Multiple Alignment

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Multiple Alignment

• BioE131/231

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Pairwise Dynamic Programming (DP)
Time O(L2), memory O(L2)
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Three-sequence DP
Time O(L3), memory O(L3)
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Multidimensional DP

• Time O(LN), memory O(LN)
• Generally impractical, e.g. for globins (99aa)

kkilobytes
Mmegabytes
Ggigabytes
Tterabytes
Ppetabytes
Eexabytes
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Progressive alignment

• Estimate a guide tree (slowest step - why?)
• Proceed up tree, building a profile for each
  internal node
• Align siblings, going from leaves to root
• Sequence-to-sequence (A-B, D-E)
• Sequence-to-profile (U-C)
• Profile-to-profile (V-W)

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Whats a profile?
Alignment
Profile
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Profile a.k.a. Position-specific Weight
Matrix (PWM)
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Sequence logos
Scale each column by its entropy (technically,
the difference between its entropy and the
maximum possible entropy)
weblogo.berkeley.edu
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Sequence logos
Globin, B helix to D helix
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Scoring schemes

• Scoring schemes up to now have been pairwise
• Several ways of scoring a multiple alignment
  column
• Entropy
• Sum-of-pairs
• Phylogenetic
• Position-specific
• Sequence-profile and profile-profile scoring

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Entropy-like scores

• If n(x) is the number of times residue x occurs
  in the column, then p(x) n(x) / N
• Rewards homogeneous columns
• Assumes each row is an independent draw from the
  same probability distribution
• Equivalent to the following

can maximize with Lagrange multipliers
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Sum-of-pairs score

• i and j are row indices
• xi is residue in row i (similarly xj)
• Q(a,b) is pairwise substitution matrix
• Problems overcounting

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Probabilistic scoring

• Recall pairwise substitution matrix is
  Q(a,b)log q(a,b)where Q is an additive score
  q is a multiplicative probability
• Strictly, q is usually not a probability per se,
  but is related to one e.g. it might be a
  likelihood ratioq(a,b) P(a,b) / (P(a)P(b))
  P(ba) / P(a) P(ab) / P(b)

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Phylogenetic score
(but... you dont actually know u,v,w,x. So what
do you do? The probabilistic answer sum them out)
...and then rearrange the sums optimally
(pruning)...
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Position-specific score

• Score for aligning two (or more) residues does
  not depend (directly) on their values
• Instead, you specify particular scores for
  aligning each pair of positions
• These can be obtained by pre-processing the
  sequences (e.g. scores derived from posterior
  probabilities from a Pair HMM), or by other means
• e.g. T-COFFEE, PROBCONS

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Profile-sequence

• Q(a,b)log q(a,b) is pairwise substitution matrix
• Aligning profile p(x) with residue y

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Profile-profile

• Q(a,b)log q(a,b) is pairwise substitution matrix
• Aligning profile p1(x) with profile p2(y)