Lecture 2: Database search Based on class by Larry Hunter

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Lecture 2 Database search(Based on class by
Larry Hunter)
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First Behind the Screen

• Databases are largely devoted to search.
• Also, integrity, security, etc.
• Search means taking a query and retrieving some
  database entry that matches it.
• We will start by discussing how to find an exact
  match, and then move to finding inexact matches
  (like BLAST search).
• Efficiency is a key want to find things fast,
  regardless of how big the database gets.

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Computational Complexity

• A key idea in computer science How much work
  does it take to solve a class of problems?
• How do we measure complexity?
• Relative to problem size
• How long does it take?
• Clock time versus operations
• Order O(?) notation
• Other resources used (particularly space)

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The complexity of search

• Compare several algorithms for exact methods
• exhaustive (linear time, constant space)
• indexed (log time, linear space)
• hash tables (constant time, linear space)
• Then look at inexact search methods
• Dynamic programming (Smith-Waterman)
• BLAST

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Linear search

• Database
• ACTGA
• TTAGG
• CGTAA
• AGAGA
• CGATA
• CCGGA
• GCCCT
• TTACG

• Test query against each target sequentially
• Worst case, query matches last target and you
  have as manytests as targets (size of database)
• Average case, test half the targets.
• Linear in the size of the database

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Data Representation
Data structures (internal representations of
data) effect computational complexity

• Linked lists
• Variable length
• Each element has a pointer to the next (doubles
  space)

• Vectors ( arrays)
• Fixed length
• Often allocate more space than necessary
• Each element has a specific position

actga
ttgaca
...
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Computational Complexity

• For linked lists
• finding the nth element takes time proportional
  to the length of the list
• insertion or deletion takes constant time
• For vectors
• finding the nth element takes constant time.
• insertion of deletion takes time proportional to
  the length of the list (have to move all
  subsequent entries).

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Indexed (binary) search

• Create an sorted set of keys that point to
  entries
• Start in the middle, then figure out which half
• Eliminate half the database each step, so need
  log2 steps at worst
• Need to build the index (takes space and time at
  each database update)

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Hash tables
f (TTACG) 8

• Map each query to an arbitrary number with a
  hash function
• Use those numbers as an index into a table
• Collisions can happen, but are rare
• Constant time lookup

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What makes a good hash function?

• Basic must map keys to a number that is within
  the size of the table
• Desired minimize collisions
• So similar keys should lead to different numbers
• Good general method map key to a number, and
  then take the remainder when divided by a prime
  number

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Pairwise Sequence Alignment

• What is an alignment, and why might it be
  significant?
• An alignment is a mapping from one sequence to
  another, identifying elements that are likely to
  have arisen from a common ancestor
• A good alignment is an indication of homology
• Alignments are NOT exact matches. We will need a
  method to find good alignments in a database...

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Similarity vs. HomologyParalogs vs. Orthologs

• Homology is an evolutionary relationship that
  either exists or does not. It cannot be partial.
• An ortholog is a homolog with shared function.
• A paralog is a homolog that arose through a gene
  duplication event. Paralogs often have divergent
  function.
• Similarity is a measure of the quality of
  alignment between two sequences. High similarity
  is evidence for homology. Similar sequences may
  be orthologs or paralogs.

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How do we compute similarity?

• Similarity can be defined by counting positions
  that are identical between two sequences
• Gaps (insertions/deletions) can be important
  abcdef abcdef abcdef
  abceef acdef a-cdef

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Not all mismatches are the same

• Some amino acids are more substitutable for each
  other than others. Serine and threonine are
  more alike than tryptophan and alanine.
• We can introduce "mismatch costs" for handling
  different substitutions.
• We don't usually use mismatch costs in aligning
  nucleotide sequences, since no substitution is
  per se better than any other.

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Many possible alignments to consider

• Without gaps, there are are NxM possible
  alignments between sequences of length N and M
• Once we start allowing gaps, there are many
  possible arrangements to consider abcbcd
  abcbcd abcbcd
  abc--d a--bcd ab--cd
• This becomes a very large number when we allow
  mismatches, since we then need to look at every
  possible pairing between elements there are
  roughly NM possible alignments.

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Exponential computations get big fast

• If nm100, there are 100100 10200
  100,000,000,000,000,000,000,000,000,000,000,000,00
  0,000,000,000,000,000,000,000,000,000,000,000,000,
  000,000,000,000,000,000,000,000,000,000,000,000,00
  0,000,000,000,000,000,000,000,000,000,000,000,000,
  000,000,000,000,000,000,000,000,000,000,000,000,00
  0,000,000,000,000 different alignments.
• And 100 amino acids is a small protein!

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Avoiding random alignments with a score function

• Not only are there many possible gapped
  alignments, but introducing too many gaps makes
  nonsense alignments possible
  s--e-----qu---en--ce sometimesquipsentice
• Need to distinguish between alignments that occur
  due to homology, and those that could be expected
  to be seen just by chance.
• Define a score function that accounts for both
  element mismatches and a gap penalty

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Match scores

• Match scores are often calculated on the basis of
  the frequency of particular mutations in very
  similar sequences.
• We can transform substitution frequencies into
  log odds scores, which can then be added together.

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Local vs. Global alignments

• A global alignment includes all elements of a
  sequence, and includes gaps
• A global alignment may or may not include "end
  gap" penalties.
• A local alignment is includes only subsequences,
  and sometimes computed without gaps.
• Local alignments can find shared domains in
  divergent proteins and are fast to compute
• Global alignments are better indicators of
  homology and take longer to compute.

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An alignment score

• An alignment score is the sum of all the match
  scores of an alignment, with a penalty subtracted
  for each gap.
• Gap penalties are usually "affine" meaning that
  the penalty for one long gap is smaller than the
  penalty for many smaller gaps that add up to the
  same size.a b c - - da c c e f d9 2 7 6
  gt 24 - (10 2) 12

Gap start continuationpenalty
Matchscore
AlignmentScore
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Finding the optimal alignment

• Given a pair of sequences and a score function,
  identify the best scoring (optimal) alignment
  between the sequences.
• Remember, exponential number of possible
  alignments (most with terrible scores).
• Computer science to the rescue dynamic
  programming identifies optimal alignments in time
  proportional to the sum of the lengths of the
  sequences

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Dynamic programming

• The name comes from an operations research task,
  and has nothing to do with writing programs.
• The key idea is to start aligning the sequences
  left to right once a prefix is optimally
  aligned, nothing about the remainder of the
  alignment changes the alignment of the prefix.
• We construct a matrix of possible alignment
  scores (NxM2 calculations worst case) and then
  "traceback" to find the optimal alignment.
• Called Needleman-Wunch or Smith-Waterman

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Alignment matrix

• Create a matrix with each sequence to be aligned
  along one edge and the score of the alignment of
  each pair of elements in a cell.
• Best local alignment is just the highest
  scoring diagonal

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Dynamic programming matrix

• Each cell has the score for the best aligned
  sequence prefix up to that position.
• Number in ( )s is thealignment score forthe
  pair of amino acids at that position.
• Gap penalty here is-12 to start and -4 to
  continue.

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Optimal alignment by traceback

• We traceback a path that gets us the highest
  score. If we don't have end gap penalties,
  then takeany path from thelast row or columnto
  the first.
• Otherwise we needto include the top and bottom
  corners

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Study guide....

• Dynamic programming alignments are a key
  technology in bioinformatics, and you should
  understand how they work.
• The method is counterintuitive
• Work some examples by hand.
• More detail and supplementary material on the
  course web site.

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How do we pick match scores?

• For match scores, two main options
• PAM based on global alignments of closely related
  sequences. Normalized to changes per 100 sites,
  then exponentiated for more distant relatives.
• BLOSUM based on local alignments in much more
  diverse sequences
• Picking the right distance is important, and may
  be hard to do. BLOSUM seems to work better for
  more evolutionarily distant sequences. BLOSUM62
  is a good default.

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Picking gap penalties

• Many different possible forms
• Most common is affine (gap open gap continue
  penalties)
• More complex penalties have been proposed.
• Penalties must be commensurate with match scores.
  Therefore, the match scoring scheme influences
  the gap penalty
• Most alignment programs suggest appropriate
  penalties for each match score option.

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Searching for optimal scores

• One possibility is to try several different match
  score and gap penalties, and choose the best
• In general, this is called parameter space search
  and it is important in many areas.
• Problems
• requires a lot computation
• we need some principled way to compare the
  results.
• Use significance testing to compare...

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The significance of an alignment

• Significance testing is the branch of statistics
  that is concerned with assessing the probability
  that a particular result could have occurred by
  chance.
• How do we calculate the probability that an
  alignment occurred by chance?
• Either with a model of evolution, or
• Empirically, by scrambling our sequences and
  calculating scores on many randomized sequences.

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For next week

• Read
• Molecular Biology Database Collection
• Entrez tutorial
• Lecture notes on class web site
• BLAST education site
• Try working some dynamic programming examples by
  hand.