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   "cells": [
    {
     "cell_type": "heading",
     "level": 1,
     "metadata": {},
     "source": [
      "Generalized dynamic programming for multiple sequence alignment"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "It's possible to generalize Smith-Waterman and Needleman-Wunsch, the dynamic programming algorithms that we explored for pairwise sequence aligment, to identify the optimal alignment of more than two sequences. Remember that our scoring scheme for pairwise alignment with Smith-Waterman looked like the following:\n",
      "\n",
      "$$\n",
      "\\begin{align}\n",
      "& F(0, 0) = 0\\\\\n",
      "& F(i, 0) = F(i-1, 0) - d\\\\\n",
      "& F(0, j) = F(0, j-1) - d\\\\\n",
      "\\\\\n",
      "& F(i, j) = max \\begin{pmatrix}\n",
      "& F(i-1, j-1) + s(c_i, c_j)\\\\\n",
      "& F(i-1, j) - d\\\\\n",
      "& F(i, j-1) - d)\\\\\n",
      "\\end{pmatrix}\n",
      "\\end{align}\n",
      "$$\n",
      "\n",
      "To generalize this to three sequences, we could create $3 \\times 3$ scoring, dynamic programming, and traceback matrices. Our scoring scheme would then look like the following:\n",
      "\n",
      "$$\n",
      "\\begin{align}\n",
      "& F(0, 0, 0) = 0\\\\\n",
      "& F(i, 0, 0) = F(i-1, 0, 0) - d\\\\\n",
      "& F(0, j, 0) = F(0, j-1, 0) - d\\\\\n",
      "& F(0, 0, k) = F(0, 0, k-1) - d\\\\\n",
      "\\\\\n",
      "& F(i, j, k) = max \\begin{pmatrix}\n",
      "F(i-1, j-1, k-1) + s(c_i, c_j) + s(c_i, c_k) + s(c_j, c_k)\\\\\n",
      "F(i, j-1, k-1) + s(c_j, c_k) - d\\\\\n",
      "F(i-1, j, k-1) + s(c_i, c_k) - d\\\\\n",
      "F(i-1, j-1, k) + s(c_i, c_j) - d\\\\\n",
      "F(i, j, k-1) - 2d\\\\\n",
      "F(i, j-1, k) - 2d\\\\\n",
      "F(i-1, j, k) - 2d\\\\\n",
      "\\end{pmatrix}\n",
      "\\end{align}\n",
      "$$\n",
      "\n",
      "However the complexity of this algorithm is much worse than for pairwise alignment. For pairwise alignment, remember that if aligning two sequences of lengths $m$ and $n$, the runtime of the algorithm will be proportional to $m \\times n$. If $n$ is longer than or as long as $m$, we simplify the statement to say that the runtime of the algorithm will be be proportional to $n^2$. This curve has a pretty scary trajectory: runtime for pairwise alignment with dynamic programming is said to scale quadratically."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# first we need to do some configuration of the notebook, don't worry about this for now\n",
      "from __future__ import division, print_function\n",
      "from functools import partial\n",
      "from IPython.core import page\n",
      "page.page = print"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 1
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import matplotlib.pyplot as plt\n",
      "\n",
      "seq_lengths = range(25)\n",
      "s2_times = [t ** 2 for t in range(25)]\n",
      "\n",
      "plt.plot(range(25), s2_times)\n",
      "plt.xlabel('Sequence Length')\n",
      "plt.ylabel('Runtime (s)')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 2,
       "text": [
        "<matplotlib.text.Text at 0x10886b350>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
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U+iC4nYApETEVQNKfgYOBV5o6qS0tXAgffgjvvZcaiBsngTfegNVWg403Th/6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\nH0ZDNoWOo057AAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x108865050>"
       ]
      }
     ],
     "prompt_number": 2
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "**The exponent in the $n^2$ term comes from the fact that, in pairwise alignment, if we assume our sequences are both of length $n$, there are $n \\times n$ cells to fill in in the dynamic programming matrix. If we were to generalize either Smith-Waterman or Needleman-Wunsch to three sequences, we would need to create a 3 dimensional array to score and traceback the alignment.** For sequences of length $n$, we would therefore have $n \\times n \\times n$ cells to fill in, and our runtime versus sequence length curve would look like the following."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "s3_times = [t ** 3 for t in range(25)]\n",
      "\n",
      "plt.plot(range(25), s3_times)\n",
      "plt.xlabel('Sequence Length')\n",
      "plt.ylabel('Runtime (s)')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 3,
       "text": [
        "<matplotlib.text.Text at 0x108861650>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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I5ooMGAB77QVDhiQTEM3KUdn3mSipgtwIzGhKJKmxQL90ux8wJqe8j6QOkjoD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\n/wNW3C+n5wmUKwAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x10886e7d0>"
       ]
      }
     ],
     "prompt_number": 3
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "That curve looks steeper than the curve for pairwise alignment, and the values on the y-axis are bigger, but it's not really clear how much of a problem this is until we plot runtime for three sequences in the context of the run times for pairwise alignment."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "plt.plot(range(25), s2_times)\n",
      "plt.plot(range(25), s3_times)\n",
      "plt.xlabel('Sequence Length')\n",
      "plt.ylabel('Runtime (s)')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 4,
       "text": [
        "<matplotlib.text.Text at 0x109209250>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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PCC5lftbdx+XZn86ZiEiB5F69ldo0lQHnDwg7nFCV2DkTM3vVzM4+zPI2ZjassAEC24As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\nVbeWxJVaJiIJIMd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q55rZyUF9DTMbFtR9Y2bXH+598nHQcOBmVj6INSN4v78E9anBZ3zH\nzBaZ2etR21wR1M0ws2fN7EMzOwHoDdxjZrOCO6IBLjCzr8zsW7VS5EiUTCQRjQeamNkSM/tfM7sA\n9g9m9xzQyd3PAoYB/xNsMwy43d1zh4841F/mDriZ1QceBi529xQiDxS6N2qdn4L6F4D7g/r/B2x2\n99+4++nAxCO8z5H0ALa4+2+JDMLXKxhCHCLDYNwFtARONLO2ZlYFeBG4LPj89YkMjrsyqH/K3Vu7\n+2Qiies4d28HXAUMLGBMkqTUzSUJx913mlkKcD6R7pu3zawfkQP1qUSe6wKRMdvWmlltoHZwEAUY\nSWSo/kMx4BwiB+opwXtVAqZErfNe8DoLuD4oX0xkwNHcOLeY2VVHeJ/D6QCcZmadg/lawK+BLCDD\n3dcCmNkcIkOJ7wK+C5IHwCjgL3k+1/7wCAY5dPdFZpZUz/WQwlMykYTk7jnAF8AXQZdVdyLJZIG7\nt41eN5+H/kQfVLM5uAVfJao8wd3/cIgQ9gav+zj4/1l+T6473PtEy6+11NfdJ0RXmFlq1P6jY8i7\n/ZGeopdZiHUlyambSxKOmZ1kZs2jqs4kMgLsEuBoMzsnWK+imbUMRoXdYmbtgvX/GLXtCuAMi2hC\npDvJiTyJrp2Z/Sp4r+p59pmfCcDtUXHWKeT75D2gfwL0MbMKUZ+72iG29eDznxicI4FIKyk3wWwH\nah4hfpFDUjKRRFQDeM3MFpjZN8ApQFpwQr4z8ETQ9TMbyL0c9mbgf81sdvQbBV1f3wMLgcFEWje4\n+8/ATcCoYB9TgJPziSX6/MtjQF0zmxfsP7UQ7wPwkpmtCqaviDywaCEwK2h9vcCBFsgvWjHuvgfo\nA4wzsxnAtmAC+BC4Ls8J+Oj30NVdclgagl4kj+Av93+7+2lhx1LSzKy6u+8Myv8LLHX3wSGHJQlA\nLRORXzIS9y/xXsFNnAuInLB/KeyAJDGoZSIiIsWmlomIiBSbkomIiBSbkomIiBSbkomIiBSbkomI\niBSbkomIiBTb/wf0pGtH4RIUmAAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x108871e10>"
       ]
      }
     ],
     "prompt_number": 4
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "And for four sequences:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "s4_times = [t ** 4 for t in range(25)]\n",
      "\n",
      "plt.plot(range(25), s2_times)\n",
      "plt.plot(range(25), s3_times)\n",
      "plt.plot(range(25), s4_times)\n",
      "plt.xlabel('Sequence Length')\n",
      "plt.ylabel('Runtime (s)')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 5,
       "text": [
        "<matplotlib.text.Text at 0x1092a8290>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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9BYcdll3wv/ZaKHNnSinxf20zK6577smeinnjjXDSSZvf3rocJxozK44IuOqq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\n",
       "text": [
        "<matplotlib.figure.Figure at 0x10928b250>"
       ]
      }
     ],
     "prompt_number": 5
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "We clearly have a problem here, and that is that **the runtime for multiple sequence alignment using full dynamic programming algoriths grows exponentially with the number of sequences to be aligned**. If $n$ is our sequence length, and $s$ is the number of sequences, that means that runtime is proportional to $n^s$. In pairwise alignment, $s$ is always equal to 2, so the problem is more manangeable. However, **for the general case of $s$ sequences, we really can't even consider Smith-Waterman or Needleman-Wunsch for more than just a few sequences.** The pattern in the plots above should illustrate why. \n",
      "\n",
      "As we explored with database searching, we need to figure out how to align fewer sequences. This is where *progressive alignment* comes in."
     ]
    },
    {
     "cell_type": "heading",
     "level": 1,
     "metadata": {},
     "source": [
      "Progressive alignment"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "<div style=\"float: right; margin-left: 30px;\"><img title=\"Image by @gregcaporaso.\" style=\"float: right; margin-left: 30px;\" src=\"files/images/confusion.png\" align=right width=330/></div>\n",
      "\n",
      "**In progressive alignment, the problem of exponential growth of runtime and space is managed by selectively aligning pairs of sequences, and aligning alignments of sequences.** What we typically do is identify a pair of closely sequences, and align those. Then, we identify the next closely related sequence to that initial pair, and align that sequence to the alignment. This concept of aligning a sequence to an alignment is new, and we'll come back to it in just a few minutes. The other concept of identifying the most closely related sequences, and then the next most closely related sequence, and so on should sound familar. It effectively means that we're traversing a tree. And herein lies our problem: **we need a tree to efficently align multiple sequences, but we need an alignment to build a good tree**. \n",
      "\n",
      "You probably have two burning questions in your mind right now:\n",
      "\n",
      "1. How do we build a tree to guide the alignment process, if we need an alignment to build a good tree?\n",
      "2. How do we align a sequence to an alignment, or an alignment to an alignment?\n",
      "\n",
      "We'll explore both of those through-out the rest of this notebook. First, let's cover the process of progressive multiple sequence alignment, just assuming for a moment that we know how to do both of those things.\n",
      "\n",
      "The process of progressive multiple sequence alignment could look like the following. First, we start with some sequences and a tree representing the relationship between those sequences. We'll call this our **guide tree**, because it's going to guide us through the process of multiple sequence alignment. In progressive multiple sequence alignment, we build a multiple sequence alignment for each internal node of the tree, where the alignment at a given internal node contains all of the sequences in the clade defined by that node.\n",
      "\n",
      "<img src=\"files/images/msa-tree-input.png\">\n",
      "\n",
      "Starting from the root node, descend the bottom branch of the tree until you get to the an internal node. If an alignment hasn't been constructed for that node yet, continue descending the tree until to get to a pair of nodes. In this case, we follow the two branches to the tips. We then align the sequences at that pair of tips (usually with Needleman-Wunsch, for multiple sequence alignment), and assign that alignment to the node connecting those tips.\n",
      "\n",
      "<img src=\"files/images/msa-tree-a1.png\">\n",
      "\n",
      "Next, we want to find what to align the resulting alignment to, so start from the root node and descend the top branch of the tree. When you get to the next node, determine if an alignment has already been created for that node. If not, our job is to build that alignment so we have something to align against. In this case, that means that we need to align `s1`, `s2`, and `s3`. We can achieve this by aligning `s1` and `s3` first, to get the alignment at the internal node connecting them.\n",
      "\n",
      "<img src=\"files/images/msa-tree-a2.png\">\n",
      "\n",
      "We can next align the alignment of `s1` and `s3` with `s2`, to get the alignment at the internal node connecting those clades.\n",
      "\n",
      "<img src=\"files/images/msa-tree-a3.png\">\n",
      "\n",
      "And finally, we can compute the alignment at the root node of the tree, by aligning the alignment of `s1`, `s2`, and `s3` with the alignment of `s4` and `s5`.\n",
      "\n",
      "<img src=\"files/images/msa-tree-final.png\">\n",
      "\n",
      "**The alignment at the root node is our multiple sequence alignment.**\n"
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Building the guide tree"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Let's address the first of our outstanding questions. **I mentioned above that *we need an alignment to build a good tree*. The key word here is *good*. We can build a very rough tree - one that we would never want to present as representing the actual relationships between the sequences in question - without first aligning the sequences.** Remember that building a UPGMA tree requires only a distance matrix, so if we can find a non-alignment-dependent way to compute distances between the sequences, we can build a rough UPGMA tree from them.\n",
      "\n",
      "Let's compute distances between the sequences based on their *word* composition. We'll define a *word* here as `k` adjacent characters in the sequence. We can then define a function that will return all of the words in a sequence as follows. These words can be defined as being overlapping, or non-overlapping. We'll go with overlapping for this example, as the more words we have, the better our guide tree should be."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from skbio import BiologicalSequence\n",
      "%psource BiologicalSequence.k_words"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "    \u001b[0;32mdef\u001b[0m \u001b[0mk_words\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mk\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0moverlapping\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mTrue\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\n",
        "\u001b[0;34m\u001b[0m        \u001b[0;34m\"\"\"Get the list of words of length k\u001b[0m\n",
        "\u001b[0;34m\u001b[0m\n",
        "\u001b[0;34m        Parameters\u001b[0m\n",
        "\u001b[0;34m        ----------\u001b[0m\n",
        "\u001b[0;34m        k : int\u001b[0m\n",
        "\u001b[0;34m            The word length.\u001b[0m\n",
        "\u001b[0;34m        overlapping : bool, optional\u001b[0m\n",
        "\u001b[0;34m            Defines whether the k-words should be overlapping or not\u001b[0m\n",
        "\u001b[0;34m            overlapping.\u001b[0m\n",
        "\u001b[0;34m\u001b[0m\n",
        "\u001b[0;34m        Returns\u001b[0m\n",
        "\u001b[0;34m        -------\u001b[0m\n",
        "\u001b[0;34m        iterator of BiologicalSequences\u001b[0m\n",
        "\u001b[0;34m            Iterator of words of length `k` contained in the\u001b[0m\n",
        "\u001b[0;34m            BiologicalSequence.\u001b[0m\n",
        "\u001b[0;34m\u001b[0m\n",
        "\u001b[0;34m        Raises\u001b[0m\n",
        "\u001b[0;34m        ------\u001b[0m\n",
        "\u001b[0;34m        ValueError\u001b[0m\n",
        "\u001b[0;34m            If k < 1.\u001b[0m\n",
        "\u001b[0;34m\u001b[0m\n",
        "\u001b[0;34m        Examples\u001b[0m\n",
        "\u001b[0;34m        --------\u001b[0m\n",
        "\u001b[0;34m        >>> from skbio.sequence import BiologicalSequence\u001b[0m\n",
        "\u001b[0;34m        >>> s = BiologicalSequence('ACACGACGTT')\u001b[0m\n",
        "\u001b[0;34m        >>> [str(kw) for kw in s.k_words(4, overlapping=False)]\u001b[0m\n",
        "\u001b[0;34m        ['ACAC', 'GACG']\u001b[0m\n",
        "\u001b[0;34m        >>> [str(kw) for kw in s.k_words(3, overlapping=True)]\u001b[0m\n",
        "\u001b[0;34m        ['ACA', 'CAC', 'ACG', 'CGA', 'GAC', 'ACG', 'CGT', 'GTT']\u001b[0m\n",
        "\u001b[0;34m\u001b[0m\n",
        "\u001b[0;34m        \"\"\"\u001b[0m\u001b[0;34m\u001b[0m\n",
        "\u001b[0;34m\u001b[0m        \u001b[0;32mif\u001b[0m \u001b[0mk\u001b[0m \u001b[0;34m<\u001b[0m \u001b[0;36m1\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\n",
        "\u001b[0;34m\u001b[0m            \u001b[0;32mraise\u001b[0m \u001b[0mValueError\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m\"k must be greater than 0.\"\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\n",
        "\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\n",
        "\u001b[0;34m\u001b[0m        \u001b[0msequence_length\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mlen\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\n",
        "\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\n",
        "\u001b[0;34m\u001b[0m        \u001b[0;32mif\u001b[0m \u001b[0moverlapping\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\n",
        "\u001b[0;34m\u001b[0m            \u001b[0mstep\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;36m1\u001b[0m\u001b[0;34m\u001b[0m\n",
        "\u001b[0;34m\u001b[0m        \u001b[0;32melse\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\n",
        "\u001b[0;34m\u001b[0m            \u001b[0mstep\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mk\u001b[0m\u001b[0;34m\u001b[0m\n",
        "\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\n",
        "\u001b[0;34m\u001b[0m        \u001b[0;32mfor\u001b[0m \u001b[0mi\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mrange\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0msequence_length\u001b[0m \u001b[0;34m-\u001b[0m \u001b[0mk\u001b[0m \u001b[0;34m+\u001b[0m \u001b[0;36m1\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mstep\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\n",
        "\u001b[0;34m\u001b[0m            \u001b[0;32myield\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mi\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0mi\u001b[0m\u001b[0;34m+\u001b[0m\u001b[0mk\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
        "\n"
       ]
      }
     ],
     "prompt_number": 6
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "for e in BiologicalSequence(\"ACCGGTGACCAGTTGACCAGTA\").k_words(3):\n",
      "    print(e)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "ACC\n",
        "CCG\n",
        "CGG\n",
        "GGT\n",
        "GTG\n",
        "TGA\n",
        "GAC\n",
        "ACC\n",
        "CCA\n",
        "CAG\n",
        "AGT\n",
        "GTT\n",
        "TTG\n",
        "TGA\n",
        "GAC\n",
        "ACC\n",
        "CCA\n",
        "CAG\n",
        "AGT\n",
        "GTA\n"
       ]
      }
     ],
     "prompt_number": 7
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "for e in BiologicalSequence(\"ACCGGTGACCAGTTGACCAGTA\").k_words(7):\n",
      "    print(e)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "ACCGGTG\n",
        "CCGGTGA\n",
        "CGGTGAC\n",
        "GGTGACC\n",
        "GTGACCA\n",
        "TGACCAG\n",
        "GACCAGT\n",
        "ACCAGTT\n",
        "CCAGTTG\n",
        "CAGTTGA\n",
        "AGTTGAC\n",
        "GTTGACC\n",
        "TTGACCA\n",
        "TGACCAG\n",
        "GACCAGT\n",
        "ACCAGTA\n"
       ]
      }
     ],
     "prompt_number": 8
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "for e in BiologicalSequence(\"ACCGGTGACCAGTTGACCAGTA\").k_words(3, overlapping=False):\n",
      "    print(e)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "ACC\n",
        "GGT\n",
        "GAC\n",
        "CAG\n",
        "TTG\n",
        "ACC\n",
        "AGT\n"
       ]
      }
     ],
     "prompt_number": 9
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "If we then have two sequences, we can compute the word counts for each and define a distance between the sequences as the fraction of words that are unique to either sequence. "
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from iab.algorithms import kmer_distance\n",
      "%psource kmer_distance"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\u001b[0;32mdef\u001b[0m \u001b[0mkmer_distance\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0msequence1\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0msequence2\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mk\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;36m3\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0moverlapping\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mTrue\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\n",
        "\u001b[0;34m\u001b[0m    \u001b[0;34m\"\"\"Compute the kmer distance between a pair of sequences\u001b[0m\n",
        "\u001b[0;34m\u001b[0m\n",
        "\u001b[0;34m    Parameters\u001b[0m\n",
        "\u001b[0;34m    ----------\u001b[0m\n",
        "\u001b[0;34m    sequence1 : BiologicalSequence\u001b[0m\n",
        "\u001b[0;34m    sequence2 : BiologicalSequence\u001b[0m\n",
        "\u001b[0;34m    k : int, optional\u001b[0m\n",
        "\u001b[0;34m        The word length.\u001b[0m\n",
        "\u001b[0;34m    overlapping : bool, optional\u001b[0m\n",
        "\u001b[0;34m        Defines whether the k-words should be overlapping or not\u001b[0m\n",
        "\u001b[0;34m        overlapping.\u001b[0m\n",
        "\u001b[0;34m\u001b[0m\n",
        "\u001b[0;34m    Returns\u001b[0m\n",
        "\u001b[0;34m    -------\u001b[0m\n",
        "\u001b[0;34m    float\u001b[0m\n",
        "\u001b[0;34m        Fraction of the set of k-mers from both sequence1 and\u001b[0m\n",
        "\u001b[0;34m        sequence2 that are unique to either sequence1 or\u001b[0m\n",
        "\u001b[0;34m        sequence2.\u001b[0m\n",
        "\u001b[0;34m\u001b[0m\n",
        "\u001b[0;34m    Raises\u001b[0m\n",
        "\u001b[0;34m    ------\u001b[0m\n",
        "\u001b[0;34m    ValueError\u001b[0m\n",
        "\u001b[0;34m        If k < 1.\u001b[0m\n",
        "\u001b[0;34m\u001b[0m\n",
        "\u001b[0;34m    Notes\u001b[0m\n",
        "\u001b[0;34m    -----\u001b[0m\n",
        "\u001b[0;34m    k-mer counts are not incorporated in this distance metric.\u001b[0m\n",
        "\u001b[0;34m\u001b[0m\n",
        "\u001b[0;34m    \"\"\"\u001b[0m\u001b[0;34m\u001b[0m\n",
        "\u001b[0;34m\u001b[0m    \u001b[0msequence1_kmers\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mset\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0msequence1\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mk_words\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mk\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0moverlapping\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\n",
        "\u001b[0;34m\u001b[0m    \u001b[0msequence2_kmers\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mset\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0msequence2\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mk_words\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mk\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0moverlapping\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\n",
        "\u001b[0;34m\u001b[0m    \u001b[0mall_kmers\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0msequence1_kmers\u001b[0m \u001b[0;34m|\u001b[0m \u001b[0msequence2_kmers\u001b[0m\u001b[0;34m\u001b[0m\n",
        "\u001b[0;34m\u001b[0m    \u001b[0mshared_kmers\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0msequence1_kmers\u001b[0m \u001b[0;34m&\u001b[0m \u001b[0msequence2_kmers\u001b[0m\u001b[0;34m\u001b[0m\n",
        "\u001b[0;34m\u001b[0m    \u001b[0mnumber_unique\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mlen\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mall_kmers\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;34m-\u001b[0m \u001b[0mlen\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mshared_kmers\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\n",
        "\u001b[0;34m\u001b[0m    \u001b[0mfraction_unique\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mnumber_unique\u001b[0m \u001b[0;34m/\u001b[0m \u001b[0mlen\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mall_kmers\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\n",
        "\u001b[0;34m\u001b[0m    \u001b[0;32mreturn\u001b[0m \u001b[0mfraction_unique\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
        "\n"
       ]
      }
     ],
     "prompt_number": 10
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "We can then use this as a distance function..."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "s1 = BiologicalSequence(\"ACCGGTGACCAGTTGACCAGT\")\n",
      "s2 = BiologicalSequence(\"ATCGGTACCGGTAGAAGT\")\n",
      "s3 = BiologicalSequence(\"GGTACCAAATAGAA\")\n",
      "\n",
      "print(s1.distance(s2, kmer_distance))\n",
      "print(s1.distance(s3, kmer_distance))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "0.75\n",
        "0.857142857143\n"
       ]
      }
     ],
     "prompt_number": 11
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "If we wanted to override the default to create (for example) a 5-mer distance function, we could use ``functools.partial``."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "fivemer_distance = partial(kmer_distance, k=5)\n",
      "\n",
      "s1 = BiologicalSequence(\"ACCGGTGACCAGTTGACCAGT\")\n",
      "s2 = BiologicalSequence(\"ATCGGTACCGGTAGAAGT\")\n",
      "s3 = BiologicalSequence(\"GGTACCAAATAGAA\")\n",
      "\n",
      "print(s1.distance(s2, fivemer_distance))\n",
      "print(s1.distance(s3, fivemer_distance))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "0.916666666667\n",
        "1.0\n"
       ]
      }
     ],
     "prompt_number": 12
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "We can now apply one of these functions to build a distance matrix for a set of sequences that we want to align."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from skbio import SequenceCollection\n",
      "query_sequences = SequenceCollection(\n",
      "                   [BiologicalSequence(\"ACCGGTGACCAGTTGACCAGT\", \"s1\"),\n",
      "                    BiologicalSequence(\"ATCGGTACCGGTAGAAGT\", \"s2\"),\n",
      "                    BiologicalSequence(\"GGTACCAAATAGAA\", \"s3\"),\n",
      "                    BiologicalSequence(\"GGCACCAAACAGAA\", \"s4\"),\n",
      "                    BiologicalSequence(\"GGCCCACTGAT\", \"s5\")])"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 13
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "guide_dm = query_sequences.distances(kmer_distance)\n",
      "print(guide_dm)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "5x5 distance matrix\n",
        "IDs:\n",
        "'s1', 's2', 's3', 's4', 's5'\n",
        "Data:\n",
        "[[ 0.          0.75        0.85714286  0.85714286  0.89473684]\n",
        " [ 0.75        0.          0.61111111  0.86363636  1.        ]\n",
        " [ 0.85714286  0.61111111  0.          0.66666667  0.95      ]\n",
        " [ 0.85714286  0.86363636  0.66666667  0.          0.83333333]\n",
        " [ 0.89473684  1.          0.95        0.83333333  0.        ]]\n"
       ]
      }
     ],
     "prompt_number": 14
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "scikit-bio also has some basic visualization functinality for these objects. For example, we can easily visualize this object as a heatmap."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "fig = guide_dm.plot(cmap='Greens')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x1091ed7d0>"
       ]
      }
     ],
     "prompt_number": 15
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "We can next use some functionality from SciPy to cluster the sequences with UPGMA, and print out a **dendrogram**."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from scipy.cluster.hierarchy import average, dendrogram, to_tree\n",
      "\n",
      "for q in query_sequences:\n",
      "    print(q)\n",
      "\n",
      "guide_lm = average(guide_dm.condensed_form())    \n",
      "guide_d = dendrogram(guide_lm, labels=guide_dm.ids, orientation='right', \n",
      "                     link_color_func=lambda x: 'black')\n",
      "guide_tree = to_tree(guide_lm)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "ACCGGTGACCAGTTGACCAGT\n",
        "ATCGGTACCGGTAGAAGT\n",
        "GGTACCAAATAGAA\n",
        "GGCACCAAACAGAA\n",
        "GGCCCACTGAT\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAWsAAAD7CAYAAACsV7WPAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nS1IDxlqSGjDWktSAsZakBv4fsqqfGsmCeYIAAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x1092a8950>"
       ]
      }
     ],
     "prompt_number": 16
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from iab.algorithms import guide_tree_from_sequences\n",
      "%psource guide_tree_from_sequences"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\u001b[0;32mdef\u001b[0m \u001b[0mguide_tree_from_sequences\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0msequences\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\n",
        "\u001b[0;34m\u001b[0m                              \u001b[0mdistance_fn\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mkmer_distance\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\n",
        "\u001b[0;34m\u001b[0m                              \u001b[0mdisplay_tree\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mFalse\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\n",
        "\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\n",
        "\u001b[0;34m\u001b[0m    \u001b[0mguide_dm\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0msequences\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mdistances\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mdistance_fn\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\n",
        "\u001b[0;34m\u001b[0m    \u001b[0mguide_lm\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0maverage\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mguide_dm\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mcondensed_form\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\n",
        "\u001b[0;34m\u001b[0m    \u001b[0mguide_tree\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mto_tree\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mguide_lm\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\n",
        "\u001b[0;34m\u001b[0m    \u001b[0;32mif\u001b[0m \u001b[0mdisplay_tree\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\n",
        "\u001b[0;34m\u001b[0m        \u001b[0mguide_d\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mdendrogram\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mguide_lm\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mlabels\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mguide_dm\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mids\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0morientation\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;34m'right'\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\n",
        "\u001b[0;34m\u001b[0m               \u001b[0mlink_color_func\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;32mlambda\u001b[0m \u001b[0mx\u001b[0m\u001b[0;34m:\u001b[0m \u001b[0;34m'black'\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\n",
        "\u001b[0;34m\u001b[0m    \u001b[0;32mreturn\u001b[0m \u001b[0mguide_tree\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
        "\n"
       ]
      }
     ],
     "prompt_number": 17
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "t = guide_tree_from_sequences(query_sequences, display_tree=True)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAWsAAAD7CAYAAACsV7WPAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nS1IDxlqSGjDWktSAsZakBv4fsqqfGsmCeYIAAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x10b46d190>"
       ]
      }
     ],
     "prompt_number": 18
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "We now have a guide tree, so we can move on to the next step of progressive alignment."
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Generalization of Needleman-Wunsch (with affine gap scoring) for progressive multiple sequence alignment"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Next, we'll address our second burning question: aligning alignments. As illustrated above, there are basically three different types of pairwise alignment we need to support for progressive multiple sequenence alignment with Needleman-Wunsch. These are:\n",
      "\n",
      "1. Alignment of a pair of sequences.\n",
      "2. Alignment of a sequence and an alignment.\n",
      "3. Alignment of a pair of alignments.\n",
      "\n",
      "Standard Needleman-Wunsch supports the first, and it is very easy to generalize it to support the latter two. The only change that is necessary is in how the alignment of two non-gap characters is scored. Recall that we previously scored an alignment of two characters by looking up the score of subsitution from one to the other in a substitution matrix. To adapt this for aligning a sequence to an alignment, or for aligning an alignment to an alignment, we compute this subsitution as the average score of aligning the pairs of characters. \n",
      "\n",
      "For example, if we want to align the alignment column from $aln1$:\n",
      "\n",
      "```\n",
      "A\n",
      "C\n",
      "```\n",
      "\n",
      "to the alignment column from $aln2$:\n",
      "\n",
      "```\n",
      "T\n",
      "G\n",
      "```\n",
      "\n",
      "we could compute the subsitution score using the matrix $m$ as:\n",
      "\n",
      "$$\n",
      "s = \\frac{m[A][T] + m[A][G] + m[C][T] + m[C][G]}{aln1_{length} \\times aln2_{length}}\n",
      "$$\n",
      "\n",
      "The following code adapts our implementation of Needleman-Wunsh to support aligning a sequence to an alignment, or aligning an alignment to an alignment."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from iab.algorithms import format_dynamic_programming_matrix, format_traceback_matrix\n",
      "from skbio.alignment._pairwise import _compute_score_and_traceback_matrices \n",
      "\n",
      "%psource _compute_score_and_traceback_matrices"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\u001b[0;32mdef\u001b[0m \u001b[0m_compute_score_and_traceback_matrices\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m\u001b[0m\n",
        "\u001b[0;34m\u001b[0m        \u001b[0maln1\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0maln2\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mgap_open_penalty\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mgap_extend_penalty\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0msubstitution_matrix\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\n",
        "\u001b[0;34m\u001b[0m        \u001b[0mnew_alignment_score\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;34m-\u001b[0m\u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0minf\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0minit_matrices_f\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0m_init_matrices_nw\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\n",
        "\u001b[0;34m\u001b[0m        \u001b[0mpenalize_terminal_gaps\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mTrue\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mgap_substitution_score\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\n",
        "\u001b[0;34m\u001b[0m    \u001b[0;34m\"\"\"Return dynamic programming (score) and traceback matrices.\u001b[0m\n",
        "\u001b[0;34m\u001b[0m\n",
        "\u001b[0;34m    A note on the ``penalize_terminal_gaps`` parameter. When this value is\u001b[0m\n",
        "\u001b[0;34m    ``False``, this function is no longer true Smith-Waterman/Needleman-Wunsch\u001b[0m\n",
        "\u001b[0;34m    scoring, but when ``True`` it can result in biologically irrelevant\u001b[0m\n",
        "\u001b[0;34m    artifacts in Needleman-Wunsch (global) alignments. Specifically, if one\u001b[0m\n",
        "\u001b[0;34m    sequence is longer than the other (e.g., if aligning a primer sequence to\u001b[0m\n",
        "\u001b[0;34m    an amplification product, or searching for a gene in a genome) the shorter\u001b[0m\n",
        "\u001b[0;34m    sequence will have a long gap inserted. The parameter is ``True`` by\u001b[0m\n",
        "\u001b[0;34m    default (so that this function computes the score and traceback matrices as\u001b[0m\n",
        "\u001b[0;34m    described by the original authors) but the global alignment wrappers pass\u001b[0m\n",
        "\u001b[0;34m    ``False`` by default, so that the global alignment API returns the result\u001b[0m\n",
        "\u001b[0;34m    that users are most likely to be looking for.\u001b[0m\n",
        "\u001b[0;34m\u001b[0m\n",
        "\u001b[0;34m    \"\"\"\u001b[0m\u001b[0;34m\u001b[0m\n",
        "\u001b[0;34m\u001b[0m    \u001b[0maln1_length\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0maln1\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0msequence_length\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\n",
        "\u001b[0;34m\u001b[0m    \u001b[0maln2_length\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0maln2\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0msequence_length\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\n",
        "\u001b[0;34m\u001b[0m    \u001b[0;31m# cache some values for quicker/simpler access\u001b[0m\u001b[0;34m\u001b[0m\n",
        "\u001b[0;34m\u001b[0m    \u001b[0maend\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0m_traceback_encoding\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m'alignment-end'\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\n",
        "\u001b[0;34m\u001b[0m    \u001b[0mmatch\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0m_traceback_encoding\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m'match'\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\n",
        "\u001b[0;34m\u001b[0m    \u001b[0mvgap\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0m_traceback_encoding\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m'vertical-gap'\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\n",
        "\u001b[0;34m\u001b[0m    \u001b[0mhgap\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0m_traceback_encoding\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m'horizontal-gap'\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\n",
        "\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\n",
        "\u001b[0;34m\u001b[0m    \u001b[0mnew_alignment_score\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;34m(\u001b[0m\u001b[0mnew_alignment_score\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0maend\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\n",
        "\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\n",
        "\u001b[0;34m\u001b[0m    \u001b[0;31m# Initialize a matrix to use for scoring the alignment and for tracing\u001b[0m\u001b[0;34m\u001b[0m\n",
        "\u001b[0;34m\u001b[0m    \u001b[0;31m# back the best alignment\u001b[0m\u001b[0;34m\u001b[0m\n",
        "\u001b[0;34m\u001b[0m    \u001b[0mscore_matrix\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mtraceback_matrix\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0minit_matrices_f\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m\u001b[0m\n",
        "\u001b[0;34m\u001b[0m        \u001b[0maln1\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0maln2\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mgap_open_penalty\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mgap_extend_penalty\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\n",
        "\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\n",
        "\u001b[0;34m\u001b[0m    \u001b[0;31m# Iterate over the characters in aln2 (which corresponds to the vertical\u001b[0m\u001b[0;34m\u001b[0m\n",
        "\u001b[0;34m\u001b[0m    \u001b[0;31m# sequence in the matrix)\u001b[0m\u001b[0;34m\u001b[0m\n",
        "\u001b[0;34m\u001b[0m    \u001b[0;32mfor\u001b[0m \u001b[0maln2_pos\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0maln2_chars\u001b[0m \u001b[0;32min\u001b[0m \u001b[0menumerate\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0maln2\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0miter_positions\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mstr\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;36m1\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\n",
        "\u001b[0;34m\u001b[0m        \u001b[0;31m# Iterate over the characters in aln1 (which corresponds to the\u001b[0m\u001b[0;34m\u001b[0m\n",
        "\u001b[0;34m\u001b[0m        \u001b[0;31m# horizontal sequence in the matrix)\u001b[0m\u001b[0;34m\u001b[0m\n",
        "\u001b[0;34m\u001b[0m        \u001b[0;32mfor\u001b[0m \u001b[0maln1_pos\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0maln1_chars\u001b[0m \u001b[0;32min\u001b[0m \u001b[0menumerate\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0maln1\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0miter_positions\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mstr\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;36m1\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\n",
        "\u001b[0;34m\u001b[0m            \u001b[0;31m# compute the score for a match/mismatch\u001b[0m\u001b[0;34m\u001b[0m\n",
        "\u001b[0;34m\u001b[0m            \u001b[0msubstitution_score\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0m_compute_substitution_score\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m\u001b[0m\n",
        "\u001b[0;34m\u001b[0m                \u001b[0maln1_chars\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0maln2_chars\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0msubstitution_matrix\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\n",
        "\u001b[0;34m\u001b[0m                \u001b[0mgap_substitution_score\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\n",
        "\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\n",
        "\u001b[0;34m\u001b[0m            \u001b[0mdiag_score\u001b[0m \u001b[0;34m=\u001b[0m \\\n",
        "                \u001b[0;34m(\u001b[0m\u001b[0mscore_matrix\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0maln2_pos\u001b[0m\u001b[0;34m-\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0maln1_pos\u001b[0m\u001b[0;34m-\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;34m+\u001b[0m \u001b[0msubstitution_score\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\n",
        "\u001b[0;34m\u001b[0m                 \u001b[0mmatch\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\n",
        "\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\n",
        "\u001b[0;34m\u001b[0m            \u001b[0;31m# compute the score for adding a gap in aln2 (vertical)\u001b[0m\u001b[0;34m\u001b[0m\n",
        "\u001b[0;34m\u001b[0m            \u001b[0;32mif\u001b[0m \u001b[0;32mnot\u001b[0m \u001b[0mpenalize_terminal_gaps\u001b[0m \u001b[0;32mand\u001b[0m \u001b[0;34m(\u001b[0m\u001b[0maln1_pos\u001b[0m \u001b[0;34m==\u001b[0m \u001b[0maln1_length\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\n",
        "\u001b[0;34m\u001b[0m                \u001b[0;31m# we've reached the end of aln1, so adding vertical gaps\u001b[0m\u001b[0;34m\u001b[0m\n",
        "\u001b[0;34m\u001b[0m                \u001b[0;31m# (which become gaps in aln1) should no longer\u001b[0m\u001b[0;34m\u001b[0m\n",
        "\u001b[0;34m\u001b[0m                \u001b[0;31m# be penalized (if penalize_terminal_gaps == False)\u001b[0m\u001b[0;34m\u001b[0m\n",
        "\u001b[0;34m\u001b[0m                \u001b[0mup_score\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;34m(\u001b[0m\u001b[0mscore_matrix\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0maln2_pos\u001b[0m\u001b[0;34m-\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0maln1_pos\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mvgap\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\n",
        "\u001b[0;34m\u001b[0m            \u001b[0;32melif\u001b[0m \u001b[0mtraceback_matrix\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0maln2_pos\u001b[0m\u001b[0;34m-\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0maln1_pos\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;34m==\u001b[0m \u001b[0mvgap\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\n",
        "\u001b[0;34m\u001b[0m                \u001b[0;31m# gap extend, because the cell above was also a gap\u001b[0m\u001b[0;34m\u001b[0m\n",
        "\u001b[0;34m\u001b[0m                \u001b[0mup_score\u001b[0m \u001b[0;34m=\u001b[0m \\\n",
        "                    \u001b[0;34m(\u001b[0m\u001b[0mscore_matrix\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0maln2_pos\u001b[0m\u001b[0;34m-\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0maln1_pos\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;34m-\u001b[0m \u001b[0mgap_extend_penalty\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\n",
        "\u001b[0;34m\u001b[0m                     \u001b[0mvgap\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\n",
        "\u001b[0;34m\u001b[0m            \u001b[0;32melse\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\n",
        "\u001b[0;34m\u001b[0m                \u001b[0;31m# gap open, because the cell above was not a gap\u001b[0m\u001b[0;34m\u001b[0m\n",
        "\u001b[0;34m\u001b[0m                \u001b[0mup_score\u001b[0m \u001b[0;34m=\u001b[0m \\\n",
        "                    \u001b[0;34m(\u001b[0m\u001b[0mscore_matrix\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0maln2_pos\u001b[0m\u001b[0;34m-\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0maln1_pos\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;34m-\u001b[0m \u001b[0mgap_open_penalty\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\n",
        "\u001b[0;34m\u001b[0m                     \u001b[0mvgap\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\n",
        "\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\n",
        "\u001b[0;34m\u001b[0m            \u001b[0;31m# compute the score for adding a gap in aln1 (horizontal)\u001b[0m\u001b[0;34m\u001b[0m\n",
        "\u001b[0;34m\u001b[0m            \u001b[0;32mif\u001b[0m \u001b[0;32mnot\u001b[0m \u001b[0mpenalize_terminal_gaps\u001b[0m \u001b[0;32mand\u001b[0m \u001b[0;34m(\u001b[0m\u001b[0maln2_pos\u001b[0m \u001b[0;34m==\u001b[0m \u001b[0maln2_length\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\n",
        "\u001b[0;34m\u001b[0m                \u001b[0;31m# we've reached the end of aln2, so adding horizontal gaps\u001b[0m\u001b[0;34m\u001b[0m\n",
        "\u001b[0;34m\u001b[0m                \u001b[0;31m# (which become gaps in aln2) should no longer\u001b[0m\u001b[0;34m\u001b[0m\n",
        "\u001b[0;34m\u001b[0m                \u001b[0;31m# be penalized (if penalize_terminal_gaps == False)\u001b[0m\u001b[0;34m\u001b[0m\n",
        "\u001b[0;34m\u001b[0m                \u001b[0mleft_score\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;34m(\u001b[0m\u001b[0mscore_matrix\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0maln2_pos\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0maln1_pos\u001b[0m\u001b[0;34m-\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mhgap\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\n",
        "\u001b[0;34m\u001b[0m            \u001b[0;32melif\u001b[0m \u001b[0mtraceback_matrix\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0maln2_pos\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0maln1_pos\u001b[0m\u001b[0;34m-\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;34m==\u001b[0m \u001b[0mhgap\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\n",
        "\u001b[0;34m\u001b[0m                \u001b[0;31m# gap extend, because the cell to the left was also a gap\u001b[0m\u001b[0;34m\u001b[0m\n",
        "\u001b[0;34m\u001b[0m                \u001b[0mleft_score\u001b[0m \u001b[0;34m=\u001b[0m \\\n",
        "                    \u001b[0;34m(\u001b[0m\u001b[0mscore_matrix\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0maln2_pos\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0maln1_pos\u001b[0m\u001b[0;34m-\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;34m-\u001b[0m \u001b[0mgap_extend_penalty\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\n",
        "\u001b[0;34m\u001b[0m                     \u001b[0mhgap\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\n",
        "\u001b[0;34m\u001b[0m            \u001b[0;32melse\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\n",
        "\u001b[0;34m\u001b[0m                \u001b[0;31m# gap open, because the cell to the left was not a gap\u001b[0m\u001b[0;34m\u001b[0m\n",
        "\u001b[0;34m\u001b[0m                \u001b[0mleft_score\u001b[0m \u001b[0;34m=\u001b[0m \\\n",
        "                    \u001b[0;34m(\u001b[0m\u001b[0mscore_matrix\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0maln2_pos\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0maln1_pos\u001b[0m\u001b[0;34m-\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;34m-\u001b[0m \u001b[0mgap_open_penalty\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\n",
        "\u001b[0;34m\u001b[0m                     \u001b[0mhgap\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\n",
        "\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\n",
        "\u001b[0;34m\u001b[0m            \u001b[0;31m# identify the largest score, and use that information to populate\u001b[0m\u001b[0;34m\u001b[0m\n",
        "\u001b[0;34m\u001b[0m            \u001b[0;31m# the score and traceback matrices\u001b[0m\u001b[0;34m\u001b[0m\n",
        "\u001b[0;34m\u001b[0m            \u001b[0mbest_score\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0m_first_largest\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mnew_alignment_score\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mleft_score\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\n",
        "\u001b[0;34m\u001b[0m                                         \u001b[0mdiag_score\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mup_score\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\n",
        "\u001b[0;34m\u001b[0m            \u001b[0mscore_matrix\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0maln2_pos\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0maln1_pos\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mbest_score\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\n",
        "\u001b[0;34m\u001b[0m            \u001b[0mtraceback_matrix\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0maln2_pos\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0maln1_pos\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mbest_score\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\n",
        "\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\n",
        "\u001b[0;34m\u001b[0m    \u001b[0;32mreturn\u001b[0m \u001b[0mscore_matrix\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mtraceback_matrix\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
        "\n"
       ]
      }
     ],
     "prompt_number": 19
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from skbio.alignment._pairwise import _traceback\n",
      "%psource _traceback"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\u001b[0;32mdef\u001b[0m \u001b[0m_traceback\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mtraceback_matrix\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mscore_matrix\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0maln1\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0maln2\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mstart_row\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\n",
        "\u001b[0;34m\u001b[0m               \u001b[0mstart_col\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mgap_character\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;34m'-'\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\n",
        "\u001b[0;34m\u001b[0m    \u001b[0;31m# cache some values for simpler\u001b[0m\u001b[0;34m\u001b[0m\n",
        "\u001b[0;34m\u001b[0m    \u001b[0maend\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0m_traceback_encoding\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m'alignment-end'\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\n",
        "\u001b[0;34m\u001b[0m    \u001b[0mmatch\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0m_traceback_encoding\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m'match'\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\n",
        "\u001b[0;34m\u001b[0m    \u001b[0mvgap\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0m_traceback_encoding\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m'vertical-gap'\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\n",
        "\u001b[0;34m\u001b[0m    \u001b[0mhgap\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0m_traceback_encoding\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m'horizontal-gap'\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\n",
        "\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\n",
        "\u001b[0;34m\u001b[0m    \u001b[0;31m# initialize the result alignments\u001b[0m\u001b[0;34m\u001b[0m\n",
        "\u001b[0;34m\u001b[0m    \u001b[0maln1_sequence_count\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0maln1\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0msequence_count\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\n",
        "\u001b[0;34m\u001b[0m    \u001b[0maligned_seqs1\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;34m[\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0me\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mrange\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0maln1_sequence_count\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\n",
        "\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\n",
        "\u001b[0;34m\u001b[0m    \u001b[0maln2_sequence_count\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0maln2\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0msequence_count\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\n",
        "\u001b[0;34m\u001b[0m    \u001b[0maligned_seqs2\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;34m[\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0me\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mrange\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0maln2_sequence_count\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\n",
        "\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\n",
        "\u001b[0;34m\u001b[0m    \u001b[0mcurrent_row\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mstart_row\u001b[0m\u001b[0;34m\u001b[0m\n",
        "\u001b[0;34m\u001b[0m    \u001b[0mcurrent_col\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mstart_col\u001b[0m\u001b[0;34m\u001b[0m\n",
        "\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\n",
        "\u001b[0;34m\u001b[0m    \u001b[0mbest_score\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mscore_matrix\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mcurrent_row\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mcurrent_col\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\n",
        "\u001b[0;34m\u001b[0m    \u001b[0mcurrent_value\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mNone\u001b[0m\u001b[0;34m\u001b[0m\n",
        "\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\n",
        "\u001b[0;34m\u001b[0m    \u001b[0;32mwhile\u001b[0m \u001b[0mcurrent_value\u001b[0m \u001b[0;34m!=\u001b[0m \u001b[0maend\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\n",
        "\u001b[0;34m\u001b[0m        \u001b[0mcurrent_value\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mtraceback_matrix\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mcurrent_row\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mcurrent_col\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\n",
        "\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\n",
        "\u001b[0;34m\u001b[0m        \u001b[0;32mif\u001b[0m \u001b[0mcurrent_value\u001b[0m \u001b[0;34m==\u001b[0m \u001b[0mmatch\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\n",
        "\u001b[0;34m\u001b[0m            \u001b[0;32mfor\u001b[0m \u001b[0maligned_seq\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0minput_seq\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mzip\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0maligned_seqs1\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0maln1\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\n",
        "\u001b[0;34m\u001b[0m                \u001b[0maligned_seq\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mappend\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mstr\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0minput_seq\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mcurrent_col\u001b[0m\u001b[0;34m-\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\n",
        "\u001b[0;34m\u001b[0m            \u001b[0;32mfor\u001b[0m \u001b[0maligned_seq\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0minput_seq\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mzip\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0maligned_seqs2\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0maln2\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\n",
        "\u001b[0;34m\u001b[0m                \u001b[0maligned_seq\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mappend\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mstr\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0minput_seq\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mcurrent_row\u001b[0m\u001b[0;34m-\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\n",
        "\u001b[0;34m\u001b[0m            \u001b[0mcurrent_row\u001b[0m \u001b[0;34m-=\u001b[0m \u001b[0;36m1\u001b[0m\u001b[0;34m\u001b[0m\n",
        "\u001b[0;34m\u001b[0m            \u001b[0mcurrent_col\u001b[0m \u001b[0;34m-=\u001b[0m \u001b[0;36m1\u001b[0m\u001b[0;34m\u001b[0m\n",
        "\u001b[0;34m\u001b[0m        \u001b[0;32melif\u001b[0m \u001b[0mcurrent_value\u001b[0m \u001b[0;34m==\u001b[0m \u001b[0mvgap\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\n",
        "\u001b[0;34m\u001b[0m            \u001b[0;32mfor\u001b[0m \u001b[0maligned_seq\u001b[0m \u001b[0;32min\u001b[0m \u001b[0maligned_seqs1\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\n",
        "\u001b[0;34m\u001b[0m                \u001b[0maligned_seq\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mappend\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m'-'\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\n",
        "\u001b[0;34m\u001b[0m            \u001b[0;32mfor\u001b[0m \u001b[0maligned_seq\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0minput_seq\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mzip\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0maligned_seqs2\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0maln2\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\n",
        "\u001b[0;34m\u001b[0m                \u001b[0maligned_seq\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mappend\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mstr\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0minput_seq\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mcurrent_row\u001b[0m\u001b[0;34m-\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\n",
        "\u001b[0;34m\u001b[0m            \u001b[0mcurrent_row\u001b[0m \u001b[0;34m-=\u001b[0m \u001b[0;36m1\u001b[0m\u001b[0;34m\u001b[0m\n",
        "\u001b[0;34m\u001b[0m        \u001b[0;32melif\u001b[0m \u001b[0mcurrent_value\u001b[0m \u001b[0;34m==\u001b[0m \u001b[0mhgap\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\n",
        "\u001b[0;34m\u001b[0m            \u001b[0;32mfor\u001b[0m \u001b[0maligned_seq\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0minput_seq\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mzip\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0maligned_seqs1\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0maln1\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\n",
        "\u001b[0;34m\u001b[0m                \u001b[0maligned_seq\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mappend\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mstr\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0minput_seq\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mcurrent_col\u001b[0m\u001b[0;34m-\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\n",
        "\u001b[0;34m\u001b[0m            \u001b[0;32mfor\u001b[0m \u001b[0maligned_seq\u001b[0m \u001b[0;32min\u001b[0m \u001b[0maligned_seqs2\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\n",
        "\u001b[0;34m\u001b[0m                \u001b[0maligned_seq\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mappend\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m'-'\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\n",
        "\u001b[0;34m\u001b[0m            \u001b[0mcurrent_col\u001b[0m \u001b[0;34m-=\u001b[0m \u001b[0;36m1\u001b[0m\u001b[0;34m\u001b[0m\n",
        "\u001b[0;34m\u001b[0m        \u001b[0;32melif\u001b[0m \u001b[0mcurrent_value\u001b[0m \u001b[0;34m==\u001b[0m \u001b[0maend\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\n",
        "\u001b[0;34m\u001b[0m            \u001b[0;32mcontinue\u001b[0m\u001b[0;34m\u001b[0m\n",
        "\u001b[0;34m\u001b[0m        \u001b[0;32melse\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\n",
        "\u001b[0;34m\u001b[0m            \u001b[0;32mraise\u001b[0m \u001b[0mValueError\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m\u001b[0m\n",
        "\u001b[0;34m\u001b[0m                \u001b[0;34m\"Invalid value in traceback matrix: %s\"\u001b[0m \u001b[0;34m%\u001b[0m \u001b[0mcurrent_value\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\n",
        "\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\n",
        "\u001b[0;34m\u001b[0m    \u001b[0;32mfor\u001b[0m \u001b[0mi\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mrange\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0maln1_sequence_count\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\n",
        "\u001b[0;34m\u001b[0m        \u001b[0maligned_seq\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;34m''\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mjoin\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0maligned_seqs1\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mi\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m-\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\n",
        "\u001b[0;34m\u001b[0m        \u001b[0mseq_id\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0m_get_seq_id\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0maln1\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mi\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mstr\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mi\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\n",
        "\u001b[0;34m\u001b[0m        \u001b[0maligned_seqs1\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mi\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mBiologicalSequence\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0maligned_seq\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mid\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mseq_id\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\n",
        "\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\n",
        "\u001b[0;34m\u001b[0m    \u001b[0;32mfor\u001b[0m \u001b[0mi\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mrange\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0maln2_sequence_count\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\n",
        "\u001b[0;34m\u001b[0m        \u001b[0maligned_seq\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;34m''\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mjoin\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0maligned_seqs2\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mi\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m-\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\n",
        "\u001b[0;34m\u001b[0m        \u001b[0mseq_id\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0m_get_seq_id\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0maln2\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mi\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mstr\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mi\u001b[0m \u001b[0;34m+\u001b[0m \u001b[0maln1_sequence_count\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\n",
        "\u001b[0;34m\u001b[0m        \u001b[0maligned_seqs2\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mi\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mBiologicalSequence\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0maligned_seq\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mid\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mseq_id\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\n",
        "\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\n",
        "\u001b[0;34m\u001b[0m    \u001b[0;32mreturn\u001b[0m \u001b[0;34m(\u001b[0m\u001b[0maligned_seqs1\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0maligned_seqs2\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mbest_score\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\n",
        "\u001b[0;34m\u001b[0m            \u001b[0mcurrent_col\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mcurrent_row\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
        "\n"
       ]
      }
     ],
     "prompt_number": 20
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from skbio.alignment import global_pairwise_align_nucleotide\n",
      "%psource global_pairwise_align_nucleotide "
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\u001b[0;32mdef\u001b[0m \u001b[0mglobal_pairwise_align_nucleotide\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mseq1\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mseq2\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mgap_open_penalty\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;36m5\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\n",
        "\u001b[0;34m\u001b[0m                                     \u001b[0mgap_extend_penalty\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;36m2\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\n",
        "\u001b[0;34m\u001b[0m                                     \u001b[0mmatch_score\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mmismatch_score\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;34m-\u001b[0m\u001b[0;36m2\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\n",
        "\u001b[0;34m\u001b[0m                                     \u001b[0msubstitution_matrix\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mNone\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\n",
        "\u001b[0;34m\u001b[0m                                     \u001b[0mpenalize_terminal_gaps\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mFalse\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\n",
        "\u001b[0;34m\u001b[0m    \u001b[0;34m\"\"\"Globally align pair of nuc. seqs or alignments with Needleman-Wunsch\u001b[0m\n",
        "\u001b[0;34m\u001b[0m\n",
        "\u001b[0;34m    Parameters\u001b[0m\n",
        "\u001b[0;34m    ----------\u001b[0m\n",
        "\u001b[0;34m    seq1 : str, BiologicalSequence, or Alignment\u001b[0m\n",
        "\u001b[0;34m        The first unaligned sequence(s).\u001b[0m\n",
        "\u001b[0;34m    seq2 : str, BiologicalSequence, or Alignment\u001b[0m\n",
        "\u001b[0;34m        The second unaligned sequence(s).\u001b[0m\n",
        "\u001b[0;34m    gap_open_penalty : int or float, optional\u001b[0m\n",
        "\u001b[0;34m        Penalty for opening a gap (this is substracted from previous best\u001b[0m\n",
        "\u001b[0;34m        alignment score, so is typically positive).\u001b[0m\n",
        "\u001b[0;34m    gap_extend_penalty : int or float, optional\u001b[0m\n",
        "\u001b[0;34m        Penalty for extending a gap (this is substracted from previous best\u001b[0m\n",
        "\u001b[0;34m        alignment score, so is typically positive).\u001b[0m\n",
        "\u001b[0;34m    match_score : int or float, optional\u001b[0m\n",
        "\u001b[0;34m        The score to add for a match between a pair of bases (this is added\u001b[0m\n",
        "\u001b[0;34m        to the previous best alignment score, so is typically positive).\u001b[0m\n",
        "\u001b[0;34m    mismatch_score : int or float, optional\u001b[0m\n",
        "\u001b[0;34m        The score to add for a mismatch between a pair of bases (this is\u001b[0m\n",
        "\u001b[0;34m        added to the previous best alignment score, so is typically\u001b[0m\n",
        "\u001b[0;34m        negative).\u001b[0m\n",
        "\u001b[0;34m    substitution_matrix: 2D dict (or similar)\u001b[0m\n",
        "\u001b[0;34m        Lookup for substitution scores (these values are added to the\u001b[0m\n",
        "\u001b[0;34m        previous best alignment score). If provided, this overrides\u001b[0m\n",
        "\u001b[0;34m        ``match_score`` and ``mismatch_score``.\u001b[0m\n",
        "\u001b[0;34m    penalize_terminal_gaps: bool, optional\u001b[0m\n",
        "\u001b[0;34m        If True, will continue to penalize gaps even after one sequence has\u001b[0m\n",
        "\u001b[0;34m        been aligned through its end. This behavior is true Needleman-Wunsch\u001b[0m\n",
        "\u001b[0;34m        alignment, but results in (biologically irrelevant) artifacts when\u001b[0m\n",
        "\u001b[0;34m        the sequences being aligned are of different length. This is ``False``\u001b[0m\n",
        "\u001b[0;34m        by default, which is very likely to be the behavior you want in all or\u001b[0m\n",
        "\u001b[0;34m        nearly all cases.\u001b[0m\n",
        "\u001b[0;34m\u001b[0m\n",
        "\u001b[0;34m    Returns\u001b[0m\n",
        "\u001b[0;34m    -------\u001b[0m\n",
        "\u001b[0;34m    skbio.Alignment\u001b[0m\n",
        "\u001b[0;34m        ``Alignment`` object containing the aligned sequences as well as\u001b[0m\n",
        "\u001b[0;34m        details about the alignment.\u001b[0m\n",
        "\u001b[0;34m\u001b[0m\n",
        "\u001b[0;34m    See Also\u001b[0m\n",
        "\u001b[0;34m    --------\u001b[0m\n",
        "\u001b[0;34m    local_pairwise_align\u001b[0m\n",
        "\u001b[0;34m    local_pairwise_align_protein\u001b[0m\n",
        "\u001b[0;34m    local_pairwise_align_nucleotide\u001b[0m\n",
        "\u001b[0;34m    skbio.alignment.local_pairwise_align_ssw\u001b[0m\n",
        "\u001b[0;34m    global_pairwise_align\u001b[0m\n",
        "\u001b[0;34m    global_pairwise_align_protein\u001b[0m\n",
        "\u001b[0;34m\u001b[0m\n",
        "\u001b[0;34m    Notes\u001b[0m\n",
        "\u001b[0;34m    -----\u001b[0m\n",
        "\u001b[0;34m    Default ``match_score``, ``mismatch_score``, ``gap_open_penalty`` and\u001b[0m\n",
        "\u001b[0;34m    ``gap_extend_penalty`` parameters are derived from the NCBI BLAST\u001b[0m\n",
        "\u001b[0;34m    Server [1]_.\u001b[0m\n",
        "\u001b[0;34m\u001b[0m\n",
        "\u001b[0;34m    This function can be use to align either a pair of sequences, a pair of\u001b[0m\n",
        "\u001b[0;34m    alignments, or a sequence and an alignment.\u001b[0m\n",
        "\u001b[0;34m\u001b[0m\n",
        "\u001b[0;34m    References\u001b[0m\n",
        "\u001b[0;34m    ----------\u001b[0m\n",
        "\u001b[0;34m    .. [1] http://blast.ncbi.nlm.nih.gov/Blast.cgi\u001b[0m\n",
        "\u001b[0;34m\u001b[0m\n",
        "\u001b[0;34m    \"\"\"\u001b[0m\u001b[0;34m\u001b[0m\n",
        "\u001b[0;34m\u001b[0m    \u001b[0;31m# use the substitution matrix provided by the user, or compute from\u001b[0m\u001b[0;34m\u001b[0m\n",
        "\u001b[0;34m\u001b[0m    \u001b[0;31m# match_score and mismatch_score if a substitution matrix was not provided\u001b[0m\u001b[0;34m\u001b[0m\n",
        "\u001b[0;34m\u001b[0m    \u001b[0;32mif\u001b[0m \u001b[0msubstitution_matrix\u001b[0m \u001b[0;32mis\u001b[0m \u001b[0mNone\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\n",
        "\u001b[0;34m\u001b[0m        \u001b[0msubstitution_matrix\u001b[0m \u001b[0;34m=\u001b[0m \\\n",
        "            \u001b[0mmake_identity_substitution_matrix\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mmatch_score\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mmismatch_score\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\n",
        "\u001b[0;34m\u001b[0m    \u001b[0;32melse\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\n",
        "\u001b[0;34m\u001b[0m        \u001b[0;32mpass\u001b[0m\u001b[0;34m\u001b[0m\n",
        "\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\n",
        "\u001b[0;34m\u001b[0m    \u001b[0;32mreturn\u001b[0m \u001b[0mglobal_pairwise_align\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mseq1\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mseq2\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mgap_open_penalty\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\n",
        "\u001b[0;34m\u001b[0m                                 \u001b[0mgap_extend_penalty\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0msubstitution_matrix\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\n",
        "\u001b[0;34m\u001b[0m                                 \u001b[0mpenalize_terminal_gaps\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mpenalize_terminal_gaps\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
        "\n"
       ]
      }
     ],
     "prompt_number": 21
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "For the sake of the examples below, I'm going to override one of the ``global_pairwise_align_nucleotide`` defaults to penalize terminal gaps. This effectively tells the algorithm that we know we have a collection of sequences that are homologous from beginning to end."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "global_pairwise_align_nucleotide = partial(global_pairwise_align_nucleotide, penalize_terminal_gaps=True)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 22
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "For example, we can still use this code to align pairs of sequences (but note that we now need to pass those sequences in as a pair of one-item lists):"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "print(query_sequences[0])\n",
      "print(query_sequences[1])\n",
      "\n",
      "aln1 = global_pairwise_align_nucleotide(query_sequences[0], query_sequences[1])\n",
      "print(aln1)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "ACCGGTGACCAGTTGACCAGT\n",
        "ATCGGTACCGGTAGAAGT\n",
        ">s1\n",
        "ACCGGTGACCAGTTGACCAGT\n",
        ">s2\n",
        "ATCGGT-ACCGGTAGA--AGT\n",
        "\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stderr",
       "text": [
        "/Users/caporaso/.virtualenvs/iab/lib/python2.7/site-packages/skbio/alignment/_pairwise.py:540: EfficiencyWarning: You're using skbio's python implementation of Needleman-Wunsch alignment. This is known to be very slow (e.g., thousands of times slower than a native C implementation). We'll be adding a faster version soon (see https://github.com/biocore/scikit-bio/issues/254 to track progress on this).\n",
        "  \"to track progress on this).\", EfficiencyWarning)\n"
       ]
      }
     ],
     "prompt_number": 23
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "We can align that alignment to one of our other sequences. "
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "\n",
      "print(query_sequences[2])\n",
      "print(global_pairwise_align_nucleotide(aln1, query_sequences[2]))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "GGTACCAAATAGAA\n",
        ">s1\n",
        "ACCGGTGACCAGTTGACCAGT\n",
        ">s2\n",
        "ATCGGT-ACCGGTAGA--AGT\n",
        ">s3\n",
        "---GGTACCAAATAGA--A--\n",
        "\n"
       ]
      }
     ],
     "prompt_number": 24
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Alternatively, we can align another pair of sequences:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "aln2 = global_pairwise_align_nucleotide(query_sequences[2], query_sequences[3])\n",
      "print(aln2)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        ">s3\n",
        "GGTACCAAATAGAA\n",
        ">s4\n",
        "GGCACCAAACAGAA\n",
        "\n"
       ]
      }
     ],
     "prompt_number": 25
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "And then align that alignment against our previous alignment:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "print(aln1)\n",
      "print(aln2)\n",
      "aln3 = global_pairwise_align_nucleotide(aln1, aln2)\n",
      "print(aln3)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        ">s1\n",
        "ACCGGTGACCAGTTGACCAGT\n",
        ">s2\n",
        "ATCGGT-ACCGGTAGA--AGT\n",
        "\n",
        ">s3\n",
        "GGTACCAAATAGAA\n",
        ">s4\n",
        "GGCACCAAACAGAA\n",
        "\n",
        ">s1\n",
        "ACCGGTGACCAGTTGACCAGT\n",
        ">s2\n",
        "ATCGGT-ACCGGTAGA--AGT\n",
        ">s3\n",
        "---GGTACCAAATAGA--A--\n",
        ">s4\n",
        "---GGCACCAAACAGA--A--\n",
        "\n"
       ]
      }
     ],
     "prompt_number": 26
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Putting it all together: progressive multiple sequence alignment"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "We can now combine all of these steps to take a set of query sequences, build a guide tree, perform progressive multiple sequence alignment, and return the guide tree (as a SciPy linkage matrix) and the alignment. "
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from skbio import TreeNode\n",
      "guide_tree = TreeNode.from_linkage_matrix(guide_lm, guide_dm.ids)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 27
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "We can view the guide tree in [newick format](http://scikit-bio.org/docs/latest/generated/skbio.io.newick.html) as follows:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "print(guide_tree)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "(s5:0.45975877193,(s1:0.410714285714,(s4:0.382575757576,(s2:0.305555555556,s3:0.305555555556):0.0770202020202):0.0281385281385):0.0490444862155);\n",
        "\n"
       ]
      }
     ],
     "prompt_number": 28
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from iab.algorithms import progressive_msa\n",
      "%psource progressive_msa"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\u001b[0;32mdef\u001b[0m \u001b[0mprogressive_msa\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0msequences\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mguide_tree\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mpairwise_aligner\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\n",
        "\u001b[0;34m\u001b[0m    \u001b[0;34m\"\"\" Perform progressive msa of sequences\u001b[0m\n",
        "\u001b[0;34m\u001b[0m\n",
        "\u001b[0;34m    Parameters\u001b[0m\n",
        "\u001b[0;34m    ----------\u001b[0m\n",
        "\u001b[0;34m    sequences : skbio.SequenceCollection\u001b[0m\n",
        "\u001b[0;34m        The sequences to be aligned.\u001b[0m\n",
        "\u001b[0;34m    guide_tree : skbio.TreeNode\u001b[0m\n",
        "\u001b[0;34m        The tree that should be used to guide the alignment process.\u001b[0m\n",
        "\u001b[0;34m    pairwise_aligner : function\u001b[0m\n",
        "\u001b[0;34m        Function that should be used to perform the pairwise alignments,\u001b[0m\n",
        "\u001b[0;34m        for example skbio.Alignment.global_pairwise_align_nucleotide. Must\u001b[0m\n",
        "\u001b[0;34m        support skbio.BiologicalSequence objects or skbio.Alignment objects\u001b[0m\n",
        "\u001b[0;34m        as input.\u001b[0m\n",
        "\u001b[0;34m\u001b[0m\n",
        "\u001b[0;34m    Returns\u001b[0m\n",
        "\u001b[0;34m    -------\u001b[0m\n",
        "\u001b[0;34m    skbio.Alignment\u001b[0m\n",
        "\u001b[0;34m\u001b[0m\n",
        "\u001b[0;34m    \"\"\"\u001b[0m\u001b[0;34m\u001b[0m\n",
        "\u001b[0;34m\u001b[0m    \u001b[0mc1\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mc2\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mguide_tree\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mchildren\u001b[0m\u001b[0;34m\u001b[0m\n",
        "\u001b[0;34m\u001b[0m    \u001b[0;32mif\u001b[0m \u001b[0mc1\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mis_tip\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\n",
        "\u001b[0;34m\u001b[0m        \u001b[0mc1_aln\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0msequences\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mc1\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mname\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\n",
        "\u001b[0;34m\u001b[0m    \u001b[0;32melse\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\n",
        "\u001b[0;34m\u001b[0m        \u001b[0mc1_aln\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mprogressive_msa\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0msequences\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mc1\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mpairwise_aligner\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\n",
        "\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\n",
        "\u001b[0;34m\u001b[0m    \u001b[0;32mif\u001b[0m \u001b[0mc2\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mis_tip\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\n",
        "\u001b[0;34m\u001b[0m        \u001b[0mc2_aln\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0msequences\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mc2\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mname\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\n",
        "\u001b[0;34m\u001b[0m    \u001b[0;32melse\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\n",
        "\u001b[0;34m\u001b[0m        \u001b[0mc2_aln\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mprogressive_msa\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0msequences\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mc2\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mpairwise_aligner\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\n",
        "\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\n",
        "\u001b[0;34m\u001b[0m    \u001b[0;32mreturn\u001b[0m \u001b[0mpairwise_aligner\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mc1_aln\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mc2_aln\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
        "\n"
       ]
      }
     ],
     "prompt_number": 29
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "msa = progressive_msa(query_sequences, guide_tree, pairwise_aligner=global_pairwise_align_nucleotide)\n",
      "print(msa)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        ">s5\n",
        "---GGC--CCA-----CTGAT\n",
        ">s1\n",
        "ACCGGTGACCAGTTGACCAGT\n",
        ">s4\n",
        "---GGCACCAAACAGA--A--\n",
        ">s2\n",
        "ATCGGTACC-GGTAGA--AGT\n",
        ">s3\n",
        "---GGTACCAAATAGA--A--\n",
        "\n"
       ]
      }
     ],
     "prompt_number": 30
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "We can now build a (hopefully) improved tree from our multiple sequence alignment. First we'll look at our original distance matrix again, and then the distance matrix generted from the progressive multiple sequence alignment."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "fig = guide_dm.plot(cmap='Greens')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x10b4f35d0>"
       ]
      }
     ],
     "prompt_number": 31
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "msa_dm = msa.distances()\n",
      "fig = msa_dm.plot(cmap='Greens')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x10b669250>"
       ]
      }
     ],
     "prompt_number": 32
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The UPGMA trees that result from these alignments are very different. First we'll look at the guide tree, and then the tree resulting from the progressive multiple sequence alignment."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "d = dendrogram(guide_lm, labels=guide_dm.ids, orientation='right', \n",
      "               link_color_func=lambda x: 'black')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAWsAAAD7CAYAAACsV7WPAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nS1IDxlqSGjDWktSAsZakBv4fsqqfGsmCeYIAAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x10b765f50>"
       ]
      }
     ],
     "prompt_number": 33
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "msa_lm = average(msa_dm.condensed_form())\n",
      "d = dendrogram(msa_lm, labels=msa_dm.ids, orientation='right', \n",
      "               link_color_func=lambda x: 'black')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAWsAAAD7CAYAAACsV7WPAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nS1IDxlqSGjDWktSAsZakBoy1JDXwfyLSyTiWENvGAAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x10b5e9a50>"
       ]
      }
     ],
     "prompt_number": 34
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "And we can wrap this all up in a single convenience function:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from iab.algorithms import progressive_msa_and_tree\n",
      "%psource progressive_msa_and_tree"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\u001b[0;32mdef\u001b[0m \u001b[0mprogressive_msa_and_tree\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0msequences\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\n",
        "\u001b[0;34m\u001b[0m                             \u001b[0mpairwise_aligner\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\n",
        "\u001b[0;34m\u001b[0m                             \u001b[0msequence_distance_fn\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mkmer_distance\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\n",
        "\u001b[0;34m\u001b[0m                             \u001b[0mguide_tree\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mNone\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\n",
        "\u001b[0;34m\u001b[0m                             \u001b[0mdisplay_aln\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mFalse\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\n",
        "\u001b[0;34m\u001b[0m                             \u001b[0mdisplay_tree\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mFalse\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\n",
        "\u001b[0;34m\u001b[0m    \u001b[0;34m\"\"\" Perform progressive msa of sequences and build a UPGMA tree\u001b[0m\n",
        "\u001b[0;34m    Parameters\u001b[0m\n",
        "\u001b[0;34m    ----------\u001b[0m\n",
        "\u001b[0;34m    sequences : skbio.SequenceCollection\u001b[0m\n",
        "\u001b[0;34m        The sequences to be aligned.\u001b[0m\n",
        "\u001b[0;34m    pairwise_aligner : function\u001b[0m\n",
        "\u001b[0;34m        Function that should be used to perform the pairwise alignments,\u001b[0m\n",
        "\u001b[0;34m        for example skbio.Alignment.global_pairwise_align_nucleotide. Must\u001b[0m\n",
        "\u001b[0;34m        support skbio.BiologicalSequence objects or skbio.Alignment objects\u001b[0m\n",
        "\u001b[0;34m        as input.\u001b[0m\n",
        "\u001b[0;34m    sequence_distance_fn : function\u001b[0m\n",
        "\u001b[0;34m        Function that returns and skbio.DistanceMatrix given an\u001b[0m\n",
        "\u001b[0;34m        skbio.SequenceCollection. This will be used to build a guide tree if\u001b[0m\n",
        "\u001b[0;34m        one is not provided.\u001b[0m\n",
        "\u001b[0;34m    guide_tree : skbio.TreeNode, optional\u001b[0m\n",
        "\u001b[0;34m        The tree that should be used to guide the alignment process.\u001b[0m\n",
        "\u001b[0;34m    display_aln : bool, optional\u001b[0m\n",
        "\u001b[0;34m        Print the alignment before returning.\u001b[0m\n",
        "\u001b[0;34m    display_tree : bool, optional\u001b[0m\n",
        "\u001b[0;34m        Print the tree before returning.\u001b[0m\n",
        "\u001b[0;34m\u001b[0m\n",
        "\u001b[0;34m    Returns\u001b[0m\n",
        "\u001b[0;34m    -------\u001b[0m\n",
        "\u001b[0;34m    skbio.alignment\u001b[0m\n",
        "\u001b[0;34m    skbio.TreeNode\u001b[0m\n",
        "\u001b[0;34m\u001b[0m\n",
        "\u001b[0;34m    \"\"\"\u001b[0m\u001b[0;34m\u001b[0m\n",
        "\u001b[0;34m\u001b[0m    \u001b[0;32mif\u001b[0m \u001b[0mguide_tree\u001b[0m \u001b[0;32mis\u001b[0m \u001b[0mNone\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\n",
        "\u001b[0;34m\u001b[0m        \u001b[0mguide_dm\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0msequences\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mdistances\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0msequence_distance_fn\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\n",
        "\u001b[0;34m\u001b[0m        \u001b[0mguide_lm\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0maverage\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mguide_dm\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mcondensed_form\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\n",
        "\u001b[0;34m\u001b[0m        \u001b[0mguide_tree\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mTreeNode\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mfrom_linkage_matrix\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mguide_lm\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mguide_dm\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mids\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\n",
        "\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\n",
        "\u001b[0;34m\u001b[0m    \u001b[0mmsa\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mprogressive_msa\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0msequences\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mguide_tree\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\n",
        "\u001b[0;34m\u001b[0m                          \u001b[0mpairwise_aligner\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mpairwise_aligner\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\n",
        "\u001b[0;34m\u001b[0m    \u001b[0;32mif\u001b[0m \u001b[0mdisplay_aln\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\n",
        "\u001b[0;34m\u001b[0m        \u001b[0;32mprint\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mmsa\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\n",
        "\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\n",
        "\u001b[0;34m\u001b[0m    \u001b[0mmsa_dm\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mmsa\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mdistances\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\n",
        "\u001b[0;34m\u001b[0m    \u001b[0mmsa_lm\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0maverage\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mmsa_dm\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mcondensed_form\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\n",
        "\u001b[0;34m\u001b[0m    \u001b[0mmsa_tree\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mTreeNode\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mfrom_linkage_matrix\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mmsa_lm\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mmsa_dm\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mids\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\n",
        "\u001b[0;34m\u001b[0m    \u001b[0;32mif\u001b[0m \u001b[0mdisplay_tree\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\n",
        "\u001b[0;34m\u001b[0m        \u001b[0;32mprint\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m\"\\nOutput tree:\"\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\n",
        "\u001b[0;34m\u001b[0m        \u001b[0md\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mdendrogram\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mmsa_lm\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mlabels\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mmsa_dm\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mids\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0morientation\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;34m'right'\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\n",
        "\u001b[0;34m\u001b[0m                   \u001b[0mlink_color_func\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;32mlambda\u001b[0m \u001b[0mx\u001b[0m\u001b[0;34m:\u001b[0m \u001b[0;34m'black'\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mleaf_font_size\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;36m24\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\n",
        "\u001b[0;34m\u001b[0m    \u001b[0;32mreturn\u001b[0m \u001b[0mmsa\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mmsa_tree\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
        "\n"
       ]
      }
     ],
     "prompt_number": 35
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "msa, tree = progressive_msa_and_tree(query_sequences, pairwise_aligner=global_pairwise_align_nucleotide, display_tree=True, display_aln=True)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        ">s5\n",
        "---GGC--CCA-----CTGAT\n",
        ">s1\n",
        "ACCGGTGACCAGTTGACCAGT\n",
        ">s4\n",
        "---GGCACCAAACAGA--A--\n",
        ">s2\n",
        "ATCGGTACC-GGTAGA--AGT\n",
        ">s3\n",
        "---GGTACCAAATAGA--A--\n",
        "\n",
        "\n",
        "Output tree:\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAWsAAAD7CAYAAACsV7WPAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nS1IDxlqSGjDWktSAsZakBoy1JDXwfyLSyTiWENvGAAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x10b4eed90>"
       ]
      }
     ],
     "prompt_number": 36
    },
    {
     "cell_type": "heading",
     "level": 1,
     "metadata": {},
     "source": [
      "Progressive alignment versus iterative alignment"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "In an iterative alignment, the output tree from the above progressive alignment is used as a guide tree, and the full process repeated. This is performed to reduce errors that result from a low-quality guide tree. "
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from iab.algorithms import iterative_msa_and_tree\n",
      "%psource iterative_msa_and_tree"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\u001b[0;32mdef\u001b[0m \u001b[0miterative_msa_and_tree\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0msequences\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\n",
        "\u001b[0;34m\u001b[0m                           \u001b[0mnum_iterations\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\n",
        "\u001b[0;34m\u001b[0m                           \u001b[0mpairwise_aligner\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\n",
        "\u001b[0;34m\u001b[0m                           \u001b[0msequence_distance_fn\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mkmer_distance\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\n",
        "\u001b[0;34m\u001b[0m                           \u001b[0mdisplay_aln\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mFalse\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\n",
        "\u001b[0;34m\u001b[0m                           \u001b[0mdisplay_tree\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mFalse\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\n",
        "\u001b[0;34m\u001b[0m    \u001b[0;34m\"\"\" Perform progressive msa of sequences and build a UPGMA tree\u001b[0m\n",
        "\u001b[0;34m    Parameters\u001b[0m\n",
        "\u001b[0;34m    ----------\u001b[0m\n",
        "\u001b[0;34m    sequences : skbio.SequenceCollection\u001b[0m\n",
        "\u001b[0;34m       The sequences to be aligned.\u001b[0m\n",
        "\u001b[0;34m    num_iterations : int\u001b[0m\n",
        "\u001b[0;34m       The number of iterations of progressive multiple sequence alignment to\u001b[0m\n",
        "\u001b[0;34m       perform. Must be greater than zero and less than five.\u001b[0m\n",
        "\u001b[0;34m    pairwise_aligner : function\u001b[0m\n",
        "\u001b[0;34m       Function that should be used to perform the pairwise alignments,\u001b[0m\n",
        "\u001b[0;34m       for example skbio.Alignment.global_pairwise_align_nucleotide. Must\u001b[0m\n",
        "\u001b[0;34m       support skbio.BiologicalSequence objects or skbio.Alignment objects\u001b[0m\n",
        "\u001b[0;34m       as input.\u001b[0m\n",
        "\u001b[0;34m    sequence_distance_fn : function\u001b[0m\n",
        "\u001b[0;34m       Function that returns and skbio.DistanceMatrix given an\u001b[0m\n",
        "\u001b[0;34m       skbio.SequenceCollection. This will be used to build a guide tree.\u001b[0m\n",
        "\u001b[0;34m    display_aln : bool, optional\u001b[0m\n",
        "\u001b[0;34m       Print the alignment before returning.\u001b[0m\n",
        "\u001b[0;34m    display_tree : bool, optional\u001b[0m\n",
        "\u001b[0;34m       Print the tree before returning.\u001b[0m\n",
        "\u001b[0;34m\u001b[0m\n",
        "\u001b[0;34m    Returns\u001b[0m\n",
        "\u001b[0;34m    -------\u001b[0m\n",
        "\u001b[0;34m    skbio.alignment\u001b[0m\n",
        "\u001b[0;34m    skbio.TreeNode\u001b[0m\n",
        "\u001b[0;34m\u001b[0m\n",
        "\u001b[0;34m   \"\"\"\u001b[0m\u001b[0;34m\u001b[0m\n",
        "\u001b[0;34m\u001b[0m    \u001b[0;32mif\u001b[0m \u001b[0mnum_iterations\u001b[0m \u001b[0;34m>\u001b[0m \u001b[0;36m5\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\n",
        "\u001b[0;34m\u001b[0m        \u001b[0;32mraise\u001b[0m \u001b[0mValueError\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m\"A maximum of five iterations is allowed.\"\u001b[0m\u001b[0;34m\u001b[0m\n",
        "\u001b[0;34m\u001b[0m                         \u001b[0;34m\"You requested %d.\"\u001b[0m \u001b[0;34m%\u001b[0m \u001b[0mnum_iterations\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\n",
        "\u001b[0;34m\u001b[0m    \u001b[0mprevious_iter_tree\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mNone\u001b[0m\u001b[0;34m\u001b[0m\n",
        "\u001b[0;34m\u001b[0m    \u001b[0;32mfor\u001b[0m \u001b[0mi\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mrange\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mnum_iterations\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\n",
        "\u001b[0;34m\u001b[0m        \u001b[0;32mif\u001b[0m \u001b[0mi\u001b[0m \u001b[0;34m==\u001b[0m \u001b[0;34m(\u001b[0m\u001b[0mnum_iterations\u001b[0m \u001b[0;34m-\u001b[0m \u001b[0;36m1\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\n",
        "\u001b[0;34m\u001b[0m            \u001b[0;31m# only display the last iteration\u001b[0m\u001b[0;34m\u001b[0m\n",
        "\u001b[0;34m\u001b[0m            \u001b[0mdisplay\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mTrue\u001b[0m\u001b[0;34m\u001b[0m\n",
        "\u001b[0;34m\u001b[0m        \u001b[0;32melse\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\n",
        "\u001b[0;34m\u001b[0m            \u001b[0mdisplay\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mFalse\u001b[0m\u001b[0;34m\u001b[0m\n",
        "\u001b[0;34m\u001b[0m        \u001b[0mprevious_iter_msa\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mprevious_iter_tree\u001b[0m \u001b[0;34m=\u001b[0m \\\n",
        "            \u001b[0mprogressive_msa_and_tree\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0msequences\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\n",
        "\u001b[0;34m\u001b[0m             \u001b[0mpairwise_aligner\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mpairwise_aligner\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\n",
        "\u001b[0;34m\u001b[0m             \u001b[0msequence_distance_fn\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0msequence_distance_fn\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\n",
        "\u001b[0;34m\u001b[0m             \u001b[0mguide_tree\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mprevious_iter_tree\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\n",
        "\u001b[0;34m\u001b[0m             \u001b[0mdisplay_aln\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mdisplay_aln\u001b[0m \u001b[0;32mand\u001b[0m \u001b[0mdisplay\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\n",
        "\u001b[0;34m\u001b[0m             \u001b[0mdisplay_tree\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mdisplay_tree\u001b[0m \u001b[0;32mand\u001b[0m \u001b[0mdisplay\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\n",
        "\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\n",
        "\u001b[0;34m\u001b[0m    \u001b[0;32mreturn\u001b[0m \u001b[0mprevious_iter_msa\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mprevious_iter_tree\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
        "\n"
       ]
      }
     ],
     "prompt_number": 37
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "msa, tree = iterative_msa_and_tree(query_sequences, pairwise_aligner=global_pairwise_align_nucleotide, num_iterations=1, display_aln=True, display_tree=True)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        ">s5\n",
        "---GGC--CCA-----CTGAT\n",
        ">s1\n",
        "ACCGGTGACCAGTTGACCAGT\n",
        ">s4\n",
        "---GGCACCAAACAGA--A--\n",
        ">s2\n",
        "ATCGGTACC-GGTAGA--AGT\n",
        ">s3\n",
        "---GGTACCAAATAGA--A--\n",
        "\n",
        "\n",
        "Output tree:\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAWsAAAD7CAYAAACsV7WPAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nS1IDxlqSGjDWktSAsZakBoy1JDXwfyLSyTiWENvGAAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x10b46df90>"
       ]
      }
     ],
     "prompt_number": 38
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "msa, tree = iterative_msa_and_tree(query_sequences, pairwise_aligner=global_pairwise_align_nucleotide, num_iterations=2, display_aln=True, display_tree=True)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        ">s5\n",
        "---GGC--CCA-----CTGAT\n",
        ">s4\n",
        "---GGCACCAAACAGA----A\n",
        ">s3\n",
        "---GGTACCAAATAGA----A\n",
        ">s1\n",
        "ACCGGTGACCAGTTGACCAGT\n",
        ">s2\n",
        "ATCGGT-ACCGGTAGA--AGT\n",
        "\n",
        "\n",
        "Output tree:\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAXIAAAD7CAYAAAB37B+tAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nAAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x10b5edb10>"
       ]
      }
     ],
     "prompt_number": 39
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "msa, tree = iterative_msa_and_tree(query_sequences, pairwise_aligner=global_pairwise_align_nucleotide, num_iterations=3, display_aln=True, display_tree=True)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        ">s5\n",
        "---GGC--CCA-----CTGAT\n",
        ">s4\n",
        "---GGCACCAAACAGA----A\n",
        ">s3\n",
        "---GGTACCAAATAGA----A\n",
        ">s1\n",
        "ACCGGTGACCAGTTGACCAGT\n",
        ">s2\n",
        "ATCGGT-ACCGGTAGA--AGT\n",
        "\n",
        "\n",
        "Output tree:\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAXIAAAD7CAYAAAB37B+tAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nAAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x10b4fe090>"
       ]
      }
     ],
     "prompt_number": 40
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "msa, tree = iterative_msa_and_tree(query_sequences, pairwise_aligner=global_pairwise_align_nucleotide, num_iterations=5, display_aln=True, display_tree=True)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        ">s5\n",
        "---GGC--CCA-----CTGAT\n",
        ">s4\n",
        "---GGCACCAAACAGA----A\n",
        ">s3\n",
        "---GGTACCAAATAGA----A\n",
        ">s1\n",
        "ACCGGTGACCAGTTGACCAGT\n",
        ">s2\n",
        "ATCGGT-ACCGGTAGA--AGT\n",
        "\n",
        "\n",
        "Output tree:\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
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       "text": [
        "<matplotlib.figure.Figure at 0x10b4ba2d0>"
       ]
      }
     ],
     "prompt_number": 41
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "\n",
      "Some references that I used in assembling these notes include [1](http://statweb.stanford.edu/~nzhang/345_web/sequence_slides3.pdf), [2](http://math.mit.edu/classes/18.417/Slides/alignment.pdf), [3](http://www.sciencedirect.com/science/article/pii/0378111988903307), [4](http://bioinformatics.oxfordjournals.org/content/23/21/2947.full), and [5](http://nar.oxfordjournals.org/content/32/5/1792.full). "
     ]
    }
   ],
   "metadata": {}
  }
 ]
}