I519 Introduction to Bioinformatics, 2011 Genome Comparison Yuzhen Ye (yye@indiana.edu) School of Informatics & Computing, IUB
Whole genome comparison/alignment Build better phylogenies Identify polymorphism Detect gene-level events Compare different assemblies of a single genome
Whole genome comparison Aligning whole genomes is a fundamentally different problem than aligning short sequences. Need to consider the presence of large-scale evolutionary events Gene duplication & loss Horizontal gene transfer Repetitive sequences (repeats) Gene rearrangement and inversion Pairwise and multiple genome comparison Multiple genome alignment provides a basis for research into comparative genomics and the study of evolutionary dynamics.
Genome evolution Genome A Point Substitution Translocation Inversion Inversion and Translocation Insertion Repeat (Duplication)
Basic algorithms: use anchoring as a heuristic to speed alignment Assumption: highly similar subsequences can be found quickly and are likely to be part of the correct global alignment. These local alignments are used to anchor a global alignment (alignment anchor), reducing the number of possible global alignments considered during a subsequent O(n2) dynamic programming step. Select a single collinear set of alignment anchors Many tools have been developed
Rearrangement free or not Free of rearrangement Assume the input sequences are free from significant rearrangements of sequence elements, selecting a single collinear set of alignment anchors Pairwise: MUMmer, GLASS, AVID, and WABA align pairs of long sequences Multiple alignment: MAVID, MLAGAN, and MGA Consider rearrangement Shuffle-LAGAN (2003, first genome comparison method described that explicitly deals with genome rearrangements) MultiPipMaker (2003) Mauve (2004, multiple) Enredo and Pecan (2008) GR-Aligner (2009, pairwise)
MUMer method MUMer combines suffix trees, the longest increasing subsequence (LIS) and SW alignment Maximal Unique Match (MUM) Identification - Identify the longest strings in Genome 1 that have one identical match in Genome 2 Naïve method: O(N 2 ) Using suffix tree: O(N) Ordered MUM Selection - Identify the longest set of MUMs such that they occur in order in each of the genomes (using a variation of the well-known algorithm to find the LIS of a sequence of integers) Processing Non-matched Regions - Classify nonmatched regions as either insertions, SNPs or highly polymorphic regions
Suffix tree Suffix tree is data structure, which allows one to find, extremely efficiently, all distinct subsequences in a given sequence. There are efficient algorithms to construct suffix trees given by Weiner (1973) and McCreight (1976) (in linear time) For the task of comparing two DNA sequences, suffix trees allow one to quickly find all subsequences shared by the two inputs. The genome alignment is then built upon this information.
Suffix tree for finding MUMs Suffix Tree for sequence gaaccgacct An internal node is a repeated sequence in the original string Leaf is a unique suffix Every unique matching sequence is represented by an internal node with exactly two child nodes, such that the child nodes are leaf nodes from different genomes
ATCGTA# # 7 A# 6 TA# 5 GTA# 4 CGTA# 3 TCGTA# 2 ATCGTA# 1 ATCGAT$ $ 14 T$ 13 AT$ 12 GAT$ 11 CGAT$ 10 TCGAT$ 9 ATCGAT$ 8 ATCGTA# # 7 $ 14 A# 6 AT$ 12 ATCGAT$ 8 ATCGTA# 1 CGAT$ 10 CGTA# 3 GAT$ 11 GTA# 4 T$ 13 TA# 5 TCGAT$ 9 TCGTA# 2 A toy example T A 0 CG 1 1 2 1 $ # TA# AT$ AT$ TA# A# CG T$ T 13 5 6 3 12 2 10 3 11 4 AT$ 9 2 TA# AT$ 4 CG TA# 8 1 G
Suffix tree & suffix array for string matching Preprocess text T, not pattern P O(m) preprocess time (m: the length of the text) O(n+k) search time (n: the length of the pattern) k is number of occurrences of P in T Match pattern P against tree starting at root until Case 1, P is completely matched Every leaf below this match point is the starting location of P in T Case 2: No match is possible P does not occur in T
A toy example of string (pattern) matching T = xabxac suffixes ={xabxac, abxac, bxac, xac, ac, c} Pattern P 1 : xa Pattern P 2 : xb 1 b b b x x x x a a a a a c c c c c c 2 3 6 5 4
Suffix array Suffix array: a sorted list of the suffixes of a given string; the start positions are sorted in lexicographical (alphabetical) order Straightforward implementation: O(m 2 logm), reduced to O(mlogm) (utilizing partial sorts) m: the length of the text Suffix array enables binary search for any substring, e.g. CAD O(nlogm), reduced to O(n + logm) if use LCP (longest common prefix) n: the length of the pattern Suffix array is more compact than a suffix tree ABRACADABRA# 11 # 10 A# 7 ABRA# 0 ABRACADABRA# 3 ACADABRA# 5 ADABRA# 8 BRA# 1 BRACADABRA# 4 CADABRA# 6 DABRA# 9 RA# 2 RACADABRA# webglimpse.net/pubs/suffix.pdf
G1 Ordered MUM selection 1 2 3 4... G2 A B C D... MUMs: Possible Selections <1,A>, <2,C>, <3,B>, <4,D> <1,A>, <2,C>, <4,D> <1,A>, <3,B>, <4,D> Then process non-matched regions (by dynamic programming algorithm) See more at www.cs.rice.edu/~nakhleh/comp571/genomealignment.ppt
LIS algorithm B positions is given by the sequence 1, 3, 2, 4, 6, 7, 5 The LIS (longest increasing sequence) is: 1, 2, 4, 6, 7 LIS problem can be solved by a dynamic programming algorithm
Mauve Mauve is a system for efficiently constructing multiple genome alignments in the presence of large-scale evolutionary events Identifies conserved genomic regions, rearrangements and inversions in conserved regions, and the exact sequence breakpoints of such rearrangements across multiple genomes. Also performs traditional multiple alignment of conserved regions to identify nucleotide substitutions and indels, using the progressive dynamic programming approach of CLUSTAL W
Mauve's anchor selection algorithm Relax anchor selection method: do not assume that the genomes under study are collinear Identifie and align regions of local collinearity called locally collinear blocks (LCBs) Each LCB is a homologous region of sequence shared by two or more of the genomes under study Does not contain any rearrangements of homologous sequence (within LCB)
Mauve algorithm 1. Find local alignments (multi-mums), using seed-and-extend hashing method (time complexity O(G 2 n + Gn loggn), G is the number of genomes and n the average genome length) 2. Use the multi-mums to calculate a phylogenetic guide tree. 3. Select a subset of the multi-mums to use as anchors these anchors are partitioned into collinear groups called LCBs, using a greedy breakpoint elimination algorithm 4. Perform recursive anchoring to identify additional alignment anchors within and outside each LCB. 5. Perform a progressive alignment of each LCB using the guide tree.
Greedy breakpoint elimination in three genomes Darling A C et al. Genome Res. 2004;14:1394-1403 2004 by Cold Spring Harbor Laboratory Press
An example of LCB identified among nine enterobacterial genomes Darling A C et al. Genome Res. 2004;14:1394-1403
LCBs identified among concatenated chromosomes of the mouse, rat, and human genomes Darling A C et al. Genome Res. 2004;14:1394-1403
Turnip vs cabbage: almost identical mtdna gene sequences In 1980s Jeffrey Palmer studied evolution of plant organelles by comparing mitochondrial genomes of the cabbage and turnip (using physical mapping) 99%-99.9% similarity between genes These surprisingly identical gene sequences differed in gene order This study helped pave the way to analyzing genome rearrangements in molecular evolution
Why we care about genome rearrangement Evolutionary and functional analysis Examples: Dynamics of Genome Rearrangement in Bacterial Populations, using comparison of eight Yersinia (pathogenic bacteria) genomes. PLoS Genet 4(7): e1000128, 2008 Genome-wide DNA excision (Oxytricha trifallax destroys 95% of its germline genome during development, including the elimination of all transposon DNA, through an exaggerated process of genome rearrangement). Science, Vol. 324. no. 5929, pp. 935 938, 2009
Transforming cabbage into turnip
Reversals and breakpoints 1 2 3 1 2 3 7 8 6 5 4 9 10 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 9 10 8 4 1, 2, 3, -8, -7, -6, -5, -4, 9, 10 7 6 5 The reversion introduced two breakpoints (disruptions in order).
Unknown ancestor ~ 75 million years ago Genome rearrangements Mouse (X chrom.) Human (X chrom.) What are the similarity blocks and how to find them? What is the architecture of the ancestral genome? What is the evolutionary scenario for transforming one genome into the other?
Comparative genomic architectures: mouse vs human genome Humans and mice have similar genomes, but their genes are ordered differently ~245 rearrangements Reversals Fusions Fissions Translocation
History of Chromosome X Rat Consortium, Nature, 2004
GRIMM Real genome architectures are represented by signed permutations Efficient algorithms to sort signed permutations have been developed GRIMM web server computes the reversal distances between signed permutations: http://nbcr.sdsc.edu/grimm/mgr.cgi