Jupyter Notebook Demo for calculating phi-psi info of a PDB file via Biopython

rp.ipynb

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   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "```yaml\n",
    "---\n",
    "title: Jupyter Notebook Demo for calculating phi-psi info of a PDB file via Biopython\n",
    "author: Zefeng Zhu\n",
    "date: 2020-08-29 17:44:27 +0800\n",
    "categories: [Notes, Programming]\n",
    "tags: [python, pdb]\n",
    "---\n",
    "```\n",
    "\n",
    "## Reference \n",
    "\n",
    "* https://warwick.ac.uk/fac/sci/moac/people/students/peter_cock/python/ramachandran/calculate/"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import Bio.PDB\n",
    "import pandas as pd"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "<Structure id=P69441_6f7u.1.B_1_214>"
     },
     "metadata": {},
     "execution_count": 2
    }
   ],
   "source": [
    "s = Bio.PDB.PDBParser().get_structure('P69441_6f7u.1.B_1_214', r'C:\\Users\\Nature\\Downloads\\P69441_6f7u.1.B_1_214.pdb')\n",
    "s"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "def yieldPhiPsi(model):\n",
    "    for chain in model:\n",
    "        polypeptides = Bio.PDB.PPBuilder().build_peptides(chain)\n",
    "        for poly_index, poly in enumerate(polypeptides):\n",
    "            phi_psi = poly.get_phi_psi_list()\n",
    "            for res_index, residue in enumerate(poly):\n",
    "                phi, psi = phi_psi[res_index]\n",
    "                yield dict(chain_id=chain.id, \n",
    "                           poly_index=poly_index, \n",
    "                           residue_name=residue.resname, \n",
    "                           author_residue_number=residue.id[1], \n",
    "                           phi_radian=phi, psi_radian=psi)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "    chain_id  poly_index residue_name  author_residue_number  phi_radian  \\\n0          A           0          MET                      1         NaN   \n1          A           0          ARG                      2   -2.056204   \n2          A           0          ILE                      3   -2.224167   \n3          A           0          ILE                      4   -1.750527   \n4          A           0          LEU                      5   -2.000557   \n..       ...         ...          ...                    ...         ...   \n423        B           0          GLU                    210   -1.056953   \n424        B           0          LYS                    211   -1.124640   \n425        B           0          ILE                    212   -1.141851   \n426        B           0          LEU                    213   -1.524915   \n427        B           0          GLY                    214    1.262624   \n\n     psi_radian  \n0      2.104546  \n1      2.062229  \n2      2.323937  \n3      2.240498  \n4      2.035448  \n..          ...  \n423   -0.725899  \n424   -0.674104  \n425   -0.784768  \n426   -0.434294  \n427         NaN  \n\n[428 rows x 6 columns]",
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     },
     "metadata": {},
     "execution_count": 4
    }
   ],
   "source": [
    "df = pd.DataFrame(yieldPhiPsi(s[0]))\n",
    "df"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "import math\n",
    "def degrees(rad_angle) :\n",
    "    \"\"\"Converts any angle in radians to degrees.\n",
    "\n",
    "    If the input is None, then it returns None.\n",
    "    For numerical input, the output is mapped to [-180,180]\n",
    "    \"\"\"\n",
    "    if rad_angle is None :\n",
    "        return None\n",
    "    angle = rad_angle * 180 / math.pi\n",
    "    while angle > 180 :\n",
    "        angle = angle - 360\n",
    "    while angle < -180 :\n",
    "        angle = angle + 360\n",
    "    return angle"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
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     "data": {
      "text/plain": "    chain_id  poly_index residue_name  author_residue_number  phi_radian  \\\n0          A           0          MET                      1         NaN   \n1          A           0          ARG                      2   -2.056204   \n2          A           0          ILE                      3   -2.224167   \n3          A           0          ILE                      4   -1.750527   \n4          A           0          LEU                      5   -2.000557   \n..       ...         ...          ...                    ...         ...   \n423        B           0          GLU                    210   -1.056953   \n424        B           0          LYS                    211   -1.124640   \n425        B           0          ILE                    212   -1.141851   \n426        B           0          LEU                    213   -1.524915   \n427        B           0          GLY                    214    1.262624   \n\n     psi_radian  phi_degree  psi_degree  \n0      2.104546         NaN  120.581629  \n1      2.062229 -117.811836  118.157034  \n2      2.323937 -127.435363  133.151792  \n3      2.240498 -100.297792  128.371088  \n4      2.035448 -114.623461  116.622557  \n..          ...         ...         ...  \n423   -0.725899  -60.558941  -41.590922  \n424   -0.674104  -64.437124  -38.623306  \n425   -0.784768  -65.423269  -44.963897  \n426   -0.434294  -87.371212  -24.883187  \n427         NaN   72.343036         NaN  \n\n[428 rows x 8 columns]",
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     },
     "metadata": {},
     "execution_count": 6
    }
   ],
   "source": [
    "df['phi_degree'] = df.phi_radian.apply(degrees)\n",
    "df['psi_degree'] = df.psi_radian.apply(degrees)\n",
    "df"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns\n",
    "plt.style.use('ggplot')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
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\n"
     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "source": [
    "sns.jointplot(x='phi_radian', y='psi_radian', data=df)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "<seaborn.axisgrid.JointGrid at 0x23b7c00bd30>"
     },
     "metadata": {},
     "execution_count": 10
    },
    {
     "output_type": "display_data",
     "data": {
      "text/plain": "<Figure size 432x432 with 3 Axes>",
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\n"
     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "source": [
    "sns.jointplot(x='phi_degree', y='psi_degree', data=df)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ]
}