1. Bioinformatics Chromosome rearrangements Chromosome and genome comparison versus gene comparison Permutations and breakpoint graphs Transforming Men into Mouse Evolutionary reconstructions Lecture 15

2. Types of chromosome rearrangements Translocations Inversions Insertions Duplications Deletions Fusions/Fissions A B C D E F K L M N O P K L M C D E F A B N O P A C B D E F K O N M L P A B C    D E FK L M N O  P A B C D E E F K L L M N O P A B C E F K L O P A B C E F K L O P A B C E F K L O P

3. Chromosome and genome comparisons versus gene comparisons Comparisons of genes, proteins and non-coding sequences is not the only way to study relations between different species. Attempts were made from 1930s to use chromosome rearrangements information for this purpose. It has been shown that genomes consist of a relatively moderate number of “conserved” so called syntenic blocks, which carry nearly the same or very similar set of genes. The latest study revealed 281 syntenic blocks, which were observed when human and mouse genomes were compared. This type of analysis is independent and different from sequence data and provide very useful information, which can not be obtained by other means. When the number of rearrangements is small (<10), tracing back rearrangements is not too demanding. However, sophisticated mathematics and specialised computer programmes are required to reconstruct chains of events using real numbers of rearrangements.

4. Transformation of cabbage in turnip

5. A most parsimonious rearrangement scenario for transformation of worm mtDNA into human (26 reversals) Red arrows show direction of reversals. You may continue this process. mtDNA of worm Ascaris suum human mtDNA

6. Permutations. Sorting by reversals. Genome rearrangements can be modelled by a combinatorial problem of sorting by reversals. This problem is known in computer science as the pancake flipping problem. A chef is sloppy and the size of pancakes vary significantly. A waiter rearrange them by flipping, thus putting pancakes in the right order. Bill Gates and Christos Papadimitriou tried to solve the problem while being undergraduates at Harvard (1979). They proved that the prefix reversal diameter of the symmetric group, d pref (n) = max  Sn d pref (  ), is less than or equal to 5/3 (n) + 5/3 and that for infinitely many n, d pref (n)  17/16(n). The pancake flipping problem thus still remains unsolved in general form. ?

7. Breakpoints, breakpoint graph, and maximum cycle decomposition The estimate of reversal distance in terms of breakpoints is not very accurate. Another parameter (size of maximum cycle decomposition of the breakpoint graph) is better and plays an important role in estimating reversal distance (Pevzner 2000). For most of biological examples, d(  ) = n + 1 – c(  ), where c(  ) is a maximum number of edge-disjoint alternative cycles and n is number of elements in permutations. This procedure reduces the reversal distance problem to the maximum cycle decomposition problem. edges vertices (nodes)

8. Modelling a signed permutation by an unsigned permutation Genes are directed fragments of DNA (5’  3’) and a sequence of n genes is represented by signed (+ or -) permutation. Every reversal changes both the order and the signs of the elements within that fragment, chromosome or genome.

9. Signed permutations and physical maps Physical maps usually do not provide information about the direction of genes, and therefore lead to representation of a genome as an unsigned permutation . But it can be done using signed permutations.

10. Optimal sorting of a permutation by five reversals Breakpoint graph of this permutation Transformation of a signed permutation into an unsigned permutation  and the breakpoint graph G(  ) Interleaving graph H  with two oriented and one unoriented component

11. Multichromosomal genomes Complications are inevitable on the way from genomes containing one chromosome to multichromosomal genomes. Internal and terminal inversion should be distinguished and translocations are considered as internal if it is neither a fusion nor fission. A new order of chromosomal segments and chromosome in a genome called concatenate. There exist 2 N concatenates in a genome with N elements (chromosomes/chromosome arms). Sometime certain types of rearrangements can be mimicked by others.

12. Translocations can be mimicked by inversions inversion

13. Evolutionary transformation of genome A into genome B fusion +1+2+3+4 +5+6+7+8 +9+10+11 -3-2-1+4 +5+6+7+8 +9+10+11 +1+2+3+4 +5+6+7+8 +9+10+11 +1+2+3+4 +5+6+7+11 +9+10+8 +1+2+3+4+5+6+7+11 +9+10+8 +1+2+3+4+5+6+7+11 +9 +10+8 inversion translocation fission A B

15. Two different most parsimonious scenarios that transform the order of the 11 synteny blocks on the mouse X chromosome into order on the human X chromosome.

16. Genome rearrangements and phylogenetic studies Cytogenetic methods could reveal only a small fraction of numerous rearrangements, which took place in evolution. Huge amount of “rearrangement” information hidden in genomes became available very recently, when whole genomes were sequenced and reassembled. In the near future the amount of information in this field will grow quickly and phylogenetic reconstructions using rearrangements data, which are independent from sequence data, will be an important area of research. This is already true for simple genome.