tuto_HH.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Interactive tutorial: *the membrane potential in action*\n",
    "\n",
    "## Objectives\n",
    "- To develop an electrical engineer's perspective of the neuronal membrane and its dynamics (Hodgkin-Huxley model)\n",
    "- To understand the different membrane components involved in the generation of action potentials\n",
    "- To develop an intuition of how action potentials are sensed by extracellular recording devices\n",
    "\n",
    "*Side objective*: to illustrate the power of physical laws and computational models to help understand neural processes."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Imports"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib widget\n",
    "from numpy import exp\n",
    "from constants import MA_CM2_TO_UA_CM2\n",
    "from simutils import interactive_simulation\n",
    "from model import Model, vtrap"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Model construction\n",
    "\n",
    "We are going to construct a pyramidal regular spiking neuron model as defined in [Pospischil et al. 2008](https://link.springer.com/article/10.1007/s00422-008-0263-8). This type of neuron constitutes the primary type of excitatory neurons in the mammalian neocortex.\n",
    "\n",
    "To better understand the involvement of the different membrane componentns in resulting membrane dynamics, we will construct this model step by step, one component at a time.\n",
    "\n",
    "At each stage, we will evaluate the model's behavior by observing its response to an applied electrical stimulus $I_{stim}$, mimicking the impact of synaptic input or artificial stimulation.   "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Step 0: a cell membrane\n",
    "\n",
    "Let's start with the simplest possible model configuration: a \"naked\" cell membrane (i.e. without ion channels). This simplistic membrane can be represented electrically by a capacitor $C_m$, enforcing a potential difference $V_m = V_{in} - V_{out}$ between the intracellular and extracellular space, known as the ***membrane potential***. You can see below the equivalent electrical circuit of this representation:\n",
    "\n",
    "![circuit](imgs/circuits-01.png)\n",
    "\n",
    "As we apply an stimulating current, the membrane potential will change according to the following governing equation:\n",
    "\n",
    "$C_m \\frac{dV_m}{dt} = i_{stim}$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "12caff28b572477fadcc7a3b2e1e37f9",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "interactive(children=(FloatSlider(value=0.0, continuous_update=False, description='I', max=60.0, min=-15.0, st…"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "34f629e0f94340c5a910c0bfa2c2a80f",
       "version_major": 2,
       "version_minor": 0
      },
      "image/png": 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",
      "text/html": [
       "\n",
       "            <div style=\"display: inline-block;\">\n",
       "                <div class=\"jupyter-widgets widget-label\" style=\"text-align: center;\">\n",
       "                    Figure\n",
       "                </div>\n",
       "                <img 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' width=700.0/>\n",
       "            </div>\n",
       "        "
      ],
      "text/plain": [
       "Canvas(toolbar=Toolbar(toolitems=[('Home', 'Reset original view', 'home', 'home'), ('Back', 'Back to previous …"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Membrane capacitance (uF/cm2)\n",
    "Cm = 1.0\n",
    "\n",
    "# Create model and run interactive simulation\n",
    "model = Model(Cm=Cm)\n",
    "interactive_simulation(model.copy());"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Questions\n",
    "- *Try varying the input current and look at the evolution of the membrane potential: what do you observe?*"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Step 1: a passive current\n",
    "\n",
    "Let's start further constructing our neuron by adding a first passive membrane current term, called the ***non-specific leakage current*** ($i_{Leak}$). Our equivalent electrical circuit now is:\n",
    "\n",
    "![circuit](imgs/circuits-02.png)\n",
    "\n",
    "And the system's governing equation becomes:\n",
    "\n",
    "$C_m \\frac{dV_m}{dt} = i_{stim} - i_{Leak}(V_m)$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "d00bef33b07f4eaf96738d6ffaa7e365",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "interactive(children=(FloatSlider(value=0.0, continuous_update=False, description='I', max=60.0, min=-15.0, st…"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "df1e35feb7f5444bbc8d51ae878c180b",
       "version_major": 2,
       "version_minor": 0
      },
      "image/png": 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",
      "text/html": [
       "\n",
       "            <div style=\"display: inline-block;\">\n",
       "                <div class=\"jupyter-widgets widget-label\" style=\"text-align: center;\">\n",
       "                    Figure\n",
       "                </div>\n",
       "                <img 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DliRrkAAAC4TF5z01ptGjt2rDp27Kj69etr5cqVmjhxog4ePKgXXnhBklRcXKzk5OQqz4mPj3cfq1ev3jmvW1FRoYqKCvdjh8PhoZ8AAAAA1WX6Orw15bHHHjvrRrSfb9u3b5ckZWZmqkePHmrXrp1Gjhyp559/XjNnzqwSVi9HVlaWoqKi3FtiYmJN/GgAAAC4ApYZ4X3kkUc0dOjQC57TrFmzc+5PS0tTZWWl9u7dq5SUFCUkJOjQoUNVzvnx8fnm/UrSxIkTlZmZ6X7scDgIvQAAACazTOCNjY1VbGzsZT13w4YN8vPzU1xcnCSpa9eu+tOf/qQzZ84oICBAkrRkyRKlpKScdzqDJAUFBSkoKOiyagAAAIBnWGZKQ3WtWrVK06ZN08aNG7Vnzx698847Gj9+vO677z53mL333nsVGBioESNG6Ouvv9Z7772n6dOnVxm9BQAAgG+wzAhvdQUFBWnu3LmaMmWKKioqlJycrPHjx1cJs1FRUVq8eLFGjx6tTp06qUGDBpo0aRJLkgEAAPggm2EYhtlFWJXD4VBUVJTKysoUGRlpdjmmqKysVElJiex2u2lL0AGoeU6nU06nU3FxcfL3r3NjJwB8TJ2b0gAAAIC6hcALAAAASyPwAgAAwNIIvAAAALA0Ai8AAAAsjcALAAAASyPwAgAAwNIIvAAAALA0Ai8AAAAsjcALAAAASyPwAgAAwNIIvAAAALA0Ai8AAAAszd/sAnD5li1bplOnTpldxgU5nU4dPXpUfn5+8vPj7yvAKlwul1wul6Kjo2W3280uB/AZ1157rRo3bmx2GXWOzTAMw+wirMrhcCgqKkplZWWKjIys8esnJSWpqKioxq8LAAA844033tDw4cPNLqPOYYTXh1177bWKi4szu4wLMgxDlZWVkiSbzWZyNQBqyo9jJf7+/vy/DVyCmJgYs0uokxjh9SBPj/D6gsrKSpWUlMhut/OxJ2AhTqdTTqdTcXFx8vdn7ASAd2NSJQAAACyNwAsAAABLI/ACAADA0gi8AAAAsDQCLwAAACyNwAsAAABLI/ACAADA0gi8AAAAsDQCLwAAACyNwAsAAABLI/ACAADA0gi8AAAAsDR/swuwMsMwJEkOh8PkSsxTWVmp8vJy2Ww2+fnx9xVgFS6XS4ZhKDg4WP7+vJUA3iQiIkI2m83sMrwKr1IeVF5eLklKTEw0uRIAAFBXlJWVKTIy0uwyvIrN+HEYEjXO5XLpwIED/KUFAABqDbnjbAReAAAAWBqTKgEAAGBpBF4AAABYGoEXAAAAlkbgBQAAgKUReAEAAGBpBF4AAABYGoEXAAAAlkbgBQAAgKUReAEAAGBpBF4AAABYGoEXAAAAlkbgBQAAgKUReAEAAGBpBF4AAABYGoEXAAAAlkbgBQAAgKUReAEAAGBpBF4AAABYGoEXAAAAlkbgBQAAgKUReAEAAGBpBF4AAABYGoEXAAAAlkbgBQAAgKUReD3IMAw5HA4ZhmF2KQAAAHWWv9kFWFl5ebmioqJUVlamyMhIs8sxhdPp1OHDh1VZWWl2KQBqmL+/v2JiYmS3280uBQAuiMALjzIMQ5WVlbLZbPLz4wMFwCpcLpcqKyv5BAuATyDwolb4+fkxCgRYjNPpNLsEAKgWhtwAAABgaQReAAAAWBqBFwAAAJbGHF4AAHBFnE6nzpw5Y3YZlhcQEMD9MJeJwAsAAC6LYRgqLi7W0aNHzS6lzoiOjlZCQoJsNpvZpfgUAi8AALgsP4bduLg4hYaGEsI8yDAMnThxQiUlJZKkhg0bmlyRbyHwAgCAS+Z0Ot1hNyYmxuxy6oSQkBBJUklJieLi4pjecAm4aa2asrOzZbPZNG7cOLNLAQDAdD/O2Q0NDTW5krrlx/5mzvSlIfBWw9q1a/Xqq6+qXbt2ZpcCAIBXYRpD7aK/Lw+B9yKOHTumwYMH67XXXlO9evXMLgcAAACXiMB7EaNHj1bv3r2Vnp5+0XMrKirkcDiqbAAAwLv06NHDK6Yo5ubmymazscpFLeCmtQuYO3eu1q9fr7Vr11br/KysLE2dOtXDVQEAgCvx8ccfKyAg4KLn9ejRQx06dNC0adM8XxQ8ihHe8ygqKtLDDz+sd955R8HBwdV6zsSJE1VWVubeioqKPFwlAAC4VPXr11dERITZZaAWEXjPIz8/XyUlJerYsaP8/f3l7++vvLw8zZgxQ/7+/nI6nWc9JygoSJGRkVU2AADgXWpqSsOKFSt04403KiQkRImJiRo7dqyOHz/uPv7WW2+pc+fOioiIUEJCgu699173OrrncuLECd1+++3q1q0b0xxqGFMazqNnz57avHlzlX3Dhg1Tq1at9Oijj7L2HQAAP2MYhk5WmrNcVoh/QK2uYLB7927ddttt+utf/6qcnByVlpZqzJgxGjNmjGbPni3ph6XDnnzySaWkpKikpESZmZkaOnSoFixYcNb1jh49qt69eys8PFxLlixhubcaRuA9j4iICLVt27bKvrCwMMXExJy1HwAASCcrz6jl25NMaXvnfU8oNCCw1trLysrS4MGD3SPFLVq00IwZM9S9e3fNmjVLwcHBGj58uPv8Zs2aacaMGbruuut07NgxhYeHu48VFxdr0KBBatGihd59910FBtbez1FXMKUBAADgEm3cuFFz5sxReHi4e8vIyJDL5VJBQYGkH6ZH9unTR0lJSYqIiFD37t0lSYWFhVWu1atXLzVv3lzvvfceYddDGOG9BLm5uWaXAACA1wrxD9DO+54wre3adOzYMf3ud7/T2LFjzzqWlJSk48ePKyMjQxkZGXrnnXcUGxurwsJCZWRk6PTp01XO7927tz766CNt3bpV1157bW39CHUKgRcAANQIm81Wq9MKzNSxY0dt3bpVzZs3P+fxzZs36/Dhw8rOzlZiYqIkad26dec8Nzs7W+Hh4erZs6dyc3PVpk0bj9VdVxF4AQAAzqO0tFQbNmyosq9hw4Z69NFHdf3112vMmDH67W9/q7CwMG3dulVLlizRSy+9pKSkJAUGBmrmzJkaOXKktmzZoieffPK87Tz33HNyOp265ZZblJubq1atWnn4J6tbmMMLAABwHu+++65SU1OrbK+99pratWunvLw87dy5UzfeeKNSU1M1adIkNWrUSJIUGxurOXPm6IMPPlCbNm2UnZ2t55577oJtvfjii7r77rt1yy23aOfOnbXx49UZNsMwDLOLsCqHw6GoqCiVlZXV2TV5KysrVVJSIrvdzlJugIU4nU45nU7FxcXJ358PC+uiU6dOqaCgQMnJydX+giZcOfr98jDCCwAAAEsj8AIAgDpn+fLlVZYU+/kGa+FzKAAAUOd07tz5rJvRYF0EXgAAUOeEhIScd0kxWA9TGgAAAGBpBF4AAABYGoEXAAAAlkbgBQAAgKUReAEAAGBpBF4AAFCn9OjRQ+PGjTO7DNQiliUDAAB1yscff6yAgACzy0At8urA63K5lJeXp+XLl2vfvn06ceKEYmNjlZqaqvT0dCUmJppdIgAA8DH169c3uwTUMq+c0nDy5En99a9/VWJion75y19q4cKFOnr0qOx2u3bt2qXJkycrOTlZv/zlL7V69WqzywUAAD6kulMaKioq9OijjyoxMVFBQUFq3ry53njjDUmS0+nUiBEjlJycrJCQEKWkpGj69OlVnj906FD1799fU6dOVWxsrCIjIzVy5EidPn3aEz8WLsArR3hbtmyprl276rXXXlOvXr3O+bHDvn379O677+rXv/61/vSnP+mBBx6o0RqysrL08ccfa/v27QoJCdENN9ygv/3tb0pJSanRdgAAsArDMGScPmFK27bAUNlsthq95v33369Vq1ZpxowZat++vQoKCvTdd99J+uFT6MaNG+uDDz5QTEyMVq5cqQcffFANGzbU3Xff7b7G0qVLFRwcrNzcXO3du1fDhg1TTEyMnnrqqRqtFRdmMwzDMLuIn9u2bZtat25drXPPnDmjwsJCXX311TVaw2233aZf//rXuu6661RZWanHH39cW7Zs0datWxUWFlatazgcDkVFRamsrEyRkZE1Wp+vqKysVElJiex2u+x2u9nlAKghTqdTTqdTcXFx8vf3yrETeNipU6dUUFCg5ORkBQcHS5JcFce163fmvN81f9Uhv6DqvT/36NFDHTp00LRp0857zs6dO5WSkqIlS5YoPT29WtcdM2aMiouL9eGHH0r6YYR33rx5KioqUmhoqCTplVde0R/+8AeVlZXJz+/SP2g/V7/j4rzyVaq6YVeSAgICajzsStKiRYuqPJ4zZ47i4uKUn5+vm266qcbbAwAA3mPDhg2y2+3q3r37ec95+eWXlZOTo8LCQp08eVKnT59Whw4dqpzTvn17d9iVpK5du+rYsWMqKipSkyZNPFU+fsYrA+9PuVyuc/4F5HK59O233yopKalW6igrK5N04YnuFRUVqqiocD92OBwerwsAAG9hCwxV81fNee+zBYZe/KRLEBIScsHjc+fO1YQJE/T888+ra9euioiI0LPPPqs1a9bUaB2oGV5505r0Q1i8++67FRYWpvj4eE2aNElOp9N9vLS0VMnJybVSi8vl0rhx49StWze1bdv2vOdlZWUpKirKvbGKBACgLrHZbPILCjNlq+n5u9dee617tahz+fLLL3XDDTdo1KhRSk1NVfPmzbV79+6zztu4caNOnjzpfrx69WqFh4eTEWqZ1wbev/zlL9q4caPeeustPfXUU/rnP/+pfv36VbmzsbamH48ePVpbtmzR3LlzL3jexIkTVVZW5t6KiopqpT4AAFCzmjZtqiFDhmj48OH69NNPVVBQoNzcXL3//vuSpBYtWmjdunX67LPPtHPnTv3lL3/R2rVrz7rO6dOnNWLECG3dulULFizQ5MmTNWbMmMuav4vL57W9/emnn+rVV1/VwIED9dvf/lbr1q1TaWmp+vTp4542UNN/zZ3LmDFjNH/+fC1btkyNGze+4LlBQUGKjIyssgEAAN80a9YsDRw4UKNGjVKrVq30wAMP6Pjx45Kk3/3udxowYIAGDRqktLQ0HT58WKNGjTrrGj179lSLFi100003adCgQerbt6+mTJlSyz8JvHKVBkkKDQ3V119/XWXaQnl5uTIyMhQSEqLXX39dzZs3rzLNoSYZhqGHHnpIn3zyiXJzc9WiRYtLvgarNLBKA2BVrNIAVgu4uKFDh+ro0aP69NNPa+ya9Pvl8doR3qSkJG3btq3KvoiICC1evFgnT57UHXfc4dH2R48erbffflvvvvuuIiIiVFxcrOLi4irzcAAAAOD9vDbw3nrrrZo9e/ZZ+8PDw/XZZ595/K+aWbNmqaysTD169FDDhg3d23vvvefRdgEAgOctX75c4eHh591gLV77OdTUqVN14MCBcx6LiIjQkiVLtH79eo+176UzPQAAQA3o3LmzNmzY4NE25syZ49Hro/q8NvDWq1dP9erVO+/xiIiICy4GDQAAcD4hISFq3ry52WWglnht4P2ptWvXatmyZSopKZHL5apy7IUXXjCpKgAAAPgCrw+8Tz/9tP785z8rJSVF8fHxVZYiq41lyQAAAODbvD7wTp8+XTk5ORo6dKjZpQAAAMAHee0qDT/y8/NTt27dzC4DAAAAPsrrA+/48eP18ssvm10GAAAAfJTXT2mYMGGCevfurauvvlpt2rRRQEBAleMff/yxSZUBAABf1KNHD3Xo0EHTpk2r0evm5ubq5ptv1pEjRxQdHV2j18aV8frAO3bsWC1btkw333yzYmJiuFENAABckY8//visAbRLda7QfMMNN+jgwYOKioq6wgpR07w+8L755pv66KOP1Lt3b7NLAQAAFlC/fn2PXDcwMFAJCQkeuTaujNfP4a1fv76uvvpqs8sAAAAW0aNHD40bN+6i5/39739XixYtFBwcrPj4eA0cOFCSNHToUOXl5Wn69Omy2Wyy2Wzau3evcnNzZbPZdPToUUk/fNNadHS05s+fr5SUFIWGhmrgwIE6ceKE3nzzTTVt2lT16tXT2LFj5XQ6PfgTw+tHeKdMmaLJkydr9uzZCg0NNbscAABwHoZh6MSJE6a0HRoaWqPTHtetW6exY8fqrbfe0g033KDvv/9ey5cvl/TDkqk7d+5U27Zt9cQTT0iSYmNjtXfv3rOuc+LECc2YMUNz585VeXm5BgwYoDvuuEPR0dFasGCB9uzZozvvvFPdunXToEGDaqx+VOX1gXfGjBnavXu34uPj1bRp07Pm3Kxfv96kygAAwE+dOHFC4eHhprR97NgxhYWF1dj1CgsLFRYWpl/96leKiIhQkyZNlJqaKkmKiopSYGCgQkNDLzqF4cyZM5o1a5b70+qBAwfqrbfe0qFDhxQeHq42bdro5ptv1rJlywi8HuT1gbd///5mlwAAAOqYXr16qUmTJmrWrJluu+023Xbbbbrjjjsu+dPm0NDQKlMzfxzA++kfBvHx8SopKamx2nE2rw+8kydPNrsEAABQDaGhoTp27JhpbdekiIgIrV+/Xrm5uVq8eLEmTZqkKVOmaO3atZe05NjPP5m22Wzn3OdyuWqibJyH1wfetWvXyuVyKS0trcr+NWvWyG63q3PnziZVBgAAfspms9XotAKz+fv7Kz09Xenp6Zo8ebKio6P1xRdfaMCAAQoMDORGMx/i9as0jB49WkVFRWft379/v0aPHm1CRQAAwOrmz5+vGTNmaMOGDdq3b5/++c9/yuVyKSUlRZLUtGlTrVmzRnv37tV3333HCK2X8/rAu3XrVnXs2PGs/ampqdq6dasJFQEAAKuLjo7Wxx9/rFtuuUWtW7fWK6+8on/961+65pprJP3wTbB2u11t2rRRbGysCgsLTa4YF2IzDMMwu4gLiYmJ0fz589W1a9cq+1euXKnevXvryJEjHm3/5Zdf1rPPPqvi4mK1b99eM2fOVJcuXar1XIfDoaioKJWVlSkyMtKjdXqryspKlZSUyG63y263m10OgBridDrldDoVFxcnf3+vnx0HDzh16pQKCgqUnJys4OBgs8upM+j3y+P1I7y33nqrJk6cqLKyMve+o0eP6vHHH1evXr082vZ7772nzMxMTZ48WevXr1f79u2VkZHBnZQAAAA+xOtHePfv36+bbrpJhw8fdq9/t2HDBsXHx2vJkiVKTEz0WNtpaWm67rrr9NJLL0mSXC6XEhMT9dBDD+mxxx676PM9OcJrGIZKSw/Iy//zqbKyUocPH/7/I7xe//cVgGpyOl1yOp2KiYlhhLeOOnOmUkePlqtJkyY+OdK4YsUK9enT97zHjxz53iPt2u3+8vO7/PdDRngvj9e/Sl111VXatGmT3nnnHW3cuFEhISEaNmyY7rnnnrOW9ahJp0+fVn5+viZOnOje5+fnp/T0dK1ateqcz6moqFBFRYX7scPh8Fh9J06cUHx8Y49dHwCAC2nSpIleeeUVnTpVcfGTvVBAQKDeeuut8x7fuHGTR9ptnpyg6Bjev2ub1wbeSZMmqV+/furUqZPCwsL04IMP1mr73333nZxOp+Lj46vsj4+P1/bt28/5nKysLE2dOrU2ygMAAFcgODjYo58Sw7t4beD99ttvdfvttyswMFB9+vRR37591bNnTwUGBppd2nlNnDhRmZmZ7scOh8Nj/zOFhobq0KFvmdIAwBRMaYCvT2kwi93O/y9m8Npez8nJkcvl0pdffql58+Zp3LhxOnjwoHr16qV+/frpV7/6lerXr++x9hs0aCC73a5Dhw5V2X/o0KHzfm92UFCQgoKCPFbTT9lsNsXFXVUrbV2JyspK2WyBrNIAWAyrNODUqVMqLz8pu91fAQHeOxhlNaz3e3m8/qa1n9q2bZvmzZunf//738rPz1eXLl3Ut29f3XPPPbrqqpoPf2lpaerSpYtmzpwp6YdfsqSkJI0ZM8b0m9Z8BcuSAdZE4IXL5dI333wju92u2NhYBQYGymazmV2WZRmGodOnT6u0tFROp1MtWrS4opvf6hqfepVq3bq1WrdurT/+8Y8qLS11h1/phwWga1pmZqaGDBmizp07q0uXLpo2bZqOHz+uYcOG1XhbAAD4Ej8/PyUnJ+vgwYM6cOCA2eXUGaGhoUpKSiLsXiKfCrw/MgxD69at04IFC9yB1xMGDRqk0tJSTZo0ScXFxerQoYMWLVp01o1sAADURYGBgUpKSlJlZaWcTqfZ5Vie3W6Xv78/I+mXwaemNBQUFCgnJ0dz5sxRaWmp0tPTNX/+fLPLOi+mNDClAbAqpjQA8CVe/ypVUVGhDz/8UG+88YZWrFghp9Op5557TiNGjKizIRIAAADV57UTQPLz8zVq1CglJCRo2rRp6t+/v4qKiuTn56eMjAzCLgAAAKrFa0d409LS9NBDD2n16tVKSUkxuxwAAAD4KK8NvD179tQbb7yhkpIS/eY3v1FGRgaTtAEAAHDJvHZKw2effaavv/5aKSkp+v3vf6+GDRvq4YcfliSCLwAAAKrNawOvJCUmJmrSpEkqKCjQW2+9pdLSUvn7+6tfv356/PHHtX79erNLBAAAgJfzqWXJJOnIkSN6++23lZOTo02bNnn1un8sS8ayZIBVsSwZAF/ic4H3p9avX6+OHTuaXcZ5EXgJvIBVEXgB+BKvf5X673//a3YJAAAA8GFeH3h79Ohx1r6f3rTmzVMaAAAAYD6vvmlN+mHO7k+3kpISLVq0SNddd50WL15sdnkAAADwcl4/whsVFXXWvl69eikwMFCZmZnKz883oSoAAAD4Cq8f4T2f+Ph47dixw+wyAAAA4OW8foR306ZNVR4bhqGDBw8qOztbHTp0MKcoAAAA+AyvD7wdOnSQzWbTz1dPu/7665WTk2NSVQAAAPAVXh94CwoKqjz28/NTbGysgoODTaoIAAAAvsTrA2+TJk3MLgEAAAA+zCtvWps7d261zy0qKtKXX35Zo+3v3btXI0aMUHJyskJCQnT11Vdr8uTJOn36dI22AwAAAM/zysA7a9YstW7dWs8884y2bdt21vGysjItWLBA9957rzp27KjDhw/XaPvbt2+Xy+XSq6++qq+//lovvviiXnnlFT3++OM12g4AAAA8z2b8/G4wL/Gf//xHM2fO1BdffKGwsDDFx8crODhYR44cUXFxsRo0aKChQ4dq/Pjxio+P93g9zz77rGbNmqU9e/ZU+zkOh0NRUVEqKytTZGSkB6vzXpWVlSopKZHdbpfdbje7HAA1xOl0yul0Ki4uTv7+Xj87DkAd57WvUn379lXfvn313XffacWKFdq3b59OnjypBg0aKDU1VampqfLzq70B6rKyMtWvX/+C51RUVKiiosL92OFweLosAAAAXITXBt4fNWjQQP379ze1hl27dmnmzJl67rnnLnheVlaWpk6dWktVAQAAoDq8cg6vpzz22GOy2WwX3LZv317lOfv379dtt92mu+66Sw888MAFrz9x4kSVlZW5t6KiIk/+OAAAAKgGr53D6wmlpaUXvcGtWbNmCgwMlCQdOHBAPXr00PXXX685c+Zc8hQK5vAyhxewKubwAvAldepVKjY2VrGxsdU6d//+/br55pvVqVMnzZ49u1bnCwMAAKDm1KnAW1379+9Xjx491KRJEz333HMqLS11H0tISDCxMgAAAFwqAu85LFmyRLt27dKuXbvUuHHjKsfq0AwQAAAAS/DKObyZmZl68sknFRYWpszMzAue+8ILL9RSVZeOObzM4QWsijm8AHyJV75KffXVVzpz5oz73+djs9lqqyQAAAD4KK8c4bUKRngZ4QWsihFeAL6EpQcAAABgaQReAAAAWBqBFwAAAJZG4AUAAIClEXgBAABgaQReAAAAWBqBFwAAAJZG4AUAAIClEXgBAABgaQReAAAAWBqBFwAAAJZG4AUAAIClEXgBAABgaQReAAAAWBqBFwAAAJZG4L2IiooKdejQQTabTRs2bDC7HAAAAFwiAu9F/PGPf1SjRo3MLgMAAACXicB7AQsXLtTixYv13HPPmV0KAAAALpO/2QV4q0OHDumBBx7Qp59+qtDQ0Go9p6KiQhUVFe7HDofDU+UBAACgmhjhPQfDMDR06FCNHDlSnTt3rvbzsrKyFBUV5d4SExM9WCUAAACqo04F3scee0w2m+2C2/bt2zVz5kyVl5dr4sSJl3T9iRMnqqyszL0VFRV56CcBAABAddkMwzDMLqK2lJaW6vDhwxc8p1mzZrr77rs1b9482Ww2936n0ym73a7BgwfrzTffrFZ7DodDUVFRKisrU2Rk5BXV7qsqKytVUlIiu90uu91udjkAaojT6ZTT6VRcXJz8/ZkdB8C71anAW12FhYVV5t8eOHBAGRkZ+vDDD5WWlqbGjRtX6zoEXgIvYFUEXgC+hFepc0hKSqryODw8XJJ09dVXVzvsAgAAwDvUqTm8AAAAqHsY4a2Gpk2bipkfAAAAvokRXgAAAFgagRcAAACWRuAFAACApRF4AQAAYGkEXgAAAFgagRcAAACWxrJkHvTjUmY//da2uqayslLl5eWy2Wzy8+PvK8AqXC6XDMNQcHAw37QGeJmIiAjZbDazy/AqvEp5UHl5uSQpMTHR5EoAAEBdUVZWpsjISLPL8Co2g29U8BiXy6UDBw547C8th8OhxMREFRUV8Yt9BejHmkNf1gz6sWbQjzWDfqwZtdmPjPCejRFeD/Lz81Pjxo093k5kZCQvQjWAfqw59GXNoB9rBv1YM+jHmkE/moNJlQAAALA0Ai8AAAAsjcDrw4KCgjR58mQFBQWZXYpPox9rDn1ZM+jHmkE/1gz6sWbQj+bipjUAAABYGiO8AAAAsDQCLwAAACyNwAsAAABLI/ACAADA0gi8Puzll19W06ZNFRwcrLS0NP3vf/8zuySv9t///ld9+vRRo0aNZLPZ9Omnn1Y5bhiGJk2apIYNGyokJETp6en65ptvzCnWi2VlZem6665TRESE4uLi1L9/f+3YsaPKOadOndLo0aMVExOj8PBw3XnnnTp06JBJFXunWbNmqV27du5F6Lt27aqFCxe6j9OHlyc7O1s2m03jxo1z76MvL27KlCmy2WxVtlatWrmP04eXZv/+/brvvvsUExOjkJAQXXvttVq3bp37OO83tY/A66Pee+89ZWZmavLkyVq/fr3at2+vjIwMlZSUmF2a1zp+/Ljat2+vl19++ZzHn3nmGc2YMUOvvPKK1qxZo7CwMGVkZOjUqVO1XKl3y8vL0+jRo7V69WotWbJEZ86c0a233qrjx4+7zxk/frzmzZunDz74QHl5eTpw4IAGDBhgYtXep3HjxsrOzlZ+fr7WrVunW265Rf369dPXX38tiT68HGvXrtWrr76qdu3aVdlPX1bPNddco4MHD7q3FStWuI/Rh9V35MgRdevWTQEBAVq4cKG2bt2q559/XvXq1XOfw/uNCQz4pC5duhijR492P3Y6nUajRo2MrKwsE6vyHZKMTz75xP3Y5XIZCQkJxrPPPuved/ToUSMoKMj417/+ZUKFvqOkpMSQZOTl5RmG8UO/BQQEGB988IH7nG3bthmSjFWrVplVpk+oV6+e8frrr9OHl6G8vNxo0aKFsWTJEqN79+7Gww8/bBgGv4/VNXnyZKN9+/bnPEYfXppHH33U+MUvfnHe47zfmIMRXh90+vRp5efnKz093b3Pz89P6enpWrVqlYmV+a6CggIVFxdX6dOoqCilpaXRpxdRVlYmSapfv74kKT8/X2fOnKnSl61atVJSUhJ9eR5Op1Nz587V8ePH1bVrV/rwMowePVq9e/eu0mcSv4+X4ptvvlGjRo3UrFkzDR48WIWFhZLow0v1n//8R507d9Zdd92luLg4paam6rXXXnMf5/3GHAReH/Tdd9/J6XQqPj6+yv74+HgVFxebVJVv+7Hf6NNL43K5NG7cOHXr1k1t27aV9ENfBgYGKjo6usq59OXZNm/erPDwcAUFBWnkyJH65JNP1KZNG/rwEs2dO1fr169XVlbWWcfoy+pJS0vTnDlztGjRIs2aNUsFBQW68cYbVV5eTh9eoj179mjWrFlq0aKFPvvsM/3+97/X2LFj9eabb0ri/cYs/mYXAMB3jR49Wlu2bKky1w/Vl5KSog0bNqisrEwffvihhgwZory8PLPL8ilFRUV6+OGHtWTJEgUHB5tdjs+6/fbb3f9u166d0tLS1KRJE73//vsKCQkxsTLf43K51LlzZz399NOSpNTUVG3ZskWvvPKKhgwZYnJ1dRcjvD6oQYMGstvtZ90he+jQISUkJJhUlW/7sd/o0+obM2aM5s+fr2XLlqlx48bu/QkJCTp9+rSOHj1a5Xz68myBgYFq3ry5OnXqpKysLLVv317Tp0+nDy9Bfn6+SkpK1LFjR/n7+8vf3195eXmaMWOG/P39FR8fT19ehujoaLVs2VK7du3i9/ESNWzYUG3atKmyr3Xr1u4pIrzfmIPA64MCAwPVqVMnLV261L3P5XJp6dKl6tq1q4mV+a7k5GQlJCRU6VOHw6E1a9bQpz9jGIbGjBmjTz75RF988YWSk5OrHO/UqZMCAgKq9OWOHTtUWFhIX16Ey+VSRUUFfXgJevbsqc2bN2vDhg3urXPnzho8eLD73/TlpTt27Jh2796thg0b8vt4ibp163bWUo07d+5UkyZNJPF+Yxqz75rD5Zk7d64RFBRkzJkzx9i6davx4IMPGtHR0UZxcbHZpXmt8vJy46uvvjK++uorQ5LxwgsvGF999ZWxb98+wzAMIzs724iOjjb+/e9/G5s2bTL69etnJCcnGydPnjS5cu/y+9//3oiKijJyc3ONgwcPurcTJ064zxk5cqSRlJRkfPHFF8a6deuMrl27Gl27djWxau/z2GOPGXl5eUZBQYGxadMm47HHHjNsNpuxePFiwzDowyvx01UaDIO+rI5HHnnEyM3NNQoKCowvv/zSSE9PNxo0aGCUlJQYhkEfXor//e9/hr+/v/HUU08Z33zzjfHOO+8YoaGhxttvv+0+h/eb2kfg9WEzZ840kpKSjMDAQKNLly7G6tWrzS7Jqy1btsyQdNY2ZMgQwzB+WCrmL3/5ixEfH28EBQUZPXv2NHbs2GFu0V7oXH0oyZg9e7b7nJMnTxqjRo0y6tWrZ4SGhhp33HGHcfDgQfOK9kLDhw83mjRpYgQGBhqxsbFGz5493WHXMOjDK/HzwEtfXtygQYOMhg0bGoGBgcZVV11lDBo0yNi1a5f7OH14aebNm2e0bdvWCAoKMlq1amX84x//qHKc95vaZzMMwzBnbBkAAADwPObwAgAAwNIIvAAAALA0Ai8AAAAsjcALAAAASyPwAgAAwNIIvAAAALA0Ai8AAAAsjcALAAAASyPwAkA15Obmymaz6ejRo6a0v3TpUrVu3VpOp9NjbVx//fX66KOPPHZ9ADAL37QGAD/To0cPdejQQdOmTXPvO336tL7//nvFx8fLZrPVek2dOnVSZmamBg8e7LE25s+fr/Hjx2vHjh3y82M8BIB18IoGANUQGBiohIQEU8LuihUrtHv3bt15550ebef2229XeXm5Fi5c6NF2AKC2EXgB4CeGDh2qvLw8TZ8+XTabTTabTXv37j1rSsOcOXMUHR2t+fPnKyUlRaGhoRo4cKBOnDihN998U02bNlW9evU0duzYKtMQKioqNGHCBF111VUKCwtTWlqacnNzL1jT3Llz1atXLwUHB7v3TZkyRR06dFBOTo6SkpIUHh6uUaNGyel06plnnlFCQoLi4uL01FNPuZ9jGIamTJmipKQkBQUFqVGjRho7dqz7uN1u1y9/+UvNnTu3ZjoTALyEv9kFAIA3mT59unbu3Km2bdvqiSeekCTFxsZq7969Z5174sQJzZgxQ3PnzlV5ebkGDBigO+64Q9HR0VqwYIH27NmjO++8U926ddOgQYMkSWPGjNHWrVs1d+5cNWrUSJ988oluu+02bd68WS1atDhnTcuXL9e999571v7du3dr4cKFWrRokXbv3q2BAwdqz549atmypfLy8rRy5UoNHz5c6enpSktL00cffaQXX3xRc+fO1TXXXKPi4mJt3LixyjW7dOmi7OzsK+xFAPAuBF4A+ImoqCgFBgYqNDRUCQkJFzz3zJkzmjVrlq6++mpJ0sCBA/XWW2/p0KFDCg8PV5s2bXTzzTdr2bJlGjRokAoLCzV79mwVFhaqUaNGkqQJEyZo0aJFmj17tp5++ulztrNv3z73+T/lcrmUk5OjiIgId1s7duzQggUL5Ofnp5SUFP3tb3/TsmXLlJaWpsLCQiUkJCg9PV0BAQFKSkpSly5dqlyzUaNGKioqksvlYh4vAMvg1QwALlNoaKg77EpSfHy8mjZtqvDw8Cr7SkpKJEmbN2+W0+lUy5YtFR4e7t7y8vK0e/fu87Zz8uTJKtMZftS0aVNFRERUaatNmzZVgupP27/rrrt08uRJNWvWTA888IA++eQTVVZWVrlmSEiIXC6XKioqLrE3AMB7McILAJcpICCgymObzXbOfS6XS5J07Ngx2e125efny263VznvpyH55xo0aKAjR45ccfuJiYnasWOHPv/8cy1ZskSjRo3Ss88+q7y8PPfzvv/+e4WFhSkkJORCPzoA+BQCLwD8TGBgoEfWu01NTZXT6VRJSYluvPHGS3re1q1ba6SGkJAQ9enTR3369NHo0aPVqlUrbd68WR07dpQkbdmyRampqTXSFgB4CwIvAPxM06ZNtWbNGu3du1fh4eGqX79+jVy3ZcuWGjx4sO6//349//zzSk1NVWlpqZYuXap27dqpd+/e53xeRkaG3nzzzStuf86cOXI6nUpLS1NoaKjefvtthYSEqEmTJu5zli9frltvvfWK2wIAb8IcXgD4mQkTJshut6tNmzaKjY1VYWFhjV179uzZuv/++/XII48oJSVF/fv319q1a5WUlHTe5wwePFhff/21duzYcUVtR0dH67XXXlO3bt3Url07ff7555o3b55iYmIkSfv379fKlSs1bNiwK2oHALwN37QGAD7gD3/4gxwOh1599VWPtfHoo4/qyJEj+sc//uGxNgDADIzwAoAP+NOf/qQmTZq4b0DzhLi4OD355JMeuz4AmIURXgAAAFja/wOsA4XurQoy+gAAAABJRU5ErkJggg==' width=700.0/>\n",
       "            </div>\n",
       "        "
      ],
      "text/plain": [
       "Canvas(toolbar=Toolbar(toolitems=[('Home', 'Reset original view', 'home', 'home'), ('Back', 'Back to previous …"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "ELeak = -70.3   # Reversal potential (mV)\n",
    "gLeak = 2.05e-5  # Maximal channel conductance (S/cm2)\n",
    "\n",
    "def i_Leak(Vm):\n",
    "    return gLeak * (Vm - ELeak) * MA_CM2_TO_UA_CM2  # uA/cm2\n",
    "\n",
    "# Update model and run interactive simulation\n",
    "model.add_current(i_Leak)\n",
    "interactive_simulation(model.copy());"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Questions\n",
    "- *In the absence of stimulus (I = 0), what can you tell about the effect of this current on the membrane?*\n",
    "- *As you vary the stimulus amplitude, which differences in voltage variations do you observe?*\n",
    "- *What do you conclude about the role of the leakage current on membrane potential?*"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Step 2: a voltage-gated sodium current\n",
    "\n",
    "Our neuron membrane so far only exhibits passive responses to inputs, which is rather trivial. To obtain a nonlinear behavior, let's now add an active ***sodium current*** term ($i_{Na}$) representing voltage-gated sodium channels. Upon opening, theses channels trigger the entry of sodium ions inside the cell, following their concentration gradient.\n",
    "\n",
    "Such channels are typically composed of voltage-densitive subunits, called *gates*, that each switch between closed and open states at specific rates $\\alpha$ abd $\\beta$ upon variation of the membrane potential. This process is captured by a kinetic scheme:\n",
    "\n",
    "$\\alpha(V_m): C -> O$  (opening)\n",
    "\n",
    "$\\beta(V_m): O -> C$   (closing)\n",
    "\n",
    "For now, let us start implementing a sodium channel composed of 3 subunits of the same *M*-gate, which together regulate the channel conductance.\n",
    "\n",
    "Our equivalent electrical circuit now is:\n",
    "\n",
    "![circuit](imgs/circuits-03.png)\n",
    "\n",
    "And the system's governing equation becomes:\n",
    "\n",
    "$C_m \\frac{dV_m}{dt} = i_{stim} - [i_{Leak}(V_m) + i_{Na}(m, V_m)]$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "eeddcd4ca026451695d2424385856bb6",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "interactive(children=(FloatSlider(value=0.0, continuous_update=False, description='I', max=60.0, min=-15.0, st…"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "8acd3015bdb44a3586ea094bc6db5042",
       "version_major": 2,
       "version_minor": 0
      },
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",
      "text/html": [
       "\n",
       "            <div style=\"display: inline-block;\">\n",
       "                <div class=\"jupyter-widgets widget-label\" style=\"text-align: center;\">\n",
       "                    Figure\n",
       "                </div>\n",
       "                <img 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' width=700.0/>\n",
       "            </div>\n",
       "        "
      ],
      "text/plain": [
       "Canvas(toolbar=Toolbar(toolitems=[('Home', 'Reset original view', 'home', 'home'), ('Back', 'Back to previous …"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "ENa = 50.0       # Reversal potential (mV)\n",
    "gNa_bar = 0.056  # Maximal channel conductance (S/cm2)\n",
    "V_T = -56.2      # Spike threshold adjustment parameter (mV)\n",
    "\n",
    "def alpha_m(Vm):\n",
    "    return 0.32 * vtrap(13 - (Vm - V_T), 4)  # ms-1\n",
    "\n",
    "def beta_m(Vm):\n",
    "    return 0.28 * vtrap((Vm - V_T) - 40, 5)  # ms-1\n",
    "\n",
    "def dm_dt(m, Vm):\n",
    "    return alpha_m(Vm) * (1 - m) - beta_m(Vm) * m  # ms-1\n",
    "\n",
    "def m_inf(Vm):\n",
    "    return alpha_m(Vm) / (alpha_m(Vm) + beta_m(Vm))  # (-)\n",
    "\n",
    "def i_Na(m, Vm):\n",
    "    return gNa_bar * m**3 * (Vm - ENa) * MA_CM2_TO_UA_CM2  # uA/cm2\n",
    "\n",
    "# Update model and run interactive simulation\n",
    "model.add_current(i_Na)\n",
    "model.add_state(dm_dt, m_inf)\n",
    "interactive_simulation(model.copy());"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Questions\n",
    "- *For zero or negative stimulus (I <= 0), do you observe any difference in behavior?*\n",
    "- *What happens when you apply a positive stimulus (I > 0)?*\n",
    "- *What do you conclude about the role of sodium channels on membrane potential?*"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Step 3: a voltage-gated potasium current \n",
    "\n",
    "Our neuron membrane now shows some depolarization ability, but reaches a plateau potential. To obtain a more dynamic behavior, let's now add an active ***potassium current*** term ($i_{K}$) representing voltage-gated potassium channels. Upon opening, theses channels trigger the exit of potassium ions outside the cell, following their concentration gradient.\n",
    "\n",
    "Let us define these potassium channels as being composed of 4 subunits of the same *N*-gate, which together regulate the channel conductance.\n",
    "\n",
    "Our equivalent electrical circuit now is:\n",
    "\n",
    "![circuit](imgs/circuits-04.png)\n",
    "\n",
    "And the system's governing equation becomes:\n",
    "\n",
    "$C_m \\frac{dV_m}{dt} = i_{stim} - [i_{Leak}(V_m) + i_{Na}(m, V_m) + i_{K}(n, V_m)]$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "753ac6e5a1b24889a59d1cbf16751270",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "interactive(children=(FloatSlider(value=0.0, continuous_update=False, description='I', max=60.0, min=-15.0, st…"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "64ac2cb8567442f0a9484bc54bba676d",
       "version_major": 2,
       "version_minor": 0
      },
      "image/png": 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erri4uGq3vfHGGyovL9e8efMUGBioyy+/XFu2bNHMmTMJvAAAALWMaUMaAgIC9Pbbb+uHH37Qk08+6dWwK0nTpk1T/fr11b59ez399NOqqKhwbcvJyVH37t0VGBjoWpeenq6dO3fqyJEjXq0TAAAAF8e0Ht7//Oc/ZjWtcePGqUOHDqpXr57Wrl2rzMxM5efna+bMmZKkgoICNW7cuNIxsbGxrm1169at9rxlZWUqKytzvS4pKfHQOwAAAMC5qjE3rV2sBx98sMqNaL9dvvvuO0lSRkaGevbsqbZt2+ruu+/WjBkz9Nxzz1UKqxciKytLkZGRriUhIcEdbw0AAAAXwTJzydx///0aNmzYWfdp0qRJtetTUlJUUVGhffv2qUWLFoqLi1NhYWGlfX59faZxv5KUmZmpjIwM1+uSkhJCLwAAgMksE3ijo6MVHR19Qcdu2bJFfn5+iomJkSSlpqbq73//u06fPq2AgABJ0vLly9WiRYszDmeQpKCgIAUFBV1QDQAAAPAMywxpOFc5OTmaNWuWtm7dqr179+qNN97QhAkTdOedd7rC7O23367AwECNHDlS33zzjd58803Nnj27Uu8tAAAAagfL9PCeq6CgIC1atEhTpkxRWVmZGjdurAkTJlQKs5GRkfrkk080evRodezYUQ0aNNCkSZOYkgwAAKAWqnGPFrYSHi3Mo4UBq+LRwgBqE58b0gAAAADfQuAFAACApRF4AQAAYGkEXgAAAFgagRcAAACWRuAFAACApRF4AQAAYGkEXgAAAFgagRcAAACWRuAFAACApRF4AQAAYGkEXgAAAFgagRcAAACW5m92AbhwLVq00A8//GB2Gb/LMAxJks1mM7kSAO7C/9fAhZkzZ46GDBlidhk+h8Bbi508eVKlpaVmlwEAAM5RRUWF2SX4JAJvLbZmzRo5HA6zyziriooKHT58WH5+frLb7WaXA8BNHA6HnE6n6tevL39/fpUA56pBgwZml+CT+JSqxRITE80u4XdVVFSoTp06stvtBF7AQhwOhxwOh2JiYgi8AGo8bloDAACApRF4AQAAYGkEXgAAAFgagRcAAACWRuAFAACApRF4AQAAYGkEXgAAAFgagRcAAACWRuAFAACApRF4AQAAYGkEXgAAAFgaD0D3IMMwJEklJSUmV2KeiooKHTt2TDabTX5+/H0FWIXT6ZRhGAoODpa/P79KgJokPDxcNpvN7DJqFD6lPOjYsWOSpISEBJMrAQAAvqK4uFgRERFml1Gj2IxfuyHhdk6nUz/++CN/aQEAAK8hd1RF4AUAAIClMagSAAAAlkbgBQAAgKUReAEAAGBpBF4AAABYGoEXAAAAlkbgBQAAgKUReAEAAGBpBF4AAABYGoEXAAAAlkbgBQAAgKUReAEAAGBpBF4AAABYGoEXAAAAlkbgBQAAgKUReAEAAGBpBF4AAABYGoEXAAAAlkbgBQAAgKUReAEAAGBpBF4AAABYGoEXAAAAlkbgBQAAgKUReAEAAGBpBF4PMgxDJSUlMgzD7FIAAAB8lr/ZBVjZsWPHFBkZqeLiYkVERJhdjikcDocOHz6siooKs0sB4Gb+/v6qX7++7Ha72aUAwFkReOFRhmGooqJCNptNfn58oQBYhdPpVEVFBd9gAagVCLzwCj8/P3qBAItxOBxmlwAA54QuNwAAAFgagRcAAACWRuAFAACApTGGFwAA1EpOp1Pl5eVml+E1AQEB3A9zgXwi8H7++ed6+umntXHjRuXn5+vdd99V//79z3rMqlWrlJGRoW+++UYJCQl6+OGHNWzYMK/UCwAAzq68vFy5ublyOp1ml+JVUVFRiouLk81mM7uUWsUnAu+JEyfUrl07jRgxQgMGDPjd/XNzc9W3b1/dfffdeuONN7RixQr9+c9/Vnx8vNLT071QMQAAOBPDMJSfny+73a6EhASfmPbSMAyVlpaqqKhIkhQfH29yRbWLTwTePn36qE+fPue8/9y5c9W4cWPNmDFDktSqVSutWbNGzzzzDIEXAACTVVRUqLS0VA0bNlRoaKjZ5XhNSEiIJKmoqEgxMTEMbzgP1v+T6ALk5OQoLS2t0rr09HTl5OSc9biysjKVlJRUWgAAgHv9Ogd0YGCgyZV4368B//Tp0yZXUrsQeKtRUFCg2NjYSutiY2NVUlKikydPnvG4rKwsRUZGupaEhARPlwoAgM/yxXGsvvie3YHA60aZmZkqLi52LQcOHDC7JAAAAJ/nE2N4z1dcXJwKCwsrrSssLFRERIRr/Ex1goKCFBQU5OnyAAAAcB7o4a1GamqqVqxYUWnd8uXLlZqaalJFAAAAuFA+EXiPHz+uLVu2aMuWLZJ+mXZsy5YtysvLk/TLUIQhQ4a49r/77ru1d+9e/e1vf9N3332nf/7zn3rrrbc0YcIEM8oHAADARfCJIQ0bNmzQNddc43qdkZEhSRo6dKgWLFig/Px8V/iVpMaNG+u///2vJkyYoNmzZ+vSSy/VK6+8wpRkAADggvXs2VNt27ZVcHCwXnnlFQUGBuruu+/WlClTzC7N8nwi8Pbs2VOGYZxx+4IFC6o9ZvPmzR6sCgAAuINhGDp52mFK2yEB9vOaOeHVV19VRkaG1q9fr5ycHA0bNkzdunVT7969PVglfCLwAgAA6zp52qHWkz42pe0dj6YrNPDc41Tbtm01efJkSVKzZs30/PPPa8WKFQReD/OJMbwAAAA1Qdu2bSu9jo+Pdz0uGJ5DDy8AAKjVQgLs2vGoOffZhASc3+N9AwICKr222WxyOp3uLAnVIPACAIBazWazndewAvgehjQAAADA0gi8AAAAsDT6/wEAALxg1apVVdYtXbrU63X4Inp4AQAAYGkEXgAAAFgagRcAAACWRuAFAACApRF4AQAAYGkEXgAAAFgagRcAAACWRuAFAACApRF4AQAAYGkEXgAAAFgagRcAAACWRuAFAACApRF4AQAAvKBnz54aO3asxo8fr7p16yo2NlYvv/yyTpw4oeHDhys8PFxNmzbVhx9+aHaplkPgBQAAtZthSOUnzFkM47xKffXVV9WgQQN9+eWXGjt2rO655x7deuut6tq1qzZt2qTrrrtOf/rTn1RaWuqhi+WbbIZxnv+lcM5KSkoUGRmp4uJiRUREmF2OKSoqKlRUVCS73S673W52OQDcxOFwyOFwKCYmRv7+/maXAx9z6tQp5ebmqnHjxgoODv4leD7R0JxiHvpRCqxzTrv27NlTDodDq1evlvTL/0eRkZEaMGCAXnvtNUlSQUGB4uPjlZOToy5dulQ5R5X3jnNCDy8AAICXtG3b1vWz3W5X/fr11aZNG9e62NhYSVJRUZHXa7My/iwHAAC1W0DoLz2tZrV9PrsHBFR6bbPZKq2z2WySJKfTefG1wYXACwAAajeb7ZyHFcA3MaQBAAAAlkbgBQAAgKUxpAEAAMALVq1aVWXdvn37qqxjAi33o4cXAAAAlkbgBQAAgKUReAEAAGBpNTrwbtq0SV9//bXr9Xvvvaf+/fvroYceUnl5uYmVAQAAoLao0YH3rrvu0q5duyRJe/fu1R//+EeFhoZq8eLF+tvf/mZydQAAwEy+eHOXL75nd6jRgXfXrl1KTk6WJC1evFjdu3fXwoULtWDBAr3zzjvmFgcAAExht9slySe/7S0tLZVU9YltOLsaPS2ZYRiuR+t9+umn+sMf/iBJSkhI0E8//WRmaQAAwCT+/v4KDQ3VoUOHFBAQID+/Gt1/5xaGYai0tFRFRUWKiopyhX6cmxodeDt16qR//OMfSktLU3Z2tubMmSNJys3NVWxsrMnVAQAAM9hsNsXHxys3N1f79+83uxyvioqKUlxcnNll1Do1OvDOmjVLd9xxh5YuXaq///3vatq0qSTp7bffVteuXU2uDgAAmCUwMFDNmjXzqWENAQEB9OxeIJtRC0c/nzp1Sna7vcaPXykpKVFkZKSKi4sVERFhdjmmqKioUFFRkex2O/+TAhbicDjkcDgUExMjf/8a3XcCADX7pjVJOnr0qF555RVlZmbq559/liTt2LFDRUVFJlcGAACA2qBG/1m+bds29erVS1FRUdq3b59GjRqlevXqacmSJcrLy9Nrr71mdokAAACo4Wp0D29GRoaGDx+u77//XsHBwa71N9xwgz7//HMTKwMAAEBtUaMD71dffaW77rqryvpLLrlEBQUFJlQEAACA2qZGB96goCCVlJRUWb9r1y5FR0ebUBEAAABqmxodeG+88UY9+uijOn36tKRf5t3Ly8vTAw88oIEDB5pcHQAAAGqDGh14Z8yYoePHjysmJkYnT55Ujx491LRpU4WHh+vxxx83uzwAAADUAjV6lobIyEgtX75cX3zxhbZu3arjx4+rQ4cOSktLM7s0AAAA1BI1uof3tddeU1lZmbp166Z7771Xf/vb35SWlqby8vILmpLshRdeUKNGjRQcHKyUlBR9+eWXZ9x3wYIFstlslZb/nSkCAAAAtUONDrzDhw9XcXFxlfXHjh3T8OHDz+tcb775pjIyMjR58mRt2rRJ7dq1U3p6+lkfYBEREaH8/HzX4mvP6wYAALCCGh14DcOQzWarsv6HH35QZGTkeZ1r5syZGjVqlIYPH67WrVtr7ty5Cg0N1bx58854jM1mU1xcnGuJjY097/cAAAAAc9XIMbzt27d3DSPo1atXpee0OxwO5ebm6vrrrz/n85WXl2vjxo3KzMx0rfPz81NaWppycnLOeNzx48eVlJQkp9OpDh066IknntDll19+xv3LyspUVlbmel3dlGoAAADwrhoZePv37y9J2rJli9LT0xUWFubaFhgYqEaNGp3XtGQ//fSTHA5HlR7a2NhYfffdd9Ue06JFC82bN09t27ZVcXGxpk+frq5du+qbb77RpZdeWu0xWVlZmjp16jnXBQAAAM+rkYF38uTJkqRGjRpp0KBBptwslpqaqtTUVNfrrl27qlWrVnrxxRf12GOPVXtMZmamMjIyXK9LSkqUkJDg8VoBAABwZjUy8P5q6NChbjlPgwYNZLfbVVhYWGl9YWGh4uLizukcAQEBat++vXbv3n3GfYKCghQUFHRRtQIAAMC9avRNaw6HQ9OnT1fnzp0VFxenevXqVVrOVWBgoDp27KgVK1a41jmdTq1YsaJSL+7v1fL1118rPj7+vN8HAAAAzFOjA+/UqVM1c+ZMDRo0SMXFxcrIyNCAAQPk5+enKVOmnNe5MjIy9PLLL+vVV1/Vt99+q3vuuUcnTpxwTW82ZMiQSje1Pfroo/rkk0+0d+9ebdq0SXfeeaf279+vP//5z+58iwAAAPCwGj2k4Y033tDLL7+svn37asqUKRo8eLAuu+wytW3bVuvWrdO4cePO+VyDBg3SoUOHNGnSJBUUFCg5OVkfffSR60a2vLw8+fn9v/x/5MgRjRo1SgUFBapbt646duyotWvXqnXr1m5/nwAAAPAcm2EYhtlFnEmdOnX07bffKjExUfHx8frvf/+rDh06aO/evWrfvn21D6WoSUpKShQZGani4mJFRESYXY4pKioqVFRUJLvdLrvdbnY5ANzE4XDI4XAoJiam0tSRAFAT1eghDZdeeqny8/MlSZdddpk++eQTSdJXX33FzWEAAAA4JzU68N58882uG83Gjh2rRx55RM2aNdOQIUM0YsQIk6sDAABAbVCjhzT81rp167R27Vo1a9ZM/fr1M7uc38WQBoY0AFbFkAYAtUmN/pT6/PPP1bVrV9eHaZcuXdSlSxdVVFTo888/V/fu3U2uEAAAADVdjR7ScM011+jnn3+usr64uFjXXHONCRUBAACgtqnRgdcwDNlstirrDx8+rDp16phQEQAAAGqbGjmkYcCAAZIkm82mYcOGVZqRweFwaNu2beratatZ5QEAAKAWqZGBNzIyUtIvPbzh4eEKCQlxbQsMDFSXLl00atQos8oDAABALVIjA+/8+fMlSdHR0ZoyZYpCQ0MlSfv27dPSpUvVqlUrNWjQwMwSAQAAUEvU6DG8mzdv1muvvSZJOnr0qLp06aIZM2aof//+mjNnjsnVAQAAoDao8YH36quvliS9/fbbio2N1f79+/Xaa6/p2WefNbk6AAAA1AY1OvCWlpYqPDxckvTJJ59owIAB8vPzU5cuXbR//36TqwMAAEBtUKMDb9OmTbV06VIdOHBAH3/8sa677jpJUlFRkc8+uQwAAADnp0YH3kmTJmnixIlq1KiRUlJSlJqaKumX3t727dubXB0AAABqA5thGIbZRZxNQUGB8vPz1a5dO/n5/ZLPv/zyS0VERKhly5YmV3d2JSUlioyMVHFxsc/2SFdUVKioqEh2u112u93scgC4icPhkMPhUExMjOvx7wBQU9X4T6m4uDjFxcVVWte5c2eTqgEAAEBtU6OHNAAAAAAXi8ALAAAASyPwAgAAwNIIvAAAALA0Ai8AAAAsjcALAAAASyPwAgAAwNIIvAAAALA0Ai8AAAAsjcALAAAASyPwAgAAwNIIvAAAALA0Ai8AAAAsjcALAAAASyPwAgAAwNIIvAAAALA0Ai8AAAAsjcALAAAASyPwAgAAwNIIvAAAALA0Ai8AAAAsjcALAAAASyPwAgAAwNIIvAAAALA0Ai8AAAAsjcALAAAASyPwAgAAwNIIvAAAALA0Ai8AAAAszacC7wsvvKBGjRopODhYKSkp+vLLL8+6/+LFi9WyZUsFBwerTZs2WrZsmZcqBQAAgLv4TOB98803lZGRocmTJ2vTpk1q166d0tPTVVRUVO3+a9eu1eDBgzVy5Eht3rxZ/fv3V//+/bV9+3YvVw4AAICLYTMMwzC7CG9ISUnRlVdeqeeff16S5HQ6lZCQoLFjx+rBBx+ssv+gQYN04sQJffDBB651Xbp0UXJysubOnXtObZaUlCgyMlLFxcWKiIhwzxupZSoqKlRUVCS73S673W52OQDcxOFwyOFwKCYmRv7+/maXAwBn5ROfUuXl5dq4caMyMzNd6/z8/JSWlqacnJxqj8nJyVFGRkaldenp6Vq6dKknSz0vbz33oHSqxOwyzsowDDmdzl9e2MytBYAb/f9dJX5+frLZ+J8bOFdJ3W5VStdrzC7D5/hE4P3pp5/kcDgUGxtbaX1sbKy+++67ao8pKCiodv+CgoIztlNWVqaysjLX65ISz4bR7ocXK04/ebQNAADgPl8VtJBE4PU2nwi83pKVlaWpU6d6rb2y1rcq79RRr7V3IQzDUHl5+S89QHQCAdZh/PL/d2BgID28wHlIbJFsdgk+yScCb4MGDWS321VYWFhpfWFhoeLi4qo9Ji4u7rz2l6TMzMxKwyBKSkqUkJBwEZWfXdJt0zx2bndhDC9gTYzhBVCb+MQsDYGBgerYsaNWrFjhWud0OrVixQqlpqZWe0xqamql/SVp+fLlZ9xfkoKCghQREVFpAQAAgLl85s/yjIwMDR06VJ06dVLnzp01a9YsnThxQsOHD5ckDRkyRJdccomysrIkSffdd5969OihGTNmqG/fvlq0aJE2bNigl156ycy3AQAAgPPkM4F30KBBOnTokCZNmqSCggIlJyfro48+ct2YlpeXJz+//9fh3bVrVy1cuFAPP/ywHnroITVr1kxLly7VFVdcYdZbAAAAwAXwmXl4zcA8vIzhBayKMbwAahOfGMMLAAAA30XgBQAAgKUReAEAAGBpBF4AAABYGncaeNCv9wN6+hHDNVlFRYWOHTsmm81WaRYMALWb0+mUYRgKDg7mpjWghgkPD+cJiL/Bp5QHHTt2TJI8+rQ1AACA/+XLs0OdCdOSeZDT6dSPP/7IX1oAAMBryB1VEXgBAABgaQyqBAAAgKUReAEAAGBpBF4AAABYGoEXAAAAlkbgBQAAgKUReAEAAGBpBF4AAABYGoEXAAAAlkbgBQAAgKUReAEAAGBpBF4AAABYGoEXAAAAlkbgBQAAgKUReAEAAGBpBF4AAABYGoEXAAAAlkbgBQAAgKUReAEAAGBpBF4AAABYGoEXAAAAluYTgXfKlCmy2WyVlpYtW571mMWLF6tly5YKDg5WmzZttGzZMi9VCwAAAHfyicArSZdffrny8/Ndy5o1a86479q1azV48GCNHDlSmzdvVv/+/dW/f39t377dixUDAADAHWyGYRhmF+FpU6ZM0dKlS7Vly5Zz2n/QoEE6ceKEPvjgA9e6Ll26KDk5WXPnzvVQlQAAAPAEn+nh/f7779WwYUM1adJEd9xxh/Ly8s64b05OjtLS0iqtS09PV05OzlnbKCsrU0lJiWspLi7WoUOH5AN/UwAAANRY/mYX4A0pKSlasGCBWrRoofz8fE2dOlVXX321tm/frvDw8Cr7FxQUKDY2ttK62NhYFRQUnLWdrKwsTZ06tcr64uJiRUREXNybqKUcDocOHz6siooKs0sB4Gb+/v6qX7++7Ha72aUAwFn5RODt06eP6+e2bdsqJSVFSUlJeuuttzRy5Ei3tZOZmamMjAzX65KSEiUkJLjt/LWRYRiqqKiQzWaTn5/PfKEAWJ7T6VRFRQXfYAGoFXwi8P5WVFSUmjdvrt27d1e7PS4uToWFhZXWFRYWKi4u7qznDQoKUlBQkNvqtBI/Pz96gQCLcTgcZpcAAOfEJ7vcjh8/rj179ig+Pr7a7ampqVqxYkWldcuXL1dqaqo3ygMAAIAb+UTgnThxorKzs7Vv3z6tXbtWN998s+x2uwYPHixJGjJkiDIzM13733ffffroo480Y8YMfffdd5oyZYo2bNigMWPGmPUWAAAAcIF8YkjDDz/8oMGDB+vw4cOKjo7WVVddpXXr1ik6OlqSlJeXV2l8adeuXbVw4UI9/PDDeuihh9SsWTMtXbpUV1xxhVlvAQAAABfIJ+bhNUtJSYkiIyN9epaGiooKFRUVyW63M4YXsBCHwyGHw6GYmBj5+/tE3wnOwuFw6PTp02aXYXkBAQH8Lr1AfEoBAIALYhiGCgoKdPToUbNL8RlRUVGKi4uTzWYzu5RahcALAAAuyK9hNyYmRqGhoYQwDzIMQ6WlpSoqKpKkM954j+oReAEAwHlzOByusFu/fn2zy/EJISEhkqSioiLFxMQwvOE8+MQsDQAAwL1+HbMbGhpqciW+5dfrzZjp80PgBQAAF4xhDN7F9b4wBF4AAABYGoEXAAD4lJ49e2r8+PFml6FVq1bJZrMxy4UXcNMaAADwKUuWLFFAQMDv7tezZ08lJydr1qxZni8KHkXgBQAAPqVevXpmlwAvY0gDAADwKe4a0rBmzRpdffXVCgkJUUJCgsaNG6cTJ064tv/73/9Wp06dFB4erri4ON1+++2ueXSrU1paqj59+qhbt24Mc3AzAi8AAHALwzBUerrclMUwDK++1z179uj666/XwIEDtW3bNr355ptas2aNxowZ49rn9OnTeuyxx7R161YtXbpU+/bt07Bhw6o939GjR9W7d285nU4tX75cUVFR3nkjPoIhDQAAwC1OVpxW89cnmdL2rjsfVWhAoNfay8rK0h133OHqKW7WrJmeffZZ9ejRQ3PmzFFwcLBGjBjh2r9JkyZ69tlndeWVV+r48eMKCwtzbSsoKNCgQYPUrFkzLVy4UIGB3nsfvoIeXgAAgPO0detWLViwQGFhYa4lPT1dTqdTubm5kqSNGzeqX79+SkxMVHh4uHr06CFJysvLq3Su3r17q2nTpnrzzTcJux5CDy8AAHCLEP8A7brzUdPa9qbjx4/rrrvu0rhx46psS0xM1IkTJ5Senq709HS98cYbio6OVl5entLT01VeXl5p/759++qdd97Rjh071KZNG2+9BZ9C4AUAAG5hs9m8OqzATB06dNCOHTvUtGnTard//fXXOnz4sKZNm6aEhARJ0oYNG6rdd9q0aQoLC1OvXr20atUqtW7d2mN1+yoCLwAAwBkcOnRIW7ZsqbQuPj5eDzzwgLp06aIxY8boz3/+s+rUqaMdO3Zo+fLlev7555WYmKjAwEA999xzuvvuu7V9+3Y99thjZ2xn+vTpcjgcuvbaa7Vq1Sq1bNnSw+/MtzCGFwAA4AwWLlyo9u3bV1pefvlltW3bVtnZ2dq1a5euvvpqtW/fXpMmTVLDhg0lSdHR0VqwYIEWL16s1q1ba9q0aZo+ffpZ23rmmWd022236dprr9WuXbu88fZ8hs3w9jwePqSkpESRkZEqLi5WRESE2eWYoqKiQkVFRbLb7bLb7WaXA8BNHA6HHA6HYmJi5O/Pl4W+6NSpU8rNzVXjxo0VHBxsdjk+g+t+YejhBQAAgKUReAEAgM9ZvXp1pSnFfrvAWvgeCgAA+JxOnTpVuRkN1kXgBQAAPickJOSMU4rBehjSAAAAAEvzicCblZWlK6+8UuHh4YqJiVH//v21c+fOsx6zYMEC2Wy2Sgt3QwIAANQ+PhF4s7OzNXr0aK1bt07Lly/X6dOndd111+nEiRNnPS4iIkL5+fmuZf/+/V6qGAAAAO7iE2N4P/roo0qvFyxYoJiYGG3cuFHdu3c/43E2m01xcXGeLg8AAAAe5BM9vL9VXFwsSapXr95Z9zt+/LiSkpKUkJCgm266Sd98881Z9y8rK1NJSUmlBQAAAObyWg+v0+lUdna2Vq9erf3796u0tFTR0dFq37690tLSlJCQ4LU6xo8fr27duumKK644434tWrTQvHnz1LZtWxUXF2v69Onq2rWrvvnmG1166aXVHpOVlaWpU6d6qnQAAOAGPXv2VHJysmbNmmV2KfASj/fwnjx5Uv/4xz+UkJCgG264QR9++KGOHj0qu92u3bt3a/LkyWrcuLFuuOEGrVu3ztPlaPTo0dq+fbsWLVp01v1SU1M1ZMgQJScnq0ePHlqyZImio6P14osvnvGYzMxMFRcXu5YDBw64u3wAAHCRlixZoscee+x39+vZs6dsNluVzDBr1iw1atTIQ9XBEzzew9u8eXOlpqbq5ZdfVu/evRUQEFBln/3792vhwoX64x//qL///e8aNWqUR2oZM2aMPvjgA33++edn7KU9k4CAALVv3167d+8+4z5BQUEKCgq62DIBAIAH/d6Qxv8VHByshx9+WAMHDqw2w6B28HgP7yeffKK33npLN9xwwxn/oSQlJSkzM1Pff/+9rr32WrfXYBiGxowZo3fffVefffaZGjdufN7ncDgc+vrrrxUfH+/2+gAAgPf07NlT48ePP6d9Bw8erKNHj+rll18+4z579uzRTTfdpNjYWIWFhenKK6/Up59+6qZq4Q4e7+Ft1arVOe8bEBCgyy67zO01jB49WgsXLtR7772n8PBwFRQUSJIiIyMVEhIiSRoyZIguueQSZWVlSZIeffRRdenSRU2bNtXRo0f19NNPa//+/frzn//s9voAALACwzBklJea0rYtMFQ2m83t542IiNDf//53Pfrooxo6dKjq1KlTZZ/jx4/rhhtu0OOPP66goCC99tpr6tevn3bu3KnExES314Tz59VpyZxOp/z8qnYqO51O/fDDDx77RzFnzhxJv/xF97/mz5+vYcOGSZLy8vIq1XbkyBGNGjVKBQUFqlu3rjp27Ki1a9eqdevWHqkRAIDazigv1e67Ikxpu+mLJbIFVQ2j7nDvvfdq9uzZmjlzph555JEq29u1a6d27dq5Xj/22GN699139Z///EdjxozxSE04P16ZlqykpES33Xab6tSpo9jYWE2aNEkOh8O1/dChQxc0zOBcGYZR7fJr2JWkVatWacGCBa7XzzzzjPbv36+ysjIVFBTov//9r9q3b++xGgEAQM0UFBSkRx99VNOnT9dPP/1UZfvx48c1ceJEtWrVSlFRUQoLC9O3336rvLw8E6pFdbzSw/vII49o69at+ve//62jR4/qH//4hzZt2qQlS5YoMDBQ0i+hFAAA1F62wFA1fdGcOehtgaEePf+dd96p6dOn6x//+EeVGRomTpyo5cuXa/r06WratKlCQkJ0yy23qLy83KM14dx5JfAuXbpUr776qmtIQf/+/dW3b1/169dP//nPfyTJI+NuAACA99hsNo8NKzCbn5+fsrKyNGDAAN1zzz2Vtn3xxRcaNmyYbr75Zkm/9Pju27fPhCpxJl4Z0nDo0CElJSW5Xjdo0ECffvqpjh07phtuuEGlpeYMcAcAADhXffv2VUpKSpU5+Zs1a6YlS5Zoy5Yt2rp1q26//XY5nU6TqkR1vBJ4ExMT9e2331ZaFx4erk8++UQnT550/UUEAABQkz355JM6depUpXUzZ85U3bp11bVrV/Xr10/p6enq0KGDSRWiOjbDC4Nnx40bp/z8fC1evLjKtmPHjql379766quvKt3IZgUlJSWKjIxUcXGxIiLMuWvVbBUVFSoqKpLdbpfdbje7HABu4nA45HA4FBMTI39/r074gxri1KlTys3NVePGjRUcHGx2OT6D635hvPIpNXXqVP3444/VbgsPD9fy5cu1adMmb5QCAAAAH+OVwFu3bl3VrVv3jNvDw8PVo0cPb5QCAACg1atXq0+fPmfcfvz4cS9WA0/z+vdQX331lVauXKmioqIqA7pnzpzp7XIAAIAP6tSpk7Zs2WJ2GfASrwbeJ554Qg8//LBatGih2NjYSlORMS0ZAADwlpCQEDVt2tTsMuAlXg28s2fP1rx58yo94QwAAADwJK9MS+ZqzM9P3bp182aTAAAA8HFeDbwTJkzQCy+84M0mAQAA4OO8OqRh4sSJ6tu3ry677DK1bt1aAQEBlbYvWbLEm+UAAADAB3g18I4bN04rV67UNddco/r163OjGgAAADzOq4H31Vdf1TvvvKO+fft6s1kAAACXnj17Kjk5WbNmzTK7FHiJV8fw1qtXT5dddpk3mwQAAKhkyZIleuyxx353v549e2r8+PGV1s2ePVtBQUFatGiRh6qDJ3g18E6ZMkWTJ09WaWmpN5sFAABwqVevnsLDw8/7uMmTJ+uhhx7Se++9pz/+8Y8eqAye4tUhDc8++6z27Nmj2NhYNWrUqMpNa5s2bfJmOQAAwAed75AGwzA0btw4vf7661q+fLm6du3q2QLhdl4NvP379/dmcwAAwIsMw9DpcocpbQcE2j1yM3xFRYXuvPNOffbZZ8rOzlbbtm3d3gY8z6uBd/Lkyd5sDgAAeNHpcocefvAjU9r+x7TrFRjk/ljz8ssvS5K2bt2qli1buv388A6vjuH96quvtH79+irr169frw0bNnizFAAAgN911VVXKSwsTI888ogqKirMLgcXyKs9vKNHj9bf/vY3paSkVFp/8OBBPfnkk9WGYQAAUDsEBNr1j2nXm9a2J7Rp00YzZsxQWlqaBg0apDfffFP+/l6NT3ADr/4X27Fjhzp06FBlffv27bVjxw5vlgIAANzMZrN5ZFiB2ZKTk7VixQqlpaXptttu05tvvlnlxnvUbF4d0hAUFKTCwsIq6/Pz873y19ILL7ygRo0aKTg4WCkpKfryyy/Puv/ixYvVsmVLBQcHq02bNlq2bJnHawQAADVPu3bt9Nlnn2nNmjW67bbbdPr0abNLwnnwauC97rrrlJmZqeLiYte6o0eP6qGHHlLv3r092vabb76pjIwMTZ48WZs2bVK7du2Unp6uoqKiavdfu3atBg8erJEjR2rz5s3q37+/+vfvr+3bt3u0TgAAUDO1adNGn332mdauXatbb71V5eXlZpeEc2QzDMPwVmMHDx5U9+7ddfjwYbVv316StGXLFsXGxmr58uVKSEjwWNspKSm68sor9fzzz0uSnE6nEhISNHbsWD344INV9h80aJBOnDihDz74wLWuS5cuSk5O1ty5c8+pzZKSEkVGRqq4uFgRERHueSP/P8MwasUDPCoqKnTo0CH5+fnJbvfM+CoA3udwOOR0OhUdHc14Rh9VVlam/Px81zenODd+fn4XNX3aqVOnlJubq8aNG3Pdz4NXP6UuueQSbdu2TW+88Ya2bt2qkJAQDR8+XIMHD/boWJjy8nJt3LhRmZmZrnV+fn5KS0tTTk5Otcfk5OQoIyOj0rr09HQtXbr0jO2UlZWprKzM9bqkpOTiCj+L0tJShYWFeez8AACcTVJSkubOnauTJ0+aXUqt0jT6EkUlxZtdhs/xSuCdNGmSbrrpJnXs2FF16tTRX/7yF2806/LTTz/J4XAoNja20vrY2Fh999131R5TUFBQ7f4FBQVnbCcrK0tTp069+IIBAIBHbd68Wffdd98Zt3/++eeeadhr36vjf3kl8P7www/q06ePAgMD1a9fP914443q1auXAgMDvdG812RmZlbqFS4pKfHYMI3Q0FB9vTpHjtM1e05Ah8OhYyUlsvv5yebn/ifgADCH4TTkcDoVHhHBcCUfZfjZZIsIVWJCooJq4e/zxgmJ6tLpyjNuv+yyyzzSbiDDEEzhlcA7b948OZ1OffHFF3r//fc1fvx45efnq3fv3rrpppv0hz/8QfXq1fNY+w0aNJDdbq8yQ0RhYaHi4uKqPSYuLu689pd+mYUiKCjo4gs+BzabTVdc1cUrbV2MiooKFRUVyW6380sRsBCHwyGHw6GYmBjG8PqoX8eShoTVqZVjSUMjwlU/NsbsMuAlXpulwc/PT1dffbWeeuop7dy5U+vXr1dKSopefPFFNWzYUN27d9f06dN18OBBt7cdGBiojh07asWKFa51TqdTK1asUGpqarXHpKamVtpfkpYvX37G/QEAAFAzmfZneatWrdSqVSv97W9/06FDh/T+++/rvffekyRNnDjR7e1lZGRo6NCh6tSpkzp37qxZs2bpxIkTGj58uCRpyJAhuuSSS5SVlSVJuu+++9SjRw/NmDFDffv21aJFi7Rhwwa99NJLbq8NAAAAnmP691CGYWjDhg1atmyZK/B6wqBBg3To0CFNmjRJBQUFSk5O1kcffeS6MS0vL09+fv+vw7tr165auHChHn74YT300ENq1qyZli5dqiuuuMJjNQIAAMD9vDoP7//Kzc3VvHnztGDBAh06dEhpaWmV5ry1Ak/Ow1tbMIYXsCbG8IL5YM3Bdb8wXv2UKisr09tvv61//etfWrNmjRwOh6ZPn66RI0f6bCAEAACAZ3nlprWNGzfq3nvvVVxcnGbNmqX+/fvrwIED8vPzU3p6OmEXAAB4Tc+ePTV+/Hizy4AXeaWHNyUlRWPHjtW6devUokULbzQJAABQrSVLlnj0Ca+oebwSeHv16qV//etfKioq0p/+9Celp6df1HOkAQAALpQn5/5HzeSVIQ0ff/yxvvnmG7Vo0UL33HOP4uPjXY/zI/gCAABvOtchDWVlZXrggQeUkJCgoKAgNW3aVP/6178k/XLj5siRI9W4cWOFhISoRYsWmj17dqXjhw0bpv79+2vq1KmKjo5WRESE7r77bpWXl3vibeEsvHbTWkJCgiZNmqRJkyZp+fLlmj9/vvz9/XXTTTfplltu0S233KIOHTp4qxwAAOBmhmHIOHnalLZtIQFu70QbMmSIcnJy9Oyzz6pdu3bKzc3VTz/9JOmXB1hdeumlWrx4serXr6+1a9fqL3/5i+Lj43Xbbbe5zrFixQoFBwdr1apV2rdvn4YPH6769evr8ccfd2utODvTpiWTpCNHjuj111/XvHnztG3bNjkcDrNK8QimJWNaMsCqmJYM1U2P5SwtV1Gn2b9zpGfEbLhPfqGB57Rvz549lZycrFmzZp1xn127dqlFixZavny50tLSzum8Y8aMUUFBgd5++21Jv/Twvv/++zpw4IBCQ0MlSXPnztVf//pXFRcXV5r//1wxLdmF8dqjhatTt25djR07Vps3b9ZXX31lZikAAAAuW7Zskd1uV48ePc64zwsvvKCOHTsqOjpaYWFheumll5SXl1dpn3bt2rnCriSlpqbq+PHjOnDggMdqR1Ve/bP8888/92ZzAADAi2whAYrZcJ9pbbtTSEjIWbcvWrRIEydO1IwZM5Samqrw8HA9/fTTWr9+vVvrgHt4NfD27Nmzyrr/HW9jtSENAAD4EpvNJts5Diuo6dq0aSOn06ns7OxqhzR88cUX6tq1q+69917Xuj179lTZb+vWrTp58qQrQK9bt05hYWFKSEjwXPGowqtDGo4cOVJpKSoq0kcffaQrr7xSn3zyiTdLAQAAOKNGjRpp6NChGjFihJYuXarc3FytWrVKb731liSpWbNm2rBhgz7++GPt2rVLjzzySLXDM8vLyzVy5Ejt2LFDy5Yt0+TJkzVmzJgLGr+LC+fVHt7IyMgq63r37q3AwEBlZGRo48aN3iwHAADgjObMmaOHHnpI9957rw4fPqzExEQ99NBDkqS77rpLmzdv1qBBg2Sz2TR48GDde++9+vDDDyudo1evXmrWrJm6d++usrIyDR48WFOmTDHh3fg2U2dp+NV3332nTp066fjx42aX4lbM0sAsDYBVMUsDmC3g9w0bNkxHjx7V0qVL3XZOrvuF8eqn1LZt2yq9NgxD+fn5mjZtmpKTk71ZCgAAAHyEVwNvcnKybDabftup3KVLF82bN8+bpQAAAB+2evVq9enT54zbrfats6/zauDNzc2t9NrPz0/R0dF0yQMAAK/q1KmTtmzZ4tE2FixY4NHz49x5NfAmJSV5szkAAIBqhYSEqGnTpmaXAS/x+JwYixYtOud9Dxw4oC+++MKD1QAAAMDXeDzwzpkzR61atdJTTz2lb7/9tsr24uJiLVu2TLfffrs6dOigw4cPe7okAAAA+BCPD2nIzs7Wf/7zHz333HPKzMxUnTp1FBsbq+DgYB05ckQFBQVq0KCBhg0bpu3btys2NtbTJQEAAMCHeGUM74033qgbb7xRP/30k9asWaP9+/fr5MmTatCggdq3b6/27dvzxBEAAAB4hFdvWmvQoIH69+/vzSYBAADg4+hWBQAAPqVnz54aP36828+7atUq2Ww2HT161O3nxsWxfODdt2+fRo4cqcaNGyskJESXXXaZJk+erPLy8rMe17NnT9lstkrL3Xff7aWqAQCApyxZskSPPfbYRZ2jutDctWtX5efnKzIy8qLODfez/APQv/vuOzmdTr344otq2rSptm/frlGjRunEiROaPn36WY8dNWqUHn30Udfr0NBQT5cLAAA8rF69eh45b2BgoOLi4jxyblwcy/fwXn/99Zo/f76uu+46NWnSRDfeeKMmTpyoJUuW/O6xoaGhiouLcy0RERFeqBgAAHjSuQ5p+Oc//6lmzZopODhYsbGxuuWWWyRJw4YNU3Z2tmbPnu36Fnjfvn1VhjQsWLBAUVFR+uCDD9SiRQuFhobqlltuUWlpqV599VU1atRIdevW1bhx4+RwODz4jmH5Ht7qFBcXn9Nfd2+88YZef/11xcXFqV+/fnrkkUfO2stbVlamsrIy1+uSkhK31AsAQG1gGIZKS0tNaTs0NFQ2m81t59uwYYPGjRunf//73+ratat+/vlnrV69WpI0e/Zs7dq1S1dccYXrm+Do6Gjt27evynlKS0v17LPPatGiRTp27JgGDBigm2++WVFRUVq2bJn27t2rgQMHqlu3bho0aJDb6kdlHg+8GRkZeuyxx1SnTh1lZGScdd+ZM2d6uhzt3r1bzz333O8OZ7j99tuVlJSkhg0batu2bXrggQe0c+fOs/YMZ2VlaerUqe4uGQCAWqG0tFRhYWGmtH38+HHVqVPHbefLy8tTnTp19Ic//EHh4eFKSkpS+/btJUmRkZEKDAx0fRN8NqdPn9acOXN02WWXSZJuueUW/fvf/1ZhYaHCwsLUunVrXXPNNVq5ciWB14M8Hng3b96s06dPu34+k/P9q+zBBx/Uk08+edZ9vv32W7Vs2dL1+uDBg7r++ut16623atSoUWc99i9/+Yvr5zZt2ig+Pl69evXSnj17XP9ofyszM7NSqC8pKVFCQsK5vB0AAFCD9O7dW0lJSWrSpImuv/56XX/99br55pvP+36e0NDQSrkhNjZWjRo1qvSHQWxsrIqKitxWO6ryeOBduXJltT9frPvvv1/Dhg076z5NmjRx/fzjjz/qmmuuUdeuXfXSSy+dd3spKSmSfukhPlPgDQoKUlBQ0HmfGwAAKwgNDdXx48dNa9udwsPDtWnTJq1atUqffPKJJk2apClTpuirr75SVFTUOZ8nICCg0mubzVbtOqfT6Y6ycQa1dgxvdHS0oqOjz2nfgwcP6pprrlHHjh01f/78C3qq25YtWyRJ8fHx530sAAC+wGazuXVYgdn8/f2VlpamtLQ0TZ48WVFRUfrss880YMAABQYGcqNZLVJrA++5OnjwoHr27KmkpCRNnz5dhw4dcm37ddzNwYMH1atXL7322mvq3Lmz9uzZo4ULF+qGG25Q/fr1tW3bNk2YMEHdu3dX27ZtzXorAADASz744APt3btX3bt3V926dbVs2TI5nU61aNFCktSoUSOtX79e+/btU1hYmMemOoN7WD7wLl++XLt379bu3bt16aWXVtpmGIakXwaU79y503VnaWBgoD799FPNmjVLJ06cUEJCggYOHKiHH37Y6/UDAADvi4qK0pIlSzRlyhSdOnVKzZo10//93//p8ssvlyRNnDhRQ4cOVevWrXXy5Enl5uaaXDHOxmb8mvrgdiUlJYqMjFRxcbHPzuFbUVGhoqIi2e122e12s8sB4CYOh0MOh0MxMTHy97d83wmqcerUKeXm5qpx48YKDg42uxyfwXW/MJZ/8AQAAAB8G4EXAAD4nNWrVyssLOyMC6yF76EAAIDP6dSpk2sGJlgfgRcAAPickJAQNW3a1Owy4CUMaQAAAIClEXgBAMAFY7In7+J6XxgCLwAAOG+/Ph731zns4R2/Xu/fPp4YZ8cYXgAAcN7sdruioqJUVFQkSQoNDZXNZjO5KusyDEOlpaUqKipSVFQUc9ufJwIvAAC4IHFxcZLkCr3wvKioKNd1x7kj8AIAgAtis9kUHx+vmJgYnT592uxyLC8gIICe3QtE4AUAABeFx8ejpuOmNQAAAFgagRcAAACWRuAFAACApRF4AQAAYGkEXgAAAFgagRcAAACWRuAFAACApRF4AQAAYGkEXgAAAFgagRcAAACWRuAFAACApRF4AQAAYGk+EXgbNWokm81WaZk2bdpZjzl16pRGjx6t+vXrKywsTAMHDlRhYaGXKgYAAIC7+ETglaRHH31U+fn5rmXs2LFn3X/ChAl6//33tXjxYmVnZ+vHH3/UgAEDvFQtAAAA3MXf7AK8JTw8XHFxcee0b3Fxsf71r39p4cKFuvbaayVJ8+fPV6tWrbRu3Tp16dLFk6UCAADAjWyGYRhmF+FpjRo10qlTp3T69GklJibq9ttv14QJE+TvX33e/+yzz9SrVy8dOXJEUVFRrvVJSUkaP368JkyYUO1xZWVlKisrc70uLi5WYmKiDhw4oIiICLe+p9qioqJChw4dks1mk5+fz3yhAFie0+mUYRiKjo4+42cpAHOEh4fLZrOZXUaN4hOfUuPGjVOHDh1Ur149rV27VpmZmcrPz9fMmTOr3b+goECBgYGVwq4kxcbGqqCg4IztZGVlaerUqVXWJyQkXFT9AAAA56q4uNhnO9rOpNYG3gcffFBPPvnkWff59ttv1bJlS2VkZLjWtW3bVoGBgbrrrruUlZWloKAgt9WUmZlZqS2n06mff/5Z9evX98hfWiUlJUpISPDpHmR34Dq6D9fSPbiO7sF1dA+uo3t48zqGh4d79Py1Ua0NvPfff7+GDRt21n2aNGlS7fqUlBRVVFRo3759atGiRZXtcXFxKi8v19GjRyv18hYWFp51HHBQUFCVAP3bXmJPiIiI4EPIDbiO7sO1dA+uo3twHd2D6+geXEdz1NrAGx0drejo6As6dsuWLfLz81NMTEy12zt27KiAgACtWLFCAwcOlCTt3LlTeXl5Sk1NveCaAQAA4H21NvCeq5ycHK1fv17XXHONwsPDlZOTowkTJujOO+9U3bp1JUkHDx5Ur1699Nprr6lz586KjIzUyJEjlZGRoXr16ikiIkJjx45VamoqMzQAAADUMpYPvEFBQVq0aJGmTJmisrIyNW7cWBMmTKg01vb06dPauXOnSktLXeueeeYZ+fn5aeDAgSorK1N6err++c9/mvEWzigoKEiTJ0926zhkX8R1dB+upXtwHd2D6+geXEf34DqayyemJQMAAIDvYmJUAAAAWBqBFwAAAJZG4AUAAIClEXgBAABgaQTeWuyFF15Qo0aNFBwcrJSUFH355Zdml1Sjff755+rXr58aNmwom82mpUuXVtpuGIYmTZqk+Ph4hYSEKC0tTd9//705xdZgWVlZuvLKKxUeHq6YmBj1799fO3furLTPqVOnNHr0aNWvX19hYWEaOHCgCgsLTaq4ZpozZ47atm3rmoQ+NTVVH374oWs71/DCTJs2TTabTePHj3et41r+vilTpshms1VaWrZs6drONTw/Bw8e1J133qn69esrJCREbdq00YYNG1zb+X3jfQTeWurNN99URkaGJk+erE2bNqldu3ZKT09XUVGR2aXVWCdOnFC7du30wgsvVLv9qaee0rPPPqu5c+dq/fr1qlOnjtLT03Xq1CkvV1qzZWdna/To0Vq3bp2WL1+u06dP67rrrtOJEydc+0yYMEHvv/++Fi9erOzsbP34448aMGCAiVXXPJdeeqmmTZumjRs3asOGDbr22mt100036ZtvvpHENbwQX331lV588UW1bdu20nqu5bm5/PLLlZ+f71rWrFnj2sY1PHdHjhxRt27dFBAQoA8//FA7duzQjBkzXHP/S/y+MYWBWqlz587G6NGjXa8dDofRsGFDIysry8Sqag9Jxrvvvut67XQ6jbi4OOPpp592rTt69KgRFBRk/N///Z8JFdYeRUVFhiQjOzvbMIxfrltAQICxePFi1z7ffvutIcnIyckxq8xaoW7dusYrr7zCNbwAx44dM5o1a2YsX77c6NGjh3HfffcZhsG/x3M1efJko127dtVu4xqenwceeMC46qqrzrid3zfmoIe3FiovL9fGjRuVlpbmWufn56e0tDTl5OSYWFntlZubq4KCgkrXNDIyUikpKVzT31FcXCxJqlevniRp48aNOn36dKVr2bJlSyUmJnItz8DhcGjRokU6ceKEUlNTuYYXYPTo0erbt2+laybx7/F8fP/992rYsKGaNGmiO+64Q3l5eZK4hufrP//5jzp16qRbb71VMTExat++vV5++WXXdn7fmIPAWwv99NNPcjgcio2NrbQ+NjZWBQUFJlVVu/163bim58fpdGr8+PHq1q2brrjiCkm/XMvAwEBFRUVV2pdrWdXXX3+tsLAwBQUF6e6779a7776r1q1bcw3P06JFi7Rp0yZlZWVV2ca1PDcpKSlasGCBPvroI82ZM0e5ubm6+uqrdezYMa7hedq7d6/mzJmjZs2a6eOPP9Y999yjcePG6dVXX5XE7xuzWP7RwgA8Z/To0dq+fXulsX44dy1atNCWLVtUXFyst99+W0OHDlV2drbZZdUqBw4c0H333afly5crODjY7HJqrT59+rh+btu2rVJSUpSUlKS33npLISEhJlZW+zidTnXq1ElPPPGEJKl9+/bavn275s6dq6FDh5pcne+ih7cWatCggex2e5U7ZAsLCxUXF2dSVbXbr9eNa3ruxowZow8++EArV67UpZde6lofFxen8vJyHT16tNL+XMuqAgMD1bRpU3Xs2FFZWVlq166dZs+ezTU8Dxs3blRRUZE6dOggf39/+fv7Kzs7W88++6z8/f0VGxvLtbwAUVFRat68uXbv3s2/x/MUHx+v1q1bV1rXqlUr1xARft+Yg8BbCwUGBqpjx45asWKFa53T6dSKFSuUmppqYmW1V+PGjRUXF1fpmpaUlGj9+vVc098wDENjxozRu+++q88++0yNGzeutL1jx44KCAiodC137typvLw8ruXvcDqdKisr4xqeh169eunrr7/Wli1bXEunTp10xx13uH7mWp6/48ePa8+ePYqPj+ff43nq1q1blakad+3apaSkJEn8vjGN2XfN4cIsWrTICAoKMhYsWGDs2LHD+Mtf/mJERUUZBQUFZpdWYx07dszYvHmzsXnzZkOSMXPmTGPz5s3G/v37DcMwjGnTphlRUVHGe++9Z2zbts246aabjMaNGxsnT540ufKa5Z577jEiIyONVatWGfn5+a6ltLTUtc/dd99tJCYmGp999pmxYcMGIzU11UhNTTWx6prnwQcfNLKzs43c3Fxj27ZtxoMPPmjYbDbjk08+MQyDa3gx/neWBsPgWp6L+++/31i1apWRm5trfPHFF0ZaWprRoEEDo6ioyDAMruH5+PLLLw1/f3/j8ccfN77//nvjjTfeMEJDQ43XX3/dtQ+/b7yPwFuLPffcc0ZiYqIRGBhodO7c2Vi3bp3ZJdVoK1euNCRVWYYOHWoYxi9TxTzyyCNGbGysERQUZPTq1cvYuXOnuUXXQNVdQ0nG/PnzXfucPHnSuPfee426desaoaGhxs0332zk5+ebV3QNNGLECCMpKckIDAw0oqOjjV69ernCrmFwDS/GbwMv1/L3DRo0yIiPjzcCAwONSy65xBg0aJCxe/du13au4fl5//33jSuuuMIICgoyWrZsabz00kuVtvP7xvtshmEY5vQtAwAAAJ7HGF4AAABYGoEXAAAAlkbgBQAAgKUReAEAAGBpBF4AAABYGoEXAAAAlkbgBQAAgKUReAEAAGBpBF4AOAerVq2SzWbT0aNHTWl/xYoVatWqlRwOh8fa6NKli9555x2PnR8AzMKT1gDgN3r27Knk5GTNmjXLta68vFw///yzYmNjZbPZvF5Tx44dlZGRoTvuuMNjbXzwwQeaMGGCdu7cKT8/+kMAWAefaABwDgIDAxUXF2dK2F2zZo327NmjgQMHerSdPn366NixY/rwww892g4AeBuBFwD+x7Bhw5Sdna3Zs2fLZrPJZrNp3759VYY0LFiwQFFRUfrggw/UokULhYaG6pZbblFpaaleffVVNWrUSHXr1tW4ceMqDUMoKyvTxIkTdckll6hOnTpKSUnRqlWrzlrTokWL1Lt3bwUHB7vWTZkyRcnJyZo3b54SExMVFhame++9Vw6HQ0899ZTi4uIUExOjxx9/3HWMYRiaMmWKEhMTFRQUpIYNG2rcuHGu7Xa7XTfccIMWLVrknosJADWEv9kFAEBNMnv2bO3atUtXXHGFHn30UUlSdHS09u3bV2Xf0tJSPfvss1q0aJGOHTumAQMG6Oabb1ZUVJSWLVumvXv3auDAgerWrZsGDRokSRozZox27NihRYsWqWHDhnr33Xd1/fXX6+uvv1azZs2qrWn16tW6/fbbq6zfs2ePPvzwQ3300Ufas2ePbrnlFu3du1fNmzdXdna21q5dqxEjRigtLU0pKSl655139Mwzz2jRokW6/PLLVVBQoK1bt1Y6Z+fOnTVt2rSLvIoAULMQeAHgf0RGRiowMFChoaGKi4s7676nT5/WnDlzdNlll0mSbrnlFv373/9WYWGhwsLC1Lp1a11zzTVauXKlBg0apLy8PM2fP195eXlq2LChJGnixIn66KOPNH/+fD3xxBPVtrN//37X/v/L6XRq3rx5Cg8Pd7W1c+dOLVu2TH5+fmrRooWefPJJrVy5UikpKcrLy1NcXJzS0tIUEBCgxMREde7cudI5GzZsqAMHDsjpdDKOF4Bl8GkGABcoNDTUFXYlKTY2Vo0aNVJYWFildUVFRZKkr7/+Wg6HQ82bN1dYWJhryc7O1p49e87YzsmTJysNZ/hVo0aNFB4eXqmt1q1bVwqq/9v+rbfeqpMnT6pJkyYaNWqU3n33XVVUVFQ6Z0hIiJxOp8rKys7zagBAzUUPLwBcoICAgEqvbTZbteucTqck6fjx47Lb7dq4caPsdnul/f43JP9WgwYNdOTIkYtuPyEhQTt37tSnn36q5cuX695779XTTz+t7Oxs13E///yz6tSpo5CQkLO9dQCoVQi8APAbgYGBHpnvtn379nI4HCoqKtLVV199Xsft2LHDLTWEhISoX79+6tevn0aPHq2WLVvq66+/VocOHSRJ27dvV/v27d3SFgDUFAReAPiNRo0aaf369dq3b5/CwsJUr149t5y3efPmuuOOOzRkyBDNmDFD7du316FDh7RixQq1bdtWffv2rfa49PR0vfrqqxfd/oIFC+RwOJSSkqLQ0FC9/vrrCgkJUVJSkmuf1atX67rrrrvotgCgJmEMLwD8xsSJE2W329W6dWtFR0crLy/PbeeeP3++hgwZovvvv18tWrRQ//799dVXXykxMfGMx9xxxx365ptvtHPnzotqOyoqSi+//LK6deumtm3b6tNPP9X777+v+vXrS5IOHjyotWvXavjw4RfVDgDUNDxpDQBqgb/+9a8qKSnRiy++6LE2HnjgAR05ckQvvfSSx9oAADPQwwsAtcDf//53JSUluW5A84SYmBg99thjHjs/AJiFHl4AAABYGj28AAAAsDQCLwAAACyNwAsAAABLI/ACAADA0gi8AAAAsDQCLwAAACyNwAsAAABLI/ACAADA0gi8AAAAsDQCLwAAACyNwAsAAABLI/ACAADA0gi8AAAAsDQCLwAAACyNwAsAAABLI/ACAADA0gi8AAAAsDQCLwAAACyNwAsAAABLI/ACAADA0gi8AAAAsDQCLwAAACzt/wMg1pAkHn5uQQAAAABJRU5ErkJggg==",
      "text/html": [
       "\n",
       "            <div style=\"display: inline-block;\">\n",
       "                <div class=\"jupyter-widgets widget-label\" style=\"text-align: center;\">\n",
       "                    Figure\n",
       "                </div>\n",
       "                <img 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' width=700.0/>\n",
       "            </div>\n",
       "        "
      ],
      "text/plain": [
       "Canvas(toolbar=Toolbar(toolitems=[('Home', 'Reset original view', 'home', 'home'), ('Back', 'Back to previous …"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "EK = -90.0      # Reversal potential (mV)\n",
    "gK_bar = 0.006  # Maximal channel conductance (S/cm2)\n",
    "\n",
    "def alpha_n(Vm):\n",
    "    return 0.032 * vtrap(15 - (Vm - V_T), 5)  # ms-1\n",
    "\n",
    "def beta_n(Vm):\n",
    "    return 0.5 * exp(-((Vm - V_T) - 10) / 40)  # ms-1\n",
    "\n",
    "def dn_dt(n, Vm):\n",
    "    return alpha_n(Vm) * (1 - n) - beta_n(Vm) * n  # ms-1\n",
    "\n",
    "def n_inf(Vm):\n",
    "    return alpha_n(Vm) / (alpha_n(Vm) + beta_n(Vm))  # (-)\n",
    "\n",
    "def i_K(n, Vm):\n",
    "    return gK_bar * n**4 * (Vm - EK) * MA_CM2_TO_UA_CM2  # uA/cm2\n",
    "\n",
    "# Update model and run interactive simulation\n",
    "model.add_current(i_K)\n",
    "model.add_state(dn_dt, n_inf)\n",
    "interactive_simulation(model.copy());"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Questions\n",
    "- *As you apply a positive stimulus, do you observe any difference in behavior?*\n",
    "- *What do you conclude about the role of potassium channels on membrane potential?*\n",
    "- *Is this membrane configuration enough to elicit multiple \"action potentials\" (or \"spikes\")?*"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Step 4: a sodium inactivation gate\n",
    "\n",
    "While the addition of potassium current offers some counterweight to our sodium current, our membrane still stabilizes around a plateau potential upon stimulation. To finally obtain a so-called \"spiking\" behavior, we must ensure repolarization. To this aim, let's add a so-called **inactivation gate** (*H*) to our sodium channels.\n",
    "\n",
    "Our governing equation is therefore slightly modified:\n",
    "\n",
    "$C_m \\frac{dV_m}{dt} = i_{stim} - [i_{Leak}(V_m) + i_{Na}(m, h, V_m) + i_{K}(n, V_m)]$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "f8ef90ff6c484fa98c2528374c06fad8",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "interactive(children=(FloatSlider(value=0.0, continuous_update=False, description='I', max=60.0, min=-15.0, st…"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "6baed0a18717465e9bf7a297db18df2d",
       "version_major": 2,
       "version_minor": 0
      },
      "image/png": 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",
      "text/html": [
       "\n",
       "            <div style=\"display: inline-block;\">\n",
       "                <div class=\"jupyter-widgets widget-label\" style=\"text-align: center;\">\n",
       "                    Figure\n",
       "                </div>\n",
       "                <img 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' width=700.0/>\n",
       "            </div>\n",
       "        "
      ],
      "text/plain": [
       "Canvas(toolbar=Toolbar(toolitems=[('Home', 'Reset original view', 'home', 'home'), ('Back', 'Back to previous …"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def alpha_h(Vm):\n",
    "    return 0.128 * exp(-((Vm - V_T) - 17) / 18)  # ms-1\n",
    "\n",
    "def beta_h(Vm):\n",
    "    return 4 / (1 + exp(-((Vm - V_T) - 40) / 5))  # ms-1\n",
    "\n",
    "def dh_dt(h, Vm):\n",
    "    return alpha_h(Vm) * (1 - h) - beta_h(Vm) * h\n",
    "\n",
    "def h_inf(Vm):\n",
    "    return alpha_h(Vm) / (alpha_h(Vm) + beta_h(Vm))\n",
    "\n",
    "def i_Na(m, h, Vm):\n",
    "    return gNa_bar * m**3 * h * (Vm - ENa) * MA_CM2_TO_UA_CM2  # uA/cm2\n",
    "\n",
    "# Update model and run interactive simulation\n",
    "model.add_state(dh_dt, h_inf)\n",
    "model.update_current(i_Na)\n",
    "interactive_simulation(model.copy());"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Questions\n",
    "- *As you apply a positive stimulus, do you observe any difference in behavior?*\n",
    "- *What do you conclude about the role of sodium inactivation gates on membrane dynamics?*"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Summary\n",
    "\n",
    "By the end of this tutorial, you should have developed a clear intuition of the key components involved in the intricate neuronal membrane dynamics. In light of this, *can you describe, in your own words, the different phases of an action potential?*\n",
    "\n",
    "YOUR DESCRIPTION:"
   ]
  }
 ],
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   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
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