRnp6e2dnZpMfEe/yJbt26zZ8/38fH58svv+TxeLdu3RJ9V/LxCen6QaoOOjo6xsbGlZWVpIOJUFlZ2cuXL9lsNqnJvSvS82358uURERFDhw7Nzs4m/Wg+cO9xOBzSN8rX1zc2NlZYHUQI0TQ9aNCgkJAQPz8/hNDIkSObv+qRoSnvcVOMEKIoytbWFmMsHPZH8Hg8Mk0a2bcIIfIgWawtiLQ3iiItSO8XDPH555/b2dlFRkYKHzY7OjoyDNPyuQZ79+69dOnS4ODgcePGFRYWkh5bZENI/yzRwuTb7Nu3L3lJHjdINnm1cGoucsPXzCw/2traFhYWpaWlYkdpS0yaNElHR+fp06fXr19vqgzpEGBra0tRVGpqqtidChknamVlJVnFaQk2mz1gwIC1a9fGxcWZmpqGhISQHUXOhQ+cXnH69OkqKirnz59vaGiQ2i4aHx+vp6cnmgURQmLHLWrx6UC+8ejoaLHl5HgQHvbtRFdPhC9fvpw4cWJgYKCent7WrVvJQpqmvby8BALBrl27RAv//PPPAoHAy8uLtEVI3sOSegzGuL6+HiH0f//3f8rKymfPnpV8QIIxfr9pfDdt2kRR1C+//EJaS0g/4927d0s24vP5fDILRkNDA4lHFLnsii2/cOGCaO5/8eLFtWvXVFVVyXgMhBBpSNm5c6fop/bu3VtXVzdu3DjRtqC3IsMcRZdQFEWukiSqgQMH9urVKyoqSmo/i5bsPdLguWPHjsbGRtIcKjRs2LDq6mryGEk0R0pFGuLeexI+MvqCDGITLjx+/DjpSiAcJUkGrYp2fJA8AoXBkGH174emadKRZMuWLaQCOn/+fITQpk2bJKdNqaurI5e82tpayXYq0aPIycnJ0tIyJSWFtL0TfD6f9K0VzjmioqJiZGSUmpoq+pQ3JiaGNKK81fDhw83NzYODg8Xu4USRzVm3bp1kwM0fNmpqalu2bEEIff7555KNkHw+/5dffiFDAnR0dEaNGlVRUUG6jguRAQnvOsGKZFQqKiqk7kv27SeffKKurn7x4kWpPX1aeCXR0NCYMmVKaWnp77//fu/ePQsLC7GTQl9fv6KiQrQzVHZ29smTJ8XW08LTYfDgwUZGRo8fPw4ICBAurK+vJ73H290cNLLpnCp3pN+jiYnJ6tWrV69evXLlygULFjg5OZGGmh49ekRHR4uWz8jI0NTUpCjq66+/joqKioqK+uqrr8i0xcJhyGvXrh0wYMCBAwcCAgKePXsWHBw8d+5chNCIESOE6yGjf7S0tH788Uc/P7+EhAQfH58ff/yxV69ep0+fbibgpgbUY4zJA8LNmzeTl19++SVCqFu3bvv37w8KCnry5Mm1a9fWrFnD5XJJ5+P09HR9ff2VK1feuHEjMTExISHht99+09TU5HA4wsG/ZPiEubm5jY3NjRs3nj17duXKFdKdTLRX96tXr0ij/+LFiyMiImJjY1evXs1isZSVlUXHEZPhE2Iji0mqHjBgAHlJhnZt27bN19c3NTU1Ojp6w4YNNE0bGRmRUXoY45CQEEVFRTabvXz5cjIZyv379w8ePDh48GDRwfJNEb2DFg4TFK5Z+FZaWproW5LDJ0hVycDA4Icffjhy5MjRo0fLy8uF35HYCGKMsfCZGXlZWVlJ9uTMmTODg4Pj4+PJaEg2mx0SEiL8VHx8PBmRuX379pCQkL///nvgwIGkJ47o8ImsrCyaptXV1VevXn348OGjR4+KDt4QI3UcIcZYIBCQG/Y///yTvCRfmb29/YkTJyIjIx8/fnzx4sVly5ZpaWmRjb137163bt02bdp0586dlJSU2NjYH3/8kcPh6OjolJaWktVevXqVnCP79+9PSkry8/Mjo9rJvCrCv04Otj59+ly+fDkoKGjXrl2amppkSyWHT0hu1J07d8iO+v7770NDQxMSEq5du+bt7S0cRVBTU0MqjsOGDTt//nxMTExYWNgff/wxb948Lpfb1L4SItO10zQ9c+bM06dP379///r16z/88AMZISocLhUTE6OgoMDhcDZu3PjkyZOwsDBy+puYmAh3SFNbQZ5Mz58/n7zcsmVL//799+3b5+/v/+zZs5CQEDJE4eOPPxZ+5MyZM6QRe/PmzQ8ePEhISLh9+/ZPP/1ka2srPAKFA+qb2jQyoJDUVkXHBxNk1OCwYcP8/f2fPn36xx9/WFhYkEN32bJlwmLkWmpqarpp0ybyRJPc1EqOIyS9kXV0dI4cOZKUlHT//n1y0zl06FDhwCrhgHqxYMhN6t69e5valtbVtRKhGD09vbFjx54+fbq2tlbyI9HR0WJdK21sbETz5cGDByV7QLi5ub169Up0PRcuXBDtXi9cldjwODHNJMKYmBiKojQ1NcnwPoZhfv75Z3L/KERRlLOzc0ZGBsa4oKBAMgAjI6Nr164J10muTefPnxedj4PFYq1atUp0FBfGOCkpSaxzaffu3cW2pSWJ8OHDh6L94ghbW9vY2FjRT0VEREj2ZeVyuadOnWpm7xGNjY3kQYW+vr7YVtTX15PLgeSVUTIRYox37NghOg+t6Mwyb02EGOPMzEzRSXYQQsbGxrdv3xb74IEDB0RnCBo4cCBpWRKbveXEiROivUXedWYZggx+79mzJ7kk8Xi8lStXik2TxGazR44cSS5zjx8/luyF0aNHD7HpP86dOyf2tY4bN664uFi0TGVlpWjvJJqmt23b1tQ4Qqnbdfv2bbGutkpKSn///bewwOvXr729vcVmO1NSUvrkk0+a2lei/vjjD7Gu0QghAwODjRs3in6tfn5+ZKoEIWdnZ9HJLpraCrFEePLkScnWlOHDh4vNGnH16lXJDsY9evQQDul7ayIkAwoRQlKHDxYXF5NBn0JTpkwh7TGiiRBj/P3334t2j29mZpljx46JXZqmTJlCbq2IdpIIKdw1flWkrq6uoKBA+JLD4WhoaIh9Q5IEAkFERASpMfTu3dvFxUXs1Kqvr4+Njc3MzKysrNFpSD4AACAASURBVDQyMrK1tZWcaBQh1NjYGBkZ+fz5cz6fb2RkZGNjI7WYqNevX5eVlWloaEjtA5aVlSUQCIyMjISPImpqasLDwzMyMshkN/369RPrWffixYuUlJTCwkJlZWVLS0tnZ2fR/sorVqzYu3fv9evXJ02aFBUVlZCQwGazhw4dKnWMEcMwUVFRycnJZMz7oEGDxCZ4e/XqVW1trampqeifEAgEWVlZioqKwjESDMMkJia+fPmyuLhYW1vb2tpasvM9QghjnJiYGBcXV1tba2hoaGFh0a9fP7H5SJuSm5vb0NAg+keFcnJyGhsblZSUxHZUbW1tXl6elpaWZB/aiooKMtWkmZkZh8Mh35Genp7Yk3/yRy0tLUW3BWMcFxcXHx9fX19PuvBJnTY9Jyfn4cOH9fX1vXv3Hjx4sEAgyM7OlgwSIVRdXU16InC5XMkbMqKkpKSyslJXV1fyUGcYhjROkm0hC8vLy8PCwnJyclRUVIyNjR0dHUXTP8Y4KSnpxYsXRUVFWlpa3bt3F7apiKqpqSHzx6qoqDg7O0sdqIMxDg0NTU5OVlFRGTFihKmpaXl5eXl5uYGBgbD7RnZ2Np/Pb2qUW2NjY0REBMk6JiYmgwYNkux/UVhYGBYWVlhYqKamZmpq6uTk1JIxgkLJyckJCQkVFRXKysq9evVycnISO84RQg0NDaGhoc+fP+dwOH379nVychI7gKVuBY/Hy8/PV1dXFx5jjY2NsbGxGRkZFRUVhoaGNjY2Up+4k355T58+bWho4HK5PXr0EC3W0NCQm5tLGp+b2qjCwsKamhqapqUO2mEYJjIyMi0tjabpjz76yNbWtra29tWrV1IvROQrQwh169aNpunXr18XFxcbGBiIHWxVVVWBgYG5ublkrlGxSx85DiXPUHKuST1020JXSYSgeaKJUN6xAACATHX1zjIAAAC6OEiEAAAAujQYUA8QQsjDw4M845R3IAAAIGvwjBAAAECXBk2jAAAAujRIhAAAALo0SIQAAAC6NEiEAAAAujRIhAAAALo0SIQAAAC6tA6QCB88eNDyH6WT2S8aAzGw5+UF9ry8wJ6Xl1Yf9dcBEqG/vz/5meaWaPVf9AYtBHteXmDPywXGuLa2Vt5RdEXCX1ptRR0gEQIAAABtBxIhAACALg0SIQAAgC4NEiEAAIAuDRIhAACALg0SIQAAgC4NEiEAAIAuDRIhAACAjqGOj+7lofhyqnVXC79QDwAAoF1Lr8K+OfhODhPyCjvoom9tIRG2zKpVqx4+fCjvKNrWzJkzv/nmG3lHAQAArY/PoIgifCuH8cvD2dXYlcua0Z31xwiWGovf2NjKk9t12kT4+PHjL774wtHRUd6BtBVfX9+4uDh5RwEAAK3pVR26n8vcysZ++Ux3dcrNhNrrQg82ooR1QD6/9f9op02ECKGePXs6OTnJO4q2kpqa+vTpU3lHAQAAH0qAUXjhG5U/D3PqyBCOjqKMAujMiRAAAEC7VVSH7uYyt7Kxfz5j+W/lb5AhxWrlJ4BvB4kQAACAjAgwiivFPtnMrWycVY1HcFluJtS+gRyuijyjgkQIAACgbRXz0KMCxicL38phuMqUZzdqpzM9nEtx2scIPkiEAAAAWh+p/PnlYZ9sJqEMD+dSnuasHc5sE1WZN32+DSRCAAAAraaEhx4WMH55+GYWo6NIeXajNvVvR5U/qSARAgAA+CAMRk8kKn8/OLJN21/lTypIhLLD4/GOHj16586d169fm5iYuLu7z5s3T1VVNTs7e9WqVcJiPXr02LZtW1BQ0MGDBxFCysrKffr0WbRokaampvxiBwAAcaX1KCCfIflPmaY8zKlN/elhXEqhHVf+pIJEKCM8Hs/Nza2xsXHt2rXdu3d/+fLlH3/8UV1dvWrVqtevX1++fPnixYukpI6ODkIoKysrOjr6p59+amxsPHny5MWLFyMjI1msjnZ8AQA6neRyTAa8RxVjZ33Kw4z1vQPbXK1jVP6kgkQoI7/99ltubm5aWpqSkhJCyN7e3svLq6qqSlhg6tSpYh/R1taeNm0aQmjEiBHGxsbp6enW1tayjBkAAIjqRvSwgLmVjW/nYEUWcjOhltuxRpuwFGl5R9YaIBHKiI+Pz+zZs0kWFFJXVxf+Pz09nfxHT09PQ0NDtBjJlwoKCm0fJgAA/Ce9CpMxD6Ty52bM8hvHstHqwJU/qbpQIpwfKAh+hWXzt2ZaUds+euNOqaCgwMzMjPw/Ojr68uXLCCE7O7u5c+cihBiGGTt2LHl306ZNs2bNQggVFhb+9NNP9fX1Fy5cmDhxorm5uWyCBwB0ZTV8FJDP3MrGvjmY82/lz92EpdQpKn9SdaFEuPtjurJRRolQR1H8jklNTa2srIz8X11dvXv37nfv3n327BlJhCwW69mzZ2If4fP55eXlGhoaO3fu9PT0lEHYAIAuS7Lyd3ccy7bTVf6k6kKJUE8J6SnJ7UsdNGhQQEDAunXrEEK9evXq1atXaWlpVFRUMx8xMTHZuXOnrAIEAHQ5tXwUVoh9spnrWZimkLsJtciGddWNpc6Rd2Sy1YUSoXytWLHCwcFh69ata9euZbPZGOOSkhJ5BwUA6IrSq/4Z8/cwHzvoUp7mrKtuLCe9LlH5kwoSoYxYWFg8evRo+fLlO3bs6NatW2VlZc+ePbdu3YoQoiiKw+liN2AAANmq46PQQuyXz9zIwuX1eLQJa14P1h8jWBpw7YFEKEsODg5BQUGVlZWvX7/mcrnC5Ne3b18ejydWeO7cueTxIQAAvDdS+fPLw/fzmD7alKc567wrq78e1XVrf9JAIpQ1DQ0NsdERAADQingCFPIK++UzPlm4pB6PMWFN604dH8rRhBFYTYBECAAAnUFGFX6Qh/3y8IM8xkqD8jCnzrrSUPlrCUiEAADQUfEZFFGEb+Uwfnk4uxq7clke5tTRIRxtRXlH1qFAIgQAgA6msA7dy2XIhJ/d1Sk3E2qvCz3IkGJB7e+9QCIEAIAOgPzOrU82cysbZ1XjEVyWmwm1fxDHSFnekXV8kAgBAKD9KqpDd3OZW9nYP5+xhMpf24BECAAA7YvUyt/egWxjFch+baLTJkJFRcWZM2eK/dpDZ1JdXQ0TkALQmRTz0KMChkz4yVWmPLtRO53p4VyKA79D2sY6bSK8dOlSaWmpvKNoWyYmJvIOAQDwQRiMnpT+M+FZQhkezqU8zVk7nNkmqlD5k51Omwg1NTU1NTXlHQUAAEhRWo8C8hm/PHwzi1FhUx7m1Kb+9DAupQCVP3notIkQAADaFWHlzy+fiSrGQ40oT3PWeke2GVT+5A0SIQAAtKGyeuSfz/jl4VvZWIlGHubUanuo/LUvbZgIKysr4+LiTE1Nu3fvLrVAXV1dUlISQqhPnz7KyjAWBgDQeSSXYzLgnfzOrYcZa50Dq5saVP7ao7ZKhGFhYV5eXn379k1JSZk1a9bu3bvFCjx58sTDw6Nnz54IoWfPnt26dcvR0bGNggEAABmo4aOAfOZWNr6TgxVYyM2EWm7HGm3CUqTlHRloVlslwm+++eb7779fvnx5QUFB7969FyxYYGdnJ1pgx44dn3zyyb59+xBCK1as2L59+6VLl9ooGAAAaDvpVZiMeSCVPzdj1oNxLBstqPx1GG2SCHNzcx8/fuzr64sQ4nK5o0ePvnz5slgipGlaS0uL/F9TU7OgoKAtIgEAgLZQy0cPX7H8igXXMjGHhdxMqEU2rGtuLDX4ndsOqE0SYU5OjpaWljDPWVhY5OTkiJXZunXrp59+WlRURFFUYmLi6dOnm1pbdXV1SUnJgwcPyEsWizVs2DCalt7WwDAMwzCtsRHg3cCelxfY87KUXoVvZaNbOUx0CXLUZo0xQ3fGULb/Vf7gq2hzzL9aWJ7FenuvpDZJhHV1dQoK//0EpKKiYm1trViZ9PT0oqKi4cOHUxRVXFz88uVLa2trqWsrKCiIj49PT08nLxUUFKytrXV1dZv6003lSNCmYM/LC+z5tlbLR5ElLN981u08GiE8yojxtmTODWRYDTWqqqoIIYnLG2hDfD6/sbERY9zC8kpKSmz2WzJdmyRCIyOj8vJyhmFIKi4pKeFyuWJlli9fvmHDhlmzZiGEevfuvXz58qdPn0pdW48ePQYMGLB69eqW/GmMsZqa2oeFD94H7Hl5gT3fRtKr/pnw5WE+dtClPM1ZV20pJ71/Kn8Y45oaBHte9kgibN2BBm2SCK2srNTV1R8/fuzi4oIQCg4O3rBhg1iZmpoa4cwvmpqaNTU1bREJAAC0XB0fhRZiv3zmZhYuq8ejTVjzerDOu7I0Fd7+WdBxtUkiVFRUXLZs2eLFizdv3hwQEMDj8SZPnowQevTo0cyZM0m/mOnTp69atYrH41EU9cMPP8yYMaMtIgEAgLcilT+/PPwgj7HSoDzMqXOudH89Cvp9dhFtNXxiw4YNRkZGf//9N5fLDQwMJI8MzczMFi1aRAr89NNPffr08fHxQQh9++23c+fObaNIAABAEk+AQl5hv3zGLw/n1ODhRiwPc+rYUI4WVP66HqrljxzlZc2aNdra2i18RlhVVaWurt7WIQFJsOflBfb8O8mswvffrPx5mrPeo/KHMa6pqYFnhLLXYZ4RAgBA+8FnUEQRvpXD+OXh7GrsymV5mFNHh3C0FeUdGWgfIBECADqnwjp0L5chE352V6fcTKi9LvQgQ4oFj/7AmyARAgA6DwFGcaXYJ5u5lY2zqvEILsvNhNo/iGMEs/qDpkEiBAB0eEV1KPAV45OFfbIZYxXKsxu105l25VJs+Kkj0AKQCAEAHZJo5S+zCo80ZrmZUDsHsI1VoOkTvBtIhACAjqSEhx4WMOTXHrjK/1T+hnMpDlT+wPuCRAgAaO8YjJ6U/jPhWUIZHs6lPM1Z253ZpqpQ+QOtABIhAKCdKq1HAfkMyX/KNOVhTm3qTw/jUgpQ+QOtChIhAKB9SS7HZMwD+Z1bDzPWeke2GVT+QJuBRAgAkL+yeuSfz/jl4VvZWIlGbibUcjvWaBOWIvzAFGh7kAgBAHIjWflb58DqpgaVPyBTkAgBADJVw0cB+cytbHwnByuwoPIH5A8SIQBAFtKrMBnzQCp/bsas++NYvbWg8gfkDxIhAKCt1PJRWCH2yWauZ2E2hdxMqEU2rGtuLDWOvCMDQISURMgwTEhISEBAQHx8fElJCZvNNjIyGjBggLu7e58+fWQfIgCgYyG/c+uTzTzMxw66lKc566oby0kPKn+gnXojEfJ4vEOHDh0+fDg9PV1BQcHCwkJHR4fH44WHh1+8eJFhmAEDBqxcuXL69OkU/HQzAEBEHR+FFmKfbOZGFqYoNNqEmteD9ccIlgZU/kC7918ijIuL8/Lyqq+vnzVr1pQpU5ycnBQV//u1roqKitDQ0IsXL3722Wd79+69c+eOtra2PAIGALQjkpW/K1D5Ax3Nf4mwsLBw1apVn332mYKCgmQ5TU3N8ePHjx8//pdfftm9e3dlZSUkQgC6JlL588tnbmbhsno82oQ1rwfrvCtLU8qVA4AO4L9EOGbMmJZ8QEdHZ/v27W0WDwCgncqowg/ysF8efpDHWGlQHubUOVe6vx48JgEdHvQaBQA0ic+giCJ8K4fxy8M5NXi4EcvDnDo2lKMFlT/QibyRCENCQng8XvMfcHNza8t4AADyl1mF7+dhvzzsl890V6fcTKi9LvRgI6j8gc7pjUQ4Z86crKys5j+AMW7LeAAA8iHAKLzwn8pfdjV25bI8zKmjQzjaim//LAAdmnjTqKKi4sSJEydOnCjaZRQA0FkV1qF7uQyZ8FNY+RtkSLGg9ge6jDcS4bFjx06ePHnjxg1/f/+ZM2fOnz//o48+kldkAIA2IsAorhT7ZDO3snFWNR7BZbmZUPsGcrgq8o4MAHl4IxGOHj169OjRr1+/vnjx4tmzZ52dnXv37u3t7e3t7W1kZCSvEAEAraKYhx4VMD5Z2CebMVahPLtRO51pVy7Fht+5BV2blDNAS0tr0aJFISEhiYmJ48eP//XXX83MzL777jvZBwcA+EACjGJK8E/xzBAfvtXfjWefM0OMqKSp7ORP2DudaTcTyIIANDt8ok+fPgsWLBAIBAcPHkxMTJRZTACAD1TCQw8LGJ8sfDuHMVKmPLtRm/rTw7kUB9IeABKkJ0Jh62hoaGjv3r23bdvm7e0t48gAAO+EwehJ6T8TniWU4eFcytOctd2ZbaoK/V4AaM4biZBhmICAgLNnz165ckVBQWH69Ok7d+4cMmSIvIIDALxVWQN1N4Mh+U+ZpjzMqU396WFcSgEqfwC0zBuJ0MnJKTExccyYMb///juMoACgnWtg0MYYwW8pCiNN8DhT6gdHqPwB8D7eSITl5eU0TYeHh4eHhy9evFjqB8rKymQSGACgOWmv8ZxHAj0lFDWuoYeBmrzDAaADeyMRzpo1q7S0VF6hAABa6Oxz5ptIwXoHenkfVnUVTPYEwAd5IxHCz0oA0M4V89BnwYL8Ghziye6lCQ2hALQCeJ4OQIdxLxc7XuNbqKHQiZAFAWg10odP+Pj4NPUzFNOmTWvLeAAAUtTx0ZoowY0s/OcIepgRpEAAWpP0RPj5558XFhZKfQt+fQIAGYsuwXMeCux1qCdebPgtCABanfREGBkZKRAIhC+Li4sfPXp06NCh3377TVaBAQAQRmh/EvNjnOAXF3qONTzIAKBNSE+E3bp1E33ZvXv3jz/+2NDQ8Ntvvx03bhyLBSckAG0uuxrPCxSwEIrxYpvBAEEA2sw7pLQxY8akpaWlpaW1XTQAAOJSBuN8g+/KpfzGQxYEoG01N+m2mJcvXyKEOBxOmwUDAEAVDeh/YYKYEnx3LNtRF1IgAG2upb1GMzIyDhw4YGZmZmVlJZPAAOiKwgrxvEDBKGMqejJb5R1uUwEA7+8deo0OHTr0wIED8IAQgLbQyKAf4wTH0phjQ9ge5lARBEB2WtRrFCHE5XKVlZVlEhIAXU7qazznkcBACcV6cYzgPANAtlrUaxQA0EYwQsfTmO+jBesd6K/6QHMLAHLwXyJsbGxsYUcYjLFAIGCz4QkGAB+kqA4tDOYX1qFQT3ZPmDINADn57w70r7/+8vDwiIiIaKY0n8+/evWqo6Njenp628cGQGd2Nxc7XefbaVMhkAUBkKv/anVjx44NCgoaMmRIz549p06d6uLi0rNnTx0dHT6fX1ZWFh8fHxYWdunSperq6u+++87CwkJ+MQPQsZGJQ29m4z9H0ENh4lAA5O2/RKivr3/8+PEVK1YcPnz44MGD27ZtEytqbm6+ZMmSxYsXGxoayjZIADqPqGI855Ggnw71xIutpSDvaAAAkp1lbG1tDx48uG/fvtjY2MTExKKiIgUFBQMDA2dn5169esklRAA6BwFGuxOYPYmCvQPpWVbQLwaA9kJ6hxeapp2dnZ2dnWUcDQCdVVY1nvdIwGGhWC+2KUyZBkB7ArelALS5SxmMyw3+eDPW/XGQBQFod2AIBABtqKIBLQsTPCnBvmPZDjBxKADtEtQIAWgrAfm47xW+KhtFTYYsCED7BTVCAFqfcOLQE0PZ480gBQLQrkEiBKCVpbzGcx4KLNWpxKkcXUV5RwMAeBtoGgWg1WCEjqUxw2/xvXuwrrjRkAUB6BCarBHm5OT4+vrm5uY2NDSILt+5c2fbRwVAx1NYhxYG8Yt5KMyT3QOmTAOg45CeCE+dOrV06dL6+npVVVUFhTdmv2hhIsQYX7x4MSwszNLS8vPPP1dVVZUsU1tb+/vvv6elpRkZGc2ePRt+8gJ0XNcymSWhgvk9WVudaA60swDQoUg/Zb/77ruhQ4dmZWVVV1eXvamF692yZcumTZtsbW39/f0nTJggWaCystLFxeX27dvW1tbV1dUJCQnvvxEAyE8dH30VLlgZyVwexd7pDFkQgI5HSo2wqKiotLR069at5ubm77fS2travXv3+vn5OTk5LViwwMzMLDQ0dPDgwaJltm/fbm5u7uPjQ1HQiAQ6qsfFeM4jgYs+lTCFrd6iHzEDALQ7Um5ftbS0VFVV6+rq3nuliYmJLBbLyckJIaSgoDB8+PCgoCCxMr6+vrNmzbpw4cKvv/6amJj43n8LALngM+ineMbjHn9zf9ZZVxqyIAAdl5QaoYKCwsqVK3fv3j148GCxB4QtVFBQoK+vL3xpYGCQn58vViYjI2PLli1jxozR1NR0dXU9ceKEl5eX1LVlZmb6+/s/e/aMvGSxWJs3b9bS0pJauK6ujqbp94gZfKAuteezqtHnEWwFFg4bKzBWaaytlWcwXWrPtx8Y49raWhYLmsJljc/nNzY2YoxbWF5BQeGtPyMv/W0OhxMbG2traztixAhdXV3Rt1rSWYbD4fD5fOHLxsZGdXV1sTI0TY8ePXrfvn0IIWNj461btzaVCDU1NU1NTYUzgCspKWlpaSkqSu+Z3tDQ0NRboE11nT1/7gVeFYVX2lHf9qVYlPxH4nadPd+uYIz5fD7sedmjaZrFYrV8z7fkZkX6aXz+/Pn6+vr6+vorV66IvdWSRGhiYlJYWMjn80kezsvLGzlypGSZ3r17k//b2trm5OQ0tTZtbe3u3bt/8cUXb/27CCGapuHuWC66wp5/3YCWhgoSytCDce1oyrSusOfbIYwx7Hm5wBgzDNO6e156qnz69GlZE1qyUnt7ez09vdu3byOEioqKAgMDPTw8yP9DQkJIGS8vr/DwcPL/sLAwW1vbVtgaANqMfz62v8LXV0IxMHEoAJ1LmzTssFisnTt3fvbZZ1evXg0LC5s/f37Pnj0RQkFBQV999VVeXh5CaPny5UOHDvXw8NDU1AwICLhx40ZbRALAh+MJ0KZYwbnn+MRQehxMHApAp9NkIuTxeJcuXYqPj8/NzTUyMurbt+/06dMlH/U1ZcaMGQMGDIiKilq6dOnHH39MFo4aNcrX15f8X19fPy4uLiAgAGN84MABHR2dD9wSANpCcjme80hgpUElTGXDlGkAdErSE2FeXt7o0aNTUlIUFRUNDQ2Liop4PN7mzZvv3bsnfLD3VpaWlpaWlqJLtLW1tbW1hS+VlJTGjx//3qED0KYwQsfTmA0xgi1O9CIb6BwIQKcl/fT+4osvCgsLL1++XFtbm5WVVVdXd//+fRaLNXfuXBnHB4BcFNYhj3v8U8+YEE82ZEEAOjcpZ3htbe3du3cPHDgwdepUYcdTd3f3s2fPxsTEZGZmyjRAAGTuaibT72pjXx0q2INtrQEPBQHo5KQ0jb5+/ZrP5/ft21dsOVlSXFxsYWEhg8gAkL2qRvRtpOBBHr7ixh5sCCkQgC5BSo1QT09PRUXl7t27Ysvv3btHURT8RgTorCKLcP9r/Do+SpgCWRCALkT6FGve3t7r1q0rKyubPn26sbFxcXGxj4/P9u3bJ02aZGBgIPsoAWhTfAbtSWT2JQsOD6Ynd4MnggB0LdJ7je7Zs6esrGzHjh07duwQLhw9evTJkydlFRgAMpJRhec+EqiwUfRktrEKVAQB6HKkJ0JlZeW//vpr8+bNwcHBpaWlmpqaLi4uDg4OMg4OgLZ29jnzTaTg2770KnsWC5IgAF1SczPL9OrVq1evXjILBQBZKuGhz4MFLyqx/3i2vQ7kQAC6rv8SIY/Hq6ioUFdXV1FRKSkpEQgEUj9gaGgoq9gAaCt+eXhBkGCKBfXXSLYiTJsMQNf2XyK8cOHCp59+un379rVr19rZ2RUVFUn9QMt/BQqAdohMHPrXS3zWlR7BhYogAEAkEQ4dOvT06dPkZ+X379//Ib9QD0D7lFyOZz8U9NCkYr3YOjBxKAAAISSaCK2tra2trcn/Z8yYIad4AGgTGKH9ScyPcYJtH8HEoQCAN0i/Inz++edPnz4VW/js2bPp06e3fUgAtLJXdWj8Xf5f6Uz4RJg4FAAgTvpFwcfHp7S0VGxhaWnp5cuX2z4kAFrT5QzG4WrjxwZUiCfbCiYOBQBIeIcf5s3NzdXV1W27UABoXZWNaFWkwC8PX3VjD4Ip0wAATXgjEd6+ffvMmTMIoYqKih9++EE07VVVVYWFhbm6uso4PgDeT0QRnvtIMNCAip/CVuPIOxoAQDv2RiKsqKhIT09HCAkEgry8vIqKCuFbWlpaCxYsWLNmjawDBOAd8Rm0LU5wNJU5OoSeCBOHAgDe5o1EOGvWrFmzZiGEPv74499++61///5yigqA95RRhec8EqixUYwXTBwKAGgR6c8IIyMjZRwHAB+OTBy63oFe3gfmDQUAtFRznWV4PF56errYyHoy4h6AdqWYhz4PFqRX4YDx7L4wcSgA4F1IT4Tl5eULFy68ceMGwzBib8EUa6C9uZ+HPw0STLWgLo5iK8AzQQDAO5KeCL/44ovAwMCDBw9ev35dT09v0qRJd+7cuXr16u7du2UcHwDN4AnQ6seCG1n4vCvtChOHAgDei5T7Z4zx7du39+zZs2TJEmNjYwsLi+nTp//+++/r1q07evSo7EMEQKqkcvzxDX5BLYr1YkMWBAC8NymJsKioqKamxsXFBSGkoKBQVVVFln/22WexsbEvX76UaYAASMAI7UtiRt7mf2vPujiKhumzAQAfQkrTqKamJkVR1dXVCCETE5Pw8HCynPxCoTAvAiAX2dXYO1BQL0ARk9jd1aEiCAD4UFJqhEpKSr169YqNjUUIubm5+fv7Hzly5PHjx8uWLVNVVe3Ro4fMgwTgH5cyGOcb/OFcKtgTsiAAoHVI7yyzYsWKkpIShNCgQYNmz569ZMkShJCiouLhw4dVVVVlGiAACKF/Jw4NeoV9x7D760EKBAC0GumJcNGiRcL/nz59esOGDRkZGb179+ZyubIKDID/hBfhuY8Egwyo6Mls1XeYKB4AAN5OStNoeXm5u7t7UFCQcImlpeXIkSMhCwLZ4zNoU6xgqh//VxfWWVcasiAAoNVJSYQCgcDPYdBGCwAAIABJREFUz09BQUH20QAgKu01drnJjyjCMZM5nuYwVB4A0CakXFz09PRsbGyio6NlHw0AQmefM0Nv8edas3zHsrkq8o4GANB5SW9pOnHixJw5czQ0NDw9PbW1tWUcE+jiiurQZ8GCgloc4snupQn9YgAAbUt6Ivz0009fvXrl7e2NEFJTU+Nw/vth07KyMhmFBrqke7l4YbBgqgV12Q0mDgUAyIL0RDh37lwyoB4AmanjozVRghtZ+M8R9DAjqAgCAGREeiJcv369jOMAXVx0CZ7zUGCvQz3xYmvDlGkAABmS3va0atUqyTlF09PTFy9e3PYhga6FwWhfEjP+Ln+9I+viKBqyIABAxqQnwnPnzhUWFootLCwsPHbsWNuHBLqQ7Go88g7/RhYT48WeYw2PBAEAcvAOl57CwkIdHZ22CwV0NWTiUFcu5TeebaYKDwUBAPLxxjNCPz+/S5cuIYQqKyt//vlnQ0ND4Vs1NTX+/v7Ozs6yDhB0RhUN6H9hgpgSfHcs21EXUiAAQJ7eSITZ2dl+fn4IoYaGhqioKCUlJeFb6urqbm5uW7ZskXWAoNMJK8TzAgWjjKnoyWwVmDINACBvb1yHPv30008//RQh1KtXr3Pnzg0YMEBOUYHOqZFBP8YJjqUxx4awPcyhIggAaBek35A/ffpUxnGATi/1NZ7zSGCghGK9OEbK8o4GAAD+1VzLVH5+fmZmZm1trehCNze3Ng4JdDYYoeNpzPfRgvUO9Fd9oGsoAKB9kZ4I4+PjFy1a9PjxY8m3MMZtHBLoVIrq0MJgfmEdCvVk94SJQwEA7Y/0RDhr1qyKiopDhw717dtXRQVm/gfv6W4u/jxYMNuauuJGw8ShAID2SUoirKioSElJuXnzpqenp+wDAp0DmTj0Zjb+cwQ9FCYOBQC0Y1ISIYvFYrFYRkZGso8GdA5RxXjOI0E/HeqJF1sLfuAZANC+SWmuUldX9/DwuH79uuyjAR2dAKOf4pkJ9/gb+7MujqIhCwIA2j/pzwjnz5+/dOnS0tLSMWPGqKuri74FvUZBU7Kq8bxHAg4LxXqxTWHKNABAByE9ES5ZsqSwsPDo0aNHjx4Vewt6jQKpruWwVj/hf92HXmXPYkESBAB0HNIT4f379xsbG2UcCuigKhrQsjBBTBHHdyzbASYOBQB0NNITob29vYzjAB1UQD6eHygYZ0YFjm4wgEeCAIAOqLmZZVJTU5OTk+vr62fPno0QqqysZLPZMKwQEMKJQ08MZY83o6qqoM0cANAhSU+EVVVVM2fOvH37NkLIxMSEJMJvv/02IyPjwYMHMg0QtEspr/GchwJLdSpxKkcXflMeANCRSZ/tY+nSpVFRUX///feVK1eEC+fMmRMYGFhTUyOr2EB7hBE6lsYMv8X37sG64kZDFgQAdHRSEiGPx7t48eK+ffumT5+uq6srXG5jY9PY2JiTkyPD8ED7UliHPO/xTz5lwjzZMH02AKBzkHItKy0tbWhocHBwEFvO4XAQQtXV1bKIC7Q/1zKZflcb++hQIZ7sHjB9NgCgs5CSCHV1dRUUFJKTk8WWh4WFURRlYWHRkvVmZ2d7enqam5u7ubmlpqY2Vay2ttbLy2v16tXvEjOQtVo++ipc8E0kc3kUe6czzYGqIACgE5FySVNSUpo0adLatWufPXtGUf/c+CclJX399dfu7u56enotWe+sWbOsra1jYmJGjRo1adIkhmGkFvv+++9fvnwZGxv73hsA2trjYuxwjV9ejxKmsIfA9NkAgE5H+r39/v37aZq2tbX19vYuLS21t7d3cHDg8Xi//fZbS1aanJwcGxu7bds2fX39NWvWVFdXBwQESBaLiIh4/Pjxp59++kFbANoMn0E/xTMe9/ib+7POutJqHHkHBAAAbUB6IjQyMoqOjt61a5eNjY2dnZ2uru769evj4uK6d+/ekpWmpKTY2NioqqoihCiKcnBwSElJEStTX1+/ZMmS48ePs1jQ0NYeZVbhEXf4fvnMEy/2TCv4jgAAnVaTA+pVVVVXrFixYsWK91hpaWmp6FTdWlpaxcXFYmU2btw4efJkW1tbPz+/5tcWFxcXFBS0c+fOfyJmsyMjIw0MDKQWrqmpETbngvf2ZwZrXRz7KxvmKxs+C6OWdJCCPS8vsOflAmNcW1sr7yi6Ij6f39jYKBAIWlheSUmJzW5u6hjUVCJMSUmpq6tzcnISXZiUlMTn8yV7k0rS1tYW7VxaWVmpo6MjWiAxMfHvv//29fVNT08vLS2tq6vLyMiwtLSUurZ+/fq5uLh89dVX5CWLxdLU1GzqT2OM1dTU3hohaMrrBrQ0VJBQhv0n0P103uHyCnteXmDPywXGmKIo2POyRxKhsrJyK65TepPXjBkz7ty5I7YwKipq3LhxLcnDVlZWL1++bGhoIC9TU1Otra1FC+Tm5rJYrAkTJri7ux86dCg2NtbDw6OptVEUpaysrP2vZrIg+EB+ebjvFb6+EoqZzH6nLAgAAB2XlERYW1ublJQ0evRoseXu7u6vXr3KzMx860o/+ugjU1PTQ4cOIYT+/vvv2traMWPGIISCg4O3b9+OEBo3btzLf23YsGHw4MGSozWALPEEaE2UwDtQcGwIvW8grUjLOyAAAJAVKYnw9evXCCHJKj9ZUlZW1pL1nj9//tSpUxoaGuvWrfv7778VFBQQQllZWSEhIWIlNTU1uVzue4QOWktyOR54k/+iEiVMZY8zg4ogAKBrkfKMUE9PT1lZOTQ01M7OTnQ5yWGmpqYtWa+Dg0NiYiKfzxd9Sjlnzpw5c+aIlfT29vb29n7nwEFrwAgdT2M2xAi2ONGLbKBrKACgK5KSCBUUFLy8vNasWdOtWzfSpIkQCg8PX7Zs2fDhw9+p9vbWvjpAjl7VoU+D+GX1KMSTba0BFUEAQBclvRKwd+9eLpc7duxYY2Pjjz/+uFu3boMGDUIInTp1SrbhgbZyJYNxuNpor0MFe0AWBAB0adJrbPr6+lFRUSdPnvT39y8sLLS3t//f//63aNEi6LHZCVQ1om8jBQ/y8BU39mBDSIEAgK6uyaZLFRWVL7/88ssvv5RlNKCtRRbhOY8EAw2ohClsmDINAABQM4kQdDJ8Bu1JZPYlC34bTE/qBv1iAADgH9ITYW1t7d69e69fv56Tk1NfXy/6VguHT4B2JaMKz30kUGGj6MlsYxVoDgUAgP9IT4Rz5sy5fv26u7v74MGDFRUVZRwTaF1nnzPfRAq+7UuvsmexIAkCAMCbpCTChoaGW7du7dq165tvvpF9QKAVlfDQ58GCF5XYfzzbHqZMAwAAaaTPLNPY2Dhy5EjZRwNa0YM87HiNb66GoidDFgQAgCZJSYT6+vq9evVKSEiQfTSgVZCJQz8PFpx1hYlDAQDgLaQ0jVIUderUqU8//dTQ0HDUqFEcDvSy70iSyvHsh4KemlSsF1sHHu8CAMDbSO8ss2DBgqysrHHjxrHZbNGf2EXQa7QdwwjtT2J+jBNs+wgmDgUAgJaSngjnzp1b3ZJfJQftxqs6tCCQ/7oBhU9kW8GUaQAA0GLSE+H69etlHAf4EJczmGVhgiW9WT840jQkQQAAeBdvn1mmsrJSQ0NDBqGA91DZiFZFCvzy8DU39iCYOBQAAN5dk0+SHjx4MGzYME1NTU1NTTU1NRcXl8uXL8syMvBWEUW4/zV+HR8lTIUsCAAA70l6jfDq1avTpk0zNDScM2eOkZFRcXHxnTt3pk2bdujQoaVLl8o4RCCJz6BtcYKjqczRIfREmDgUAAA+gPREuGrVKnd39+vXryspKZElv/7668KFC9etW7dw4UKYdE2+0qvw3EcCNTaK8YKJQwEA4ENJqUwUFxenp6dv3LhRmAURQjRNb9mypaKiIi0tTYbhAXFnnzMf3+BPt2TdHQdZEAAAWgH8DFOHUcxDnwULMqpwwHh2X5gyDQAAWon0KdasrKy2bt0q+gNMDMNs3rxZU1PTxsZGhuGBf9zPw47X+BZqKHoyZEEAAGhN0muEP//887Rp06ysrCZPnszlcouKinx9fZ8/f37o0CF4QChjPAFa/VhwIwv/4UoP50IKBACAViY9EU6ZMuXu3btbt249duz/27vzgCbOvA/gTy5u5BYCCAJa8T7QinggaxU8EKx4H1WoL56ta7Wt2nU9q9baatWuWi8srC7UEyyKeAJKrQqioHiACmIgBgQJEJLMvH/M7jSEUzkiyffz18wzD8/8MoT58cw8M89euVzO4/H69OkTFRUVFBTUwvHpuLuF9LTLSnczTso4vgX+AwEAaAa13iMcPnz48OHD5XJ5aWmpkZEROoItjH1x6FZP3owOeEACAKC5qCfCrKwsY2NjW1tbZlUgEFhYWBBCJBJJcXGxk5MTn4/xNc3ueSn9yRWlTEmSA/iuprgcCgDQjKp0NU6cONGxY8eMjIzq9cRicY8ePXbu3NlSgemuqGyq3ymFt5CT4I8sCADQ7Kokwp07d44bN87Hx6d6PXd39wULFvz0008tFZguKpGTmZeVq25Rsb781X3w+mwAgJbwVyJUKBRJSUnjxo2rreq4ceOys7OfP3/eIoHpnOsFdJ8TCkM+uRnI72ONHAgA0EL+uuFXXFwsk8kcHR1rq+rg4EAIEYlETk5OLRGazmBeHLr3AbVnEM/fCeNiAABa1F+J0MTEhBDy6tWr2qoym9QmrIdGevCannZZaWNAbgUKhEaajgYAQPf81f/Q19fv0qXL6dOna6t66tQpU1PTDh06tEhgOuHwI2pwjGJmB26sHx9ZEABAI6pciJs9e3Z4eHhERET1eleuXNmyZcuMGTMEAkFLxabNCsrJ2DjljnQq0Z//eTcubgkCAGhKlYcCP/vss5iYmOnTp//6668BAQGurq48Hu/Zs2fnzp07fvw48wJSTQWqTc7l0iEJyvHtOb99xNfDPUEAAI2qkgj19PRiY2OXL1++Z8+ec+fOseU8Hm/y5Mnbt2+3tLRs8Qi1SrmCfP2n8vRz+t8+vCF26AcCAGie+mtiDA0Nt23btnr16mvXrj179kypVDo4OHh5ebHvmoF3dvMVPf2Ssocl53YgXhwKAPC+qPl9aebm5qNGjWrhULQYRZMd6dSGVOWPnrxpeHEoAMD7BC8ObQmzrihzpfTtcXxHY1wOBQB4vyARNrszOXSymL4zjm+Igw0A8P7Bubl5lcjJvETlQW8esiAAwPsJ96ua17I/lGOcOMPscUUUAOA9hX5KM7rykj6TQ98bj4MMAPD+Uu8RxsfHjx071t3d3dvbe+PGjQqFQiNhaYFyBZmTqNzlxTXX03QoAABQuyqdlaSkJD8/Py6X6+bmlpaWdvXq1fz8/G3btmkquFbtn7eV/aw5Ac64+AwA8F6rcpretWuXtbV1RkbG/fv3X758OX78+D179lRWVmoquNYrVUL/+oj60ZOn6UAAAKAeVRLho0ePZs6cycwvYWBgsGLFioqKCszE+7YUFAm+qtzqyWtrqOlQAACgPlUSoVgsFgqF7Kq9vT1T2NJBtXKb7lBCIzLVDRdFAQBagfoHNNI03QJxaI3MYnpHhvJmIEaKAgC0Durn6x9++IGdj1AulxNCgoODmcnrGTdv3myx4FodiiafJijX9OG1w6vUAABaiSqJsHv37i9fvmRXBQKBh4dHi4fUiu3MoLiEhHbGRVEAgFajSiKMjo7WVBxa4FkpvS5FeXUMH51BAIBWBH2XJhOaqFzandfZHHkQAKA1qZII586de/z4cWaZpun09PSSkhJNRNX6HHpIicrIku74xwIAoJWpcuKOjY3NzMxkluVyebdu3eLi4jQRVSvzqoIs/1N5YAhPgDwIANDa4MzdBOYnKUM6cftY46IoAEDrg8fdGivmOX2nkD48FEcSAKBVwum7UYoryfwkZYQPzwBvFQUAaJ3UE2FCQgKfzyeEKJVKQsjp06ezs7NVKyxbtqzFgnv/ffGHMsCZM9gOF0UBAFor9UQYGxsbGxvLrv76669qFd4qEd6/f7+ysrJ79+5cbg03I2Uy2cOHD7lcbqdOnZjs27pceknHv6DvYt5dAIDWrMpJ/PLly8xr1RpPJpONHTs2KyvL2NiYw+HEx8dbWVmpVvjPf/4zb948BwcHpVJZXl5+7NixPn36NMmuW0aZgsxJUO7w4poKNB0KAAA0QpVE6OLi0lTt/vrrrxKJJD09XSAQBAUFff/99xs3blSt8MEHH6SlpTk6OhJCvvjii88//zwhIaGp9t4C/nFLOdCW4++EYbcAAK1bc53HIyMjp0+frqenx+FwgoODIyMj1Sr07t2byYKEEC8vL5FI1EyRNIcbYjriMfV9f4yQAQBo9ar0CF+9erVy5cqRI0cGBgYSQlJSUoYNG8Zu5fF4V69e7dy5c0Paff78Odu/dHFxycnJoSiqxjuFFEXt3bv3448/rq2psrIyiUQSHx/PhuHt7V1jUy2jkiIhV5XbB/BsDDQVAgAANJkqifCnn36KioratGkTs6pQKIqKikaPHm1kZEQIuXHjxvr169lJmupWXl6ur6/PLBsYGMjlcrlczpaoWrly5atXr/75z3/W1lROTs7du3efPHnCrPJ4PBcXF2tr6xorS6VSDqd5x3B+e4/nYMAZ3VZRWtqs+2llWuDIQ41w5DWCpumysjJNR6GLFAqFXC5nnmtoCAMDg3oHY1bZfOzYsVmzZllYWKgW/vzzz05OToSQgwcPLlq0SKFQNGSEp62tbWFhIbMskUgsLS1rzILr1q2Ljo6+dOkSk2tr1KlTJ09Pz6+++qrenRJCaJpWnT2xyT14Te9/orgVyDcxRn+wiuY+8lAbHHmNoGmaw+HgyLc8JhEaGho2YZt/XWCUyWQPHjwYMmRIbVX79esnlUrZnlnd+vXrl5SUxCwnJib27du3ep0ffvghPDz8/PnzNjY2bxm2ZlA0CUlQrvfgOWLeXQAAbfFX3660tJSiKNXuoJubW2RkJHsR0tzcnBBSXFzckHbnz5/v5eXVu3dvc3Pzb7/9ln0esU+fPmvWrPH39w8PD//yyy+/+eYbZhJEPp8fHBzcVJ+qmWxPp/S45FN3jBQFANAefyVCU1NTDoeTn5/PllhaWk6YMIFdZQZ2mpmZNaTdrl27njlzZvfu3TKZbP/+/X5+fkx5YGAgc6HVxsZm6dKlFRUVWVlZhBCB4H1/HO/pG3rTHWWSP+bdBQDQKn8lQj09va5du54+fXrixIk1Vo2OjjYzM3Nzc2tg04MGDRo0aJBa4apVq5gFX19fX1/ftw9YM2hCQhOVX/bgdWiDPAgAoFWqXOWbPXv20aNHo6KiqtdLSkraunXr9OnTW+O70BrvQCZVVEkWd8NFUQAAbVMlqy1cuPDkyZOTJk06fPiwv7+/q6srIeTFixdxcXGRkZHt27dfu3athuLUJFE5Wf6n8txIPg+9QQAArVMlEerp6Z09e/bLL7/ct29fTEwMW87lcidMmLBjxw5LS8sWj1DzFiQp53Xm9rZCGgQA0ELq1zmNjIx27ty5du3axMTEnJwcpVIpFAoHDRokFAo1Ep/G/ZZNZbymI3x08YIwAIAuqPn8bmlpOXbs2BYO5T1UXEmWJFNH/oZ5dwEAtBZGf9RlcbLyYxfOQFtcFAUA0Fq44leri3n05Zf03Y9xiAAAtBl6hDVT0mRekvJfA3km7/uD/gAA0ChIhDWLzKKs9ImfIy6KAgBoOVz3qwFNyMY71JYPMUIGAED7oUdYg9PPKD6HjEB3EABAByAR1mDzHeofvblIgwAAugCJUF3cC/p1JQlwxpEBANAJON2r25Ci/KY3F/1BAAAdgURYxfUCOldKJrrgsAAA6Aqc8atYe1u5vBeXj6MCAKAzcMr/S4qETi8iMzvimAAA6BCc9P+yLoVa1oOrh0MCAKBLcNb/r/uv6eQCKqQTDggAgG7Bef+/1qdQi7vxjPCmHQAAHYNESAghWW/oc7lUqDuOBgCAzsGpnxBCNqZSC7tyzfQ0HQcAALQ4XAokuVL6+FMqcwLmWwIA0EXoEZLv0qhPO3GtDTQdBwAAaIKu9wgLykn4Yyp9PLqDAAA6Std7hD/cU07vwBUaaToOAADQEJ3uERZXkv2Z1M1AnT4IAAA6Tqd7hNvuUQHOXGcTzDQBAKC7dLczJFWQf91XXh2ju0cAAACILvcId2VQw+y5H5ihOwgAoNN0tD9UoSTb71Fn/XiaDgQAADRMR3uE+zKp/m053S3RHQQA0HW62COUU2TrXSryb+gOAgCATvYIDz+iOpmRfjboDgIAgO71CJU0+S6N2jcY3UEAACBEB3uE/8mirA3IYDt0BwEAgBBd6xHShGy6Q33fH91BAAD4L93qEZ56RvE5ZLgDuoMAAPBfupUIv02lVvXhIg0CAABLhxLhuVxaKidjnXToIwMAQL10KCtsSFV+05uL/iAAAKjSlUR4vYDOKyMTXHTl8wIAQAPpSmJYc1u5oheXrysfFwAAGkonMkOKhM4oItM76MSHBQCAt6ITuWHtberLnlw9nfisAADwdrQ/OWS8pv8QUyEfaP8nBQCAd6D96WF9CvX3bjxD3XqFDgAANJSWJ8InJfSFPGpuZy3/mAAA8M60PENsvEPN78wzFWg6DgAAeF9p8xVDcQU5/pR6PBFpEAAAaqXNPcIDmdT49lxLfU3HAQAA7zGtTYQUTfY+wN1BAACoh9bmibgXdBs94mGNV4sCAEBdtDYR7rlPzUd3EAAA6qOdqeJlGbkioia7aeenAwCAJqSdqWJ/JjXJlYunJgAAoF5amAhpQg49ouZ00sKPBgAATa4ZnyP8/fffExISHBwcgoODjYyMqld48ODB0aNHuVzutGnT3Nzcmmq/51/Q5nqkD4bJAABAAzRXt2n79u0LFixo27bt2bNnR4wYQdO0WoX09PT+/fsrlcqysrJ+/fo9efKkqXa97wH1KbqDAADQMM3SI5TL5Zs3b46IiPDx8Vm4cKGrq+vFixeHDRumWufHH38MDg5et24dIaSoqGjHjh3btm1r/K4lMk58HvXLYNweBACABmmWnlNmZmZRUdGQIUMIIQKBwMfH59KlS2p1Ll265OvryyyPGDGieoV3c0HEDXDmmuk1SWMAAKD9mqVH+PLlSysrKx6Px6za2tq+fPlSrY5IJLKxsWEr5OXl1dbas2fPLl68+OjRI2bV0NBw5cqV5ubmNVYe3VY60ZVbUSFv7GeAt1RRUSEQoCOuATjyGkHTdEVFBZ+vza9rfj8pFAq5XM7hNHQUiEAgYJNRbZrlt8jn8ymKYlcVCkX1P1Qej8fWqbECy8TExMHBoW/fvuwPmpqa1lbfQE9gpI+TggYIBAKcjjUCR14jaJrGkdcIJgU2/MhzufVf+GyWRCgUCiUSiUwm09fXJ4Tk5eV17dpVrY69vT3bC8zLy7O3t6+tNSsrqw4dOsydO7chu+bxePUmf2gOOPKagiOvETRN48hrBE3TFEU17ZFvlnuEnTp1cnZ2jo6OJoQUFxfHx8ePHj2aEFJUVJScnMzUGTNmzG+//cYsHzt2bMyYMU2y67NnzzZJO/BWaJrGkdcImUzWVPfX4a0UFRVdv35d01Hootzc3LS0tKZts1kSIYfD2bhx47x580JDQwcPHuzn5+fh4UEISU5OHjlyJFNn8eLFly9fDgoKCggISE1NnT9/fpPsOiQkpKSkpEmagoYrKSn59NNPNR2FLnr48OGKFSs0HYUuun79+tatWzUdhS46e/bsL7/80rRtNted3vHjx/fo0SMpKWny5MlDhw5lCj09PWNjY5llR0fHe/funTt3jsvl+vr6mpqaNlMkAACgNao/ld54zTjkqWPHjh07dlQtsbCw8PT0ZFfNzMwmTpzYfAEAAADUC29gAQAAndYKHoJ5/PhxWlpafHx8QyqXl5cHBgZiKFcLY16VN3z4cE0HonOkUumzZ89w5FueRCJ5/vw5jnzLy83NffPmTcOP/Lhx4+odg8JpjuutTSs1NfXJkydmZmYNqZydne3i4tLcIUF1OPIaQVFUTk6Os7OzpgPROZWVlWKx2MHBQdOB6JzS0tLy8nL2fSz1cnFxqXdSh1aQCAEAAJoP7hECAIBOQyIEAACdhkQIAAA6DYkQAAB0Wit4fKI2YrE4Li7OyMjIz8/P0NCwegW5XB4XFyeRSIYNG4bBXU2loqIiMTExLy/PxcVl0KBB1SdDEYvFd+7cYVd79+5tZWXVsjFqp8TExIqKCmbZ2tq6V69e1eu8evUqLi7OwMDAz8/PyMioZQPUTiUlJTdu3FAt6datm52dnWrJgwcPcnNz2dWPPvqohYLTRjRNP3ny5OnTp56eniYmJmx5UVHR2bNnBQKBn5+fajlLqVTGx8eLRCJvb+/27du/1U5b66jRzMzMwYMHjxgxoqCgQCQSJSUlqb2kTaFQDBs2TC6Xd+7c+eTJk9HR0V5eXpqKVpvY2Nh07tzZzc0tKSnJxcUlJiZGbT6UkydPzp49m502a+PGjewyNIazs7NQKGS+5/3791+/fr1ahUePHg0cOHD48OESiSQ3N/fatWtt2rTRRKRaJTMzc+HChcyyTCZLSEi4evXq4MGDVevMmzcvPj6eOflyOJy4uLiWj1M7SKVSR0dHHo9XWFiYkpLSs2dPpvzZs2cDBgwYPHiwVCp9+PDh9evX1f69pml61KhRYrG4V69eJ0+ePHr06Nv9O0K3Tp988snixYtpmqYoytvbe8eOHWoVjh075u7uLpPJaJresmXLRx99pIEotdHjx4+ZhTdv3rRt2zYmJkatwokTJ4YMGdLicWk/JyenlJSUOioEBwcvWrSIpmmKonx8fLZt29ZSoemKiIgIFxcXiqLUyufOnbthwwaNhKRlFApFdnY2TdP6+vqpqals+cKFC0NCQpjl0aNHVz/a58+fd3JykkqlNE3v2bPH09PzrfbbWu8RRkdHBwUFEUI6apesAAAR+UlEQVQ4HM7HH38cExOjViEmJsbf319PT48QEhQUdOHChfLycg0EqnXYR1NNTExMTExkMln1OlKp9Ny5c3/++adcLm/Z6LTcnTt3zp8/n5+fX+PWmJiY8ePHE0I4HM748eOr/1FAI+3fvz8kJKTGudFfvHgRGxubmZnZ8lFpEx6PV+NVTfa7TQip8bsdExMzatQo5nZAUFBQcnKyWCxu+H5bZSKsqKgoLCxkb/s5ODi8ePFCrc6LFy9UKxBC2HmAoUlEREQoFIoaX3Qkk8l27do1bdq0Hj16ZGdnt3xsWsnc3PzIkSObNm1yc3PbsWOH2lbmRSeOjo7Mao1/FNAY2dnZV69enTlzZvVNfD7/zp07P//888CBA4OCghQKRcuHp8Vomn758mXd323VE76lpaWhoeFbff9b5WAZpVJJCGH/L+PxeNW/eUqlksv9b5pnauLb2YQSExP//ve/nzhxovr8Wf7+/oGBgYQQiqJmzJixbNkydgZmaIzbt28zL9FNSkr629/+FhAQ4OTkxG5VKpU0Tdf9RwGNcfDgwREjRrRr1676pm3btjG/mqKior59+x46dAjTczYhmqaVSmXDT/i11alDq+wRGhsbm5qasj3f/Px8e3t7tTpCobCgoIBZFovFNE1XrwPv5o8//hg/fnxERMTAgQOrb2XfeM7lcidNmpSSktKy0Wkt9sAOHDhQKBSqTdJtaGhoYWFR9x8FvDOKosLCwoKDg2vcyv5qLCws/Pz88J1vWlwu19bWtuEnfKlUWlpa+lbf/1aZCAkhPj4+7NCsuLg4Zu5fmqYlEgnTXxw6dOj58+dpmmYqeHh4YO7fJpGamhoYGLhv3z7Vi6LMkacoSq3y7du3a/wPGhojLy9PJBIxB7aysvL169dM+dChQ8+dO8css38U0CTi4uKkUumYMWPYEplMxh55Fk3TKSkp+M43udq+2xKJhOn5MSd85hQUFxfXqVMnoVDY8PZb6+MT165dGzly5LJlywoKCiIjI1NTU+3s7IqLi83NzTMyMjp37iyVSnv27Onl5dW9e/fvvvtu796948aN03TUrZ5cLrezsxMKhWxfMCgoaPjw4SKRSCgUZmVlubi4LFq0iMvltmvXLiMjIyoqKjo6Gmfkxrt27dp3333Xr18/hUIRFhbWv3//I0eOEEIiIiL+8Y9/ZGVlEUKSk5N9fX2XLl0qkUiOHDmSmpr6VucCqMOECROcnJy2bt3KloSFhX377bfM6Bhvb+8hQ4aYmJjExcVlZWXdunXL0tJSc8G2bsuXLy8sLNy/f39gYKCVldWWLVvatGmTmprq7e29ePHisrKyAwcO3Lp1q3379jRNc7nc5OTk/v37y+XyPn36uLu7e3p6bt26dfPmzTNmzGj4TnmrV69utk/UjNq1azdq1Kj09HRLS8tdu3YxvWAej9euXbv+/fsbGBjo6elNmzZNJBK9fv161apVI0aM0HTIWsLS0rJ///72/+Pu7m5ra8vj8ZydnT/88EN9fX0HBweJRPLq1asOHTrs2LGDfRIIGsPMzIzD4RQUFPB4vE8//fTrr79mbpkYGxt36dKlW7duhBBHR8fRo0dnZGSYmZnt2rULL5FoQuXl5VOmTFGdDI458l27diWE2NraFhQUlJWVeXt7/+tf/8Ljm41RUFBgbW09evRoNzc3e3v7Xr16CQQCOzu7gICA+/fvGxkZ7dy5k31k08HBYcCAAcbGxjweb9q0aRKJRCKRfPnllwEBAW+109baIwQAAGgSrfUeIQAAQJNAIgQAAJ2GRAgAADoNiRAAAHQaEiEAAOg0JEIAANBpSIQA9WDe2KTpKDQpLi4uPj6++dq/devWtWvXmrZNqVQaFRX15s2bpm0WtBISIbQaFEV5eXm5ubn98ccfapsWL17cvXt3tcK7d++6uroyb2AhhBw9etTV1fXu3bsN3F12dnZISIiNjY2JiYmpqam9vX1oaCjzDpf3k0gk2rt3r0gkakwjr1+/3rt379OnT1ULN27c+P333zcquDr36OfnpzrDe90++OADNze3tWvXqpXPnz/fzc1tyJAhzKqxsfHWrVu//fbbpowVtBQSIbQaly9fvn79el5e3r59+9Q25efnV5/vSSaTZWdnl5SUMKslJSXZ2dkVFRUN2VdycrKHh0dMTMyiRYt+//332NjYJUuWXLlyZfbs2Y3/IM3k8ePHoaGhjx49akwjL1++DA0NTU1NVS0MCQn55JNPGhddrb777jsbGxtmetGGyMrKysvL2717t+r0Aq9fvz548GBeXt7z58/ZwhUrVmzbtg3zr0G9kAih1Thw4ICzs/PChQuPHj3arNcqpVJpUFCQqanp7du3V61aNXLkSD8/v6VLl967d2/BggWqNeVyuUgkqmPOZ7lc/urVq9q2lpaWikSiGt/uVFxcnJ+fX8eLn8Ri8VtNNKNQKEQiUWVlJVvy+vXrBh7G6dOnT5kyRa2QCZ55x32NSkpKpFJp3S3LZLJ9+/bNnDlTdQ6deo0dO1YsFrNvYSaEHDlyRF9f39vbW7XaqFGjzM3Nf/nll4a3DLoJiRBah+Li4hMnTsycOXP27NmlpaXHjx9vvn2Fh4e/ePFi8+bNaq/r5PP5EydOZJZlMtnnn39uaWkpFArbtGnj7++venGvU6dOK1asWL9+vZWVlY2NjY2NzYEDB1SbunDhQr9+/dq0aSMUCo2MjGbNmsVuOnv2bM+ePc3Nze3s7BwdHQ8dOsRu+uKLL3r16nXx4sUOHTq0bdvWxMRk1qxZTG6LjY0dNWoUIWT06NGWlpaWlpaJiYmEkJ49ey5ZsmTdunXW1tZCofDkyZMKhWLKlClWVlYWFhampqbt27ffvXs3035ycrKnpychZMaMGUwjp0+fJoQEBQVNnTqVDSMtLW3QoEFM8La2tps2bWITdmxsrKWl5YULF0aMGGFubt6mTZv+/fvXMTnzmTNnxGLxxx9/zJasWbPGzc1NtU71Ejs7uxEjRoSFhbElhw4dmjp1qqGhodrvy9/f//Dhw7XtHYCBRAitw5EjR8rKyqZNm9alSxcPD4+DBw82377i4+N5PJ7qnDvVzZkzZ9euXStXrkxNTT18+PD169c/+ugjtmtYXFx88ODBK1euHD9+PCkpqU+fPvPmzXv27Bmz9eLFi35+fgKB4MyZM+np6VFRUexkBXFxcWPGjOnSpUtiYmJKSsrkyZNnz57NZv2ysrKsrKz58+evXr365s2bX3/9dVhY2P79+wkhffv2ZW6brVmzJjIyMjIyknkfdHFxcURERHR0dFhYWEJCgoeHB0VRHA5n//799+7du3Hjhq+v77x582JiYggh7u7uP/74IyFk2bJlTCNMXpRIJIWFhUwMeXl5Pj4++fn50dHRt2/fnjp16vLlyzds2MBslcvlRUVFwcHBQ4YMSU5OjoiIePz48aJFi2o7jBcvXrSysurYsSNbUl5erja9UfUSQsisWbNOnTrF9LYzMzNv3Lih+s8Ea8CAAVlZWWq3PAHU0QCtwYcffujl5cUs//TTTxwO5/Hjx+zWyZMn1/YN3717N1Nnz549hJAbN240ZF9CobCOCllZWRwOZ8mSJWzJyZMnCSEHDhxgVm1tbZ2cnMrKypjVFy9eEEJ27drFrHp4eDg7O5eXl1dvuUePHoMGDaIoii0ZOXKkp6cnszx37lxCSFJSkmqow4cPZ5YTEhIIIVevXlVt0NnZ2czMrLCwsO7PO2XKFGY5IyODEHLixAnVCkOHDvX19WWWV6xYweVy09PT2a1jxowxNTWVSqU0TZ86dYoQsmLFCnbrmjVruFxuRUVFjbsePHgw+2tlfPXVV5aWlnWU8Hi8zz77TCaTWVtb79y5k6bpZcuWderUiabpwMBAZ2dn1Z9NSkoihJw8ebKOjw/Ab4lkC9A46enpN27cYK/gTZ06denSpWFhYapDB/X19dUuP2ZnZ3/zzTfvsDuKouq+ZXXnzh2apidNmsSW+Pv7GxkZqY6mGTp0KHulzt7e3tzcPCcnhxBSWFh4+/btr7/+2sDAQK1ZkUiUlpYWEhJy4cIFttDe3j4hIYGmaWbeJTMzMy8vL3Zrly5dkpOT6/44Q4cOtbCwUC2RyWRRUVH3799nelSvX79+8uRJ3Y2wUlNTu3fv3qVLF7Zk0qRJMTExKSkp7CyVI0eOVI2Qoqjc3Fy1y5sMsVhcY3m99PT0Jk2aFBYWFhoaGh4evnjx4hqrWVlZEULYucsBaoRECK0Ak+GYkf1MibOz86FDh1avXs1mLD6fr3ofixBy8+bNd0uEQqEwLS1NJpPp6+vXWIG5yMnMgsngcrlCoVAikbAlalOz6uvrMzfzJBIJTdOOjo7Vm83PzyeEHD16VO0OqEAgKC0tNTU1JYSopTS22TrY2tqqrubk5AwePFgqlfr5+VlbW+vr6+vr6xcXF9fdCOv58+dqwTN3UlU/u2qQenp6hJDaguTz+XUMt6nbJ598smvXri1bthQUFEyfPr3GOnK5nBAiEAjebRegI5AI4X0nl8vDw8MNDAw2b97MFlIUVVxcHB8f3xxTLg8ZMiQ6OvrSpUt+fn41VjA2NiaEiMVi1ZRQUFDA3FGrm7m5OflfzlPDTOi6du3aJUuWvFvkNVLr3e7bt6+wsPDRo0dsgrx7927De4TGxsZq42CZ/pbqpLUNZ2trq9Yan89XGw3LPgCjpl+/ft26dVu1apWvr6/qPyWqmPSs9q8AgBoMloH3XUxMTEFBwdGjRwtViMViKyurZhoyM2vWrDZt2qxYsaL66H/mOiST8M6cOcOWX7ly5c2bNwMGDKi3cRsbmy5duhw/frx6T6h9+/bOzs6//fYbRVHvELaJiQkhpN4HJbOzs9u1a8fmhqKiItW3utTbiKen5507d5jLvIyYmBgDA4PevXu/Q8z9+vXLyMhQzXwODg4lJSVisZhZpSiKufdZo2XLlg0dOrSOwThpaWkcDsfDw+MdYgPdgUQI77uDBw9aWFiodc4EAkFQUNDJkyeLioreqrX4+Pj/qIiMjKxex9ra+sCBA/fu3fPy8oqMjHz69GlOTk50dPSYMWO++uorQki3bt1Gjhy5efPmo0ePFhcXX7t2LSQkxN7evrYLdGrWrl177969KVOm3L9/v6ysLCMjgxmryeFwNm7ceP369RkzZmRkZJSXlz99+vTf//73unXrGtKsq6urkZHR3r17ExISbt26VdvbxXr16vXgwYPw8HCZTPbgwYMJEyao5iGhUGhpaXno0KErV67cunWr+uFdsGABn8+fPHlyenp6YWHhjz/+eOTIkdDQUKY7+7aGDx9eVlam+vz+sGHDeDze559/npOT8/jx4zlz5rCjbaubOXPm+fPna+u4E0KuXbvWq1evtm3bvkNsoEM0PFgHoE4ikUggEPzf//1f9U1Xrlwh/xuKOXnyZGNjY7UKf/75J6k2alQNh8OpbdcJCQkDBw5khqgQQrhcro+PDzsms7CwMCAggN3ao0ePtLQ09mdtbW0XL16s2pqtra3qKNOwsDDVszM7JpOm6fDwcNXnF62srDZs2MBsmjt3bvv27VWbDQ0NdXV1Vf3Zjh07MrflLl68SNO0s7Pz3LlzVX+koqJi7NixTOM8Hm/BggWzZs1iRl0yTp061bVrV+b+aFRUFF111ChN0+fPn3d2dmZbmDdvnkwmY3+WEHLv3j3V1gghGRkZNR5kiqI6duy4bNky1cLt27czd/U4HM7MmTOXLFlSfdRoja2pjRotLS01MTFhB+sC1IZD1/7qCoDWgvk2Vx/qqVQquVwuk65omq5+yZHD4dQ9QFQikWRnZxsaGnbo0KH62BmRSPT8+XMLCwvVJ+EaSKlU3r9/v7y8vF27dnZ2dqqbKIp6+PBhSUmJjY2Nk5MTj8d728brlZOTIxKJXF1dmXGVdWOOm+qBoijqwYMHpaWlHTt2VBu/87Z27ty5YcOGrKws1cfh37x58+jRIzs7u9pu/jXEvn37li9f/uTJk3frrYLuQCIEAE1SKBQ9e/acM2dObY9AvBu5XO7u7v7FF1/Mnz+/CZsFrYRECAAaJpFIKisrhUJhE7ZZWVmZm5vr5OTE52NsPNQDiRAAAHQaRo0CAIBOQyIEAACdhkQIAAA6DYkQAAB02v8DPRVBNntoXWQAAAAASUVORK5CYII=\" />"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Import Catalyst.jl for good measure\n",
    "using Catalyst, Plots, DifferentialEquations\n",
    "\n",
    "# Functions\n",
    "k_old(kθ, km, R_T) = kθ * km * R_T # k_old\n",
    "α(km, x, n) = (km * x^n)/(1 + (km * x^n)) # activation Hill function\n",
    "\n",
    "# Parameters\n",
    "p_T = 1 # Total RNAP concentration\n",
    "r_T = 1 # Total ribosome concentration\n",
    "k1θ₁ = k1θ₂ = k1θ₃ =  1.67 # Transcrption elongation rate\n",
    "k2θ₁ = k2θ₂ = k2θ₃ =  1.67 # Translation elongation rate\n",
    "gᵀ₁ = gᵀ₂ = gᵀ₃ = 0.06 # Total gene concentration = 60 copies\n",
    "δ₁ = δ₂ = δ₃ = 0.0833 # mRNA degradation rate\n",
    "λ = 0.0067 # Dilution rate\n",
    "k1m₁ = k1m₃ = 1 # Binding constant between DNA and RNAP\n",
    "k1m₂ = 1/6 # Binding constant between DNA and RNAP\n",
    "k2m₁ = k2m₂ = k2m₃ = 1/15 # Binding constant between mRNA and ribosome\n",
    "kma₁ = 10 # Binding constant between activated LuxR and DNA 2\n",
    "kma₂ = 100 # Binding constant between activated NahR and DNA 3\n",
    "k_hat₁ = [252, 1] # Binding constant between inactive LuxR and AHL \n",
    "k_hat₂ = [100, 1] # Binding constant between inactive NahR and SAL\n",
    "n = 1 # Cooperativity coefficient for activated TFs and DNA\n",
    "nᴵ1 = 1.4 # Cooperativity coefficient for AHL\n",
    "nᴵ2 = 4 # Cooperativity coefficient for SAL\n",
    "\n",
    "AHL = [0.01, 0.02, 0.05, 0.08, 0.1, 0.5,1, 5, 10] # Inducer 1 concentration\n",
    "SAL = 100 # Inducer 2 concentration\n",
    "\n",
    "vect= []\n",
    "\n",
    "# Reaction system specification\n",
    "@variables t\n",
    "@species x₁(t) x₂(t)\n",
    "\n",
    "# Node 1 rates\n",
    "k1₁ = k_old(k1θ₁, k1m₁, p_T) * gᵀ₁\n",
    "k2₁ = k_old(k2θ₁, k1m₂, r_T) \n",
    "\n",
    "# Node 2 rates\n",
    "k1₂ = k_old(k1θ₂, k1m₂, p_T) * gᵀ₂ * α(k1m₁, x₁, n)\n",
    "k2₂ = k_old(k2θ₂, k2m₂, r_T)\n",
    "\n",
    "# Node 3 rates\n",
    "k1₃ = k_old(k1θ₃, k1m₃, p_T) * gᵀ₃ * α(k1m₂ , x₂ , n)\n",
    "k2₃ = k_old(k2θ₃, k2m₂, r_T)\n",
    "\n",
    "# Find the estimate of the steady-state value for GFP production for all AHL concentrations\n",
    "for i = 1:length(AHL)\n",
    "    # Node 1\n",
    "    node_1 = @reaction_network begin\n",
    "        @species m₁(t)=0.0 m₂(t)=0.0 m₃(t)=0.0 x₁(t)=0.0 x₂(t)=0.0 x₃(t)=0.0 x⁰₁(t)=0.0 x⁰₂(t)=0.0 I₁(t)=$AHL[$i] I₂(t)=100.0\n",
    "        $k1₁, ∅ --> m₁\n",
    "        $k2₁, m₁ --> x⁰₁\n",
    "        $δ₁, m₁ --> ∅\n",
    "        $λ, x⁰₁ --> ∅\n",
    "    end\n",
    "\n",
    "    # Edge 1\n",
    "    edge_1 = @reaction_network begin\n",
    "        ($k_hat₁[1], $k_hat₁[2]), x⁰₁ + $nᴵ1*I₁ <--> x₁\n",
    "        $λ, x₁ --> ∅\n",
    "    end\n",
    "\n",
    "    # Node 2 \n",
    "    node_2 = @reaction_network begin\n",
    "        $k1₂, ∅ --> m₂\n",
    "        $k2₂, m₂ --> x⁰₂\n",
    "        $δ₂, m₂ --> ∅\n",
    "        $λ, x⁰₂ --> ∅ \n",
    "    end\n",
    "\n",
    "    # Edge 2\n",
    "    edge_2 = @reaction_network begin\n",
    "        ($k_hat₂[1], $k_hat₂[2]), x⁰₂ + $nᴵ2*I₂ <--> x₂\n",
    "        $λ, x₂ --> ∅\n",
    "    end\n",
    "\n",
    "    # Node 3\n",
    "    node_3 = @reaction_network begin\n",
    "        $k1₃ , ∅ --> m₃\n",
    "        $k2₃, m₃ --> x₃\n",
    "        $δ₃, m₃ --> ∅\n",
    "        $λ, x₃ --> ∅ \n",
    "    end\n",
    "\n",
    "    # Combine nodes\n",
    "    @named rxn_sys = extend(extend(extend(extend(node_1, edge_1), node_2), edge_2), node_3)\n",
    "    # Convert to ODE system\n",
    "    tspan = (0, 1000)\n",
    "    u0 = []\n",
    "    p = []\n",
    "    ode_sys = convert(ODESystem, rxn_sys, combinatoric_ratelaws=false)\n",
    "    prob = ODEProblem(ode_sys, u0, tspan, p)\n",
    "    sol = solve(prob,Rosenbrock23())\n",
    "    push!(vect, maximum(sol[2,:]))\n",
    "end\n",
    "\n",
    "plot(AHL, vect,\n",
    "    xlabel = \"AHL Concentration (uM)\",\n",
    "    ylabel = \"GFP Concentration (uM)\",\n",
    "    label = \"GFP\", fmt = :png, title = \"Dose Response Without Resource Conservation\"\n",
    ")\n",
    "# savefig(\"no-resource-conservation-simulation\")\n"
   ]
  }
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