DNA sequences alignment measurement

Lecture 13

Introduction

• Measurement of “strength” alignment

• Nucleic acid and amino acid substitutions

• Measurement of alignment gaps

Measurement of aligned sequences• When aligning sequences (DNA/AA ) it is assumed that:

– they have a common ancestor; – the differences between the sequences is the result of

mutations– important areas like coding sequences (CDS) will be

conserved. There is a bias “against” mutations in these areas– Furthermore there is a bias in the types of mutations:

substitutions more likely that insertions/deletions….

• The dot plot gives a visual representation of sequence alignment regions. But how do we measure the strength of these alignments.

Measurement of aligned sequences

• One way is to count the mismatches: the “difference” between the sequences. – Hamming distance; :

• The distance corresponds to mismatches for strings of equal length. – agtc – cgta Distance is 2 (give another example)

• If the sequences (strings) are not of equal length then use:– The Levenshtein distance: is the minimum number of edit operations

(alter/ insert/delete) to required to turn one string into another:• ag- tcc• cgctca what is the levensthein distance?

• The latter technique has the advantage of allowing the inclusions of gaps

Measurement of matching• But what about the biological plausibility of

these approaches to measuring “differences” between sequences (strings):

• DNA sequences (string mismatches) are different:– due to the probability of substitution; insertions,

deletions is not the same. – Certain types of mutations like inversions;

translocations; duplications …. Complicate the assessment of similarity; e.g. how would you treat tandem repeats; inverted repeats….

Nucleic Acid mutations• In sequence alignment we are trying to determine have the

differences (similarity) occurred due to:– chance (random mutations)– They had a common origin (degree of conservatism)

• One approach would be to count the percentage of matches but there is now a need to include the bias associated with possible substitutions.

• However, similarity does not necessarily imply common ancestor or visa versa Zvelebil and Baum (2008 p. 74) suggest this can occur in convergent evolution/divergent evolution.

• So the results need to be contextualised the findings of alignment tests. (bat and bird both have wings…)

Alignment Scoring methods• In general sequences are given a score at each

matching position and the one with the largest score is optimal and is chosen; however suboptimal may also need to be considered.

• The most basic approach is obtained by measuring the percentage of similarity.

• Given that not all “changes” occur with equal chance there is a need to develop:– A nucleotide substitution matrix

•

Nucleotide scoring Matrix• While it is know that certain mutations are more

likely to occur than others: e.g. transitions a<->g is more common than transversions c<->t.

• However since the probability of such difference is insignificant in relation to the chance of a mutation itself the differences are mostly ignored. The following shows a typical scoring matrix for nucleotides.

Adapted from Baxevanis p. 303

Nucleic acid scoring Matrix• The values are based on the probability of a

type of substitution occurring (expected value); this includes a nucleotide substituting with itself.

• These expected values are calculated by getting the ratio of :– number of “observed changes” /number of

changes “due to chance”• These values are obtained by examining large

numbers of DNA sequences.

Nucleic acid scoring Matrix

• Then calculate 10*log 10

(“expected value”).• This ensures that

adjacent nucleotides expected values can now be added as opposed to being multiplied in determining the alignment score.

Nucleic acid scoring Matrix• A expected value greater of 1 indicates the

substitution has the same change of occurrence as it is was occurring randomly.

• A value greater than 1 indicates a bias in favour or the substitution

• A values less than 1 indicates a bias against the substitution.

• A value of 5 will give what expected value?

Measuring Protein similarity

• Deriving a matrix for proteins is more complex because:• There are 20 amino acids so much higher set of

substitutions. • The amino acids have properties that affect the

structure and so the protein functionality.• Therefore substitutions can be conserved or semi-

conserved • Observations shows that conserved substitutions

• e.g. Hydrophobic <-> hydrophobic mutations are more common • semi conserved; e.g. hydrophilic <-> hydrophobic

The PAM matrix• The PAM, developed in the 1970’s by M. Dayhoff, was

derived from all types of sequences both in conserved and un-conserved regions of the protein.

• The PAM (point accepted mutation) Matrix is a measure of the chances of one amino acid being substitute by another.

• The PAM “1” matrix was “derived” from very similar sequences (close in terms of evolution ) and represented one point “accepted” mutation per 100 residues.

• It assumed that a substitution was independent of previous mutations at this position.

• This meant it could be used to derive matrices over longer “evolutionary distances” or more mutations per 100 residues.

The PAM MATRIX • The number of times the matrix is “multiplied” by itself represents

the number of mutations per 100 residues• So a PAM 100 represents 100 mutations per 100 residues: this of

course does mean that the 100 residues changed.• The most common the PAM 250 represents 250 per 100 residues.

• The original PAM 1 was derived in a similar way to the nucleotide substitution matrix:– 10 log10(expected value)

– (the number of observed changes were divided by number of changes based on AA frequency ( as if changes occurred by chance) : expected value.)

Dayhoff PAM (250) Matrix • A H<->N has a value of 2 or an

expected value 1.6 (occurred 1.6 times more often that would be expected.

• A same amino acid substitution can range from C <-> C has a high score 12; while V <-> V (4)

• A hydrophobic <-> Hydrophobic V<->A (0); while V<-> I is (4)

• A hydrophilic <-> hydrophilic K <-> T (0); K<-> R (3)

• A hydrophilic <-> hydrophobic: K <-> V (-2)

Blosum matrix • Another matrix the Blosum (Blocks Substitution ) Matrix used

a larger data set than the PAM • This allowed the Bolsum to look at mutations within “blocks”

of conserved sequences as opposed to point mutations on individual sequences in both conserved and variable.

• The bolsum number ; e.g. 62 matrix, unlike the PAM number, e.g.120, indicates that the substitution probabilities are derived from sequences with that much similarity or conservation.

• So the Blosum 62 is obtained from blocks sharing 62% conservation .

• In addition these results are obtained directly as opposing to being derived as in the case of the PAM matrix.

The Blosum and PAM matrices

Adapted from Zvelebil e baum p 82

The two matrices opposite are the Blosum 62 and PAM 120

The following shows scores from the Blosum 62 matrixSame resisdues:C<->C (9)V<->V (4)Hydrophobic to hydrophobic V<->A (O)V<-> I (3)Hydrophilic to HydrophilicK <-> T (-1)K<-> R (2)Hydrophobic to hydrophilicK<-> V (-2)

The trend is the same.

PAM and Bolsum Matrices• In the PAM matrix the as the number

increases so does evolutionary distance while it is the reverse it the Bolsum Matrix.

• According to Baxevanis (2003) the following represents the equivalence and most appropriate use of both matrices– PAM250 and the Bolsum 45– PAM160 and the Bolsum 62

•

PAM and Bolsum MatrixMatrix Best in determining

PAM 40/ Bolsum 90 Short similar (conserved) alignments

PAM 250 Longer more divergent alignments

Pam 160/ Bolsum 80 Detecting members of protein families

Bolsum 62 In finding all potential similarities

Adapted from Baxevanis 2005

An excellent review of scoring matrices can be found at : Henikoff and Henikoff 2000

20

Dot plot Matrix: imperfect match

• Some alignments require gaps to increase the matching score; the gaps are used represent inclusion/deletion mutations

• The diagram shows that most of the 2 sequences are aligned. Where there are gaps indicates areas of non-alignment or mismatches: gaps or substitutions Adapted from: dotplot example

Measurement of alignment gaps • Gaps represents insertions and deletions• Baxevanis (2005) suggest that no more than “one gap

in 20 pairs is a good rule of thumb”.• Gaps in alignments are penalised; given a negative

scoring value. • The penalty associated with the using gaps is

dependent on – Opening the gap (introducing an insertion or deletion)– Extending the gap (as opposed to opening a new gap)– The length of the gap (the number of

deletions/insertions).

Gap penalties • There is no overall agreement on what values should

be assigned to gap penalties (Zvelebil e Baum 2008). • The purpose of an insertion is to increase the strength

of the alignment. • So choosing a high score will eliminate sequences with

gaps while of the score is too low then alignments with more and larger gaps will be chosen.

• The value should also be dependent on how closely “related” the alignments must be :– So sequences with a very strict match would use a high gap

score. – Alignment between distantly related species would use a

low gap score.

Potential Exam Questions• What is the purpose of measuring the strength

of an alignment (3 marks)• Explain two differences between analysing a

string (sequence) and a DNA string. (4 marks)• Describe how you would measure the

similarity between two DNA sequences (10 marks)

• Discuss the use of gap penalties in a sequence alignment score (13 marks)

References

• Baxevanis A.D. 2005 Bioinformatics: a practical guide to the analysis of genes and proteins chapter 11; Wiley

• Lesk, A. 2008; Introduction to bioinformatics, 3rd edition, oxford university press

• Zvelebil e Baum (2008) Understanding Bioinformatics