Genetic information is stored in DNA molecules as sequences of nucleotides. DNA exists as paired strands that run in opposite directions and are complementary to each other. The genome contains an organism's complete set of DNA and is organized into chromosomes. Genomes can differ between species through point mutations that change single nucleotides or genome rearrangements that modify multiple nucleotides. Rearrangements include reversals, translocations, fissions, and fusions that change the order of genes within and between chromosomes. The minimum number of edits needed to transform one genome into another, including point mutations and rearrangements, defines their edit distance and can provide insights into evolutionary relationships.

3. Basic Biology: DNA
 Genetic information is stored in
deoxyribonucleic acid (DNA)
molecules.
 A single DNA molecule is a sequence
of nucleotides
 adenine (A)
 cytosine (C)
 guanine (G)
 thymine (T)
nitrogenous
base
pentose
sugar
phosphate
Nucleotide DNA molecule

4. Basic Biology: DNA
 Paired DNA strands are in
reverse complementary
orientation.
One in forward, 5’ to 3’ direction
The other in reverse, 3’ to 5’
direction
 Both strands are
complementary.
A pairs with a T
G pairs with a C
forward
strand
reverse
strand
5’
3’
3’
5’
Image modified with the permission of the
National Human Genome Research Institute
(NHGRI), artist Darryl Leja.

5. Basic Biology: Genome
• The genome is the
entire hereditary
information of an
organism.
• Genomes are
partitioned into
chromosomes.
• A chromosome can
be linear
(eukaryotes), or
circular
(prokaryotes). Image modified with the permission of the
National Human Genome Research Institute
(NHGRI), artist Darryl Leja.

6. The Human Karyogram
Karyotype of a human male.
Courtesy: National Human Genome Research Institute

7. Changes in Genomic Sequences
 Genomes of different species (even of
closely related individuals) differ from
one another.
 These differences are caused by
point mutations, in which only one
nucleotide is changed, and
genome rearrangements, where multiple
nucleotides are modified.

8. Point Mutations
 Insertion …ATGGCG… → …
ATGTGCG…
 Deletion …ATGTGCG…→ …
ATGGCG…
 Substitution …ATGTGCG… → …
ATGCGCG…
…ATG-GCATGTGCGATGTGCG…
…ATGTGCATG-GCGATGCGCG…
DNA sequence alignment showing matches, mismatches,
and insertions/deletions

9. Genome Rearrangements
 Reversal
 Translocation
 Fission
 Fusion
1 2 3 4 5 6 7 8 9 1 2 3 6 5 4 7 8 9
1 2 3 4 5 6 7 8 9
10 11 12 13 14 15
1 2 3 4 13 14 15
10 11 12 5 6 7 8 9
1 2 3 4 5 6 7 8 9 1 2 3 4
5 6 7 8 9
1 2 3 4
5 6 7 8 9
1 2 3 4 5 6 7 8 9

10. Reversal:
A reversal is an operation that transforms one
signed permutation into another, reversing the
order or a contiguous protein and flipping the
sign.
Translocation:
It is process of exchange of genetic material
between chromosomes. A balanced translocation
results in no gain or loss of material.
Furthermore, while an unbalanced translocation
may result in trisomy or monosomy of a
particular chromosome segments.

11. Fission:
It is the division of a single entity into two or
more parts and then regeneration of those parts
into separate entities resembling the original.
Fusion:
It is the process in which several unicellular cells
combine to form a multinuclear cell.

12. Genome Rearrangements

13. Signed Reversals
5’ ATGCCTGTACTA 3’
3’ TACGGACATGAT 5’
5’ ATGTACAGGCTA 3’
3’ TACATGTCCGAT 5’
Break
and
Invert
Taken and modified from An Introduction to Bioinformatics Algorithms by Neil Jones and Pavel Pevzner

14. Levenshtein’s Edit Distance
 Let A and B be two sequences
(genomes). The minimum number of
edit operations that transforms A into B
defines the edit distance, dedit, between
A and B.
 Possible edit operations:
point mutations
genome rearrangements

15. A Word Puzzle
 To transform a start word into a target
word, change, add, or delete characters
until the target is reached.
 Example: start “spices” target “lice”:
○ spices → slices → slice → lice
○ spices → spice→ slice→ lice

16. Edit Distance Using Point
Mutations
S1=AGCTT, S2=AGCCTG, S3=ACAG
AGCTT AGCTG AGCCTG
⇒ dedit(S1,S2) = 2
AGCTT AGCTG AGCAG ACAG
⇒ dedit(S1,S3) = 2
AGCCTG AGCTG AGCAG ACAG
⇒ dedit(S2,S3) = 2
T→G insert C
T→G T→A delete G
delete C T→A delete G

17. Edit Distance and Evolution
 The edit distance is often used to infer evolutionary
relationships.
 Parsimony assumption: the minimum number of changes
reflects the true evolutionary distance
Parsimonious phylogeny inferred from edit distances

18. Levenshtein’s Edit Distance
 Let A and B be two sequences
(genomes). The minimum number of
edit operations that transforms A into B
defines the edit distance, dedit, between
A and B.
 Possible edit operations:
point mutations
genome rearrangements

19. Rearrangements and Anagrams
 An anagram is a rearrangement of a
word or phrase into another word or
phrase.
○ eleven plus two → twelve plus one
○ forty five → over fifty
Please visit the Internet Anagram web
server at
http://wordsmith.org/anagram/.

20. Rearrangements and Anagrams
Dot plot: “spendit” vs. “stipend” Dot plot: Mouse genome vs. Human genome

21. Genome Comparison: Human -
Mouse
 Humans and mice
have similar genomes,
but their genes are in a
different order.
 How many edits
(rearrangements) are
needed to transform
human into mouse?
 245 rearrangements
Taken and modified from An Introduction to Bioinformatics Algorithms by Neil Jones and Pavel Pevzner

22. Transforming Mice into Humans
a) Mouse and
human share a
common ancestor
b) They share the
same genes, but in a
different order
c) A series of
rearrangements transforms
one genome into the other

23. Web Tools
 GRIMM Web Server
computes signed and unsigned reversal
distances between permutations.
 Cinteny
a web server for synteny identification and
the analysis of genome rearrangement

24. DCJ Genome Rearrangements
 The DCJ model uses Double-Cut-and-
Join genome rearrangement operations.
 DCJ operations break and rejoin one or
two intergenic regions (possibly on
different chromosomes).

25. Genome Representation
 In the DCJ model, a genome is
grouped into chromosomes
(linear/circular).
 A gene g on the forward strand
is represented by [-g,+g]
 A gene g on the reverse strand
is represented by [+g,-g]
 Telomeres are represented by
the special symbol ‘o’.
 An adjacency (intergenic
region) is encoded by the
unordered pair of neighboring
gene/telomere ends.
Example.
 linear c1=(o 1 -2 3 4 o)
 circular c2=(5 6 7)

26. Research paper on DCJ rearrangements
http://www.lirmm.fr/~rivals/CoCoGEN/articles/B
erard_RECOMBCG08.pdf