example-nupack.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "05d6af13-b07f-4ad8-95f8-328a8caeecdc",
   "metadata": {},
   "outputs": [],
   "source": [
    "from nupack import *"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "31ecf7d0-55a1-493e-bcb9-2ddaa9078f7c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<b>Complex results:</b> <table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th>Complex</th>\n",
       "      <th>Pfunc</th>\n",
       "      <th>ΔG (kcal/mol)</th>\n",
       "      <th>MFE (kcal/mol)</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <td>(h1)</td>\n",
       "      <td>4.1569e+23</td>\n",
       "      <td>-33.518</td>\n",
       "      <td>-33.345</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>(h2)</td>\n",
       "      <td>1.5822e+25</td>\n",
       "      <td>-35.761</td>\n",
       "      <td>-35.622</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>(i1)</td>\n",
       "      <td>2.1724e+2</td>\n",
       "      <td>-3.316</td>\n",
       "      <td>-2.706</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>(i1+h1)</td>\n",
       "      <td>1.1616e+36</td>\n",
       "      <td>-51.181</td>\n",
       "      <td>-50.495</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>(i1+h1+h2)</td>\n",
       "      <td>1.1069e+71</td>\n",
       "      <td>-100.821</td>\n",
       "      <td>-99.892</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>(i1+h1+h1+h2)</td>\n",
       "      <td>1.8703e+105</td>\n",
       "      <td>-149.395</td>\n",
       "      <td>-148.587</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>(i1+h1+h2+h1+h2)</td>\n",
       "      <td>1.4406e+130</td>\n",
       "      <td>-184.712</td>\n",
       "      <td>-182.289</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>"
      ],
      "text/plain": [
       "Result(complexes={<Complex (i1+h1)>: nupack.analysis.ComplexResult({model: Model('stacking', 'rna06.json', T=310.15 K), pfunc: 1.161613899468506633953300688E+36, free_energy: -51.181048305342266, mfe_stack: -49.281341552734375, pairs: [[0.3025 0.0000 0.0000 ... 0.0000 0.0000 0.0000]\n",
       " [0.0000 0.0025 0.0000 ... 0.0000 0.0000 0.0000]\n",
       " [0.0000 0.0000 0.0006 ... 0.0000 0.0000 0.0000]\n",
       " ...\n",
       " [0.0000 0.0000 0.0000 ... 0.9948 0.0000 0.0000]\n",
       " [0.0000 0.0000 0.0000 ... 0.0000 0.9248 0.0000]\n",
       " [0.0000 0.0000 0.0000 ... 0.0000 0.0000 0.9408]], mfe: [StructureEnergy(Structure('(((((((((((((((((((((((.+.))))))))))))))))))))))).......(((........)))...'), energy=-50.49506759643555, stack_energy=-49.281341552734375)]}), <Complex (i1+h1+h2)>: nupack.analysis.ComplexResult({model: Model('stacking', 'rna06.json', T=310.15 K), pfunc: 1.106895179448519683215212122E+71, free_energy: -100.82089603921848, mfe_stack: -98.5126953125, pairs: [[0.0268 0.0000 0.0000 ... 0.0000 0.0000 0.0000]\n",
       " [0.0000 0.0004 0.0000 ... 0.0000 0.0000 0.0000]\n",
       " [0.0000 0.0000 0.0003 ... 0.0000 0.0000 0.0000]\n",
       " ...\n",
       " [0.0000 0.0000 0.0000 ... 0.0030 0.0000 0.0000]\n",
       " [0.0000 0.0000 0.0000 ... 0.0000 0.0031 0.0000]\n",
       " [0.0000 0.0000 0.0000 ... 0.0000 0.0000 0.0093]], mfe: [StructureEnergy(Structure('(((((((((((((((((((((((.+.)))))))))))))))))))))))((((((((((((((((((((((((+..((((.(......).))))....))))))))))))))))))))))))'), energy=-99.89205932617188, stack_energy=-98.5126953125), StructureEnergy(Structure('(((((((((((((((((((((((.+.)))))))))))))))))))))))((((((((((((((((((((((((+..((((.(......).))))....))))))))))))))))))))))))'), energy=-99.89205932617188, stack_energy=-98.5126953125)]}), <Complex (h1)>: nupack.analysis.ComplexResult({model: Model('stacking', 'rna06.json', T=310.15 K), pfunc: 415688784219339821186925.0992, free_energy: -33.518126998661025, mfe_stack: -33.04999542236328, pairs: [[1.0000 0.0000 0.0000 ... 0.0000 0.0000 0.0000]\n",
       " [0.0000 1.0000 0.0000 ... 0.0000 0.0000 0.0000]\n",
       " [0.0000 0.0000 1.0000 ... 0.0000 0.0000 0.0000]\n",
       " ...\n",
       " [0.0000 0.0000 0.0000 ... 0.0003 0.0000 0.0000]\n",
       " [0.0000 0.0000 0.0000 ... 0.0000 0.0046 0.0000]\n",
       " [0.0000 0.0000 0.0000 ... 0.0000 0.0000 0.0579]], mfe: [StructureEnergy(Structure('......((((((((((((((((((......))))))))))))))))))'), energy=-33.34527587890625, stack_energy=-33.04999542236328)]}), <Complex (h2)>: nupack.analysis.ComplexResult({model: Model('stacking', 'rna06.json', T=310.15 K), pfunc: 15822017583277137929101323.17, free_energy: -35.76105444687244, mfe_stack: -35.44999694824219, pairs: [[0.1960 0.0000 0.0000 ... 0.0000 0.0000 0.0000]\n",
       " [0.0000 0.0015 0.0000 ... 0.0000 0.0000 0.0000]\n",
       " [0.0000 0.0000 0.0004 ... 0.0000 0.0000 0.0000]\n",
       " ...\n",
       " [0.0000 0.0000 0.0000 ... 1.0000 0.0000 0.0000]\n",
       " [0.0000 0.0000 0.0000 ... 0.0000 0.9998 0.0000]\n",
       " [0.0000 0.0000 0.0000 ... 0.0000 0.0000 0.9996]], mfe: [StructureEnergy(Structure('((((((((((((((((((......))))))))))))))))))......'), energy=-35.62165451049805, stack_energy=-35.44999694824219)]}), <Complex (i1)>: nupack.analysis.ComplexResult({model: Model('stacking', 'rna06.json', T=310.15 K), pfunc: 217.2402606876066240353846713, free_energy: -3.3164245170562565, mfe_stack: -2.049999713897705, pairs: [[0.9068 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000\n",
       "  0.0047 0.0000 0.0000 0.0000 0.0000 0.0000 0.0005 0.0000 0.0000 0.0000\n",
       "  0.0037 0.0842 0.0000 0.0000]\n",
       " [0.0000 0.7509 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0114\n",
       "  0.0001 0.0001 0.0000 0.0000 0.1155 0.0000 0.0000 0.0000 0.0000 0.0000\n",
       "  0.1205 0.0015 0.0000 0.0000]\n",
       " [0.0000 0.0000 0.3607 0.0000 0.0000 0.0000 0.0000 0.0000 0.0122 0.0000\n",
       "  0.0000 0.0000 0.0000 0.1153 0.0000 0.0000 0.0000 0.0000 0.0026 0.5089\n",
       "  0.0000 0.0000 0.0002 0.0000]\n",
       " [0.0000 0.0000 0.0000 0.1449 0.0000 0.0000 0.0000 0.0121 0.0000 0.0000\n",
       "  0.0000 0.0000 0.1152 0.0005 0.0000 0.0000 0.0000 0.0032 0.7237 0.0005\n",
       "  0.0000 0.0000 0.0000 0.0000]\n",
       " [0.0000 0.0000 0.0000 0.0000 0.2733 0.0000 0.0000 0.0000 0.0000 0.0000\n",
       "  0.0000 0.0000 0.0005 0.0000 0.0000 0.0000 0.0000 0.7248 0.0003 0.0000\n",
       "  0.0000 0.0000 0.0008 0.0003]\n",
       " [0.0000 0.0000 0.0000 0.0000 0.0000 0.2772 0.0000 0.0000 0.0000 0.0002\n",
       "  0.0034 0.0000 0.0000 0.0000 0.0000 0.0000 0.7186 0.0000 0.0000 0.0000\n",
       "  0.0000 0.0006 0.0000 0.0000]\n",
       " [0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.9864 0.0000 0.0000 0.0000\n",
       "  0.0001 0.0018 0.0000 0.0000 0.0113 0.0000 0.0000 0.0000 0.0000 0.0000\n",
       "  0.0003 0.0002 0.0000 0.0000]\n",
       " [0.0000 0.0000 0.0000 0.0121 0.0000 0.0000 0.0000 0.1770 0.0000 0.0000\n",
       "  0.0000 0.0001 0.0000 0.0000 0.7082 0.0000 0.0000 0.0000 0.0000 0.0000\n",
       "  0.0000 0.1025 0.0000 0.0000]\n",
       " [0.0000 0.0000 0.0122 0.0000 0.0000 0.0000 0.0000 0.0000 0.8769 0.0000\n",
       "  0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0001 0.0000 0.0000 0.0000\n",
       "  0.1104 0.0004 0.0000 0.0000]\n",
       " [0.0000 0.0114 0.0000 0.0000 0.0000 0.0002 0.0000 0.0000 0.0000 0.8723\n",
       "  0.0000 0.0000 0.0000 0.0050 0.0000 0.0001 0.0000 0.0000 0.0000 0.1107\n",
       "  0.0000 0.0000 0.0001 0.0002]\n",
       " [0.0047 0.0001 0.0000 0.0000 0.0000 0.0034 0.0001 0.0000 0.0000 0.0000\n",
       "  0.8782 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.1104 0.0025\n",
       "  0.0000 0.0000 0.0005 0.0002]\n",
       " [0.0000 0.0001 0.0000 0.0000 0.0000 0.0000 0.0018 0.0001 0.0000 0.0000\n",
       "  0.0000 0.8829 0.0000 0.0000 0.0000 0.0000 0.0000 0.1108 0.0041 0.0002\n",
       "  0.0000 0.0000 0.0000 0.0000]\n",
       " [0.0000 0.0000 0.0000 0.1152 0.0005 0.0000 0.0000 0.0000 0.0000 0.0000\n",
       "  0.0000 0.0000 0.8175 0.0000 0.0000 0.0000 0.0443 0.0000 0.0000 0.0000\n",
       "  0.0001 0.0224 0.0000 0.0000]\n",
       " [0.0000 0.0000 0.1153 0.0005 0.0000 0.0000 0.0000 0.0000 0.0000 0.0050\n",
       "  0.0000 0.0000 0.0000 0.8487 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000\n",
       "  0.0304 0.0000 0.0000 0.0000]\n",
       " [0.0000 0.1155 0.0000 0.0000 0.0000 0.0000 0.0113 0.7082 0.0000 0.0000\n",
       "  0.0000 0.0000 0.0000 0.0000 0.1341 0.0000 0.0000 0.0000 0.0001 0.0309\n",
       "  0.0000 0.0000 0.0000 0.0000]\n",
       " [0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0001\n",
       "  0.0000 0.0000 0.0000 0.0000 0.0000 0.9998 0.0000 0.0000 0.0000 0.0000\n",
       "  0.0000 0.0000 0.0000 0.0000]\n",
       " [0.0005 0.0000 0.0000 0.0000 0.0000 0.7186 0.0000 0.0000 0.0001 0.0000\n",
       "  0.0000 0.0000 0.0443 0.0000 0.0000 0.0000 0.2361 0.0000 0.0000 0.0000\n",
       "  0.0000 0.0000 0.0002 0.0001]\n",
       " [0.0000 0.0000 0.0000 0.0032 0.7248 0.0000 0.0000 0.0000 0.0000 0.0000\n",
       "  0.0000 0.1108 0.0000 0.0000 0.0000 0.0000 0.0000 0.1610 0.0000 0.0000\n",
       "  0.0000 0.0002 0.0000 0.0000]\n",
       " [0.0000 0.0000 0.0026 0.7237 0.0003 0.0000 0.0000 0.0000 0.0000 0.0000\n",
       "  0.1104 0.0041 0.0000 0.0000 0.0001 0.0000 0.0000 0.0000 0.1589 0.0000\n",
       "  0.0000 0.0000 0.0000 0.0000]\n",
       " [0.0000 0.0000 0.5089 0.0005 0.0000 0.0000 0.0000 0.0000 0.0000 0.1107\n",
       "  0.0025 0.0002 0.0000 0.0000 0.0309 0.0000 0.0000 0.0000 0.0000 0.3462\n",
       "  0.0000 0.0000 0.0000 0.0000]\n",
       " [0.0037 0.1205 0.0000 0.0000 0.0000 0.0000 0.0003 0.0000 0.1104 0.0000\n",
       "  0.0000 0.0000 0.0001 0.0304 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000\n",
       "  0.7346 0.0000 0.0000 0.0000]\n",
       " [0.0842 0.0015 0.0000 0.0000 0.0000 0.0006 0.0002 0.1025 0.0004 0.0000\n",
       "  0.0000 0.0000 0.0224 0.0000 0.0000 0.0000 0.0000 0.0002 0.0000 0.0000\n",
       "  0.0000 0.7879 0.0000 0.0000]\n",
       " [0.0000 0.0000 0.0002 0.0000 0.0008 0.0000 0.0000 0.0000 0.0000 0.0001\n",
       "  0.0005 0.0000 0.0000 0.0000 0.0000 0.0000 0.0002 0.0000 0.0000 0.0000\n",
       "  0.0000 0.0000 0.9984 0.0000]\n",
       " [0.0000 0.0000 0.0000 0.0000 0.0003 0.0000 0.0000 0.0000 0.0000 0.0002\n",
       "  0.0002 0.0000 0.0000 0.0000 0.0000 0.0000 0.0001 0.0000 0.0000 0.0000\n",
       "  0.0000 0.0000 0.0000 0.9991]], mfe: [StructureEnergy(Structure('..((((.(......).))))....'), energy=-2.7062697410583496, stack_energy=-2.049999713897705), StructureEnergy(Structure('..((((.(......).))))....'), energy=-2.7062697410583496, stack_energy=-2.049999713897705)]}), <Complex (i1+h1+h1+h2)>: nupack.analysis.ComplexResult({model: Model('stacking', 'rna06.json', T=310.15 K), pfunc: 1.870252102861376941918336110E+105, free_energy: -149.39462011014734, mfe_stack: -147.34405517578125, pairs: [[0.0268 0.0000 0.0000 ... 0.0000 0.0000 0.0000]\n",
       " [0.0000 0.0004 0.0000 ... 0.0000 0.0000 0.0000]\n",
       " [0.0000 0.0000 0.0003 ... 0.0000 0.0000 0.0000]\n",
       " ...\n",
       " [0.0000 0.0000 0.0000 ... 0.0030 0.0000 0.0000]\n",
       " [0.0000 0.0000 0.0000 ... 0.0000 0.0031 0.0000]\n",
       " [0.0000 0.0000 0.0000 ... 0.0000 0.0000 0.0093]], mfe: [StructureEnergy(Structure('(((((((((((((((((((((((.+.)))))))))))))))))))))))((((((((((((((((((((((((+((((((((((((((((((((((((.......(((........)))...+))))))))))))))))))))))))))))))))))))))))))))))))'), energy=-148.5873260498047, stack_energy=-147.34405517578125)]}), <Complex (i1+h1+h2+h1+h2)>: nupack.analysis.ComplexResult({model: Model('stacking', 'rna06.json', T=310.15 K), pfunc: 1.440617358479057566874421800E+130, free_energy: -184.71203522163236, mfe_stack: -180.72540283203125, pairs: [[0.0268 0.0000 0.0000 ... 0.0000 0.0000 0.0000]\n",
       " [0.0000 0.0004 0.0000 ... 0.0000 0.0000 0.0000]\n",
       " [0.0000 0.0000 0.0003 ... 0.0000 0.0000 0.0000]\n",
       " ...\n",
       " [0.0000 0.0000 0.0000 ... 0.0030 0.0000 0.0000]\n",
       " [0.0000 0.0000 0.0000 ... 0.0000 0.0031 0.0000]\n",
       " [0.0000 0.0000 0.0000 ... 0.0000 0.0000 0.0093]], mfe: [StructureEnergy(Structure('(((((((((((((((((((((((.+.)))))))))))))))))))))))(((((((((((((((((((((((.+((((((((((((((((((......)))))))))))))))))).....(+((((((((((((((((((((((((.......(((........)))...+))))))))))))))))))))))))))))))))))))))))))))))))'), energy=-182.28887939453125, stack_energy=-180.72540283203125)]})})"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Import NUPACK Python module\n",
    "from nupack import *\n",
    "\n",
    "# Define physical model\n",
    "my_model = Model(material='rna', celsius=37)\n",
    "\n",
    "# Define strand species\n",
    "i1 = Strand('AGTCTAGGATTCGGCGTGGGTTAA', name='i1')\n",
    "h1 = Strand('TTAACCCACGCCGAATCCTAGACTCAAAGTAGTCTAGGATTCGGCGTG', name='h1')\n",
    "h2 = Strand('AGTCTAGGATTCGGCGTGGGTTAACACGCCGAATCCTAGACTACTTTG', name='h2')\n",
    "\n",
    "# Define complexes\n",
    "poly1 = Complex([i1, h1])\n",
    "poly2 = Complex([i1, h1, h2])\n",
    "poly3 = Complex([i1, h1, h1, h2])\n",
    "poly4 = Complex([i1, h1, h2, h1, h2])\n",
    "\n",
    "# Define complex set comprising all monomers plus additional specified complexes\n",
    "my_set = ComplexSet(strands=[i1, h1, h2], complexes=SetSpec(max_size=1, include=[poly1, poly2, poly3, poly4]))\n",
    "\n",
    "# Analyze the set of complexes\n",
    "# Calculate pfunc, pairs, mfe for each complex\n",
    "# Calculate equilibrium complex concentrations (default) for each tube ensemble\n",
    "set_result = complex_analysis(complexes=my_set, compute=['pfunc', 'pairs', 'mfe'], model=my_model)\n",
    "set_result"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "f5ab3eff-4558-41cb-88a2-83bdf7dadb41",
   "metadata": {},
   "outputs": [
    {
     "ename": "AttributeError",
     "evalue": "'Result' object has no attribute 'pairs'",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mAttributeError\u001b[0m                            Traceback (most recent call last)",
      "Cell \u001b[0;32mIn[6], line 1\u001b[0m\n\u001b[0;32m----> 1\u001b[0m \u001b[43mset_result\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mpairs\u001b[49m()\n",
      "\u001b[0;31mAttributeError\u001b[0m: 'Result' object has no attribute 'pairs'"
     ]
    }
   ],
   "source": [
    "set_result.pairs()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "4b03da67-394d-4ba9-b90b-f93010a608f4",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<b>Complex results:</b> <table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th>Complex</th>\n",
       "      <th>Pfunc</th>\n",
       "      <th>ΔG (kcal/mol)</th>\n",
       "      <th>MFE (kcal/mol)</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <td>(h1)</td>\n",
       "      <td>3.4039e+10</td>\n",
       "      <td>-14.946</td>\n",
       "      <td>-14.263</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>(h2)</td>\n",
       "      <td>8.6511e+9</td>\n",
       "      <td>-14.102</td>\n",
       "      <td>-12.088</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>(i1)</td>\n",
       "      <td>5.4252e+65</td>\n",
       "      <td>-93.286</td>\n",
       "      <td>-90.222</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>(h1+h1)</td>\n",
       "      <td>3.8858e+33</td>\n",
       "      <td>-47.668</td>\n",
       "      <td>-46.830</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>(h1+h2)</td>\n",
       "      <td>3.8835e+25</td>\n",
       "      <td>-36.314</td>\n",
       "      <td>-33.609</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>(h2+h2)</td>\n",
       "      <td>2.6331e+25</td>\n",
       "      <td>-36.075</td>\n",
       "      <td>-32.893</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>(i1+h1)</td>\n",
       "      <td>6.0564e+89</td>\n",
       "      <td>-127.413</td>\n",
       "      <td>-123.260</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>(i1+h2)</td>\n",
       "      <td>7.8068e+98</td>\n",
       "      <td>-140.341</td>\n",
       "      <td>-136.972</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>(i1+i1)</td>\n",
       "      <td>3.2764e+144</td>\n",
       "      <td>-205.086</td>\n",
       "      <td>-198.325</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>(h1+h1+h1)</td>\n",
       "      <td>5.6429e+53</td>\n",
       "      <td>-76.280</td>\n",
       "      <td>-73.919</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>(h1+h1+h2)</td>\n",
       "      <td>1.2714e+48</td>\n",
       "      <td>-68.266</td>\n",
       "      <td>-65.039</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>(h1+h2+h2)</td>\n",
       "      <td>5.1243e+40</td>\n",
       "      <td>-57.772</td>\n",
       "      <td>-52.493</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>(h2+h2+h2)</td>\n",
       "      <td>6.3088e+39</td>\n",
       "      <td>-56.481</td>\n",
       "      <td>-50.842</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>(i1+h1+h1)</td>\n",
       "      <td>4.4686e+109</td>\n",
       "      <td>-155.608</td>\n",
       "      <td>-150.350</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>(i1+h1+h2)</td>\n",
       "      <td>8.7110e+116</td>\n",
       "      <td>-165.953</td>\n",
       "      <td>-163.051</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>(i1+h2+h1)</td>\n",
       "      <td>1.0163e+129</td>\n",
       "      <td>-183.078</td>\n",
       "      <td>-177.741</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>(i1+h2+h2)</td>\n",
       "      <td>1.5787e+115</td>\n",
       "      <td>-163.481</td>\n",
       "      <td>-159.806</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>(i1+i1+h1)</td>\n",
       "      <td>3.3315e+161</td>\n",
       "      <td>-229.222</td>\n",
       "      <td>-220.994</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>(i1+i1+h2)</td>\n",
       "      <td>9.4293e+177</td>\n",
       "      <td>-252.569</td>\n",
       "      <td>-245.075</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>(i1+i1+i1)</td>\n",
       "      <td>1.1784e+217</td>\n",
       "      <td>-308.053</td>\n",
       "      <td>-298.128</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>(i1+h1+h1+h2)</td>\n",
       "      <td>1.3818e+137</td>\n",
       "      <td>-194.620</td>\n",
       "      <td>-190.140</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>(i1+h1+h2+h1+h2)</td>\n",
       "      <td>5.7262e+165</td>\n",
       "      <td>-235.232</td>\n",
       "      <td>-230.624</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>"
      ],
      "text/plain": [
       "Result(complexes={<Complex (h1+h1+h1)>: nupack.analysis.ComplexResult({model: Model('stacking', 'rna06.json', T=310.15 K), pfunc: 5.642933897519917856391356837E+53, free_energy: -76.2804286111048, mfe_stack: -70.41271209716797, pairs: [[0.8415 0.0000 0.0000 ... 0.0000 0.0000 0.0000]\n",
       " [0.0000 0.8489 0.0000 ... 0.0000 0.0000 0.0000]\n",
       " [0.0000 0.0000 0.8529 ... 0.0000 0.0000 0.0000]\n",
       " ...\n",
       " [0.0000 0.0000 0.0000 ... 0.2414 0.0000 0.0000]\n",
       " [0.0000 0.0000 0.0000 ... 0.0000 0.9812 0.0000]\n",
       " [0.0000 0.0000 0.0000 ... 0.0000 0.0000 0.9976]], mfe: [StructureEnergy(Structure('...(((((((....)))))))....(((((((((((.(((........((....))..+...((((((((..((((((((.......(((.................((....))..+)))))))))))..))))))))....))))))))))).)))........((....))..'), energy=-73.91905975341797, stack_energy=-70.41270446777344), StructureEnergy(Structure('...(((((((....)))))))....(((((((((((.(((........((....))..+...((((((((..((((((((.......(((.................((....))..+)))))))))))..))))))))....))))))))))).)))........((....))..'), energy=-73.91905975341797, stack_energy=-70.41270446777344), StructureEnergy(Structure('...(((((((....)))))))....(((((((((((.(((........((....))..+...((((((((..((((((((.......(((.................((....))..+)))))))))))..))))))))....))))))))))).)))........((....))..'), energy=-73.91905975341797, stack_energy=-70.41270446777344), StructureEnergy(Structure('...(((((((....)))))))....(((((((((((.(((........((....))..+...((((((((..((((((((.......(((.................((....))..+)))))))))))..))))))))....))))))))))).)))........((....))..'), energy=-73.91905975341797, stack_energy=-70.41270446777344), StructureEnergy(Structure('...(((((((....)))))))....(((((((((((.(((........((....))..+...((((((((..((((((((.......(((.................((....))..+)))))))))))..))))))))....))))))))))).)))........((....))..'), energy=-73.91905975341797, stack_energy=-70.41270446777344), StructureEnergy(Structure('...(((((((....)))))))....(((((((((((.(((........((....))..+...((((((((..((((((((.......(((.................((....))..+)))))))))))..))))))))....))))))))))).)))........((....))..'), energy=-73.91905975341797, stack_energy=-70.41270446777344), StructureEnergy(Structure('...(((((((....)))))))....(((((((((((.(((........((....))..+...((((((((..((((((((.......(((.................((....))..+)))))))))))..))))))))....))))))))))).)))........((....))..'), energy=-73.91905975341797, stack_energy=-70.41270446777344), StructureEnergy(Structure('...(((((((....)))))))....(((((((((((.(((........((....))..+...((((((((..((((((((.......(((.................((....))..+)))))))))))..))))))))....))))))))))).)))........((....))..'), energy=-73.91905975341797, stack_energy=-70.41270446777344), StructureEnergy(Structure('(((((((((((..((((((((....(((((((((((.(((........((....))..+...(((((((....)))))))....))))))))))).)))........((....))..+...))))))))..)))))))).......))).................((....))..'), energy=-73.91905212402344, stack_energy=-70.41271209716797), StructureEnergy(Structure('...((((((((..((((((((.......(((.................((....))..+)))))))))))..))))))))....(((((((((((.(((........((....))..+...(((((((....)))))))....))))))))))).)))........((....))..'), energy=-73.91905212402344, stack_energy=-70.41270446777344), StructureEnergy(Structure('(((((((((((..((((((((....(((((((((((.(((........((....))..+...(((((((....)))))))....))))))))))).)))........((....))..+...))))))))..)))))))).......))).................((....))..'), energy=-73.91905212402344, stack_energy=-70.41271209716797), StructureEnergy(Structure('(((((((((((..((((((((....(((((((((((.(((........((....))..+...(((((((....)))))))....))))))))))).)))........((....))..+...))))))))..)))))))).......))).................((....))..'), energy=-73.91905212402344, stack_energy=-70.41271209716797), StructureEnergy(Structure('(((((((((((..((((((((....(((((((((((.(((........((....))..+...(((((((....)))))))....))))))))))).)))........((....))..+...))))))))..)))))))).......))).................((....))..'), energy=-73.91905212402344, stack_energy=-70.41271209716797), StructureEnergy(Structure('(((((((((((..((((((((....(((((((((((.(((........((....))..+...(((((((....)))))))....))))))))))).)))........((....))..+...))))))))..)))))))).......))).................((....))..'), energy=-73.91905212402344, stack_energy=-70.41271209716797), StructureEnergy(Structure('...((((((((..((((((((.......(((.................((....))..+)))))))))))..))))))))....(((((((((((.(((........((....))..+...(((((((....)))))))....))))))))))).)))........((....))..'), energy=-73.91905212402344, stack_energy=-70.41270446777344), StructureEnergy(Structure('(((((((((((..((((((((....(((((((((((.(((........((....))..+...(((((((....)))))))....))))))))))).)))........((....))..+...))))))))..)))))))).......))).................((....))..'), energy=-73.91905212402344, stack_energy=-70.41271209716797), StructureEnergy(Structure('(((((((((((..((((((((....(((((((((((.(((........((....))..+...(((((((....)))))))....))))))))))).)))........((....))..+...))))))))..)))))))).......))).................((....))..'), energy=-73.91905212402344, stack_energy=-70.41271209716797), StructureEnergy(Structure('...((((((((..((((((((.......(((.................((....))..+)))))))))))..))))))))....(((((((((((.(((........((....))..+...(((((((....)))))))....))))))))))).)))........((....))..'), energy=-73.91905212402344, stack_energy=-70.41270446777344), StructureEnergy(Structure('...((((((((..((((((((.......(((.................((....))..+)))))))))))..))))))))....(((((((((((.(((........((....))..+...(((((((....)))))))....))))))))))).)))........((....))..'), energy=-73.91905212402344, stack_energy=-70.41270446777344), StructureEnergy(Structure('(((((((((((..((((((((....(((((((((((.(((........((....))..+...(((((((....)))))))....))))))))))).)))........((....))..+...))))))))..)))))))).......))).................((....))..'), energy=-73.91905212402344, stack_energy=-70.41271209716797), StructureEnergy(Structure('...((((((((..((((((((.......(((.................((....))..+)))))))))))..))))))))....(((((((((((.(((........((....))..+...(((((((....)))))))....))))))))))).)))........((....))..'), energy=-73.91905212402344, stack_energy=-70.41270446777344), StructureEnergy(Structure('...((((((((..((((((((.......(((.................((....))..+)))))))))))..))))))))....(((((((((((.(((........((....))..+...(((((((....)))))))....))))))))))).)))........((....))..'), energy=-73.91905212402344, stack_energy=-70.41270446777344), StructureEnergy(Structure('...((((((((..((((((((.......(((.................((....))..+)))))))))))..))))))))....(((((((((((.(((........((....))..+...(((((((....)))))))....))))))))))).)))........((....))..'), energy=-73.91905212402344, stack_energy=-70.41270446777344), StructureEnergy(Structure('...((((((((..((((((((.......(((.................((....))..+)))))))))))..))))))))....(((((((((((.(((........((....))..+...(((((((....)))))))....))))))))))).)))........((....))..'), energy=-73.91905212402344, stack_energy=-70.41270446777344)]}), <Complex (i1+i1)>: nupack.analysis.ComplexResult({model: Model('stacking', 'rna06.json', T=310.15 K), pfunc: 3.276384382512205841758711700E+144, free_energy: -205.0862811646502, mfe_stack: -195.26763916015625, pairs: [[0.1636 0.0000 0.0000 ... 0.0000 0.0000 0.0000]\n",
       " [0.0000 0.0874 0.0000 ... 0.0000 0.0000 0.0000]\n",
       " [0.0000 0.0000 0.5597 ... 0.0000 0.0000 0.0000]\n",
       " ...\n",
       " [0.0000 0.0000 0.0000 ... 0.9976 0.0000 0.0000]\n",
       " [0.0000 0.0000 0.0000 ... 0.0000 0.9885 0.0000]\n",
       " [0.0000 0.0000 0.0000 ... 0.0000 0.0000 0.9879]], mfe: [StructureEnergy(Structure('((.((((((((..((((((((..(((((((((((((((((((((((((.(((((.......((((((((((..(((((.(((((((((((((((((((((((((((((((..(((((.((((.....................)))).)))))..))))))..((((((((..((((((((..((..(((....))).....+)).))))))))..))))))))..))))))))))))))))))))))))).))))).......))))))))))..))))).)))))))))))))))))))))))))((((((..(((((.((((.....................)))).)))))..))))))..))))))))..))))))))..))..(((....))).....'), energy=-198.3245849609375, stack_energy=-195.26763916015625)]}), <Complex (i1)>: nupack.analysis.ComplexResult({model: Model('stacking', 'rna06.json', T=310.15 K), pfunc: 5.425204821628086317936734853E+65, free_energy: -93.28574969297006, mfe_stack: -88.6930923461914, pairs: [[0.1636 0.0000 0.0000 ... 0.0000 0.0000 0.0000]\n",
       " [0.0000 0.0874 0.0000 ... 0.0000 0.0000 0.0000]\n",
       " [0.0000 0.0000 0.5597 ... 0.0000 0.0000 0.0000]\n",
       " ...\n",
       " [0.0000 0.0000 0.0000 ... 0.9976 0.0000 0.0000]\n",
       " [0.0000 0.0000 0.0000 ... 0.0000 0.9885 0.0000]\n",
       " [0.0000 0.0000 0.0000 ... 0.0000 0.0000 0.9879]], mfe: [StructureEnergy(Structure('((.((((((((..((((((((..(((((((((((((((((((((((((.(((((((.((......)).))...))))).)))))))))))))))))))))))))((((((..(((((.((((.....................)))).)))))..))))))..))))))))..))))))))..))..(((....))).....'), energy=-90.22162628173828, stack_energy=-88.6930923461914)]}), <Complex (i1+h1+h2+h1+h2)>: nupack.analysis.ComplexResult({model: Model('stacking', 'rna06.json', T=310.15 K), pfunc: 5.726172573704851471476883690E+165, free_energy: -235.23212891071043, mfe_stack: -223.9254150390625, pairs: [[0.9832 0.0000 0.0000 ... 0.0000 0.0000 0.0023]\n",
       " [0.0000 0.8736 0.0000 ... 0.0000 0.0000 0.0006]\n",
       " [0.0000 0.0000 0.6211 ... 0.0000 0.0000 0.0002]\n",
       " ...\n",
       " [0.0000 0.0000 0.0000 ... 0.9819 0.0000 0.0000]\n",
       " [0.0000 0.0000 0.0000 ... 0.0000 0.9837 0.0000]\n",
       " [0.0023 0.0006 0.0002 ... 0.0000 0.0000 0.9969]], mfe: [StructureEnergy(Structure('..(.(((((((......((((....(((((((.(........((((((((((((((((((((((((((((((((..........((((((..((((....))))..))))))(((((((((((((((((((((((((((((((...........(((((.(((.((.....................(((....))).....+...(((((((....))))))).......))))).))))).........((....))..+...(((((((....)))))))...)))))))))))))))))))))))))))))))...+...(((((((....)))))))...))))))))))))))))))))))))))))))))..+...(((((((....)))))))..).))))))).....)))).....))))))).)...'), energy=-230.62379455566406, stack_energy=-223.9254150390625), StructureEnergy(Structure('..(.(((((((......((((....(((((((.(........((((((((((((((((((((((((((((((((..........((((((..((((....))))..))))))(((((((((((((((((((((((((((((((...........(((((.(((.((.....................(((....))).....+...(((((((....))))))).......))))).))))).........((....))..+...(((((((....)))))))...)))))))))))))))))))))))))))))))...+...(((((((....)))))))...))))))))))))))))))))))))))))))))..+...(((((((....)))))))..).))))))).....)))).....))))))).)...'), energy=-230.62379455566406, stack_energy=-223.9254150390625), StructureEnergy(Structure('..(.(((((((......((((....(((((((.(........((((((((((((((((((((((((((((((((..........((((((..((((....))))..))))))(((((((((((((((((((((((((((((((...........(((((.(((.((.....................(((....))).....+...(((((((....))))))).......))))).))))).........((....))..+...(((((((....)))))))...)))))))))))))))))))))))))))))))...+...(((((((....)))))))...))))))))))))))))))))))))))))))))..+...(((((((....)))))))..).))))))).....)))).....))))))).)...'), energy=-230.62379455566406, stack_energy=-223.9254150390625), StructureEnergy(Structure('..(.(((((((......((((....(((((((.(........((((((((((((((((((((((((((((((((..........((((((..((((....))))..))))))(((((((((((((((((((((((((((((((...........(((((.(((.((.....................(((....))).....+...(((((((....))))))).......))))).))))).........((....))..+...(((((((....)))))))...)))))))))))))))))))))))))))))))...+...(((((((....)))))))...))))))))))))))))))))))))))))))))..+...(((((((....)))))))..).))))))).....)))).....))))))).)...'), energy=-230.62379455566406, stack_energy=-223.9254150390625), StructureEnergy(Structure('..(.(((((((......((((....(((((((.(........((((((((((((((((((((((((((((((((..........((((((..((((....))))..))))))(((((((((((((((((((((((((((((((...........(((((.(((.((.....................(((....))).....+...(((((((....))))))).......))))).))))).........((....))..+...(((((((....)))))))...)))))))))))))))))))))))))))))))...+...(((((((....)))))))...))))))))))))))))))))))))))))))))..+...(((((((....)))))))..).))))))).....)))).....))))))).)...'), energy=-230.62379455566406, stack_energy=-223.9254150390625), StructureEnergy(Structure('..(.(((((((......((((....(((((((.(........((((((((((((((((((((((((((((((((..........((((((..((((....))))..))))))(((((((((((((((((((((((((((((((...........(((((.(((.((.....................(((....))).....+...(((((((....))))))).......))))).))))).........((....))..+...(((((((....)))))))...)))))))))))))))))))))))))))))))...+...(((((((....)))))))...))))))))))))))))))))))))))))))))..+...(((((((....)))))))..).))))))).....)))).....))))))).)...'), energy=-230.62379455566406, stack_energy=-223.9254150390625), StructureEnergy(Structure('..(.(((((((......((((....(((((((.(........((((((((((((((((((((((((((((((((..........((((((..((((....))))..))))))(((((((((((((((((((((((((((((((...........(((((.(((.((.....................(((....))).....+...(((((((....))))))).......))))).))))).........((....))..+...(((((((....)))))))...)))))))))))))))))))))))))))))))...+...(((((((....)))))))...))))))))))))))))))))))))))))))))..+...(((((((....)))))))..).))))))).....)))).....))))))).)...'), energy=-230.62379455566406, stack_energy=-223.9254150390625), StructureEnergy(Structure('..(.(((((((......((((....(((((((.(........((((((((((((((((((((((((((((((((..........((((((..((((....))))..))))))(((((((((((((((((((((((((((((((...........(((((.(((.((.....................(((....))).....+...(((((((....))))))).......))))).))))).........((....))..+...(((((((....)))))))...)))))))))))))))))))))))))))))))...+...(((((((....)))))))...))))))))))))))))))))))))))))))))..+...(((((((....)))))))..).))))))).....)))).....))))))).)...'), energy=-230.62379455566406, stack_energy=-223.9254150390625)]}), <Complex (h1+h2)>: nupack.analysis.ComplexResult({model: Model('stacking', 'rna06.json', T=310.15 K), pfunc: 38834887211317504200471296.95, free_energy: -36.31445904643149, mfe_stack: -32.33135223388672, pairs: [[0.4275 0.0000 0.0000 ... 0.0000 0.0000 0.0000]\n",
       " [0.0000 0.3487 0.0000 ... 0.0000 0.0000 0.0000]\n",
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       " ...\n",
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       " [0.0000 0.0000 0.0000 ... 0.0000 0.0000 0.9967]], mfe: [StructureEnergy(Structure('((((((((((....))))))).......)))((((((((.((((....((....))..+(..(((((((....)))))))..).....))))....))).)))))............'), energy=-33.60948944091797, stack_energy=-32.33135223388672), StructureEnergy(Structure('((((((((((....))))))).......)))((((((((.((((....((....))..+(..(((((((....)))))))..).....))))....))).)))))............'), energy=-33.60948944091797, stack_energy=-32.33135223388672), StructureEnergy(Structure('((((((((((....))))))).......)))((((((((.((((....((....))..+(..(((((((....)))))))..).....))))....))).)))))............'), energy=-33.60948944091797, stack_energy=-32.33135223388672), StructureEnergy(Structure('((((((((((....))))))).......)))((((((((.((((....((....))..+(..(((((((....)))))))..).....))))....))).)))))............'), energy=-33.60948944091797, stack_energy=-32.33135223388672)]}), <Complex (i1+i1+h2)>: nupack.analysis.ComplexResult({model: Model('stacking', 'rna06.json', T=310.15 K), pfunc: 9.429294640948385435700523900E+177, free_energy: -252.56910602011394, mfe_stack: -241.85586547851562, pairs: [[0.0595 0.0000 0.0000 ... 0.0000 0.0000 0.0000]\n",
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       " [0.0000 0.0000 0.0000 ... 0.0000 0.0000 0.9994]], mfe: [StructureEnergy(Structure('(((((.........)))))(((.(((((((((((((((((((((((((.(((((.......((((((((((..(((((.(((((((((((((((((((((((((((((((..(((((.((((.....................)))).)))))..))))))..((((((((..((((((((..((..(((....))).....+)).))))))))..))))))))..))))))))))))))))))))))))).))))).......))))))))))..))))).))))))))))))))))))))))))).)))...((((((((((((((((((((((((((((((((.............(((.(..(((..((.........))..))).).)))..........+...(((((((....)))))))...))))))))))))))))))))))))))))))))..'), energy=-245.07534790039062, stack_energy=-241.85586547851562)]}), <Complex (i1+h2+h2)>: nupack.analysis.ComplexResult({model: Model('stacking', 'rna06.json', T=310.15 K), pfunc: 1.578731684963866681887270474E+115, free_energy: -163.48149396738322, mfe_stack: -156.96270751953125, pairs: [[0.1481 0.0000 0.0000 ... 0.0000 0.0000 0.0002]\n",
       " [0.0000 0.1098 0.0000 ... 0.0000 0.0000 0.0001]\n",
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       " ...\n",
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       " [0.0002 0.0001 0.0000 ... 0.0000 0.0000 0.9992]], mfe: [StructureEnergy(Structure('(((((.........)))))(((.(((((((((((((((((((((((((.(((((((.((......)).))...))))).))))))))))))))))))))))))).)))...((((((((((((((((((((((((((((((((..............((.....)).................((((((((..((((.....+...(((((((....))))))).))).)..)))))...)))..................+...(((((((....)))))))...))))))))))))))))))))))))))))))))..'), energy=-159.80630493164062, stack_energy=-156.96270751953125), StructureEnergy(Structure('(((((.........)))))(((.(((((((((((((((((((((((((.(((((((.((......)).))...))))).))))))))))))))))))))))))).)))...((((((((((((((((((((((((((((((((..............((.....)).................((((((((..((((.....+...(((((((....))))))).))).)..)))))...)))..................+...(((((((....)))))))...))))))))))))))))))))))))))))))))..'), energy=-159.80630493164062, stack_energy=-156.96270751953125)]}), <Complex (i1+h1+h1)>: nupack.analysis.ComplexResult({model: Model('stacking', 'rna06.json', T=310.15 K), pfunc: 4.468595125391209853953858649E+109, free_energy: -155.60796013996202, mfe_stack: -147.06271362304688, pairs: [[0.5256 0.0000 0.0000 ... 0.0000 0.0000 0.0000]\n",
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       " [0.0000 0.0000 0.0000 ... 0.9562 0.0000 0.0000]\n",
       " [0.0000 0.0000 0.0000 ... 0.0000 0.9914 0.0000]\n",
       " [0.0001 0.0001 0.0001 ... 0.0000 0.0000 0.9954]], mfe: [StructureEnergy(Structure('...(((((((....)))))))....(((((((((((.(((........((....))..+...(((((((....)))))))....))))))))))).)))((((....((....))..+(..(((((((....)))))))..).....)))).........................'), energy=-65.03946685791016, stack_energy=-61.862701416015625), StructureEnergy(Structure('...(((((((....)))))))....(((((((((((.(((........((....))..+...(((((((....)))))))....))))))))))).)))((((....((....))..+(..(((((((....)))))))..).....)))).........................'), energy=-65.03946685791016, stack_energy=-61.862701416015625), StructureEnergy(Structure('...(((((((....)))))))....(((((((((((.(((........((....))..+...(((((((....)))))))....))))))))))).)))((((....((....))..+(..(((((((....)))))))..).....)))).........................'), energy=-65.03946685791016, stack_energy=-61.862701416015625), StructureEnergy(Structure('...(((((((....)))))))....(((((((((((.(((........((....))..+...(((((((....)))))))....))))))))))).)))((((....((....))..+(..(((((((....)))))))..).....)))).........................'), energy=-65.03946685791016, stack_energy=-61.862701416015625), StructureEnergy(Structure('...(((((((....)))))))....(((((((((((.(((........((....))..+...(((((((....)))))))....))))))))))).)))((((....((....))..+(..(((((((....)))))))..).....)))).........................'), energy=-65.03946685791016, stack_energy=-61.862701416015625), StructureEnergy(Structure('...(((((((....)))))))....(((((((((((.(((........((....))..+...(((((((....)))))))....))))))))))).)))((((....((....))..+(..(((((((....)))))))..).....)))).........................'), energy=-65.03946685791016, stack_energy=-61.862701416015625), StructureEnergy(Structure('...(((((((....)))))))....(((((((((((.(((........((....))..+...(((((((....)))))))....))))))))))).)))((((....((....))..+(..(((((((....)))))))..).....)))).........................'), energy=-65.03946685791016, stack_energy=-61.862701416015625), StructureEnergy(Structure('...(((((((....)))))))....(((((((((((.(((........((....))..+...(((((((....)))))))....))))))))))).)))((((....((....))..+(..(((((((....)))))))..).....)))).........................'), energy=-65.03946685791016, stack_energy=-61.862701416015625)]}), <Complex (i1+h2)>: nupack.analysis.ComplexResult({model: Model('stacking', 'rna06.json', T=310.15 K), pfunc: 7.806753175732111283138120173E+98, free_energy: -140.34137346365642, mfe_stack: -135.28135681152344, pairs: [[0.0595 0.0000 0.0000 ... 0.0000 0.0000 0.0000]\n",
       " [0.0000 0.0296 0.0000 ... 0.0000 0.0000 0.0000]\n",
       " [0.0000 0.0000 0.0108 ... 0.0000 0.0000 0.0000]\n",
       " ...\n",
       " [0.0000 0.0000 0.0000 ... 0.2926 0.0000 0.0000]\n",
       " [0.0000 0.0000 0.0000 ... 0.0000 0.8142 0.0000]\n",
       " [0.0000 0.0000 0.0000 ... 0.0000 0.0000 0.9994]], mfe: [StructureEnergy(Structure('(((((.........)))))(((.(((((((((((((((((((((((((.(((((((.((......)).))...))))).))))))))))))))))))))))))).)))...((((((((((((((((((((((((((((((((.............(((.(..(((..((.........))..))).).)))..........+...(((((((....)))))))...))))))))))))))))))))))))))))))))..'), energy=-136.972412109375, stack_energy=-135.28135681152344)]}), <Complex (h2+h2)>: nupack.analysis.ComplexResult({model: Model('stacking', 'rna06.json', T=310.15 K), pfunc: 26330810088315842355520460.68, free_energy: -36.074969576929874, mfe_stack: -31.781349182128906, pairs: [[0.6420 0.0000 0.0000 ... 0.0000 0.0000 0.0000]\n",
       " [0.0000 0.9166 0.0000 ... 0.0000 0.0000 0.0000]\n",
       " [0.0000 0.0000 0.9295 ... 0.0000 0.0000 0.0000]\n",
       " ...\n",
       " [0.0000 0.0000 0.0000 ... 0.7099 0.0000 0.0000]\n",
       " [0.0000 0.0000 0.0000 ... 0.0000 0.9962 0.0000]\n",
       " [0.0000 0.0000 0.0000 ... 0.0000 0.0000 0.9887]], mfe: [StructureEnergy(Structure('(..(((((((....)))))))..)......(.(((.(((..((((((.(.........+(..(((((((....)))))))..)......).))).)))..)))))).).........'), energy=-32.8929443359375, stack_energy=-31.781349182128906)]})})"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import nupack\n",
    "\n",
    "# Define the sequences for the three strands\n",
    "seq1 = \"GGGATTCATTTCACATCTCCTAATCCAGTCGTGGATGGGCTCTGTTTCCGTATTCTGTGAAGCCCTAGGGTCCGATACAGAAACAGAGCCCATCCACGACTGGAATGGCTCTGTTTCATCTTAAAGTCCTTGTAACAGTCGTCAAGACGAAACTAAGCCATAGAGGAGATGACAAATGAATAACCTGGCGGCAGCGCAAAAG\"\n",
    "seq2 = \"GGGCCAGTGACTTGTCACTGGGAACGGACCCTAGGGCTTCACAGAATACGGAAACGAC\"\n",
    "seq3 = \"GGGCTCACCTGCCAAGGTGAGAGCGACGACTGTTACAAGGACTTTAAGATGAAACGAC\"\n",
    "\n",
    "# Define the concentrations of each strand in moles/liter\n",
    "c1 = 2e-6\n",
    "c2 = 2e-6\n",
    "c3 = 2e-6\n",
    "\n",
    "# Set the temperature and salt concentration for the calculation\n",
    "temp = 37.0\n",
    "# salt = 0.15\n",
    "\n",
    "# Define physical model\n",
    "my_model = Model(material='rna', celsius=37)\n",
    "\n",
    "# Define strand species\n",
    "i1 = Strand(seq1, name='i1')\n",
    "h1 = Strand(seq2, name='h1')\n",
    "h2 = Strand(seq3, name='h2')\n",
    "\n",
    "# Define complexes\n",
    "poly1 = Complex([i1, h1])\n",
    "poly2 = Complex([i1, h1, h2])\n",
    "poly3 = Complex([i1, h1, h1, h2])\n",
    "poly4 = Complex([i1, h1, h2, h1, h2])\n",
    "\n",
    "# Define complex set comprising all monomers plus additional specified complexes\n",
    "my_set = ComplexSet(strands=[i1, h1, h2], complexes=SetSpec(max_size=3, include=[poly1, poly2, poly3, poly4]))\n",
    "\n",
    "# Analyze the set of complexes\n",
    "# Calculate pfunc, pairs, mfe for each complex\n",
    "# Calculate equilibrium complex concentrations (default) for each tube ensemble\n",
    "set_result = complex_analysis(complexes=my_set, compute=['pfunc', 'pairs', 'mfe'], model=my_model)\n",
    "set_result"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "e7d7d366-3589-4c52-976a-0f6351f65a4e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<b>Concentration results:</b> <table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th>Complex</th>\n",
       "      <th>tube (M)</th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <td>(i1+h2+h1)</td>\n",
       "      <td>2.000e-06</td>\n",
       "      <td></td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>(i1+h2)</td>\n",
       "      <td>1.848e-12</td>\n",
       "      <td></td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>(h1)</td>\n",
       "      <td>1.561e-12</td>\n",
       "      <td></td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>(h1+h1)</td>\n",
       "      <td>1.482e-13</td>\n",
       "      <td></td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>(h2)</td>\n",
       "      <td>1.885e-14</td>\n",
       "      <td></td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>(h1+h1+h1)</td>\n",
       "      <td>1.789e-17</td>\n",
       "      <td></td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>(i1+h1+h2)</td>\n",
       "      <td>1.714e-18</td>\n",
       "      <td></td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>(i1+h1+h2+h1+h2)</td>\n",
       "      <td>3.704e-19</td>\n",
       "      <td></td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>(i1)</td>\n",
       "      <td>3.248e-20</td>\n",
       "      <td></td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>(i1+h1)</td>\n",
       "      <td>3.016e-20</td>\n",
       "      <td></td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>(i1+i1+h2)</td>\n",
       "      <td>2.423e-20</td>\n",
       "      <td></td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>(i1+h2+h2)</td>\n",
       "      <td>1.477e-21</td>\n",
       "      <td></td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>(i1+h1+h1+h2)</td>\n",
       "      <td>2.261e-22</td>\n",
       "      <td></td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>(h1+h2)</td>\n",
       "      <td>7.038e-23</td>\n",
       "      <td></td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>(h2+h2)</td>\n",
       "      <td>2.268e-24</td>\n",
       "      <td></td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>(h1+h1+h2)</td>\n",
       "      <td>1.916e-24</td>\n",
       "      <td></td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>(i1+h1+h1)</td>\n",
       "      <td>1.850e-24</td>\n",
       "      <td></td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>(i1+i1)</td>\n",
       "      <td>2.130e-28</td>\n",
       "      <td></td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>(h1+h2+h2)</td>\n",
       "      <td>3.671e-33</td>\n",
       "      <td></td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>(h2+h2+h2)</td>\n",
       "      <td>2.148e-35</td>\n",
       "      <td></td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>(i1+i1+h1)</td>\n",
       "      <td>1.801e-35</td>\n",
       "      <td></td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>(i1+i1+i1)</td>\n",
       "      <td>8.321e-43</td>\n",
       "      <td></td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>"
      ],
      "text/plain": [
       "Result(tubes={<Tube tube>: <nupack.analysis.TubeResult object at 0x7f718f9316c0>})"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# specify strand concentrations for ComplexSet set1\n",
    "concentration_results1 = complex_concentrations(tube=my_set, data=set_result,\n",
    "    concentrations={i1: 2e-6, h1: 2e-6, h2: 2e-6})\n",
    "concentration_results1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "6dc2ac3f-b6f2-4e23-b300-f8ee13aaced9",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<b>Concentration results:</b> <table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th>Complex</th>\n",
       "      <th>tube1 (M)</th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <td>(i1+h2+h1)</td>\n",
       "      <td>2.000e-06</td>\n",
       "      <td></td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>(i1+h2)</td>\n",
       "      <td>1.852e-12</td>\n",
       "      <td></td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>(h1)</td>\n",
       "      <td>1.557e-12</td>\n",
       "      <td></td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>(h1+h1)</td>\n",
       "      <td>1.475e-13</td>\n",
       "      <td></td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>(i1)</td>\n",
       "      <td>6.102e-16</td>\n",
       "      <td></td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>(i1+h1)</td>\n",
       "      <td>5.652e-16</td>\n",
       "      <td></td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>(i1+i1+h2)</td>\n",
       "      <td>4.562e-16</td>\n",
       "      <td></td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>(h1+h1+h1)</td>\n",
       "      <td>1.778e-17</td>\n",
       "      <td></td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>(i1+h1+h2)</td>\n",
       "      <td>1.714e-18</td>\n",
       "      <td></td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>(h2)</td>\n",
       "      <td>1.006e-18</td>\n",
       "      <td></td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>(i1+i1)</td>\n",
       "      <td>7.517e-20</td>\n",
       "      <td></td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>(i1+h1+h1)</td>\n",
       "      <td>3.460e-20</td>\n",
       "      <td></td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>(i1+h2+h2)</td>\n",
       "      <td>7.896e-26</td>\n",
       "      <td></td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>(i1+i1+h1)</td>\n",
       "      <td>6.342e-27</td>\n",
       "      <td></td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>(h1+h2)</td>\n",
       "      <td>3.747e-27</td>\n",
       "      <td></td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>(h1+h1+h2)</td>\n",
       "      <td>1.018e-28</td>\n",
       "      <td></td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>(i1+i1+i1)</td>\n",
       "      <td>5.515e-30</td>\n",
       "      <td></td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>(h2+h2)</td>\n",
       "      <td>6.456e-33</td>\n",
       "      <td></td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>(h1+h2+h2)</td>\n",
       "      <td>1.043e-41</td>\n",
       "      <td></td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>(h2+h2+h2)</td>\n",
       "      <td>3.262e-48</td>\n",
       "      <td></td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>"
      ],
      "text/plain": [
       "Result(tubes={<Tube tube1>: <nupack.analysis.TubeResult object at 0x7f718f968b20>})"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# specify tube\n",
    "tube1 = Tube(strands={i1: 2e-6, h1: 2e-6, h2: 2e-6}, complexes=SetSpec(max_size=3), name='tube1')\n",
    "\n",
    "# calculate the partition function for each complex in the tube\n",
    "complex_results2 = complex_analysis(complexes=tube1, model=my_model, compute=['pfunc'])\n",
    "# use strand concentrations previously specified for tube1\n",
    "concentration_results2 = complex_concentrations(tube=tube1, data=complex_results2)\n",
    "concentration_results2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "599b337c-b443-4bcf-95f0-0646c1089fb1",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(Decimal('8.710995856118022188803954930E+116'), -165.9532788951629)"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "partition_function = pfunc(strands=[i1, h1, h2], model=my_model)\n",
    "partition_function "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "1cf3a057-1005-4f05-bc39-5716aaecfd5e",
   "metadata": {},
   "outputs": [
    {
     "ename": "RuntimeError",
     "evalue": "C++: : \"pair list length doesn't match sequence length\" (State.cc, line 27)\nlen(pairs) = 8\nn = 324\n",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mRuntimeError\u001b[0m                              Traceback (most recent call last)",
      "Cell \u001b[0;32mIn[14], line 1\u001b[0m\n\u001b[0;32m----> 1\u001b[0m dGstruc \u001b[38;5;241m=\u001b[39m \u001b[43mstructure_energy\u001b[49m\u001b[43m(\u001b[49m\u001b[43mstrands\u001b[49m\u001b[38;5;241;43m=\u001b[39;49m\u001b[43m[\u001b[49m\u001b[43mi1\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mh1\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mh2\u001b[49m\u001b[43m]\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mstructure\u001b[49m\u001b[38;5;241;43m=\u001b[39;49m\u001b[38;5;124;43m'\u001b[39;49m\u001b[38;5;124;43m((((+))))\u001b[39;49m\u001b[38;5;124;43m'\u001b[39;49m\u001b[43m,\u001b[49m\n\u001b[1;32m      2\u001b[0m \u001b[43m    \u001b[49m\u001b[43mmodel\u001b[49m\u001b[38;5;241;43m=\u001b[39;49m\u001b[43mmy_model\u001b[49m\u001b[43m)\u001b[49m\n\u001b[1;32m      3\u001b[0m \u001b[38;5;28mprint\u001b[39m(dGstruc)\n",
      "File \u001b[0;32m~/miniconda3/lib/python3.10/site-packages/nupack/model.py:261\u001b[0m, in \u001b[0;36mstructure_energy\u001b[0;34m(strands, structure, model, distinguishable)\u001b[0m\n\u001b[1;32m    259\u001b[0m \u001b[38;5;124;03m'''Free energy of a given secondary structure in (kcal/mol)'''\u001b[39;00m\n\u001b[1;32m    260\u001b[0m check_instance(model, Model)\n\u001b[0;32m--> 261\u001b[0m \u001b[38;5;28;01mreturn\u001b[39;00m \u001b[43mmodel\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mstructure_energy\u001b[49m\u001b[43m(\u001b[49m\u001b[43mstrands\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mstructure\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mdistinguishable\u001b[49m\u001b[43m)\u001b[49m\n",
      "File \u001b[0;32m~/miniconda3/lib/python3.10/site-packages/nupack/rebind/render.py:238\u001b[0m, in \u001b[0;36mrender_function.<locals>.wrap\u001b[0;34m(_orig, _bind, _old, *args, **kwargs)\u001b[0m\n\u001b[1;32m    236\u001b[0m bound \u001b[38;5;241m=\u001b[39m _bind(\u001b[38;5;241m*\u001b[39margs, \u001b[38;5;241m*\u001b[39m\u001b[38;5;241m*\u001b[39mkwargs)\n\u001b[1;32m    237\u001b[0m bound\u001b[38;5;241m.\u001b[39mapply_defaults()\n\u001b[0;32m--> 238\u001b[0m \u001b[38;5;28;01mreturn\u001b[39;00m \u001b[43m_old\u001b[49m\u001b[43m(\u001b[49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[43mbound\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43margs\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43m_fun_\u001b[49m\u001b[38;5;241;43m=\u001b[39;49m\u001b[43m_orig\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[43mbound\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mkwargs\u001b[49m\u001b[43m)\u001b[49m\n",
      "File \u001b[0;32m~/miniconda3/lib/python3.10/site-packages/nupack/model.py:235\u001b[0m, in \u001b[0;36mModel.structure_energy\u001b[0;34m(self, strands, structure, distinguishable, _fun_)\u001b[0m\n\u001b[1;32m    233\u001b[0m \u001b[38;5;28;01mif\u001b[39;00m \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39mmaterial \u001b[38;5;241m==\u001b[39m \u001b[38;5;124m'\u001b[39m\u001b[38;5;124mDNA/RNA\u001b[39m\u001b[38;5;124m'\u001b[39m \u001b[38;5;129;01mand\u001b[39;00m \u001b[38;5;28misinstance\u001b[39m(strands, Complex):\n\u001b[1;32m    234\u001b[0m     strands \u001b[38;5;241m=\u001b[39m standardize_alphabet([strands], \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39malphabet())[\u001b[38;5;241m0\u001b[39m]\n\u001b[0;32m--> 235\u001b[0m \u001b[38;5;28;01mreturn\u001b[39;00m \u001b[43m_fun_\u001b[49m\u001b[43m(\u001b[49m\u001b[38;5;28;43mself\u001b[39;49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mSequenceList\u001b[49m\u001b[43m(\u001b[49m\u001b[43mstrands\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43malphabet\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;241;43m=\u001b[39;49m\u001b[43m \u001b[49m\u001b[38;5;28;43mself\u001b[39;49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43malphabet\u001b[49m\u001b[43m(\u001b[49m\u001b[43m)\u001b[49m\u001b[43m)\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mPairList\u001b[49m\u001b[43m(\u001b[49m\u001b[43mstructure\u001b[49m\u001b[43m)\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mdistinguishable\u001b[49m\u001b[43m)\u001b[49m\u001b[38;5;241m.\u001b[39mcast(\u001b[38;5;28mfloat\u001b[39m)\n",
      "\u001b[0;31mRuntimeError\u001b[0m: C++: : \"pair list length doesn't match sequence length\" (State.cc, line 27)\nlen(pairs) = 8\nn = 324\n"
     ]
    }
   ],
   "source": [
    "dGstruc = structure_energy(strands=[i1, h1, h2], structure='((((+))))',\n",
    "    model=my_model)\n",
    "print(dGstruc)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "214479b2-c0f2-42b8-abcc-5508937c08f0",
   "metadata": {},
   "outputs": [],
   "source": [
    "strn = [i1, h1, h2]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "f1ee6063-11c9-4ef5-9f75-4cd12f644044",
   "metadata": {},
   "outputs": [
    {
     "ename": "RuntimeError",
     "evalue": "C++: : \"pair list length doesn't match sequence length\" (State.cc, line 27)\nlen(pairs) = 6\nn = 324\n",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mRuntimeError\u001b[0m                              Traceback (most recent call last)",
      "Cell \u001b[0;32mIn[17], line 1\u001b[0m\n\u001b[0;32m----> 1\u001b[0m probability \u001b[38;5;241m=\u001b[39m \u001b[43mstructure_probability\u001b[49m\u001b[43m(\u001b[49m\u001b[43mstrands\u001b[49m\u001b[38;5;241;43m=\u001b[39;49m\u001b[43mstrn\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mstructure\u001b[49m\u001b[38;5;241;43m=\u001b[39;49m\u001b[38;5;124;43m'\u001b[39;49m\u001b[38;5;124;43m(((+)))\u001b[39;49m\u001b[38;5;124;43m'\u001b[39;49m\u001b[43m,\u001b[49m\n\u001b[1;32m      2\u001b[0m \u001b[43m    \u001b[49m\u001b[43mmodel\u001b[49m\u001b[38;5;241;43m=\u001b[39;49m\u001b[43mmy_model\u001b[49m\u001b[43m)\u001b[49m\n\u001b[1;32m      3\u001b[0m \u001b[38;5;28mprint\u001b[39m(probability)\n",
      "File \u001b[0;32m~/miniconda3/lib/python3.10/site-packages/nupack/analysis.py:269\u001b[0m, in \u001b[0;36mstructure_probability\u001b[0;34m(strands, structure, model)\u001b[0m\n\u001b[1;32m    267\u001b[0m strands \u001b[38;5;241m=\u001b[39m anonymous_complex(strands, alphabet \u001b[38;5;241m=\u001b[39m model\u001b[38;5;241m.\u001b[39malphabet())\n\u001b[1;32m    268\u001b[0m res \u001b[38;5;241m=\u001b[39m complex_analysis([strands], model, compute\u001b[38;5;241m=\u001b[39m[\u001b[38;5;124m'\u001b[39m\u001b[38;5;124mpfunc\u001b[39m\u001b[38;5;124m'\u001b[39m])[strands]\n\u001b[0;32m--> 269\u001b[0m e \u001b[38;5;241m=\u001b[39m \u001b[43menergy\u001b[49m\u001b[43m(\u001b[49m\u001b[43mstrands\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mstructure\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mmodel\u001b[49m\u001b[43m)\u001b[49m\n\u001b[1;32m    270\u001b[0m \u001b[38;5;28;01mreturn\u001b[39;00m numpy\u001b[38;5;241m.\u001b[39mexp(\u001b[38;5;241m-\u001b[39mmodel\u001b[38;5;241m.\u001b[39mbeta \u001b[38;5;241m*\u001b[39m (e \u001b[38;5;241m-\u001b[39m res\u001b[38;5;241m.\u001b[39mfree_energy))\n",
      "File \u001b[0;32m~/miniconda3/lib/python3.10/site-packages/nupack/analysis.py:258\u001b[0m, in \u001b[0;36menergy\u001b[0;34m(strands, structure, model)\u001b[0m\n\u001b[1;32m    256\u001b[0m bonus \u001b[38;5;241m=\u001b[39m \u001b[38;5;28mgetattr\u001b[39m(strands, \u001b[38;5;124m'\u001b[39m\u001b[38;5;124menergy\u001b[39m\u001b[38;5;124m'\u001b[39m, \u001b[38;5;241m0.0\u001b[39m)\n\u001b[1;32m    257\u001b[0m strands \u001b[38;5;241m=\u001b[39m anonymous_complex(strands, alphabet \u001b[38;5;241m=\u001b[39m model\u001b[38;5;241m.\u001b[39malphabet())\n\u001b[0;32m--> 258\u001b[0m \u001b[38;5;28;01mreturn\u001b[39;00m \u001b[43mmodel\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mstructure_energy\u001b[49m\u001b[43m(\u001b[49m\u001b[43mstrands\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mstructure\u001b[49m\u001b[43m)\u001b[49m \u001b[38;5;241m+\u001b[39m bonus\n",
      "File \u001b[0;32m~/miniconda3/lib/python3.10/site-packages/nupack/rebind/render.py:238\u001b[0m, in \u001b[0;36mrender_function.<locals>.wrap\u001b[0;34m(_orig, _bind, _old, *args, **kwargs)\u001b[0m\n\u001b[1;32m    236\u001b[0m bound \u001b[38;5;241m=\u001b[39m _bind(\u001b[38;5;241m*\u001b[39margs, \u001b[38;5;241m*\u001b[39m\u001b[38;5;241m*\u001b[39mkwargs)\n\u001b[1;32m    237\u001b[0m bound\u001b[38;5;241m.\u001b[39mapply_defaults()\n\u001b[0;32m--> 238\u001b[0m \u001b[38;5;28;01mreturn\u001b[39;00m \u001b[43m_old\u001b[49m\u001b[43m(\u001b[49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[43mbound\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43margs\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43m_fun_\u001b[49m\u001b[38;5;241;43m=\u001b[39;49m\u001b[43m_orig\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[43mbound\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mkwargs\u001b[49m\u001b[43m)\u001b[49m\n",
      "File \u001b[0;32m~/miniconda3/lib/python3.10/site-packages/nupack/model.py:235\u001b[0m, in \u001b[0;36mModel.structure_energy\u001b[0;34m(self, strands, structure, distinguishable, _fun_)\u001b[0m\n\u001b[1;32m    233\u001b[0m \u001b[38;5;28;01mif\u001b[39;00m \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39mmaterial \u001b[38;5;241m==\u001b[39m \u001b[38;5;124m'\u001b[39m\u001b[38;5;124mDNA/RNA\u001b[39m\u001b[38;5;124m'\u001b[39m \u001b[38;5;129;01mand\u001b[39;00m \u001b[38;5;28misinstance\u001b[39m(strands, Complex):\n\u001b[1;32m    234\u001b[0m     strands \u001b[38;5;241m=\u001b[39m standardize_alphabet([strands], \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39malphabet())[\u001b[38;5;241m0\u001b[39m]\n\u001b[0;32m--> 235\u001b[0m \u001b[38;5;28;01mreturn\u001b[39;00m \u001b[43m_fun_\u001b[49m\u001b[43m(\u001b[49m\u001b[38;5;28;43mself\u001b[39;49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mSequenceList\u001b[49m\u001b[43m(\u001b[49m\u001b[43mstrands\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43malphabet\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;241;43m=\u001b[39;49m\u001b[43m \u001b[49m\u001b[38;5;28;43mself\u001b[39;49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43malphabet\u001b[49m\u001b[43m(\u001b[49m\u001b[43m)\u001b[49m\u001b[43m)\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mPairList\u001b[49m\u001b[43m(\u001b[49m\u001b[43mstructure\u001b[49m\u001b[43m)\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mdistinguishable\u001b[49m\u001b[43m)\u001b[49m\u001b[38;5;241m.\u001b[39mcast(\u001b[38;5;28mfloat\u001b[39m)\n",
      "\u001b[0;31mRuntimeError\u001b[0m: C++: : \"pair list length doesn't match sequence length\" (State.cc, line 27)\nlen(pairs) = 6\nn = 324\n"
     ]
    }
   ],
   "source": [
    "probability = structure_probability(strands=strn, structure='(((+)))',\n",
    "    model=my_model)\n",
    "print(probability)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "c44f28ec-c428-47c6-b153-d2bcad726fc9",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[0.0595 0.0000 0.0000 ... 0.0000 0.0000 0.0000]\n",
      " [0.0000 0.0296 0.0000 ... 0.0000 0.0000 0.0000]\n",
      " [0.0000 0.0000 0.0108 ... 0.0000 0.0000 0.0000]\n",
      " ...\n",
      " [0.0000 0.0000 0.0000 ... 0.2926 0.0000 0.0000]\n",
      " [0.0000 0.0000 0.0000 ... 0.0000 0.8142 0.0000]\n",
      " [0.0000 0.0000 0.0000 ... 0.0000 0.0000 0.9994]]\n"
     ]
    }
   ],
   "source": [
    "probability_matrix = pairs(strands=strn,  model=my_model)\n",
    "print(probability_matrix)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "7f564536-b333-41ab-8c1d-6c0cf26114ce",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[5.94915886e-02, 0.00000000e+00, 0.00000000e+00, ...,\n",
       "        0.00000000e+00, 0.00000000e+00, 3.40686516e-10],\n",
       "       [0.00000000e+00, 2.95902177e-02, 0.00000000e+00, ...,\n",
       "        0.00000000e+00, 0.00000000e+00, 3.41957125e-10],\n",
       "       [0.00000000e+00, 0.00000000e+00, 1.08296901e-02, ...,\n",
       "        0.00000000e+00, 0.00000000e+00, 3.43880850e-11],\n",
       "       ...,\n",
       "       [0.00000000e+00, 0.00000000e+00, 0.00000000e+00, ...,\n",
       "        2.92628984e-01, 0.00000000e+00, 0.00000000e+00],\n",
       "       [0.00000000e+00, 0.00000000e+00, 0.00000000e+00, ...,\n",
       "        0.00000000e+00, 8.14216936e-01, 0.00000000e+00],\n",
       "       [3.40686516e-10, 3.41957125e-10, 3.43880850e-11, ...,\n",
       "        0.00000000e+00, 0.00000000e+00, 9.99449620e-01]])"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "probability_matrix.to_array()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "eaaa7726-9171-4e3f-a147-6c48a7e52638",
   "metadata": {},
   "outputs": [],
   "source": [
    "mfe_structures = mfe(strands=strn, model=my_model)\n",
    "print('Free energy of MFE proxy structure: %.2f kcal/mol' % mfe_structures[0].energy)\n",
    "print('MFE proxy structure in dot-parens-plus notation: %s' % mfe_structures[0].structure)\n",
    "print('MFE proxy structure as structure matrix:\\n%s' % mfe_structures[0].structure.matrix())"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fba64d21-92fa-4d5e-a3dc-92161f55423a",
   "metadata": {},
   "source": [
    "# GC Content Similarity "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "5290695c-f26c-4f4f-8a8e-140f63e6988c",
   "metadata": {},
   "outputs": [],
   "source": [
    "import nupack\n",
    "from nupack import *\n",
    "a = Domain('N10', name='a')\n",
    "b = Domain('N20', name='b')\n",
    "C = TargetStrand([a, b, a], name='Strand C')\n",
    "\n",
    "# similarity constraint for a concatenation of domains\n",
    "sim1 = Similarity([a, ~a, b], 'S5K35', limits=[0.25, 0.75])\n",
    "\n",
    "# similarity constraint for a target strand\n",
    "sim2 = Similarity(C, 'S30K10', limits=[0.25, 0.75]) # for a strand\n",
    "\n",
    "# use similarity constraint to enforce 45-55% GC content\n",
    "sim3 = Similarity([a, b], 'S30', limits=[0.45, 0.55])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "fa593da5-a355-4140-930d-570e8016c051",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "SimilarityConstraint\n",
      "    domains: [NNNNNNNNNN,\n",
      "        NNNNNNNNNN,\n",
      "        NNNNNNNNNNNNNNNNNNNN]\n",
      "    reference: SSSSSKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK\n",
      "    range: (0.25 : 0.75)\n",
      "    weight: 1\n"
     ]
    }
   ],
   "source": [
    "print(sim1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "95b3720f-e747-41ea-883e-87835e62012a",
   "metadata": {},
   "outputs": [
    {
     "ename": "TypeError",
     "evalue": "descriptor '__dict__' for 'Similarity' objects doesn't apply to a 'Similarity' object",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mTypeError\u001b[0m                                 Traceback (most recent call last)",
      "Cell \u001b[0;32mIn[8], line 1\u001b[0m\n\u001b[0;32m----> 1\u001b[0m \u001b[38;5;28;01mfor\u001b[39;00m att \u001b[38;5;129;01min\u001b[39;00m \u001b[38;5;28;43mdir\u001b[39;49m\u001b[43m(\u001b[49m\u001b[43msim3\u001b[49m\u001b[43m)\u001b[49m:\n\u001b[1;32m      2\u001b[0m     \u001b[38;5;28mprint\u001b[39m (att, \u001b[38;5;28mgetattr\u001b[39m(sim3))\n",
      "\u001b[0;31mTypeError\u001b[0m: descriptor '__dict__' for 'Similarity' objects doesn't apply to a 'Similarity' object"
     ]
    }
   ],
   "source": [
    "for att in dir(sim3):\n",
    "    print (att, getattr(sim3))"
   ]
  }
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