CHEM101.6_Exercise_0_Butane_OpenMM.ipynb

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            "order": null,
            "_view_module_version": "1.2.0",
            "grid_template_areas": null,
            "object_position": null,
            "object_fit": null,
            "grid_auto_columns": null,
            "margin": null,
            "display": null,
            "left": null
          }
        }
      }
    }
  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/github/paulrobustelli/CHEM101.6/blob/main/Butane_OpenMM.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "pj2BWZxUDbEE"
      },
      "source": [
        "# **Hello there!**\n",
        "\n",
        "This is a Jupyter notebook for running Molecular Dynamics (MD) simulations of Alkanes using the OpenMM engine "
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "CY5Hv721m9xM",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 521
        },
        "outputId": "a1ea6933-3ba0-4145-ccd7-bf18e5b2c8b1"
      },
      "source": [
        "#@title ### **Video Demonstration**\n",
        "#@markdown Check the timelapse movie to understand how the pipeline works\n",
        "from IPython.display import YouTubeVideo\n",
        "YouTubeVideo('pVa0mQS6xeo', width=800, height=500)"
      ],
      "execution_count": 1,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
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              "        "
            ],
            "text/plain": [
              "<IPython.lib.display.YouTubeVideo at 0x7feac27c5c90>"
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          },
          "metadata": {},
          "execution_count": 1
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Lh96y6mGFY1D"
      },
      "source": [
        "---\n",
        "---\n",
        "# **Setting the environment for MD calculation**\n",
        "\n",
        "Firstly, we need to install all necessary libraries and packages for our simulation. The main packages we will be installing are:\n",
        "\n",
        "1.    Anaconda (https://docs.conda.io/en/latest/miniconda.html)\n",
        "2.    OpenMM (https://openmm.org/)\n",
        "3.    PyTraj (https://amber-md.github.io/pytraj/latest/index.html)\n",
        "4.    py3Dmol (https://pypi.org/project/py3Dmol/)\n",
        "5.    Numpy (https://numpy.org/)\n",
        "6.    Matplotlib (https://matplotlib.org/)\n",
        "7.    AmberTools (https://ambermd.org/AmberTools.php)"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "wH1oMiVUlxO_",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "7942265a-6c80-4505-bc7c-80681294ead5"
      },
      "source": [
        "#@title **Install dependencies**\n",
        "#@markdown It will take a few minutes, please, drink a coffee and wait. ;-)\n",
        "# install dependencies\n",
        "!pip -q install py3Dmol 2>&1 1>/dev/null\n",
        "!pip install --upgrade MDAnalysis 2>&1 1>/dev/null\n",
        "!pip install biopandas 2>&1 1>/dev/null\n",
        "# install conda\n",
        "!wget -qnc https://repo.anaconda.com/miniconda/Miniconda3-latest-Linux-x86_64.sh \n",
        "!bash Miniconda3-latest-Linux-x86_64.sh -bfp /usr/local 2>&1 1>/dev/null\n",
        "!rm Miniconda3-latest-Linux-x86_64.sh\n",
        "!conda install -y -q -c conda-forge openmm=7.6 python=3.7 pdbfixer 2>&1 1>/dev/null\n",
        "!conda install -c conda-forge ambertools --yes 2>&1 1>/dev/null\n",
        "!conda install -c ambermd pytraj  --yes 2>&1 1>/dev/null\n",
        "#load dependencies\n",
        "import sys\n",
        "sys.path.append('/usr/local/lib/python3.7/site-packages/')\n",
        "from biopandas.pdb import PandasPdb\n",
        "import openmm as mm\n",
        "from openmm import *\n",
        "from openmm.app import *\n",
        "from openmm.unit import *\n",
        "import os\n",
        "import urllib.request  \n",
        "import numpy as np\n",
        "import MDAnalysis as mda\n",
        "import py3Dmol\n",
        "from __future__ import print_function\n",
        "import pytraj as pt\n",
        "import platform\n",
        "import scipy.cluster.hierarchy\n",
        "from scipy.spatial.distance import squareform\n",
        "import scipy.stats as stats\n",
        "import matplotlib.pyplot as plt\n",
        "import pandas as pd\n",
        "from scipy.interpolate import griddata\n",
        "import seaborn as sb\n",
        "from statistics import mean, stdev\n",
        "from pytraj import matrix\n",
        "from matplotlib import colors\n",
        "from IPython.display import set_matplotlib_formats\n",
        "#%matplotlib inline\n",
        "#set_matplotlib_formats('png')\n",
        "#plt.figure(figsize=(5,7))"
      ],
      "execution_count": 2,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            ""
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "fDQnAKJLFxtt"
      },
      "source": [
        "## Using Google Drive to store simulation data\n",
        "\n",
        "Google Colab does not allow users to keep data on their computing nodes. However, we can use Google Drive to read, write, and store our simulations files. Therefore, we suggest to you to:\n",
        "\n",
        "1.   Create a folder in your own Google Drive and copy the necessary input files there.\n",
        "2.   Copy the path of your created directory. We will use it below."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Lm7Akepv_vl-",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "0939d94a-f430-4cce-d747-97b2d4d16c65"
      },
      "source": [
        "#@title ### **Import Google Drive**\n",
        "#@markdown Click in the \"Run\" buttom to make your Google Drive accessible.\n",
        "from google.colab import drive\n",
        "\n",
        "drive.flush_and_unmount()\n",
        "drive.mount('/content/drive', force_remount=True)"
      ],
      "execution_count": 13,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Mounted at /content/drive\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "lOKg9eH_ueRn",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "12426d86-5011-4cd9-92dd-eadceded207a"
      },
      "source": [
        "#@title **Check if you correctly allocated GPU nodes**\n",
        "\n",
        "gpu_info = !nvidia-smi\n",
        "gpu_info = '\\n'.join(gpu_info)\n",
        "if gpu_info.find('failed') >= 0:\n",
        "  print('Select the Runtime > \"Change runtime type\" menu to enable a GPU accelerator, ')\n",
        "  print('and then re-execute this cell.')\n",
        "else:\n",
        "  print(gpu_info)"
      ],
      "execution_count": 4,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Tue Nov 30 22:01:10 2021       \n",
            "+-----------------------------------------------------------------------------+\n",
            "| NVIDIA-SMI 495.44       Driver Version: 460.32.03    CUDA Version: 11.2     |\n",
            "|-------------------------------+----------------------+----------------------+\n",
            "| GPU  Name        Persistence-M| Bus-Id        Disp.A | Volatile Uncorr. ECC |\n",
            "| Fan  Temp  Perf  Pwr:Usage/Cap|         Memory-Usage | GPU-Util  Compute M. |\n",
            "|                               |                      |               MIG M. |\n",
            "|===============================+======================+======================|\n",
            "|   0  Tesla K80           Off  | 00000000:00:04.0 Off |                    0 |\n",
            "| N/A   73C    P8    33W / 149W |      3MiB / 11441MiB |      0%      Default |\n",
            "|                               |                      |                  N/A |\n",
            "+-------------------------------+----------------------+----------------------+\n",
            "                                                                               \n",
            "+-----------------------------------------------------------------------------+\n",
            "| Processes:                                                                  |\n",
            "|  GPU   GI   CI        PID   Type   Process name                  GPU Memory |\n",
            "|        ID   ID                                                   Usage      |\n",
            "|=============================================================================|\n",
            "|  No running processes found                                                 |\n",
            "+-----------------------------------------------------------------------------+\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "eLX8IGZO7MIg",
        "outputId": "a08b83ab-7682-4f2d-f893-e8c63fa503dd"
      },
      "source": [
        "from simtk import unit\n",
        "from openmm import app\n",
        "\n",
        "#Lets Load in our Butane Molecule and Force Field from Our Google Drive\n",
        "PDB_file_name = 'butane.pdb'\n",
        "forcefield_file_name = 'butane.gaff2.xml' \n",
        "Google_Drive_Path = '/content/drive/MyDrive/CHEM101.6/Butane' #@param {type:\"string\"}\n",
        "workDir = Google_Drive_Path\n",
        "initial_pdb = os.path.join(workDir, str(PDB_file_name))\n",
        "force_field = os.path.join(workDir,str(forcefield_file_name))\n",
        "print(initial_pdb)\n",
        "print(force_field )\n",
        "\n",
        "pdb = mm.app.PDBFile(initial_pdb)\n",
        "forcefield = mm.app.ForceField(force_field)\n",
        "\n",
        "\n",
        "system = forcefield.createSystem(pdb.topology, nonbondedMethod=mm.app.NoCutoff, constraints=mm.app.HBonds)\n",
        "integrator = mm.LangevinIntegrator(298.15*unit.kelvin, 5.0/unit.picoseconds, 2.0*unit.femtoseconds)\n",
        "integrator.setConstraintTolerance(1e-5)\n",
        "\n",
        "platform = mm.Platform.getPlatformByName('Reference')\n",
        "simulation = app.Simulation(pdb.topology, system, integrator, platform)\n",
        "simulation.context.setPositions(pdb.positions)"
      ],
      "execution_count": 40,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "/content/drive/MyDrive/CHEM101.6/Butane/butane.pdb\n",
            "/content/drive/MyDrive/CHEM101.6/Butane/butane.gaff2.xml\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "OA1RPmp18Ocw",
        "outputId": "46e7cf7f-d554-4ac3-f305-75dcc3899226"
      },
      "source": [
        "integrator = mm.LangevinIntegrator(298.15*unit.kelvin, 5.0/unit.picoseconds, 2.0*unit.femtoseconds)\n",
        "integrator.setConstraintTolerance(1e-5)\n",
        "\n",
        "print('Minimizing...')\n",
        "\n",
        "st = simulation.context.getState(getPositions=True,getEnergy=True)\n",
        "print(F\"Potential energy before minimization is {st.getPotentialEnergy()}\")\n",
        "\n",
        "simulation.minimizeEnergy(maxIterations=100)\n",
        "\n",
        "st = simulation.context.getState(getPositions=True,getEnergy=True)\n",
        "print(F\"Potential energy after minimization is {st.getPotentialEnergy()}\")"
      ],
      "execution_count": 47,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Minimizing...\n",
            "Potential energy before minimization is 5.295784483017471 kJ/mol\n",
            "Potential energy after minimization is 5.295543508947829 kJ/mol\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "hxKf7uhQ-kBZ",
        "outputId": "0b00624d-0011-4fce-d0c0-3dc2b4c160e0"
      },
      "source": [
        "from sys import stdout\n",
        "\n",
        "print('Equilibrating...')\n",
        "\n",
        "simulation.reporters.append(app.StateDataReporter(stdout, 100, step=True, \n",
        "    potentialEnergy=True, temperature=True, separator=','))\n",
        "simulation.context.setVelocitiesToTemperature(150.0*unit.kelvin)\n",
        "simulation.step(2500)"
      ],
      "execution_count": 49,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Equilibrating...\n",
            "#\"Step\",\"Potential Energy (kJ/mole)\",\"Temperature (K)\"\n",
            "100,30.141760285407493,262.9486052648526\n",
            "200,33.8926801562416,348.09445655702\n",
            "300,55.994071653301404,366.0136405419244\n",
            "400,54.24842375179601,289.0307002468811\n",
            "500,45.2128663417995,365.3051316316242\n",
            "600,35.19999667321129,233.8858661398986\n",
            "700,26.67592490128446,340.5430402157909\n",
            "800,34.784536338777116,252.83953584933127\n",
            "900,30.047732377737628,173.8565592390809\n",
            "1000,30.07483289279336,153.08152399988532\n",
            "1100,26.858483853709018,254.63734211014173\n",
            "1200,27.910438613634035,352.15652735892314\n",
            "1300,47.71719988112596,171.70074006044825\n",
            "1400,39.81715231859009,329.2049804597984\n",
            "1500,45.99278999223017,273.9888698425713\n",
            "1600,25.956957762751934,321.19901601528915\n",
            "1700,32.68588828305849,268.7648764009242\n",
            "1800,34.12331521932133,389.27416786415273\n",
            "1900,31.00992473575137,271.2848279052134\n",
            "2000,27.340059260451387,310.7694303574131\n",
            "2100,40.6453010605359,336.72624429166484\n",
            "2200,40.39859482956306,289.1053896058646\n",
            "2300,31.508056076957637,208.38982739362834\n",
            "2400,25.859843933780933,175.04814319412694\n",
            "2500,44.02807185864983,406.68453580611697\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "G70V9fa6-s65",
        "outputId": "0de4dbcc-cc88-4f5b-85c9-ece460490695"
      },
      "source": [
        "import time as time\n",
        "\n",
        "print('Running Production...')\n",
        "\n",
        "# Begin timer\n",
        "tinit=time.time()\n",
        "\n",
        "# Clear simulation reporters\n",
        "simulation.reporters.clear()\n",
        "\n",
        "# Reinitialize simulation reporters. We do this because we want different information printed from the production run than the equilibration run.\n",
        "# output basic simulation information below every 250000 steps - (which is equal to 2 fs(250,000) = 500,000 fs = 500 ps)\n",
        "simulation.reporters.append(app.StateDataReporter(stdout, 250000, \n",
        "    step=True, time=True, potentialEnergy=True, temperature=True, \n",
        "    speed=True, separator=','))\n",
        "\n",
        "# write out a trajectory (i.e., coordinates vs. time) to a DCD\n",
        "# file every 100 steps - 0.2 ps\n",
        "simulation.reporters.append(app.DCDReporter('ethane_sim.dcd', 100))\n",
        "\n",
        "# run the simulation for 1.0x10^7 steps - 20 ns\n",
        "simulation.step(10000000)\n",
        "\n",
        "# End timer\n",
        "tfinal=time.time()\n",
        "print('Done!')\n",
        "print('Time required for simulation:', tfinal-tinit, 'seconds')"
      ],
      "execution_count": 50,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Running Production...\n",
            "#\"Step\",\"Time (ps)\",\"Potential Energy (kJ/mole)\",\"Temperature (K)\",\"Speed (ns/day)\"\n",
            "250000,500.0000000016593,39.511268730648524,317.384018666217,0\n",
            "500000,999.9999999901769,29.694501452629122,275.92529600473466,1.22e+04\n",
            "750000,1499.9999999783536,44.28588525491841,350.07384580167127,1.21e+04\n",
            "1000000,1999.9999999665301,37.28139867077346,287.0072359586417,1.21e+04\n",
            "1250000,2499.9999999547067,44.30333309964481,530.6915535111848,1.2e+04\n",
            "1500000,2999.9999999428833,32.833865583669855,338.00543482360206,1.2e+04\n",
            "1750000,3499.99999993106,47.87336295615768,347.88334359928496,1.2e+04\n",
            "2000000,3999.9999999192364,47.76379073855511,299.2020084130648,1.2e+04\n",
            "2250000,4499.9999999992715,62.58231665991362,309.9144192727793,1.2e+04\n",
            "2500000,5000.000000101135,34.40396058013606,232.95465784728395,1.2e+04\n",
            "2750000,5500.000000202998,45.63810515555039,272.25260931691014,1.2e+04\n",
            "3000000,6000.000000304862,58.92993416468104,256.1436970220182,1.2e+04\n",
            "3250000,6500.000000406725,37.18736517107332,263.9358733135043,1.2e+04\n",
            "3500000,7000.0000005085885,35.927428762263986,525.9283456407989,1.2e+04\n",
            "3750000,7500.000000610452,50.64049196271137,263.0855170897695,1.19e+04\n",
            "4000000,8000.000000712315,38.056630578583295,447.2626913344051,1.19e+04\n",
            "4250000,8500.000000814178,26.28559218882462,276.30382589718107,1.19e+04\n",
            "4500000,9000.000000916041,52.02549550776459,402.3575886861548,1.19e+04\n",
            "4750000,9500.000001017905,49.6451021308591,241.4691124864579,1.19e+04\n",
            "5000000,10000.000001119768,31.285826742062497,329.39007865550985,1.19e+04\n",
            "5250000,10500.000001221631,37.99043015334174,361.050372321356,1.19e+04\n",
            "5500000,11000.000001323495,41.06043803029211,325.5563434699779,1.19e+04\n",
            "5750000,11500.000001425358,51.63448698699891,259.9013847305428,1.19e+04\n",
            "6000000,12000.000001527222,41.75695453500834,209.81914838646946,1.19e+04\n",
            "6250000,12500.000001629085,57.70668957988845,392.73703806062,1.19e+04\n",
            "6500000,13000.000001730948,58.55277415493524,329.35516406886194,1.19e+04\n",
            "6750000,13500.000001832812,50.76141058526323,253.68499822405087,1.19e+04\n",
            "7000000,14000.000001934675,41.03491018931456,379.40491644759436,1.19e+04\n",
            "7250000,14500.000002036539,27.330402004243417,294.47729852710637,1.19e+04\n",
            "7500000,15000.000002138402,60.405396702603966,327.0692377311667,1.19e+04\n",
            "7750000,15500.000002240266,50.203611313443766,349.9703238930527,1.19e+04\n",
            "8000000,16000.000002342129,24.708825108544104,238.30986903077533,1.19e+04\n",
            "8250000,16500.00000244399,36.70353298464422,201.96461576184961,1.19e+04\n",
            "8500000,17000.000002545854,29.58115404180868,324.9613078703551,1.19e+04\n",
            "8750000,17500.000002647717,33.6462584912426,206.14652873908392,1.19e+04\n",
            "9000000,18000.00000274958,29.273559785829068,269.3325550328233,1.19e+04\n",
            "9250000,18500.000002851444,45.33114508090459,381.21263775821245,1.19e+04\n",
            "9500000,19000.000002953308,52.11648890617858,400.3599203471326,1.19e+04\n",
            "9750000,19500.00000305517,60.524260858426096,310.184829471833,1.19e+04\n",
            "10000000,20000.000003157034,67.67872985302998,266.39756549713763,1.19e+04\n",
            "Done!\n",
            "Time required for simulation: 144.80857491493225 seconds\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "01YETJ-X--5U",
        "outputId": "bb068a12-466d-49f0-9797-5045d3faa08f"
      },
      "source": [
        "!pip install nglview 2>&1 1>/dev/null\n",
        "!conda install -c conda-forge mdtraj  --yes 2>&1 1>/dev/null"
      ],
      "execution_count": 52,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "\u001b[33mWARNING: Running pip as the 'root' user can result in broken permissions and conflicting behaviour with the system package manager. It is recommended to use a virtual environment instead: https://pip.pypa.io/warnings/venv\u001b[0m\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "S7txpJFO_xSQ",
        "outputId": "f3e63f04-67ee-44cc-feb7-7f629c591847"
      },
      "source": [
        "import mdtraj as md\n",
        "traj = md.load('ethane_sim.dcd', top=initial_pdb)\n"
      ],
      "execution_count": 55,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<mdtraj.Trajectory with 100000 frames, 14 atoms, 1 residues, without unitcells at 0x7fea7880b8d0>"
            ]
          },
          "metadata": {},
          "execution_count": 55
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 317,
          "referenced_widgets": [
            "2f87206d8a7240a8bc28bedb46ffe524",
            "1dbca630db2543ff9784f6f91f80e2cd",
            "8fe24a18868c438187dc53ef24ac0c47",
            "ca93df9ece0849f6a858e1ef75387970",
            "f79b90fb27da4c9eb6ce6b8b06c52e46",
            "c344760dfaf34cb3afd6b03ec8b8eead",
            "a172355f75e24fc4a2b371239faf6134",
            "f41de2ecc4304f09b4d7af6df86ef396",
            "da6f7c12f92a46b7b3aba04ba25b31e6",
            "c19adbbaed054fd9a630835c7b8c0051",
            "6e59172c44c645e8b11cbdebf38ee024",
            "d0d7174a01664ddc96f282cc68e53ad0",
            "33270d05de3a405c9e1c8f3d97f0e2c7"
          ]
        },
        "id": "o62FhIWVAWAT",
        "outputId": "e50a3f7a-f4ec-46ec-ed9f-e7b27c2f6dfd"
      },
      "source": [
        "import ipywidgets\n",
        "from ipywidgets import interact, fixed\n",
        "import warnings\n",
        "warnings.filterwarnings('ignore')\n",
        "from google.colab import output\n",
        "output.enable_custom_widget_manager()\n",
        "\n",
        "import nglview as ngl\n",
        "\n",
        "visualize = ngl.show_mdtraj(traj)\n",
        "visualize"
      ],
      "execution_count": 58,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "application/vnd.jupyter.widget-view+json": {
              "model_id": "2f87206d8a7240a8bc28bedb46ffe524",
              "version_minor": 0,
              "version_major": 2
            },
            "text/plain": [
              "NGLWidget(max_frame=99999)"
            ]
          },
          "metadata": {
            "application/vnd.jupyter.widget-view+json": {
              "colab": {
                "custom_widget_manager": {
                  "url": "https://ssl.gstatic.com/colaboratory-static/widgets/colab-cdn-widget-manager/a8874ba6619b6106/manager.min.js"
                }
              }
            }
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 483
        },
        "id": "qWG80bj3BE1s",
        "outputId": "f34928bf-3bab-4f3a-9c40-ce3947cba336"
      },
      "source": [
        "atoms, bonds = traj.topology.to_dataframe()\n",
        "atoms"
      ],
      "execution_count": 59,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/html": [
              "<div>\n",
              "<style scoped>\n",
              "    .dataframe tbody tr th:only-of-type {\n",
              "        vertical-align: middle;\n",
              "    }\n",
              "\n",
              "    .dataframe tbody tr th {\n",
              "        vertical-align: top;\n",
              "    }\n",
              "\n",
              "    .dataframe thead th {\n",
              "        text-align: right;\n",
              "    }\n",
              "</style>\n",
              "<table border=\"1\" class=\"dataframe\">\n",
              "  <thead>\n",
              "    <tr style=\"text-align: right;\">\n",
              "      <th></th>\n",
              "      <th>serial</th>\n",
              "      <th>name</th>\n",
              "      <th>element</th>\n",
              "      <th>resSeq</th>\n",
              "      <th>resName</th>\n",
              "      <th>chainID</th>\n",
              "      <th>segmentID</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>0</th>\n",
              "      <td>1</td>\n",
              "      <td>C1</td>\n",
              "      <td>C</td>\n",
              "      <td>1</td>\n",
              "      <td>NBU</td>\n",
              "      <td>0</td>\n",
              "      <td></td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>2</td>\n",
              "      <td>H11</td>\n",
              "      <td>H</td>\n",
              "      <td>1</td>\n",
              "      <td>NBU</td>\n",
              "      <td>0</td>\n",
              "      <td></td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2</th>\n",
              "      <td>3</td>\n",
              "      <td>H12</td>\n",
              "      <td>H</td>\n",
              "      <td>1</td>\n",
              "      <td>NBU</td>\n",
              "      <td>0</td>\n",
              "      <td></td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>4</td>\n",
              "      <td>H13</td>\n",
              "      <td>H</td>\n",
              "      <td>1</td>\n",
              "      <td>NBU</td>\n",
              "      <td>0</td>\n",
              "      <td></td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>4</th>\n",
              "      <td>5</td>\n",
              "      <td>C2</td>\n",
              "      <td>C</td>\n",
              "      <td>1</td>\n",
              "      <td>NBU</td>\n",
              "      <td>0</td>\n",
              "      <td></td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>5</th>\n",
              "      <td>6</td>\n",
              "      <td>H21</td>\n",
              "      <td>H</td>\n",
              "      <td>1</td>\n",
              "      <td>NBU</td>\n",
              "      <td>0</td>\n",
              "      <td></td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>6</th>\n",
              "      <td>7</td>\n",
              "      <td>H22</td>\n",
              "      <td>H</td>\n",
              "      <td>1</td>\n",
              "      <td>NBU</td>\n",
              "      <td>0</td>\n",
              "      <td></td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>7</th>\n",
              "      <td>8</td>\n",
              "      <td>C3</td>\n",
              "      <td>C</td>\n",
              "      <td>1</td>\n",
              "      <td>NBU</td>\n",
              "      <td>0</td>\n",
              "      <td></td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>8</th>\n",
              "      <td>9</td>\n",
              "      <td>H31</td>\n",
              "      <td>H</td>\n",
              "      <td>1</td>\n",
              "      <td>NBU</td>\n",
              "      <td>0</td>\n",
              "      <td></td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>9</th>\n",
              "      <td>10</td>\n",
              "      <td>H32</td>\n",
              "      <td>H</td>\n",
              "      <td>1</td>\n",
              "      <td>NBU</td>\n",
              "      <td>0</td>\n",
              "      <td></td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>10</th>\n",
              "      <td>11</td>\n",
              "      <td>C4</td>\n",
              "      <td>C</td>\n",
              "      <td>1</td>\n",
              "      <td>NBU</td>\n",
              "      <td>0</td>\n",
              "      <td></td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>11</th>\n",
              "      <td>12</td>\n",
              "      <td>H41</td>\n",
              "      <td>H</td>\n",
              "      <td>1</td>\n",
              "      <td>NBU</td>\n",
              "      <td>0</td>\n",
              "      <td></td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>12</th>\n",
              "      <td>13</td>\n",
              "      <td>H42</td>\n",
              "      <td>H</td>\n",
              "      <td>1</td>\n",
              "      <td>NBU</td>\n",
              "      <td>0</td>\n",
              "      <td></td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>13</th>\n",
              "      <td>14</td>\n",
              "      <td>H43</td>\n",
              "      <td>H</td>\n",
              "      <td>1</td>\n",
              "      <td>NBU</td>\n",
              "      <td>0</td>\n",
              "      <td></td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>"
            ],
            "text/plain": [
              "    serial name element  resSeq resName  chainID segmentID\n",
              "0        1   C1       C       1     NBU        0          \n",
              "1        2  H11       H       1     NBU        0          \n",
              "2        3  H12       H       1     NBU        0          \n",
              "3        4  H13       H       1     NBU        0          \n",
              "4        5   C2       C       1     NBU        0          \n",
              "5        6  H21       H       1     NBU        0          \n",
              "6        7  H22       H       1     NBU        0          \n",
              "7        8   C3       C       1     NBU        0          \n",
              "8        9  H31       H       1     NBU        0          \n",
              "9       10  H32       H       1     NBU        0          \n",
              "10      11   C4       C       1     NBU        0          \n",
              "11      12  H41       H       1     NBU        0          \n",
              "12      13  H42       H       1     NBU        0          \n",
              "13      14  H43       H       1     NBU        0          "
            ]
          },
          "metadata": {},
          "execution_count": 59
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 295
        },
        "id": "8IkYIlYkBLeP",
        "outputId": "26651f37-e370-4133-86c3-056ca61800bc"
      },
      "source": [
        "bond_indices = [4, 7] # atoms to define the bond length\n",
        "bond_length = md.compute_distances(traj, [bond_indices])\n",
        "\n",
        "bondcounts, binedges, otherstuff = plt.hist(bond_length, bins=120)\n",
        "plt.title('C-C bond length histogram')\n",
        "plt.xlabel('Bond length (nm)')\n",
        "plt.ylabel('Counts')\n",
        "plt.show()"
      ],
      "execution_count": 70,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 295
        },
        "id": "o2fyETQ3DNcJ",
        "outputId": "ea55283f-952c-4101-a6cd-96487d99a91c"
      },
      "source": [
        "kB = 8.31446/1000 # Boltzmann constant in kJ/mol\n",
        "Temp = 298.15 # simulation temperature\n",
        "bondcounts[bondcounts==0] = 0.1 # get rid of any bins with 0 counts/infinite energy\n",
        "pmf = -kB*Temp*np.log(bondcounts) # W(x) = -kT*ln[p(x)] = -kT*ln[n(x)] + C\n",
        "pmf = pmf - np.min(pmf) # subtract off minimum value so that energies start from 0\n",
        "\n",
        "bincenters = (binedges[1:] + binedges[:-1])/2 # compute centers of histogram bins\n",
        "\n",
        "plt.plot(bincenters, pmf)\n",
        "plt.xlabel('Bond length (nm)')\n",
        "plt.ylabel('Relative free energy (kJ/mol)')\n",
        "plt.title('C-C bond length pmf')\n",
        "plt.show()"
      ],
      "execution_count": 72,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 295
        },
        "id": "ukZa6k5uChho",
        "outputId": "691cefdf-1458-49ae-e5eb-d42a0bff2cdd"
      },
      "source": [
        "bond_indices = [4, 5] # many possibilities!\n",
        "bondlength = md.compute_distances(traj, [bond_indices])\n",
        "\n",
        "lengthcounts, binedges, otherstuff = plt.hist(bondlength, bins=100)\n",
        "plt.title('C-H bond length')\n",
        "plt.xlabel('Bond length (nm)')\n",
        "plt.ylabel('Counts')\n",
        "plt.show()"
      ],
      "execution_count": 78,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 295
        },
        "id": "vHKuVS7ADa8z",
        "outputId": "ad47b4de-75d5-4dee-d8c2-f1a2699eb23f"
      },
      "source": [
        "kB = 8.31446/1000 # Boltzmann constant in kJ/mol\n",
        "Temp = 298.15 # simulation temperature\n",
        "lengthcounts[lengthcounts==0] = 0.1 # get rid of any bins with 0 counts/infinite energy\n",
        "pmf = -kB*Temp*np.log(lengthcounts) # W(x) = -kT*ln[p(x)] = -kT*ln[n(x)] + C\n",
        "pmf = pmf - np.min(pmf) # subtract off minimum value so that energies start from 0\n",
        "\n",
        "bincenters = (binedges[1:] + binedges[:-1])/2 # compute centers of histogram bins\n",
        "\n",
        "plt.plot(bincenters, pmf)\n",
        "plt.xlabel('Bond length (nm)')\n",
        "plt.ylabel('Relative free energy (kJ/mol)')\n",
        "plt.title('C-H bond length pmf')\n",
        "plt.show()"
      ],
      "execution_count": 79,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 299
        },
        "id": "T5oNvZGHBfs4",
        "outputId": "f4cd44cb-3bf3-4e29-f9ec-5e543c6a3923"
      },
      "source": [
        "phi_indices = [0, 4, 7, 10] # atoms to define the torsion angle\n",
        "phi = md.compute_dihedrals(traj, [phi_indices])\n",
        "\n",
        "phicounts, binedges, otherstuff = plt.hist(phi, bins=90) # create a histogram with 90 bins\n",
        "plt.title('H-C-C-H torsion angle')\n",
        "plt.xlabel(r'$\\phi$ (rad)')\n",
        "plt.ylabel('Counts')\n",
        "plt.show()"
      ],
      "execution_count": 63,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 299
        },
        "id": "XTqsagjkB9XZ",
        "outputId": "f98bc37f-5f93-4f2a-c3bf-cf1209b4281a"
      },
      "source": [
        "kB = 8.31446/1000 # Boltzmann constant in kJ/mol\n",
        "Temp = 298.15 # simulation temperature\n",
        "phicounts[phicounts==0] = 0.1 # get rid of any bins with 0 counts/infinite energy\n",
        "pmf = -kB*Temp*np.log(phicounts) # W(x) = -kT*ln[p(x)] = -kT*ln[n(x)] + C\n",
        "pmf = pmf - np.min(pmf) # subtract off minimum value so that energies start from 0\n",
        "\n",
        "bincenters = (binedges[1:] + binedges[:-1])/2 # compute centers of histogram bins\n",
        "\n",
        "plt.plot(bincenters, pmf)\n",
        "plt.title('H-C-C-H torsion pmf')\n",
        "plt.xlabel(r'$\\phi$ (rad)')\n",
        "plt.ylabel('Relative free energy (kJ/mol)')\n",
        "plt.show()"
      ],
      "execution_count": 64,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 295
        },
        "id": "7m47X3aGCHL_",
        "outputId": "b1bac94a-fc45-4a0d-8cc4-e9e94a51c7d5"
      },
      "source": [
        "angle_indices = [0, 4, 7] # or could do [4, 7, 10]\n",
        "bondangle = md.compute_angles(traj, [angle_indices])\n",
        "\n",
        "anglecounts, binedges, otherstuff = plt.hist(bondangle, bins=100)\n",
        "plt.title('C-C-C bond angle')\n",
        "plt.xlabel('Bond angle (rad)')\n",
        "plt.ylabel('Counts')\n",
        "plt.show()"
      ],
      "execution_count": 66,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 279
        },
        "id": "HlyahiMcCa3e",
        "outputId": "de006418-a006-4ee3-b8dd-485772df079d"
      },
      "source": [
        "anglecounts[anglecounts==0] = 0.1\n",
        "pmf = -kB*Temp*np.log(anglecounts)\n",
        "pmf = pmf - np.min(pmf)\n",
        "\n",
        "bincenters = (binedges[1:] + binedges[:-1])/2\n",
        "\n",
        "\n",
        "plt.plot(bincenters, pmf)\n",
        "plt.xlabel('Bond angle (rad)')\n",
        "plt.ylabel('Relative free energy (kJ/mol)')\n",
        "plt.show()"
      ],
      "execution_count": 67,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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6HvhoA/+47AjWFZZTXd/U3OZh9IBEG/EbY1qpbWhiXWE5Vx8zbL/HfnHqaCa2WCd3fEb3r5nbVR0mflW9SETGAZcBVwMDcS/BuA6YB/xRVWt7JEo/6p8Uw+xZI/jr/A0sySth5fYygOY2D6PTk3hhcT5NLiU8rOOFkY0xoWPFtlIampRp7bSDmZCZ7JcF0rtTp6eaVXUt8D89FItjrj1uGC8u3srv31tLRnIsg/rEMiA5BoAxAxOpbXCxtaS61YUaxpjQleNZ56OjdjCBLrDOODgkLiqC208fzcrtZXy4dmerRVvGDHCvK59baHV+Y4zbkrwSRvZPCNo+Xpb4Pc6fksnEzGRcSqs2ziP7J9qFXMaEmDeXbaeovP1KdpNLWZq/l+ys9rv+BgNL/B5hYcI9545nSN84Zo1Ka94eGxXOsH7xNpffmBBRVF7LbS+v4Lmv89t9fMOuCipqG5nWzjofweKAiV9E3hCRszwzfHq1I4b2YeHtJzCoT1yr7e6ZPVbqMSYUrPMM8lo2W2spx9Puve063sHEl2T+D+BSYKOI3Csio/0cU8AZPSCR/JLqVmtpGmN6J+91O/klHST+/L2kJ0UzqE9sT4bVrXzp1TNfVS8DDgfygPki8pWIXCUikf4OMBCMGZCEKmzcVXngnY0xQc17Pm/rnvZX58vJc9f32y7eFEx8Kt+ISD/gSuAnwDLgb7g/CD7yW2QBZOxA98yetTazx5heL7fQnfj3VjdQXtvQ6rGC0hoKSmuYFqTTOL18qfG/CXwOxAHnqOq5qvqyqt4MJPg7wEAwpG8ciTERrCooczoUY4wfNTa52FRcydB+7vN8W9vU+b31/WCe0QO+jfj/rqrjVPX/VLWw5QOqmu2nuAKKiDBpUDIrt5c6HYoxxo/y9lRR3+ji1HHpzfdbysnbS3xUePP1PcHKl8TfR0S+1+Z2koj093t0AWTSoBRyCyuobWhyOhRjjJ+s85R5Th0/AID8PW1btpdw+NA+RARYt82D5cvqANcA04FPPfePx920bZiI/E5Vn/VTbAFl8qBkGl1K7s4KpgxOcTocY4wfrN9ZQXiY+xt+akJ0q1JPVV0jG3ZVNH8oBDNfPrYigbGqeqGqXgiMAxT3Eoy/8mdwgWTiIHeyt3KPMb1X7s4KhqfGEx0RztB+ceSX7Cv1rC4ow6UwZXBgN2DzhS+Jf5Cq7mpxvwgYrKolQEMHz0FE5opIkYisbrHtHhEpEJHlntuZhx56z8pIjiE1IYoV2+wErzG9Ve7OckZ76vdD+8a1GvF7O/dOGhT83/h9Sfyfich7InKFiFyBuz//ZyISD3Q2/H0aOL2d7X9V1Sme27yDD9kZIsLEzGRWFdiI35jeqLKuke17a5pP3A7pF0dheW3zeb3l20vJTIklNSHayTC7hS8XcP0U+CcwxXN7BrhRVatU9YROnrcQKOmuQAPBpEEpbCqqpKrOruA1prfx9uMaPcC9smxWv3hUYfte96h/xbbSXnN+r9PELyLhIpKrqq+r6m2e22uqqp097wBuEpGVnlJQh1dBiMh1IpIjIjnFxcVdeLvuM3mwu3vnmh12IZcxvY038bcc8YN7Zs+eyjq2761h0qDgr+/DARK/qjYB60VkSDe936PACNzfHAqBv3Ty3nNUNVtVs9PS0jrarUdNzLQTvMb0Vrk7y0mIjmjuwTO0777E763vT+4lI35fpnP2AdaIyGKg+RS3qp57sG/W8iSxiDwBvHewr+GktMRoMpJjWLHdTvAa09vk7qxgVHpCcw+evvFRJERHsLWkmrKaBsKEVmvpBjNfEv9d3fVmIjKwxdW/FwCrO9s/EE0clMwqG/Eb06uoKut3VnDmxIHN20SEIX3jyNtThQCH9U8gPtqXlBn4DngUqrpARIYCI1V1vojEAeEHep6IvIj7Yq9UEdkO3A0cLyJTcF8HkAdc34XYHTFpUAr/WbOLsuoGkuNCojmpMb3ex+uKKKtpYFxGUqvtWalx5BZWUFrTwEljek+zggMmfhG5FrgO6Iu7Pp8JPAac1NnzVPWSdjY/dQgxBpTJ3gu5Cko5dmRgnHswxhy65dtKufnFZUzMTOZ7UzNbPTakbzzzVu0EYFIvqe+Db/P4bwRmAuUAqroR6D0ffQdp4qBkIsOFl5ZsczoUY0wX5e2u4uqnl5CWGM3cK6ftV8rxdukEmNILLtzy8iXx16lqvfeOiETgLtWEpOTYSG45aSTvryxk3qrCAz/BGBOQKusaueKfiwH419VHkpa4/4VZ3pk9URFhzVf09ga+JP4FInInECsipwCvAu/6N6zANnvWCCZmJvPrt1azu7LO6XCMMYfg43W7yN9TzYMXT2FYany7+wz1bB83MImoiODuyNmSL0dyB1AMrMJ9MnYe8Gt/BhXoIsLD+MsPJlNZ28hdb62ma9ezGWOc8Nn6YvrGRzHzsNQO9xmQFENCdATZQb7iVlu+zOpxAU94bsZjVHoit50yivs+yOWD1Ts5o8U0MGNMYGtyKQs2FDNrVBrhYR2vnRseJrx14wzSk2J6MDr/82XpxZki8pGIbBCRzSKyRUQ290Rwge7aY4cxLDWeZxblOx2KMeYgrNxeSklVPcePPvDMvMP6J5IY07umbvtyNcJTwG24F1+x5adaiAgP4/wpmTz48QZ2lNaQkRLrdEjGGB98ur6YMIHjQnRKti81/jJV/beqFqnqHu/N75EFifOnZqAK76zY4XQoxhgffba+iKlD+tAnPsrpUBzhS+L/VET+LCLTReRw783vkQWJof3iOXxICm8tK3A6FGOMD4or6li5vYwTfCjz9Fa+lHqO8vzMbrFNgRO7P5zgdMHUTO56ew3rCssZOzDpwE8wxjhmwQZ3m/cTelELhoPly6yeDhdbMW5nTcrgt++u5a3lBZb4jQlwn64von9iNONC+P+qL7N60kXkKRH5t+f+OBG5xv+hBY++8VHMGpXG28t24HLZnH5jAlVDk4uFG4o5YXT/5vbLociXGv/TwH+ADM/9DcCt/gooWJ0/NZOd5bV8vcXOexsTiFSVhz7ZREVtIyeMCd36PviW+FNV9RXABaCqjdi0zv2cPDadhOgIXl9qJ3mNCTQ19U3c9OIy/v7xRi6YmsnJY9OdDslRviT+KhHph6cxm4gcDdgSVG3ERoVz7pQM3l+1g7KaBqfDMcZ4lFTVc9HjXzFvVSF3nDGGB34wmYjw3tN351D4cvT/BbwDjBCRL4FngJv9GlWQuvTIIdQ2uGxqpzEB5MH5G8gtrODJH2cze9aIkK7tex0w8avqt8AsYAbuJm3jVXWlvwMLRhMyk5mYmcyLi7da4zZjAkBBaQ0vLd7GRdmDOSnEyzst+fR9R1UbVXWNqq5WVatjdOLSo4aQu7OCZdtsXV5jnPbIp5sAuOnEwxyOJLCEdqHLD86ZnEF8VDgvfLPV6VCMCWnbSqp5Zck2fnjkYDKtj1Yrlvi7WUJ0BOdOyeS9lXaS1xgnPfTJRsLChJ8eb6P9tny5gEtE5Eci8hvP/SEicqT/QwtedpLXGGdt2FXB698WcNlRQxiQ3Lt66XcHX0b8/wCmA5d47lcAj/gtol5g4qBkDh+SwkOfbKSkqv7ATzDGdAtV5dWcbVzwyJckxkRww6wRTocUkHxJ/Eep6o1ALYCq7gVCs5fpQfjjBRMpq2ngN2+vdjoUY0JCcUUdN77wLb98bSUTMpN5/2fH0r+XrZzVXXzpztkgIuHsu4ArDc9VvKZjYwcmcctJI7n/ww2cMaGQsybZ0ozG+MOO0hrmLNzMi4u34lLlV6eP4brjhne6pGKo8yXx/x14E0gXkT8C3yfEF1v31exZI/jPml3c9fZqjhrel9SEaKdDMqZXeWtZAb98bQWq7vboNxw/guFpCU6HFfB8uYDreeB24H+BQuB8VX3V34H1BhHhYfzlB5OprG3krres5GNMd2pyKX/5aD2jByTy2S+P588XTbak7yNfp3OmAtWq+jCwW0SG+TGmXmVUeiK3nDySf6/eyQerdzodjjG9xoINRWwrqWH2rBEM6hPndDhBxZfpnHcDvwL+27MpEnjOn0H1NtcdN5xxA5P4zdurbW6/Md3kmUX59E+M5rTxA5wOJej4MuK/ADgXqAJQ1R1Aoj+D6m0iw8O478JJ7K6s4//mrXM6HGOCXv6eKhZsKOaSI4cQGeKdNg+FL39i9eruOOad1RPvywuLyFwRKRKR1S229RWRj0Rko+dnn0MLO/hMHJTMtccO56Ul2/jqu91Oh2NMUHv+m62EiXDJkUOcDiUo+ZL4XxGRx4EUEbkWmA884cPzngZOb7PtDuBjVR0JfOy5HzJuPXkUQ/vFcetLy9m4q8LpcIwJSrUNTbySs43TxqfbVbmHqNPEL+7G1S8DrwGvA6OB36jqQwd6YVVdCJS02Xwe8C/P7/8Czj/YgINZbFQ4T/w4GwUunvM1qwtsPRtjDtY7K3ZQWt3A5UdnOR1K0Oo08XtKPPNU9SNV/aWq/kJVP+rC+6WraqHn951Ahw2yReQ6EckRkZzi4uIuvGVgGZWeyCvXTycmIoxLnviapfl7nQ7JmKChqsz9Yguj0hM4enhfp8MJWr6Uer4VkWnd/cYtzxt08PgcVc1W1ey0tN61MPKw1HhevWEG/eKjuOSJr3l2UZ4t3GKMDxZu3E3uzgp+cuxwW0mrC3zq1QMsEpHvRGSliKwSkUNdgWuXiAwE8PwsOsTXCXqZKbG8fsMMZozox11vr+GG576lrNqmehrTmTkLvyM9KZrzpmQ4HUpQ6zDxt7hI6zRgBHAicA5wtufnoXgHuMLz+xXA24f4Or1Cv4Ro5l4xjTvPHMP8dbu44B9fUl3f6HRYxgSk1QVlfLlpD1fNHEZ0RLjT4QS1zkb8r3l+zlXV/La3A72wiLwILAJGi8h2EbkGuBc4RUQ2Aid77oe0sDDhuuNG8M+rprF5dxUPzt/odEjGBKTHF24mITqCS4+yKZxd1VmTtjARuRMYJSL/1fZBVX2gsxdW1Us6eOikg4gvZBw7Mo0fThvMU19s4bwpGYzPSHY6JGMCxraSauatKuSaY4aRFBPpdDhBr7PE/0Pc0y0jsCt1e8QdZ7hLPne+uZo3bphhbWVNSHvo4418nOs+Dbinqg4BrpqZ5WhMvUWHiV9V1wP3ichKVf13D8YUslLiorjr7HHc8tJynv8mnx9Pz3I6JGMcUVhWw98+3siw1HgGpsSSFBvJFdOzGJhsi6Z3hwP247ek37POnZzBa0u386cP1nPa+AGk2wpCJgT966t8XKrMvXIag/ta583uZt2NAoyI8PvzJlDf5OIP71tDNxN6quoaeeGbfM6YMNCSvp9Y4g9AWanx/PT4Eby7YgdfbLSGbia0vLZ0O+W1jVx9jC374S++9OOPE5G7ROQJz/2RInK2/0MLbbNnjWBovzh+8/Zq6hqbnA7HmB7R5FL++eUWpg5J4YihIdO8t8f5MuL/J1AHTPfcLwD+4LeIDAAxkeH87rwJbN5dxZwFm50Ox5ge8fG6XeTtqeYaG+37lS+Jf4Sq/gloAFDVasDmGfaAWaPSOGviQB7+dBPbSqqdDscYv6prbOKRTzeRmRLL6baqll/5tBCLiMSybyGWEbi/AZge8OuzxxImwr3/znU6FGP8xuVSfv7KClZsL+OOM8YQYatq+ZUvf7r3AB8Ag0XkedwLqNzuz6DMPgOTY5k9awTvryrkm817nA7HGL/447x1vLeykDvOGMM5k60Bm78dMPGr6ofA94ArgReBbFX9zL9hmZauO244Gckx/PbdtTS5rH2z6V2e/HwzT32xhStnZHH9ccOdDick+DKr513gVOAzVX1PVW1+YQ+LjQrnjjPHsrawnFdztjkdjjHdpriijvs+yOW08en85uxx1mO/h/hS6rkfOBZYKyKvicj3RcQuJ+1h50waSPbQPtz/4XrKa61vv+kdXlq8lYYm5VenjyHMelP1GF9KPQtU9afAcOBx4AeE8AIqThER7jl3PCVV9fz5g/VOh2NMlzU2uXhh8VaOHZnK8LQEp8MJKT6dOvfM6rkQmA1MY9+C6aYHTchM5ooZWTz3TT7fbrW1ek1wm7+uiMKyWi4/eqjToYQcX2r8rwDrcK/A9TDueVsSRx0AABYDSURBVP03+zsw076fnzqa9MQY7nxjFQ1NLqfDMeaQPft1HhnJMZw4pr/ToYQcX0b8T+FO9rNV9VNVtWzjoIToCH573nhyd1bw1BdbnA7HmEOyqaiSLzft4bKjh9qcfQd02JZZRE5U1U+AeOC8tmfbVfUNP8dmOnDa+AGcOi6dB+dv4KyJ1sHQBJ/nvs4nMly4eNpgp0MJSZ191M7y/DynnZs1aXPYPeeOJ0yE37671ulQjDkoG3dV8NrS7Zw5cSCpCdFOhxOSOluB627Pr79T1VY1BRGxDkoOy0iJ5eYTR3LfB7l8mlvECVYnNUFg+95qLn9qMbFR4fzi1NFOhxOyfCmuvd7Otte6OxBz8K45ZhjD0+K559011DZY62YT2HZX1nH5U4uprm/kmauPtBKlgzpM/CIyRkQuBJJF5HstblcCdgFXAIiKCOO3544nf081cxZa62YTuEqq6rli7mIKy2qYe+U0xg5McjqkkNbZmrujcdfyU3DX9b0qgGv9GZTx3bEj0zhz4gAe+XQTp45PZ8wA+w9lAsu2kmqumLuYgtIaHr/8CLKz+jodUsgT1c6bfonIdFVd1EPxtCs7O1tzcnKcDCGg7Sit4dyHv6SmvpH7L5rMGRMHOh2SMQCs3VHOFf9cTF1DE09dOY1plvR7lIgsVdXsttt9qfEvE5EbReQfIjLXe/NDjOYQZaTE8t7NxzAyPZEbnv+W+z7ItS6exnGfri/i4scXEREmvHbDDEv6AcSXxP8sMAA4DVgADMJd7jEBZEByDC9ffzSXHjWERz/7jivmLmZPpa2XY3qeqvLEws1c8/QSBveN442fzmBUeqLTYZkWfEn8h6nqXUCVqv4LOAs4yr9hmUMRHRHO/14wkT9dOInFeSWc/dAX1tPH9Ki6xiZ+/uoK/jhvHWdMGMhrN0xnYHKs02GZNnxJ/N4ewKUiMgFIBmzSeAD7wbTBvHHDDCLChYsfX8S8VYVOh2RCQE19E9c+s5Q3vi3gtpNH8fClU4mL6mz+iHGKL4l/joj0Ae4C3gHWAn/ya1SmyyZkJvPeTccyMTOZn7+ygg27rDpn/KeitoEr5i7m843F/OnCSdxy8khbVCWAHXBWj1/eVCQP93mCJqCxvbPOLdmsnkO3q7yWs/7+OUmxkbx940wSYyKdDsn0MmXVDVw+9xvW7ijnrxdPsTVzA0hHs3o6a9L2X529oKo+0MWYTrBlHP0vPSmGhy45nB899Q2/en0lj1x6uI3ETLepbWjimn8tIbewgscvP4KTxqY7HZLxQWelnsQD3EyQmD6iH7efNpp5q3Zy/bNLmb92F/WN1l3bdE2TS/nZi8tYunUvD1w82ZJ+EOmsSdtv/fi+CnwoIgo8rqpz/PheBrjuuOGU1zbwwjdb+XDtLpJjI/mfM8fyA2uLaw6BqnL3O6v5cO0u7j5nHGdPsvJOMPFlBa5RIvKxiKz23J8kIr/u4vseo6qHA2cAN4rIce2873UikiMiOcXFxV18OyMi/PK0MSz+n5P555XTGNk/gV+/tZqNdtLXHKTKukZ+/uoKnvt6K9fPGs5VM61Zb7DxZVbPE8B/45nWqaorgR925U1VtcDzswh4EziynX3mqGq2qmanpaV15e1MC5HhYZwwpj+P/ugI4qPD+cVrK2m0JRyNj5ZvK+Wsv3/OW8sKuOWkkfzqtDFOh2QOgS+JP05VF7fZ1niobygi8SKS6P0dOBVYfaivZw5NWmI0vz1vAiu2lfKkLeFofPD28gIufPQrGpuUl6+fzm2njCIszCYKBCNfEv9uERmBuy6PiHwf6MoVQenAFyKyAlgMvK+qH3Th9cwhOmfSQE4fP4AHPtrApiIr+ZiOrdlRxu2vreSIIX2Yd8ux1ncnyPmS+G8EHgfGiEgBcCsw+1DfUFU3q+pkz228qv7xUF/LdI2I8PvzJxAfFc5NLyyjsu6Qv8iZXqy0up7Zzy2lT1wUj1x2OMmxdi1IsDtg4vck6pOBNGAM7rV4j/F3YKZnpCVG8/dLprKxqJKbXvjW6v2mlSaXcstLy9lZVss/fnQ4aYm2Rm5v0NkKXEki8t8i8rCInAJUA1cAm4Af9FSAxv+OHZnGH86fwGfri7nn3TU4cTW3CTxFFbXc/OK3LNhQzD3njufwIX2cDsl0k846KD0L7AUW4V5x638AAS5Q1eU9EJvpQZccOYT8PdU8tuA7BvWJY/asEU6HZBzicikvLN7KfR/kUtfg4penjebSI4c4HZbpRp0l/uGqOhFARJ7EfUJ3iKrW9khkpsfdftpotu+t5t5/51Lb0MQtJ1mjrVBTXd/Ijc9/y6fri5kxoh9/OH8Cw9MSnA7LdLPOEr+3HTOq2iQi2y3p925hYcKDF08hNjKcB+dvZG9VPXefM96m7IWI0up6rn56Ccu3lfK788Zz+dFD7YO/l+os8U8WkXLP7wLEeu4LoKpqq3r3QhHhYfzp+5NIiYvkic+3sLuqnnu/N9G6evZyO8tq+fHcb8jbXc0/Ljuc0yfYus29WWe9esJ7MhATOESEO88cS2pCNPd9kMvK7aU8ePEUjhhqc7d7o20l1Vz65NfsrWrg6aunMWNEqtMhGT/zZR6/CUEiwvWzRvDq7OkAXPTYIh7+ZKPDUZnu9l1xJRc9toiK2kZeuPYoS/ohwhK/6dQRQ/sy72fHctakDO7/cAMvL9nqdEimm6wuKOPixxfR6HLx0nVHM2lQitMhmR5iC2KaA0qMieTBi6dQWl3PXW+tYWR6os3pDmI5eSU8vnAz89ftIj0xhuevPYoRNnMnpNiI3/gkPEx46JKpDEiOYfazSykqtwlewaausYmf/CuH7z+2iCV5Jdx8wmG8/7NjLOmHIBvxG5+lxEUx58dHcMEjX/Gjp77hnEkZTB6cwpQhKSTZrJ+A1uRSbn1pOfPX7eKXp43mqplZxEXZf/9QZX/z5qCMGZDEw5dO5X/nreMvH20AIDE6gldvmM6YATbDNxCpKr9+axX/Xr2TX581lp8cO9zpkIzDJBj6smRnZ2tOTo7TYZg2ymsbWLGtlP96ZQWJ0RG8fdNMm+8fYFwu5b4Pcnl84WZuPGEEv7SFU0KKiCxV1ey2263Gbw5ZUkwkx45M46FLppK3p4o73lhlDd4CSFlNA9c9m8PjCzdz2VFD+MWpo50OyQQIS/ymy44e3o9fnDaa91cW8syifKfDMcDaHeWc+/AX7o6r54zjD+dPsPYLppnV+E23mH3cCJZsKeH3762ltLqB2ccPJzrCLv7uaasLypizcDPvryokNSGKl68/2q64NvuxxG+6RViY8OAPp3Lnm6v46/wNvL2igD+cN4HpI/rZSNPPVJUFG4p54vPNfLlpDwnREVw9M4vrZ40gNcEWTjH7s5O7ptt9tr6Iu95ezbaSGgb1iWXWqDROGN2fE8f0t06f3UhVeWt5AY99tpn1uyoYkBTDVTOzuOSoITa91gAdn9y1xG/8oqa+iTeWbefT3GK++m431fVNHD86jb9dPJXkOEtKXdXQ5OLON1bx6tLtjBmQyLXHDuecyRlERdhpO7OPJX7jmPpGFy8t2crv31vLwORYHvvREYzLsDn/h6qspoGfPr+ULzft4ZaTRnLrybZgjmmfTec0jomKCOPH07N4+frp1DU28b1Hv+ShjzdSWdfodGhBpbq+kTeXbefCR7/im80l3H/RZG47ZZQlfXPQbMRvelRxRR3/8+YqPly7iz5xkVw/awRXzsgiJtJmAHVkw64KHlvwHR+s3kl1fROD+sTypwsnMeMwa6FsOmelHhNQlm8r5YGPNrBwQzGD+8ZyzznjOWlsutNhBZSte6p5cP4G3lxeQFxkOOdMzuCCqZlMy+prJ8mNTyzxm4D01Xe7+c3ba9hUVMnJY9P50dFDGJeRRP/EGKdDc8ymokoeX/Adby4rIDxMuHJGFrNnjaBPfJTToZkgY4nfBKz6Rhdzv9zC3+ZvpKahCYDUhChmjerP5dOHMmVw714gpKqukY1FlazfWc4nuUV8uHYXUeFh/HDaYH56wmGkJ4Xuh6DpGkv8JuCV1zawpqCcdYXlrC4o4z9rdlJV38TEzGSuPiaLcyZlEBHeO+YjqCpffbeHOQs3s3BjMd7/hsmxkVx+9FCunJllF1+ZLrPEb4JORW0Dby0r4JlF+WwsqmR4ajw3nXgY50zOIDJIPwAam1y8v6qQxxdsZm1hOakJ0fxw2mAmDUpm9IBEBveJs/q96TaW+E3QcrmUD9fu5MH5G8ndWQFAVHgYMZFhTByUzO/Pm8DwAF9FqrahiTe+LeCxBd+xtaSaw/oncN2xwzl3SobNaDJ+Y4nfBD2XS/k4t4g1O8qobXBRVdfI28sLqGt0eVaVGkZ4gIyW6xqb2FZSQ05eCR/nFvHFxt3UNDQxeVAyPz3hME4Zm24je+N3AZX4ReR04G9AOPCkqt7b2f6W+E1HisprufPNVcxfV0RGcgzpyTGkxEaSkeLuEXTMyFS/LzFYWFZDTt5eVu8oY+2Ocr4rqqSwvLa5bp+RHMNJY9M5Y+IApg+3pnWm5wRM4heRcGADcAqwHVgCXKKqazt6jiV+0xlV5Z0VO/hw7S7Kqhsoq2lgy+4qKusaiYoIY1JmMjGR4YSFCQnR4UwelMK0YX0ZlZ7Ihl0VLN9aynfFlYxKTyQ7qw9jBiTR0OSioLSGXWW19EuIZmi/uFYlmYYmF5/kFvHi4q0s2OA+ORsZLoxKT2RUeiJD+sYxtF8c4zKSGJ2eaMneOKKjxO9EW+YjgU2quhlARF4CzgM6TPzGdEZEOG9KJudNyWzeVt/oai6zrNpeRnV9I00K+XuqmLdq536vkRAd0dxCIioijPpGV5v3gIFJMYSFCVV1jVTVNVHf5GJAUgw3nziSU8elMyo90ZqkmaDgROLPBLa1uL8dOKrtTiJyHXAdwJAhQ3omMtNrREWEMeOw1HbbGhRX1LE0v4RNRZUc1j+RqUNSSE+KoaDUXZNfXVBGUkwkmX1iGZAUw+6qerYUV5G/pwoE4qMiiIsOZ9rQvhw/Oq3XTDE1oSNgF2JR1TnAHHCXehwOx/QiaYnRnD5h4H7bM1NiyWzzzcGY3siJoUoBMLjF/UGebcYYY3qAE4l/CTBSRIaJSBTwQ+AdB+IwxpiQ1OOlHlVtFJGbgP/gns45V1XX9HQcxhgTqhyp8avqPGCeE+9tjDGhzqYjGGNMiLHEb4wxIcYSvzHGhBhL/MYYE2KCojuniBQD+U7H0U1Sgd1OB+EQO/bQFcrH7+SxD1XVtLYbgyLx9yYiktNe06RQYMcemscOoX38gXjsVuoxxpgQY4nfGGNCjCX+njfH6QAcZMceukL5+APu2K3Gb4wxIcZG/MYYE2Is8RtjTIixxO8nIjJXRIpEZHUHjyeLyLsiskJE1ojIVT0do7/4cOx9RORNEVkpIotFZEJPx+gPIjJYRD4VkbWev9Nb2tlHROTvIrLJc/yHOxFrd/Px2MeIyCIRqRORXzgRpz/4eOyXef6+V4nIVyIy2YlYvSzx+8/TwOmdPH4jsFZVJwPHA3/xrE/QGzxN58d+J7BcVScBPwb+1hNB9YBG4OeqOg44GrhRRMa12ecMYKTndh3waM+G6De+HHsJ8DPg/p4Ozs98OfYtwCxVnQj8HodP+Fri9xNVXYj7H3qHuwCJIiJAgmffxp6Izd98OPZxwCeefXOBLBFJ74nY/ElVC1X1W8/vFcA63GtMt3Qe8Iy6fQ2kiMj+60AGGV+OXVWLVHUJ0OBAiH7j47F/pap7PXe/xr3yoGMs8TvnYWAssANYBdyiqi5nQ+oxK4DvAYjIkcBQHP6P0N1EJAuYCnzT5qFMYFuL+9vZ/8MhqHVy7L2ej8d+DfDvnoinI5b4nXMasBzIAKYAD4tIkrMh9Zh7cY90lwM3A8uAJmdD6j4ikgC8DtyqquVOx9OT7Ng7P3YROQF34v9VT8bWliMrcBkArgLuVfeFFJtEZAswBljsbFj+5/lPcRW4T3birn9udjSobiIikbj/8z+vqm+0s0sBMLjF/UGebUHPh2PvtXw5dhGZBDwJnKGqe3oyvrZsxO+crcBJAJ769mh6SfI7EBFJaXEi+yfAwt4wOvR8iD0FrFPVBzrY7R3gx57ZPUcDZapa2GNB+omPx94r+XLsIjIEeAO4XFU39GR87cZjV+76h4i8iHu2TiqwC7gbiARQ1cdEJAP37JeBgOAe/T/nSLDdzIdjnw78C/cJ7jXANS1OfAUtETkG+Bz3ORvv+Zo7gSHQfOyC+/zO6UA1cJWq5jgQbrfy8dgHADlAkmefSmBcsH/o+3jsTwIXsq+9fKOTHTst8RtjTIixUo8xxoQYS/zGGBNiLPEbY0yIscRvjDEhxhK/McaEGEv8JmCJSJOILPd0MP1WRGZ00+seLyLvdcdrdfIeV4rIwwf5nKki8lQX3/dpEfm+5/eXRGRkV17P9E6W+E0gq1HVKZ4Opv8N/J/TAfnZncDf224UkUO9wv5R4PYuRWR6JUv8JlgkAXuhuaf9n0Vktae/+cWe7ceLyGci8pqI5IrI854LphCR0z3bvsXTIK4tEckSkc893y6av2Ec4HXP9Gxb6umzv983CRFJE5HXRWSJ5zaznX0SgUmqusJz/x4ReVZEvgSe7SQ2EZGHRWS9iMwH+rd42c+Bk7vwwWF6KfsHYQJZrKeRWwzuK5xP9Gz/Hu7GdpNxXx28REQWeh6bCozH3fX0S2CmiOQAT3ievwl4uYP3KwJOUdVaT4nkRcB7dWVHr/s4cJyqbvFcsdyevwF/VdUvPJfu/wd3Z9aWsoG2C9eMA45R1RoRiesgtgtwt/sYB6QDa4G5AKrqEpFNnj+npR3EZkKQJX4TyGpUdQqAp83DM+JeresY4EVVbQJ2icgCYBpQDixW1e2e5ywHsnC3Btiiqhs925/DvQhKW5G4u6ROwd0tdFSLxzp63c2qusWzz4sdvO7JwDjPlwSAJBFJUNXKFvsMBIrbPO8dVa05QGzHtfiz2CEin7R5jSLcHWAt8ZtmlvhNUFDVRSKSCqQdYNe6Fr83cXD/xm/D3VtoMu4yaG03vW4YcLSq1nayTw3ubzYtVfkYW2diPK9tTDOr8ZugICJjgHBgD+7a9cUiEi4iabhHvZ21s/au8jXCc/+SDvZLBgo9C+Jc7nm/zqwHhot78Q2AizvY70Pc6w54j2VKO/usAw7r5L06im0h+/4sBgIntHneKPYvIZkQZ4nfBLJYz3TO5bjr8ld4ShpvAitxr+T1CXC7qu7s6EU8I+3rgPc9J3eLOtj1H8AVIrIC99oIVR3s533dGuCnwAcishSoAMra2fVnQLa4F9teC8xu57VygWTPSd6Die1NYCPu2v4zwCLvE8Td7rumsz8bE5qsO6cxXeCt1Xtm+TwCbFTVvx7ia90GVKjqk90U221Auap26doA0/vYiN+YrrnW841kDe5yzONdeK1HaX0uoatKca97YEwrNuI3xpgQYyN+Y4wJMZb4jTEmxFjiN8aYEGOJ3xhjQowlfmOMCTH/D78+8bYrZIpbAAAAAElFTkSuQmCC\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "bu4VSAK2Cf_r"
      },
      "source": [
        ""
      ],
      "execution_count": null,
      "outputs": []
    }
  ]
}