Evolution

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Evolution

• Doug Raiford
• Lesson 4

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Darwinian Evolution

• Heritable traits
• Variation in population (parental combinations
  and mutations)
• Visible, phenotypical differences lead to
  different survival rates

Parental combinations and mutational changes
Natural Selection
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Meiosis

• Parental combinations

Each of us has two copies of each
chromosome (diploid)

• One allele from each parent
• Allele one of a series of different forms of a
  gene
• Each chromatid has a copy of each gene

Sperm and egg only one copy
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DNA and evolution

• Over time, genes accumulate mutations
• Environmental factors
• Radiation
• Oxidation
• Mistakes in replication or repair
• Evolution change in allele frequency over time

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Classification

• In the past phenotypical differences were used to
  classify
• Now that have sequenced genomes can look at
  similarity of DNA
• Chimps and humans 99 identical
• Diverged about 6 million years ago

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Homologs, Paralogs, and Orthologs

• To compare, species must look at similar genes
• Homologous genes
• Orthologous genes
• Separated by speciation
• Paralogous genes
• Similar due to gene duplication event

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Why do homologs drift apart?Types of mutations

• Point mutations
• Insertions, deletions
• Duplications, inversions, translocations
• Remember paralogs?
• Causes
• Radiation (cosmic, UV, X-ray)
• Replication (mitosis) or crossover (meiosis)

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If we want to compare two homologous genes

• Point mutations (substitutions),
  easyACGTCTGATACGCCGTATAGTCTATCTACGTCTGATTCGCCC
  TATCGTCTATCT

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Insertions and deletions

• Indels are difficult, must align
  sequencesACGTCTGATACGCCGTATAGTCTATCTCTGATTCGCAT
  CGTCTATCTACGTCTGATACGCCGTATAGTCTATCT----CTGATTC
  GC---ATCGTCTATCT

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Deletions

• Codon deletionACG ATA GCG TAT GTA TAG CCG
• Effect depends on the protein, position, etc.
• Almost always deleterious
• Sometimes lethal
• Frame shift mutation (muscular dystrophy and
  sickle-cell) ACG ATA GCG TAT GTA TAG CCG ACG
  ATA GCG ATG TAT AGC CG?
• Almost always lethal

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Insertion or deletion?

• 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
  knownACGTCTGATACGCCGTATCGTCTATCTACGTCTGAT---CC
  GTATCGTCTATCT

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Does it change the protein?

• Synonymous
• Serine
• UCU to UCT
• No change in protein
• Non-synonymous
• Serine to tyrosine
• UCU to UAU

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Nature experiments

• Gene duplication event
• One can continue to perform function
• Other can accumulate mutations experiment
• Paralogs

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Why align sequences?

• Already said
• Can then measure differences between genes to
  determine evolutionary distance
• see where indels and substitutions are
• Why else?
• What if wanted to do a database search?
• Databases great at perfect matches
• But to find homologous genes need fuzzy matches

Database of sequences
Sequence query
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But, how to align?

• Exhaustively, could try all possible alignments

From---ACGTACT---- ToACGT-------ACT
And everything in between
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Exhaustive placement of spaces

• Could setup a loop and place gaps in all possible
  locations

Or, could solverecursively
---ACGT ACT---- --A-CGT ACT---- --AC-GT ACT----
. . . ACGT--- ----ACT

• Tricky
• Have to avoid all gap-gap situations
• Must find a way to look at ALL possibles

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Recursion

• A function that calls itself
• Can often be an elegant solution to difficult
  problems
• Elegant non-obvious solution that is much more
  simple in design than the problem would suggest

Example factorial Definition of f(n) return
nf(n-1)
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A more practical example

• Factorial recurrence relation
• factorial(n) n factorial(n-1)
• Define f(n) return n f(n-1)
• Example f(3)
• 3 f(2)
• 2 f(1)
• 1
• 3 2 1
• How did the program know to stop at f(1)?

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Base case

• To know when to stop, must have a base case
• Base case for factorial is when n equals 1

Example my answer factorial(10) print
"answer\n" sub factorial my passedArg
shift check base case if(passedArg 1)
return 1 else if base case not
satisfied, recurse return passedArg
factorial(passedArg - 1)
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What does this have to do with aligning?

• Recursive solutions can usually be found by
  breaking a problem into sub problems
• Insert no gap, recurse on rest
• Insert a gap in string 1, recurse on rest
• Insert a gap in string 2, recurse on rest

Add score from matching to score from
First character of string 1 First character of string 2 rest of string 1 rest of string 2
Gap First character of string 2 string 1 rest of string 2
First character of string 1 Gap rest of string 1 string 2
Three sub-problems
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Example
t g c g _ tg c g t g _ cg

• atg
• acg

a tg a cg _ atg a cg a tg _ acg
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Scoring

• When scoring alignments there must be a gap
  penalty, a mismatch penalty, and a bonus for a
  match
• For any two strings the best alignment score with
  be the maximum of three possibilities
• Recurrence relations

Match or mismatch of first chars allign(rest of
string1, rest of string2) Gap penalty
allign(string1, rest of string2) Gap penalty
allign(string1 starting at pos 2, string2)
max
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What is the base case?

• If down to empty string for either
• Return gap penalty the length of the non-empty
  string (return 0 if both empty)

Base Case
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Pseudo code

• Definition of allign(string1, string2)
• If base case satisfied return base score
• Otherwise
• Return the max of
• Gap penalty allign(string1, rest of string2)
• Match or mismatch of first chars allign(rest of
  string1, rest of string2)
• Gap penalty allign(string1 starting at pos 2,
  string2)

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Example

• These two strings
• atagcgcc
• ataggcc
• Align like
• atagcgcc
• atag_gcc

Have now taken a problem in biology and mapped it
to a common problem-solving technique in computer
science Recursion
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Life is good, but

• The previous example (an 8 character string
  aligned with a 7 character string) took 103,342
  invocations of allign
• Why?

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Is exponential bad?

• Aligning two strings of size 500
• More invocations of align than there are
  subatomic particles in the universe
• If took one nanosecond per invocation
• Universe is 14 Billion years old
• It would take 8.2 10208 times the age of the
  universe to calculate the alignment score

Exponential bad Corollary Tree exponential
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Complexity analysis

• Fixed best
• Linear next best
• Polynomial (n2) not bad
• Exponential (3n) very bad
• Big O notation
• O(1), O(n), O(n3), O(3n)

Big ONotation
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Next lesson

• Speeding things up
• Dynamic programming solution

Dynamic Programming
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