example_rna_folding.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "56f0b47e",
   "metadata": {},
   "source": [
    "# Example: RNA Folding on the Dynex Platform"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "33b030eb",
   "metadata": {},
   "source": [
    "In biology and chemistry, the properties of a molecule are not solely determined by a set of atoms but also by the shape of the molecule. In genetics, the shape of an RNA molecule is largely determined by how it bends back on itself. The sequence of A’s, U’s, G’s, and C’s that make up RNA has certain pairs that are drawn together to form hydrogen bonds. A sequence of several bonds in a row is called a stem, and a stem provides sufficient force to keep the molecule folded together. RNA molecules naturally form some stems while avoiding others in a manner that minimizes the free energy of the system.\n",
    "\n",
    "This demo program takes an RNA sequence and applies a quadratic model in pursuit of the optimal stem configuration."
   ]
  },
  {
   "attachments": {
    "Single_Stem.png": {
     "image/png": 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"
    }
   },
   "cell_type": "markdown",
   "id": "989f5d68",
   "metadata": {},
   "source": [
    "![Single_Stem.png](attachment:Single_Stem.png)\n",
    "Fig.1 - An RNA sequence with a single stem of length 4."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "60f35aa4",
   "metadata": {},
   "source": [
    "Predicting the existence of stems is important to predicting the properties of the RNA molecule. However, prediction is complicated by two important factors.\n",
    "\n",
    "First, stems are not allowed to overlap. A simple case of overlapping can be illustrated by Figure 1. The stem expressed by the pink lines can be denoted with the tuple (2, 5, 12, 15). Here, indexing starts with 0 at the far left C and continues along the sequence represented by the gray edges, ending with index 16 at the bottom-most C. The indices of the eight nucleotides in the stem are labeled in the figure. The four pink edges illustrate the four bonds that make up the stem. While there are eight nucleotides in the stem, bonded along pink lines, the 4-tuple completely determines the stem. However, the smaller stems (2, 4, 13, 15) and (3, 5, 12, 14) also need to be considered, even though the optimal solution will not include them in this case. Note that by default, we will only consider stems with length at least 3, as smaller stems are unlikely to form and sustain bonds.\n",
    "\n",
    "Second, the intertwining phenomenon known as a pseudoknot is less energetically favorable. In Figure 2, we see an example of such a pseudoknot, where one side of a stem occurs in between the two sides of a different stem. The use of a quadratic objective allows us to make pseudoknots less likely to occur in optimal solutions, increasing overall accuracy. Specifically, we include a quadratic term for each pair of stems that, if present, form a pseudoknot. The positive coefficient on this quadratic term discourages the forming of pseudoknots without explicitly disallowing them."
   ]
  },
  {
   "attachments": {
    "pseudoknot2.png": {
     "image/png": 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"
    }
   },
   "cell_type": "markdown",
   "id": "3f277b1b",
   "metadata": {},
   "source": [
    "![pseudoknot2.png](attachment:pseudoknot2.png)\n",
    " Fig.2 - A pseudoknot formed by a stem of length 3 and a stem of length 5."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f462df19",
   "metadata": {},
   "source": [
    "This demo is loosely based on the work in [1], which is in turn inspired by [2]."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8d964a5e",
   "metadata": {},
   "source": [
    "## Problem Formulation "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3898c884",
   "metadata": {},
   "source": [
    "In predicting the stems of an RNA molecule, we build a quadratic model with three contributing factors.\n",
    "\n",
    "1. Each potential stem is encoded as a binary variable, linearly weighted by the negative square of the length, k.\n",
    "\n",
    "2. Each potential pseudoknot is encoded as a quadratic term, weighted by to the product of the two lengths times a positive parameter c.\n",
    "\n",
    "3. Overlapping stems are not allowed. Potential overlaps give rise to constraints in the model."
   ]
  },
  {
   "attachments": {
    "model.png": {
     "image/png": "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"
    }
   },
   "cell_type": "markdown",
   "id": "4e92c23b",
   "metadata": {},
   "source": [
    "![model.png](attachment:model.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "dd51f017",
   "metadata": {},
   "source": [
    "Here, each xi is a binary variable indicating the inclusion/exclusion of the ith stem. Each constant ki is the length of said stem. The indexing set S is the set of all pairs of stems that form a pseudoknot. Finally, c is a tunable parameter adjusting the impact of pseudoknots. It is set to 0.3 by default. If c = 0, the affect of pseudoknots is ignored, while c > 1 eliminates all pseudoknots from optimal solutions. This formulation (and default choice of c) is loosely based on [1].\n",
    "\n",
    "In the printed solution, each stem is denoted by four numbers. The first two numbers correspond to the beginning and ending indices of the first side of the stem. Similarly, the last two numbers correspond to the beginning and ending indices of the second side of the stem."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f2e0ebdd",
   "metadata": {},
   "source": [
    "## Code Specifics "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9b95369c",
   "metadata": {},
   "source": [
    "By default, the minimum stem length is set to 3. A stem of length 5 thus contains two stems of length 4 and three stems of length 3 under inclusion. The stem dictionary records the maximal stems (under inclusion) as keys, where each key maps to a list of the associated stems weakly contained within the maximal stem.\n",
    "\n",
    "No two stems contained in the same maximal key can both be in an optimal solution, so we treat them all as overlapping, regardless of if it is literally the case. This particular case of overlapping is enforced by treating the set of stems contained in a maximal stem as a single discrete variable by use of the add_discrete method.\n",
    "\n",
    "We further use the stem dictionary structure to avoid comparing all combinations of stems when searching for pseudoknots and overlaps.\n",
    "\n",
    "Plotting uses a randomized process to find a reasonable layout. For this reason, the plot will change in successive runs, even if the solution does not.\n",
    "\n",
    "Input text files should have a number at the beginning of each line, followed by a sequence of A, C, G, U, and T's. The file reader ignores the leading number and is not sensitive to spaces, upper vs. lower case, or line breaks. By convention, spaces are used to separate every 10 letters and the number at the beginning of each line is included to keep track of the location in the sequence. For instance, if there are 30 letters on each line, then there would be three groups of 10 letters on each line, with the leading numbers increasing by 30 each line."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6d361347",
   "metadata": {},
   "source": [
    "## References "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "bd5c9d31",
   "metadata": {},
   "source": [
    "[1] Fox DM, MacDermaid CM, Schreij AM, Zwierzyna M, Walker RC. \"RNA folding using quantum computers,\" PLOS Computational Biology.\n",
    "\n",
    "[2] Kai, Zhang, et al. \"An efficient simulated annealing algorithm for the RNA secondary structure prediction with Pseudoknots,\" BMC Genomics."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "929047af",
   "metadata": {},
   "source": [
    "## Code "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "4c52a895",
   "metadata": {},
   "outputs": [],
   "source": [
    "from collections import defaultdict\n",
    "from itertools import product, combinations\n",
    "import click\n",
    "import matplotlib\n",
    "import numpy as np\n",
    "import networkx as nx\n",
    "import dimod\n",
    "import matplotlib.pyplot as plt\n",
    "import dynex\n",
    "import dimod"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ff031eea",
   "metadata": {},
   "source": [
    "## Helper functions"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "987c863f",
   "metadata": {},
   "source": [
    "Read properly formatted RNA text file and returns a matrix of possible hydrogen bonding pairs:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "17846966",
   "metadata": {},
   "outputs": [],
   "source": [
    "def text_to_matrix(file_name, min_loop):\n",
    "    \"\"\" Reads properly formatted RNA text file and returns a matrix of possible hydrogen bonding pairs.\n",
    "\n",
    "    Args:\n",
    "        file_name (str):\n",
    "            Path to text file.\n",
    "        min_loop (int):\n",
    "            Minimum number of nucleotides separating two sides of a stem.\n",
    "\n",
    "    Returns:\n",
    "        :class: `numpy.ndarray`:\n",
    "            Numpy matrix of 0's and 1's, where 1 represents a possible bonding pair.\n",
    "    \"\"\"\n",
    "\n",
    "    # Requires text file of RNA data written in same format as examples.\n",
    "    with open(file_name) as f:\n",
    "        rna = \"\".join((\"\".join(line.split()[1:]) for line in f.readlines())).lower()\n",
    "\n",
    "    # Create a dictionary of all indices where each nucleotide occurs.\n",
    "    index_dict = defaultdict(list)\n",
    "\n",
    "    # Create a dictionary giving list of indices for each nucleotide.\n",
    "    for i, nucleotide in enumerate(rna):\n",
    "        index_dict[nucleotide].append(i)\n",
    "\n",
    "    # List of possible hydrogen bonds for stems.\n",
    "    # Recall that 't' is sometimes used as a stand-in for 'u'.\n",
    "    hydrogen_bonds = [('a', 't'), ('a', 'u'), ('c', 'g'), ('g', 't'), ('g', 'u')]\n",
    "\n",
    "    # Create a upper triangular 0/1 matrix indicating where bonds may occur.\n",
    "    bond_matrix = np.zeros((len(rna), len(rna)), dtype=bool)\n",
    "    for pair in hydrogen_bonds:\n",
    "        for bond in product(index_dict[pair[0]], index_dict[pair[1]]):\n",
    "            if abs(bond[0] - bond[1]) > min_loop:\n",
    "                bond_matrix[min(bond), max(bond)] = 1\n",
    "\n",
    "    return bond_matrix\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "126e1165",
   "metadata": {},
   "source": [
    "Takes a matrix of potential hydrogen binding pairs and returns a dictionary of possible stems:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "061ca56d",
   "metadata": {},
   "outputs": [],
   "source": [
    "def make_stem_dict(bond_matrix, min_stem, min_loop):\n",
    "    \"\"\" Takes a matrix of potential hydrogen binding pairs and returns a dictionary of possible stems.\n",
    "\n",
    "    The stem dictionary records the maximal stems (under inclusion) as keys,\n",
    "    where each key maps to a list of the associated stems weakly contained within the maximal stem.\n",
    "    Recording stems in this manner allows for faster computations.\n",
    "\n",
    "    Args:\n",
    "        bond_matrix (:class: `numpy.ndarray`):\n",
    "            Numpy matrix of 0's and 1's, where 1 represents a possible bonding pair.\n",
    "        min_stem (int):\n",
    "            Minimum number of nucleotides in each side of a stem.\n",
    "        min_loop (int):\n",
    "            Minimum number of nucleotides separating two sides of a stem.\n",
    "\n",
    "    Returns:\n",
    "        dict: Dictionary of all possible stems with maximal stems as keys.\n",
    "    \"\"\"\n",
    "\n",
    "    stem_dict = {}\n",
    "    n = bond_matrix.shape[0]\n",
    "\n",
    "    # Iterate through matrix looking for possible stems.\n",
    "    for i in range(n + 1 - (2 * min_stem + min_loop)):\n",
    "        for j in range(i + 2 * min_stem + min_loop - 1, n):\n",
    "            if bond_matrix[i, j]:\n",
    "                k = 1\n",
    "                # Check down and left for length of stem.\n",
    "                # Note that bond_matrix is strictly upper triangular, so loop will terminate.\n",
    "                while bond_matrix[i + k, j - k]:\n",
    "                    bond_matrix[i + k, j - k] = False\n",
    "                    k += 1\n",
    "\n",
    "                if k >= min_stem:\n",
    "                    # A 4-tuple is used to represent the stem.\n",
    "                    stem_dict[(i, i + k - 1, j - k + 1, j)] = []\n",
    "\n",
    "    # Iterate through all sub-stems weakly contained in a maximal stem under inclusion.\n",
    "    for stem in stem_dict.keys():\n",
    "        stem_dict[stem].extend([(stem[0] + i, stem[0] + k, stem[3] - k, stem[3] - i)\n",
    "                                for i in range(stem[1] - stem[0] - min_stem + 2)\n",
    "                                for k in range(i + min_stem - 1, stem[1] - stem[0] + 1)])\n",
    "\n",
    "    return stem_dict"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8f0830c8",
   "metadata": {},
   "source": [
    "Checks if 2 stems use any of the same nucleotides:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "57433e0f",
   "metadata": {},
   "outputs": [],
   "source": [
    "def check_overlap(stem1, stem2):\n",
    "    \"\"\" Checks if 2 stems use any of the same nucleotides.\n",
    "\n",
    "    Args:\n",
    "        stem1 (tuple):\n",
    "            4-tuple containing stem information.\n",
    "        stem2 (tuple):\n",
    "            4-tuple containing stem information.\n",
    "\n",
    "    Returns:\n",
    "         bool: Boolean indicating if the two stems overlap.\n",
    "    \"\"\"\n",
    "\n",
    "    # Check for string dummy variable used when implementing a discrete variable.\n",
    "    if type(stem1) == str or type(stem2) == str:\n",
    "        return False\n",
    "\n",
    "    # Check if any endpoints of stem2 overlap with stem1.\n",
    "    for val in stem2:\n",
    "        if stem1[0] <= val <= stem1[1] or stem1[2] <= val <= stem1[3]:\n",
    "            return True\n",
    "    # Check if endpoints of stem1 overlap with stem2.\n",
    "    # Do not need to check all stem1 endpoints.\n",
    "    for val in stem1[1:3]:\n",
    "        if stem2[0] <= val <= stem2[1] or stem2[2] <= val <= stem2[3]:\n",
    "            return True\n",
    "\n",
    "    return False\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1162b114",
   "metadata": {},
   "source": [
    "Creates a dictionary with all possible pseudoknots as keys and appropriate penalties as values. The penalty is the parameter c times the product of the lengths of the two stems in the knot."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "d33c457b",
   "metadata": {},
   "outputs": [],
   "source": [
    "def pseudoknot_terms(stem_dict, min_stem=3, c=0.3):\n",
    "    \"\"\" Creates a dictionary with all possible pseudoknots as keys and appropriate penalties as values.\n",
    "\n",
    "    The penalty is the parameter c times the product of the lengths of the two stems in the knot.\n",
    "\n",
    "    Args:\n",
    "        stem_dict (dict):\n",
    "            Dictionary with maximal stems as keys and list of weakly contained sub-stems as values.\n",
    "        min_stem (int):\n",
    "            Smallest number of consecutive bonds to be considered a stem.\n",
    "        c (float):\n",
    "            Parameter factor of the penalty on pseudoknots.\n",
    "\n",
    "    Returns:\n",
    "         dict: Dictionary with all possible pseudoknots as keys and appropriate penalty as as value pair.\n",
    "    \"\"\"\n",
    "\n",
    "    pseudos = {}\n",
    "    # Look within all pairs of maximal stems for possible pseudoknots.\n",
    "    for stem1, stem2 in product(stem_dict.keys(), stem_dict.keys()):\n",
    "        # Using product instead of combinations allows for short asymmetric checks.\n",
    "        if stem1[0] + 2 * min_stem < stem2[1] and stem1[2] + 2 * min_stem < stem2[3]:\n",
    "            pseudos.update({(substem1, substem2): c * (1 + substem1[1] - substem1[0]) * (1 + substem2[1] - substem2[0])\n",
    "                            for substem1, substem2\n",
    "                            in product(stem_dict[stem1], stem_dict[stem2])\n",
    "                            if substem1[1] < substem2[0] and substem2[1] < substem1[2] and substem1[3] < substem2[2]})\n",
    "    return pseudos"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a1acc651",
   "metadata": {},
   "source": [
    "Creates a constrained quadratic model to optimize most likely stems from a dictionary of possible stems:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "489690ba",
   "metadata": {},
   "outputs": [],
   "source": [
    "def build_cqm(stem_dict, min_stem, c):\n",
    "    \"\"\" Creates a constrained quadratic model to optimize most likely stems from a dictionary of possible stems.\n",
    "\n",
    "    Args:\n",
    "        stem_dict (dict):\n",
    "            Dictionary with maximal stems as keys and list of weakly contained sub-stems as values.\n",
    "        min_stem (int):\n",
    "            Smallest number of consecutive bonds to be considered a stem.\n",
    "        c (float):\n",
    "            Parameter factor of the penalty on pseudoknots.\n",
    "\n",
    "    Returns:\n",
    "         :class:`~dimod.ConstrainedQuadraticModel`: Optimization model for RNA folding.\n",
    "    \"\"\"\n",
    "\n",
    "    # Create linear coefficients of -k^2, prioritizing inclusion of long stems.\n",
    "    # We depart from the reference paper in this formulation.\n",
    "    linear_coeffs = {stem: -1 * (stem[1] - stem[0] + 1) ** 2 for sublist in stem_dict.values() for stem in sublist}\n",
    "\n",
    "    # Create constraints for overlapping and and sub-stem containment.\n",
    "    quadratic_coeffs = pseudoknot_terms(stem_dict, min_stem=min_stem, c=c)\n",
    "\n",
    "    bqm = dimod.BinaryQuadraticModel(linear_coeffs, quadratic_coeffs, 'BINARY')\n",
    "\n",
    "    cqm = dimod.ConstrainedQuadraticModel()\n",
    "    cqm.set_objective(bqm)\n",
    "\n",
    "    # Add constraint disallowing overlapping sub-stems included in same maximal stem.\n",
    "    for stem, substems in stem_dict.items():\n",
    "        if len(substems) > 1:\n",
    "            # Add the variable for all zeros case in one-hot constraint\n",
    "            zeros = 'Null:' + str(stem)\n",
    "            cqm.add_variable(zeros, 'BINARY')\n",
    "            cqm.add_discrete(substems + [zeros], stem)\n",
    "\n",
    "    for stem1, stem2 in combinations(stem_dict.keys(), 2):\n",
    "        # Check maximal stems first.\n",
    "        if check_overlap(stem1, stem2):\n",
    "            # If maximal stems overlap, compare list of smaller stems.\n",
    "            for stem_pair in product(stem_dict[stem1], stem_dict[stem2]):\n",
    "                if check_overlap(stem_pair[0], stem_pair[1]):\n",
    "                    cqm.add_constraint(dimod.quicksum([dimod.Binary(stem) for stem in stem_pair]) <= 1)\n",
    "\n",
    "    return cqm"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b20c20d3",
   "metadata": {},
   "source": [
    "## RNA Folding Example: Tobacco Mild Greed Mosaic Virus"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "66f3946c",
   "metadata": {},
   "source": [
    "The folder 'rna-data' contains multiple RNA sequences, including the HIV virus. For demonstration purposes we are using the \"Tobamovirus\", which is the Tobacco Mild Green Mosaic Virus:\n",
    "\n",
    "https://rnavlab.utep.edu/static/PKB_files/PKB92"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b4760de9",
   "metadata": {},
   "source": [
    "By default, the minimum stem length is set to 3. A stem of length 5 thus contains two stems of length 4 and three stems of length 3 under inclusion. The stem dictionary records the maximal stems (under inclusion) as keys, where each key maps to a list of the associated stems weakly contained within the maximal stem.\n",
    "\n",
    "No two stems contained in the same maximal key can both be in an optimal solution, so we treat them all as overlapping, regardless of if it is literally the case. This particular case of overlapping is enforced by treating the set of stems contained in a maximal stem as a single discrete variable by use of the add_discrete method.\n",
    "\n",
    "We further use the stem dictionary structure to avoid comparing all combinations of stems when searching for pseudoknots and overlaps. First we define the parameters:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "622dae7c",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Defining the parameters:\n",
    "path     = \"rna-data/TMGMV_UPD-PK1.txt\"\n",
    "min_stem = 3 # Minimum length for a stem to be considered\n",
    "min_loop = 2 # Minimum number of nucleotides separating two sides of a stem\n",
    "c = 0.3      # Multiplier for the coefficient of the quadratic terms for pseudoknots"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0b73cd9c",
   "metadata": {},
   "source": [
    "Then we load the RNA sequence and convert it into a matrix. Input text files should have a number at the beginning of each line, followed by a sequence of A, C, G, U, and T's. The file reader ignores the leading number and is not sensitive to spaces, upper vs. lower case, or line breaks. By convention, spaces are used to separate every 10 letters and the number at the beginning of each line is included to keep track of the location in the sequence. For instance, if there are 30 letters on each line, then there would be three groups of 10 letters on each line, with the leading numbers increasing by 30 each line."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "fddbcfc8",
   "metadata": {},
   "outputs": [],
   "source": [
    "# load RNA sequence:\n",
    "matrix = text_to_matrix(path, min_loop)\n",
    "stem_dict = make_stem_dict(matrix, min_stem, min_loop)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "02541c0a",
   "metadata": {},
   "source": [
    "The problem can be expresses as a Constrained Quadratic Model (CQM):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "bef1419f",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "<ipython-input-6-343e14dbb60c>:33: DeprecationWarning: Parameter order CQM.add_variable(v, vartype) is deprecated since dimod 0.11.0 and will be removed in 0.13.0. Use CQM.add_variable(vartype, v) instead.\n",
      "  cqm.add_variable(zeros, 'BINARY')\n"
     ]
    }
   ],
   "source": [
    "cqm = build_cqm(stem_dict, min_stem, c)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cf5ecdb6",
   "metadata": {},
   "source": [
    "Binary Quadratic Models (BQM) and Constrained Quadratic Models can be easily converted between each other. Here a 2-tuple containing a binary quadratic model and a function that converts samples over the binary quadratic model back into samples for the constrained quadratic model is returned:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "id": "c451137f",
   "metadata": {},
   "outputs": [],
   "source": [
    "bqm, invert = dimod.cqm_to_bqm(cqm) # Convert CQM->BQM"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "73e2daf1",
   "metadata": {},
   "source": [
    "Next we sample the (converted) CQM problem on the Dynex neuromorphic platform to find the optimal state witht the lowest energy using Ising/QUBU sampling. We choose to run the computation on 1024 individual Dynex chips for an integration time of maximum 1000 steps. Note that the Dynex platform supports up to 150 million individual Dynex chips (at the time of writing this example)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "id": "8e7fd29b",
   "metadata": {},
   "outputs": [],
   "source": [
    "# run on Dynex:\n",
    "model = dynex.BQM(bqm);\n",
    "sampler = dynex.DynexSampler(model);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "id": "fc90f89a",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "time: 0.05s #workers: 2 #chips: 1152 #steps: 1010 global falsified softs: 15 global energy: 199270.0\n",
      "FINISHED READ AFTER 0.05 SECONDS\n",
      "SAMPLESET LOADED\n",
      "MALLOB: JOB UPDATED: 285\n"
     ]
    }
   ],
   "source": [
    "sampleset = sampler.sample(num_reads=1024, annealing_time = 1000);\n",
    "sample_set = invert(sampler.assignments); # return to original CQM variable classes"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9af8d7fa",
   "metadata": {},
   "source": [
    "sampler.assignments contains the best assignment which was found by the Dynex sampler. We will be using this assignment to extract the stems and find the pseudoknots:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "id": "bc06e0e5",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Number of stems in best solution: 2\n",
      "Stems in best solution: (2, 4, 20, 22) (14, 16, 24, 26)\n",
      "\n",
      "Number of variables (stems): 17\n",
      "\n",
      "Number of pseudoknots in best solution: 1\n",
      "Pseudoknots: ((2, 4, 20, 22), (14, 16, 24, 26))\n"
     ]
    }
   ],
   "source": [
    "# Extract best feasible sample.\n",
    "solution = sample_set \n",
    "\n",
    "# Extract stems with a positive indicator variable.\n",
    "bonded_stems = [stem for stem, val in solution.items() if val == 1 and type(stem) == tuple]\n",
    "\n",
    "print('\\nNumber of stems in best solution:', len(bonded_stems))\n",
    "print('Stems in best solution:', *bonded_stems)\n",
    "\n",
    "print('\\nNumber of variables (stems):', len(solution))\n",
    "\n",
    "# Find pseudoknots using product instead of combinations allows for short asymmetric checks.\n",
    "pseudoknots = [(stem1, stem2) for [stem1, stem2] in product(bonded_stems, bonded_stems)\n",
    "               if stem1[1] < stem2[0] and stem2[1] < stem1[2] and stem1[3] < stem2[2]]\n",
    "\n",
    "print('\\nNumber of pseudoknots in best solution:', len(pseudoknots))\n",
    "if pseudoknots:\n",
    "    print('Pseudoknots:', *pseudoknots)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a78387d7",
   "metadata": {},
   "source": [
    "Now we will visualize the found solution. Note that plotting uses a randomized process to find a reasonable layout. For this reason, the plot will change in successive runs, even if the solution does not."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "id": "64c06bd5",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.LineCollection at 0x7f93ecb1dc40>"
      ]
     },
     "execution_count": 52,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "with open(path) as f:\n",
    "    rna = \"\".join((\"\".join(line.split()[1:]) for line in f.readlines())).lower()\n",
    "    \n",
    "# Create graph with edges from RNA sequence and stems. Nodes are temporarily labeled by integers.\n",
    "G = nx.Graph()\n",
    "rna_edges = [(i, i + 1) for i in range(len(rna) - 1)]\n",
    "stem_edges = [(stem[0] + i, stem[3] - i) for stem in bonded_stems for i in range(stem[1] - stem[0] + 1)]\n",
    "G.add_edges_from(rna_edges + stem_edges)\n",
    "\n",
    "# Assign each nucleotide to a color.\n",
    "color_map = []\n",
    "for node in rna:\n",
    "    if node == 'g':\n",
    "        color_map.append('tab:red')\n",
    "    elif node == 'c':\n",
    "        color_map.append('tab:green')\n",
    "    elif node == 'a':\n",
    "        color_map.append('y')\n",
    "    else:\n",
    "        color_map.append('tab:blue')\n",
    "\n",
    "options = {\"edgecolors\": \"tab:gray\", \"node_size\": 200, \"alpha\": 0.8}\n",
    "\n",
    "pos = nx.spring_layout(G, iterations=5000)  # max(3000, 125 * len(rna)))\n",
    "nx.draw_networkx_nodes(G, pos, node_color=color_map, **options)\n",
    "labels = {i: rna[i].upper() for i in range(len(rna))}\n",
    "nx.draw_networkx_labels(G, pos, labels, font_size=10, font_color=\"whitesmoke\")\n",
    "nx.draw_networkx_edges(G, pos, edgelist=rna_edges, width=3.0, alpha=0.5)\n",
    "nx.draw_networkx_edges(G, pos, edgelist=stem_edges, width=4.5, alpha=0.7, edge_color='tab:pink')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "aafe0da1",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.8.8"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}