{ "metadata": { "name": "", "signature": "sha256:7922e95e19c2edf0b7a2a8c6bb49659489498fbe0e3bdcb627161e949cf6eeb8" }, "nbformat": 3, "nbformat_minor": 0, "worksheets": [ { "cells": [ { "cell_type": "code", "collapsed": false, "input": [ "#Collaborators: Alan Wu, Fred Landis\n", "\n", "#Problem 1\n", "\n", "#We can see that there exist $4^{(6/2)} = 4^3 = 64$ different reverse palindromic recognition sites of length 6. \n", "#This is because, as we imagine constructing the palindromic sequence, we have four possible options for the first entry, but any of these choices immediately fixes the last entry. \n", "#This process continues for $n/2$ entries where $n$ is the total length of interest. \n", "#We thus see that the problem is reduced to finding the possible combinations of half the original string length. \n", "#The fraction of $2N$-mers, that are reverse palindromic is $\\frac{4^N}{4^{2N}} = \\frac{1}{4^N}$. \n", "#We see this as the numerator (before simplification) is the number of possible reverse palindromes in a $2N$-mer, and the denominator (before simplification) is all possible strings for a $2N$-mer. \n", "#The following code produces all such possible recognition sites: \n", "\n", "import itertools\n", "\n", "sizeOfPalindrome = 6\n", "reversePalindromes = []\n", "\n", "#essentially performs a \"repeat\"-dimensional cartesian product\n", "halfPermutations = itertools.product('ATGC',repeat=sizeOfPalindrome/2) \n", "\n", "for permutation in halfPermutations:\n", "\treversePalindromes.append(''.join(permutation)+''.join(reversed(['A' if b=='T' else 'C' if b=='G' else 'T' if b=='A' else 'G' for b in permutation])))\n", "print reversePalindromes\n", "\n", "#The following reverse palidromes were produced by my code: \n", "#['AAATTT', 'AATATT', 'AAGCTT', 'AACGTT', 'ATATAT', 'ATTAAT', 'ATGCAT', 'ATCGAT', 'AGATCT', 'AGTACT', \n", "#'AGGCCT', 'AGCGCT', 'ACATGT', 'ACTAGT', 'ACGCGT', 'ACCGGT', 'TAATTA', 'TATATA', 'TAGCTA', 'TACGTA', \n", "#'TTATAA', 'TTTAAA', 'TTGCAA', 'TTCGAA', 'TGATCA', 'TGTACA', 'TGGCCA', 'TGCGCA', 'TCATGA', 'TCTAGA', \n", "#'TCGCGA', 'TCCGGA', 'GAATTC', 'GATATC', 'GAGCTC', 'GACGTC', 'GTATAC', 'GTTAAC', 'GTGCAC', 'GTCGAC', \n", "#'GGATCC', 'GGTACC', 'GGGCCC', 'GGCGCC', 'GCATGC', 'GCTAGC', 'GCGCGC', 'GCCGGC', 'CAATTG', 'CATATG', \n", "#'CAGCTG', 'CACGTG', 'CTATAG', 'CTTAAG', 'CTGCAG', 'CTCGAG', 'CGATCG', 'CGTACG', 'CGGCCG', 'CGCGCG', \n", "#'CCATGG', 'CCTAGG', 'CCGCGG', 'CCCGGG']" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "['AAATTT', 'AATATT', 'AAGCTT', 'AACGTT', 'ATATAT', 'ATTAAT', 'ATGCAT', 'ATCGAT', 'AGATCT', 'AGTACT', 'AGGCCT', 'AGCGCT', 'ACATGT', 'ACTAGT', 'ACGCGT', 'ACCGGT', 'TAATTA', 'TATATA', 'TAGCTA', 'TACGTA', 'TTATAA', 'TTTAAA', 'TTGCAA', 'TTCGAA', 'TGATCA', 'TGTACA', 'TGGCCA', 'TGCGCA', 'TCATGA', 'TCTAGA', 'TCGCGA', 'TCCGGA', 'GAATTC', 'GATATC', 'GAGCTC', 'GACGTC', 'GTATAC', 'GTTAAC', 'GTGCAC', 'GTCGAC', 'GGATCC', 'GGTACC', 'GGGCCC', 'GGCGCC', 'GCATGC', 'GCTAGC', 'GCGCGC', 'GCCGGC', 'CAATTG', 'CATATG', 'CAGCTG', 'CACGTG', 'CTATAG', 'CTTAAG', 'CTGCAG', 'CTCGAG', 'CGATCG', 'CGTACG', 'CGGCCG', 'CGCGCG', 'CCATGG', 'CCTAGG', 'CCGCGG', 'CCCGGG']\n" ] } ], "prompt_number": 6 }, { "cell_type": "code", "collapsed": false, "input": [ "#Problem 2\n", "\n", "#The frequencies of the palindromic sequences in the dataset are produced by the following code. \n", "#NOTE: HumChr01.seq must be in this file's path\n", "\n", "#It appears as though the more frequently occurring sequences are those that are made of predominately 'T's and 'A's, \n", "#while the less frequently occurring recognition sites are those that are made of predominately 'G's and 'C's. \n", "\n", "\n", "with open(\"HumChr01.seq\", 'r') as sequenceFile:\n", "\tfullSequence = sequenceFile.read()\n", "\n", "reversePalindroneFrequencies = {}\n", "\n", "for reversePalindrone in reversePalindromes:\n", "\treversePalindroneFrequencies[reversePalindrone] = fullSequence.count(reversePalindrone)\n", "\n", "print reversePalindroneFrequencies\n", "\n", "#The following frequencies were produced by my code: \n", "#{'ACTAGT': 30370, 'TATATA': 144759, 'TCGCGA': 1127, 'TACGTA': 9337, \n", "#'CGGCCG': 7651, 'CTTAAG': 50087, 'TGCGCA': 7005, 'CCTAGG': 48979,\n", "# 'CTCGAG': 9957, 'GAGCTC': 50049, 'ACATGT': 79458, 'TTCGAA': 8091, \n", "#'ATTAAT': 106729, 'AGTACT': 42704, 'AGATCT': 60179, 'ACGCGT': 1631, \n", "#'CGTACG': 839, 'GGCGCC': 19486, 'AGCGCT': 8579, 'TGGCCA': 107911, \n", "#'ATCGAT': 6471, 'TGTACA': 61405, 'TGATCA': 56893, 'GACGTC': 5317, \n", "#'TTTAAA': 252188, 'AAGCTT': 64394, 'GCTAGC': 22197, 'CATATG': 66900, \n", "#'CTATAG': 39287, 'TCATGA': 74262, 'AACGTT': 11841, 'CTGCAG': 105663, \n", "#'ATGCAT': 66729, 'GCATGC': 43792, 'TAGCTA': 46642, 'AATATT': 170369, \n", "#'CGCGCG': 3460, 'CACGTG': 20824, 'CCGCGG': 5530, 'TCCGGA': 7704, \n", "#'ATATAT': 161388, 'GATATC': 32152, 'CAATTG': 40935, 'CGATCG': 978, \n", "#'ACCGGT': 4216, 'AAATTT': 192451, 'CCCGGG': 31941, 'GCCGGC': 10460, \n", "#'GGGCCC': 40294, 'GTGCAC': 38168, 'GTATAC': 31467, 'GTTAAC': 29507, \n", "#'TAATTA': 101323, 'GGTACC': 22705, 'GCGCGC': 5048, 'CAGCTG': 89432, \n", "#'GAATTC': 60248, 'TTATAA': 120196, 'GGATCC': 30113, 'TTGCAA': 68694, \n", "#'GTCGAC': 2342, 'TCTAGA': 61946, 'AGGCCT': 67067, 'CCATGG': 59851}" ], "language": "python", "metadata": {}, "outputs": [] }, { "cell_type": "code", "collapsed": false, "input": [ "#Problem 3\n", "\n", "#The following code produces a histogram which displays the distribution of lengths of the segments of our sample when cut at recognition sites \"CGTAC/G\". \n", "#That is, when the sequence of nucleotides CGTACG are found, a cut is made between the last 'C' and 'G'. \n", "\n", "import matplotlib.pyplot\n", "import re \n", "\n", "cutStrands = re.sub(\"(?<=CGTAC)(?=G)\",\"jaretrulz\",fullSequence).split(\"jaretrulz\") #super hacky because re.split sucks\n", "matplotlib.pyplot.hist([len(s) for s in cutStrands], bins=100, range=(0,3000000))\n", "matplotlib.pyplot.show()" ], "language": "python", "metadata": {}, "outputs": [] }, { "cell_type": "code", "collapsed": false, "input": [ "HapllLengths = [68, 114, 133, 162, 387, 557, 649, 813, 1737, 2012, 2325, 7342]\n", "BstUILengths = [235, 316, 1403, 1455, 1562, 1589, 1633, 1666, 6440]\n", "HapllAndBstUILengths = [9, 68, 99, 114, 133, 136, 162, 183, 387, 513, 557, 754, 813, 1032, 1455, 1562, 1633, 1666, 2012, 3011]\n", "\n", "def powerSet(inputSet):\n", "\tpowerSet = [[]]\n", "\tfor element in inputSet:\n", "\t\tpowerSet.extend([subset + [element] for subset in powerSet])\n", "\treturn powerSet\n", "\n", "def determineOrderOfSegments(digestionSetA, digestionSetB, combinedDigestionSets):\n", "\tpowerSetHits = []\n", "\tfor setToTry in powerSet(combinedDigestionSets):\n", "\t\tif sum(setToTry) in digestionSetA + digestionSetB:\n", "\t\t\tpowerSetHits.extend([setToTry])\n", "\t\n", "\tsolutionFound = False\n", "\n", "\tremainingLengthsToExplain = [\"init\"]\n", "\n", "\twhile not remainingLengthsToExplain:\n", "\t\tremainingLengthsToExplain = digestionSetA + digestionSetB\n", "\t\tusedPowerSetElements = []\n", "\t\tfor powerSetHit in powerSetHits:\n", "\t\t\tfor powerSetElement in powerSetHit:\n", "\t\t\t\tif powerSetElement in usedPowerSetElements:\n", "\t\t\t\t\tbreak\n", "\t\t\tremainingLengthsToExplain.remove(sum(powerSetHit))\n", "\t\t\tusedPowerSetElements.extend(powerSetHit)\n", "\t\tprint sorted(usedPowerSetElements)\n", "\n", "determineOrderOfSegments(HapllLengths, BstUILengths, HapllAndBstUILengths)" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 11 } ], "metadata": {} } ] }