1. Last lecture summary

2. New generation sequencing (NGS)
The completion of human genome was just a start of modern DNA sequencing era – “high-throughput next generation sequencing” (NGS).
New approaches, reduce time and cost.
Holly Grail of sequencing – complete human genome below $ 1000.
1st generation – Sanger dideoxy method
2nd generation – sequencing by synthesis (pyrosequencing)
3rd generation – single molecule sequencing

3. cDNA, EST libraries cDNA – reverse transcriptase, contains
only expressed genes (no introns)
cDNA library – a collection of
different DNA sequences that have
been incorporated into a vector
EST – Expressed Sequence Tag
short, unedited (single-pass read),
randomly selected subsequence (
bps) of cDNA sequence generated either
from 5’ or from 3’
higher quality in the middle
cDNA/EST – direct evidence of transcriptome
- Because usually the desired gene sequences still represent only a tiny proportion of the total cDNA population, the cDNA fragments are amplified by cloning/PCR.

4. What is sequence alignment ?
CTTTTCAAGGCTTA
GGCTTATTATTGC
Fragments overlaps
CTTTTCAAGGCTTA
GGCTATTATTGC
navozeni squence alignmentu na prikladech, kdy se tento objevuje v predchozim vykladu
nahore je presny overlap
dole je priblizny overlap, jsou ukazana dve zarovnani, zarovnani s vlozenou mezerou je vice optimalni
CTTTTCAAGGCTTA
GGCT-ATTATTGC

5. What is sequence alignment ?
CCCCATGGTGGCGGCAGGTGACAG
CATGGGGGAGGATGGGGACAGTCCGG TTACCCCATGGTGGCGGCTTGGGAAACTT
TGGCGGCTCGGGACAGTCGCGCATAAT
CCATGGTGGTGGCTGGGGATAGTA
TGAGGCAGTCGCGCATAATTCCG
“EST clustering”
CCCCATGGTGGCGGCAGGTGACAG
CATGGGGGAGGATGGGGACAGTCCGG TTACCCCATGGTGGCGGCTTGGGAAACTT
TGGCGGCTCGGGACAGTCGCGCATAAT
CCATGGTGGTGGCTGGGGATAGTA
TGAGGCAGTCGCGCATAATTCCG
toto je pouze demonstracni zarovnani
nahore jsou EST sekvence
clustering vede ke konsensualni sekvenci
ale ty sekvence musime nejak takhle setridit
samozrejme jsou tam chyby, caste na koncich ESTU, dve jsou ukazany (ale mam jich tam vic)
TTACCCCATGGTGGCGGCTGGGGACAGTCGCGCATAATTCCG
consensus

6. Sequence alphabet Adenine A Thymine T Cytosine G Guanine C Name
side chain charge at physiological pH 7.4
Name
3 letters
1 letter
Positively charged side chains
Arginine
Arg R
Histidine
His H
Lysine
Lys K
Negatively charged side chains
Aspartic Acid
Asp D
Glutamic Acid
Glu E
Polar uncharged side chains
Serine
Ser S
Threonine
Thr T
Asparagine
Asn N
Glutamine
Gln Q
Special
Cysteine
Cys C
Selenocysteine
Sec U
Glycine
Gly G
Proline\
Pro P
Hydrophobic side chains
Alanine
Ala A
Leucine
Leu L
Isoleucine
Ile I
Methionine
Met M
Phenylalanine
Phe F
Tryptophan
Trp W
Tyrosine
Tyr Y
Valine
Val V
Adenine A
Thymine T
Cytosine G
Guanine C

7. Sequence alignment Procedure of comparing sequences
Point mutations – easy
More difficult example
However, gaps can be inserted to get something like this
ACGTCTGATACGCCGTATAGTCTATCT ACGTCTGATTCGCCCTATCGTCTATCT
gapless alignment
ACGTCTGATACGCCGTATAGTCTATCT CTGATTCGCATCGTCTATCT
Gaps correspond to inserion in one sequnce, or deletion in another. (indel)
Comparing two genes it is generally impossible to tell if an indel is an insertion in one gene, or a deletion in another, unless ancestry is known: ACGTCTGATACGCCGTATCGTCTATCT ACGTCTGAT---CCGTATCGTCTATCT
ACGTCTGATACGCCGTATAGTCTATCT ----CTGATTCGC---ATCGTCTATCT
gapped alignment
insertion × deletion
indel

8. Why align sequences – continuation
The draft human genome is available
Automated gene finding is possible
Gene: AGTACGTATCGTATAGCGTAA
What does it do?
One approach: Is there a similar gene in another species?
Align sequences with known genes
Find the gene with the “best” match

9. Flavors of sequence alignment
pair-wise alignment × multiple sequence alignment
- párové/násobné zarovnání
- Sequences that are quite similar and approximately the same length are suitable candidates for global alignment.
- Local alignments are more suitable for aligning sequences that are similar along some of their lengths but dissimilar in others, sequences that differ in length, or sequences that share a conserved region or domain.

10. Flavors of sequence alignment
global alignment × local alignment
global
align entire sequence
stretches of sequence with the highest density of matches are aligned, generating islands of matches or subalignments in the aligned sequences
- párové/násobné zarovnání
- Sequences that are quite similar and approximately the same length are suitable candidates for global alignment.
- Local alignments are more suitable for aligning sequences that are similar along some of their lengths but dissimilar in others, sequences that differ in length, or sequences that share a conserved region or domain.
local

11. New stuff

12. Evolution
common ancestors
wikipedia.org

13. Evolution of sequences
The sequences are the products of molecular evolution.
When sequences share a common ancestor, they tend to exhibit similarity in their sequences, structures and biological functions.
DNA1
DNA2
Protein1
Protein2
- similar sequences produce similar proteins – this is probably the most powerful idea of bioinformatics because it enables us to make predictions. Often little is known about the function of new sequence from a genome sequencing program, but if similar sequences can be found in a database for which functional or structural information is available, then this can be used as the basis of a prediction of function or structure for the new sequence.
Sequence similarity
Similar 3D structure
Similar function
Similar sequences produce similar proteins
However, this statement is not a rule. See Gerlt JA, Babbitt PC. Can sequence determine function? Genome Biol. 2000;1(5) PMID:

14. Homology
During the time period, the molecular sequences undergo random changes, some of which are selected during the process of evolution.
Selected sequences accumulate mutations, they diverge over time.
Two sequences are homologous when they are descended from a common ancestor sequence.
Traces of evolution may still remain in certain portions of the sequences to allow identification of the common ancestry.
Residues performing key roles are preserved by natural selection, less crucial residues mutate more frequently.

15. Orhology, paralogy I
Orthologs – homologous proteins from different species that possess the same function (e.g. corresponding kinases in signal transduction pathway in humans and mice)
Paralogs – homologous proteins that have different function in the same species (e.g. two kinases in different signal transduction pathways of humans)
However, these terms are controversially discussed:
Jensen RA. Orthologs and paralogs - we need to get it right. Genome Biol. 2001;2(8), PMID: and references therein
two flavors of homology
transfers phosphate groups from high-energy donor molecules, such as ATP, to specific substrates

16. Orthology, paralogy II Orthologs – genes separated by the
event of speciation
Sequences are direct descendants of a
common ancestor.
Most likely have similar domain structure, 3D structure and biological function.
Paralogs – genes separated by the event of genetic duplication
Gene duplication: An extra copy of a gene. Gene duplication is a key mechanism in evolution. Once a gene is duplicated, the identical genes can undergo changes and diverge to create two different genes.

17. Gene duplication Unequal cross-over
Entire chromosome is replicated twice
This error will result in one of the daughter cells having an extra copy of the chromosome. If this cell fuses with another cell during reproduction, it may or may not result in a viable zygote.
Retrotransposition
Sequences of DNA are copied to RNA and then back to DNA instead of being translated into proteins resulting in extra copies of DNA being present within cell.
Gene duplication is believed to play a major role in evolution;
Duplications typically arise from an event termed
unequal crossing-over (recombination) that occurs between misaligned homologous chromosomes during meiosis (germ cell formation). The chance of this event happening is a function of the degree of sharing of repetitive elements between two chromosomes. The recombination products of such an event are a duplication at the site of the exchange and a reciprocal deletion.
Another way that gene duplication can occur is if the entire chromosome is replicated twice. This error will result in one of the daughter cells having an extra copy of the chromosome and all the extra genetic material. If this cell fuses with another cell during reproduction, it may or may not result in a viable zygote.
The last way that gene duplication can occur is through retrotransposition. During retrotransposition, sequences of DNA are copied to RNA and then back to DNA instead of being translated into proteins. This results in extra copies of that DNA being present within the cell, which can rejoin with the chromosomes that are already present. Any genes found along these sequences of DNA will have been duplicated in the process.

18. Unequal cross-over
Homologous chromosomes are misaligned during meiosis.
The probability of misalignment is a function of the degree of sharing of repetitive elements.
The underlying DNA sequence homology of the similar maternal and paternal chromosome pairs guides this search and eventual alignment along the entire length of each chromosome. The alignment is further mediated and cemented by a three-dimensional zipperlike structure surrounding each set of paired homologous chromosomes, the synaptonemal complex.
Read more: Meiosis - Biology Encyclopedia - cells, plant, body, human, process, different, chromosomes, DNA, organs

19. Comparing sequences through alignment – patterns of conservation and variation can be identified.
The degree of sequence conservation in the alignment reveals evolutionary relatedness of different sequences
The variation between sequences reflects the changes that have occurred during evolution in the form of substitutions and/or indels.
Identifying the evolutionary relationships between sequences helps to characterize the function of unknown sequences.
Protein sequence comparison can identify homologous sequences from common ancestor 1 billions year ago (BYA). DNA sequences typically only 600 MYA.

20. Scoring systems I
DNA and protein sequences can be aligned so that the number of identically matching pairs is maximized.
Counting the number of matches gives us a score (3 in this case). Higher score means better alignment.
This procedure can be formalized using substitution matrix.
A T T G T
A – - G A C A T A T C G 1
Identity matrix

21. Scoring systems II
For nucleotide sequences identity matrix is usually good enough.
For protein sequences identity matrix is not sufficient to describe biological and evolutionary proceses.
It’s because amino acids are not exchanged with the same probability as can be conceived theoretically.
For example substitution of aspartic acids D by glutamic acid E is frequently observed. And change from aspartic acid to tryptophan W is very rare.
Why is that?
Triplet-based genetic code
GAT (D) → GAA (E), GAT (D) → TGG (W)
Both D and E have similar properties, but D and W differ considerably. D is hydrophylic, W is hydrophobic, D → W mutation can greatly alter 3D structure and consequently function.

22. Genetic code

23. Gaps or no gaps
three examples of gapless alignments between two short sequences
three examples of gapped alignments between two short sequences

24. Scoring DNA sequence alignment (1)
Match score: +1
Mismatch score: +0
Gap penalty: –1
ACGTCTGATACGCCGTATAGTCTATCT ||||| ||| || |||||||| ----CTGATTCGC---ATCGTCTATCT
Matches: 18 × (+1)
Mismatches: 2 × 0
Gaps: 7 × (– 1)
Score = +11

25. Length penalties
We want to find alignments that are evolutionarily likely.
Which of the following alignments seems more likely to you?
ACGTCTGATACGCCGTATAGTCTATCT ACGTCTGAT ATAGTCTATCT ACGTCTGATACGCCGTATAGTCTATCT AC-T-TGA--CG-CGT-TA-TCTATCT
We can achieve this by penalizing more for a new gap, than for extending an existing gap  
- It’s more likely that longer stretches of sequence are deleted.

26. Scoring DNA sequence alignment (2)
Match/mismatch score: +1/+0
Origination/length penalty: –2/–1
ACGTCTGATACGCCGTATAGTCTATCT ||||| ||| || |||||||| ----CTGATTCGC---ATCGTCTATCT
Matches: 18 × (+1)
Mismatches: 2 × 0
Origination: 2 × (–2)
Length: 7 × (–1)
Score = +7

27. Substitution matrices
Substitution (score) matrices show scores for amino acids substitution. Higher score means higher probability of mutation.
Conservative substitutions – conserve the physical and chemical properties of the amino acids, limit structural/functional disruption
Substitution matrices should reflect:
Physicochemical properties of amino acids.
Different frequencies of individual amino acids occuring in proteins.
Interchangeability of the genetic code.

28. PAM matrices I
How to assign scores? Let’s get nature – evolution – involved!
If you choose set of proteins with very similar sequences, you can do alignment manually.
Also, if sequences in your set are similar, then there is high probability that amino acid difference are due to single mutation.
From the frequencies of mutations in the set of similar protein sequences probabilities of substitutions can be derived.
This is exactly the approach take by Margaret Dayhoff in 1978 to construct PAM (Accepted Point Mutation) matrices.
Dayhoff, M.O., Schwartz, R. and Orcutt, B.C. (1978). "A model of Evolutionary Change in Proteins". Atlas of protein sequence and structure (volume 5, supplement 3 ed.). Nat. Biomed. Res. Found.. pp. 345–358.

29. PAM matrices II
Alignments of 71 groups of very similar (at least 85% identity) protein sequences substitutions were found.
These mutations do not significantly alter the protein function. Hence they are called accepted mutations (accepted by natural selection).
Probabilities that any one amino acid would mutate into any other were calculated.
If I know probabilities of individual amino acids, what is the probability for the given sequence?
Product
Thus probabilities are converted to logarithms, and an alignment score can be calculated by summation.
Excellent discussion of the derivation and use of PAM matrices: George DG, Barker WC, Hunt LT. Mutation data matrix and its uses. Methods Enzymol. 1990,183: PMID:

30. PAM matrices III
Dayhoff’s definition of accepted mutation was thus based on empirically observed amino acids substitutions.
The used unit is a PAM. Two sequences are 1 PAM apart if they have 99% identical residues.
PAM1 matrix is the result of computing the probability of one substitution per 100 amino acids.
PAM1 matrix represents probabilities of point mutations over certain evolutionary time.
in Drosophila 1 PAM corresponds to ~2.62 MYA
in Human 1 PAM corresponds to ~4.58 MYA
- Henikoff S, Henikoff JG. Amino acid substitution matrices. Advances in Protein Chemistry. 54: 73-97, 2000
- odhad delky 1 PAM prevzat z Introduction to Computational Biology – An Evolutionary Approach, by B. Haubold, T. Wiehe

31. PAM1 matrix
numbers are multiplied by

32. Higher PAM matrices
What to do if I want get probabilities over much longer evolutionary time?
i.e. I want to align sequences with far less than 85% identity.
Dayhoff proposed a model of evolution that is a Markov process.
We already met (in Lin Alg lecture) linear dynamical system, which is a case of Markov process.

33. Linear dynamical system I
A new species of frog has been introduced into an area where it has too few natural predators. In an attempt to restore the ecological balance, a team of scientists is considering introducing a species of bird which feeds on this frog. Experimental data suggests that the population of frogs and birds from one year to the next can be modeled by linear relationships. Specifically, it has been found that if the quantities Fk and Bk represent the populations of the frogs and birds in the kth year, then
𝐵 𝑘+1 =0.6 𝐵 𝑘 +0.4 𝐹 𝑘
𝐹 𝑘+1 =−0.35 𝐵 𝑘 +1.4 𝐹 𝑘
The question is this: in the long run, will the introduction of the birds reduce or eliminate the frog population growth?

34. Linear dynamical system II
𝐹 𝑘+1 𝐵 𝑘+1 = − 𝐹 𝑘 𝐵 𝑘
So this system evolves in time according to x(k+1) = Ax(k). Such a system is called discrete linear dynamical system, matrix A is called transition matrix.
If we need to know the state of the system in time k = 50, we have to compute x(50) = A50 x(0).
And the same is true for Dayhoff’s model of evolution.
If we need to obtain probability matrices for higher percentage of accepted mutations (i.e. covering longer evolutionary time), we do matrix powers.
Let’s say we want PAM120 – 120 mutations fixed on average per 100 residues. We do PAM1120.

35. Higher PAM matrices
Biologically, the PAM120 matrix means that in 100 amino acids there have been 50 substitutions, while in PAM250 there have been 2.5 amino acid mutation at each side.
This may sound unusual, but remember, that over evolutionary time, it is possible that an alanine was changed to glycine, then to valine, and then back to alanine.
These are called silent substituions.

36. PAM 120 small, polar small, nonpolar polar or acidic basic
Zvelebil, Baum, Understanding bioinformatics.
PAM 120
Positive score – frequency of substitutions is greater than would have occurred by random chance.
Zero score – frequency is equal to that expected by chance.
Negative score – frequency is less than would have occurred by random chance.
small, polar
small, nonpolar
polar or acidic
basic
large, hydrophobic
aromatic

37. PAM matrices assumptions
Mutation of amino acid is independent of previous mutations on the same position (Markov process requirement).
Only PAM1 was “measured”, all other are extrapolations (i.e. predictions based on some model).
Each amino acid position is equally mutable.
Mutations are assumed to be independent of surrounding residues.
Forces responsible for sequence evolution over short time are the same as these over longer times.
PAM matrices are based on protein sequences available in 1978 (bias towards small, globular proteins)
New generation of Dayhoff-type – e.g. PET91

38. How to calculate score? substitution matrix 2 - BLOSUM62 shown here
Selzer, Applied bioinformatics.
How to calculate score?
substitution matrix 2
- BLOSUM62 shown here

39. Protein vs. DNA sequences
Given the choice of aligning DNA or protein, it is often more informative to compare protein sequences.
There are several reasons for this:
Many changes in DNA do not change the amino acid that is specified.
Many amino acids share related biophysical properties. Though these amino acids are not identical, they can be more easily substituted each with other. These relationships can be accounted for using scoring systems.
When is it appropriate to compare nucleic sequences?
confirming the identity of DNA sequence in database search, searching for polymorphisms, confirming identity of cloned cDNA
When nucleotide sequence is analyzed, it is usually preferable to study the protein sequences.
Particularly 3rd position in codon does not change the coded amino acid.