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Incoming links: Multiple sequence alignment
Multiple sequence alignment Created 2026-10-20 Updated 2026-11-05
A multiple sequence alignment places three or more sequences in corresponding columns, inserting gaps where needed. The arrangement represents a hypothesis about positional correspondence and can support phylogenetics or detection of conserved motifs. A column can be reliably aligned in one region and ambiguous in another. Adding sequences can clarify shared structure but also introduce difficult divergent regions, so the alignment itself requires evaluation before downstream inference. [ref]
Amino acid substitution matrices from protein blocks by Steven Henikoff and Jorja G. Henikoff. 1992, conserved protein blocks and aligned positions
A time-calibrated phylogenetic tree combines evidence about ancestry with evidence about elapsed time. First identify homologous RNA or protein sequences, preferably orthologous loci whose splits reflect the species divergences of interest. A multiple sequence alignment proposes corresponding ancestral positions. Conserved ribosomal RNA can compare distant lineages, whereas faster-evolving regions help resolve recent splits; amino acid alignments can retain useful deep information after many nucleotide sites have changed repeatedly.
A phylogenetics model estimates a topology and branch lengths in substitutions per site, using explicit substitution probabilities rather than treating every observed mismatch as one historical change. Repeated substitutions, unequal rates among sites, selection, and compositional bias can make observed mismatch fractions underestimate the amount of change. Multiple loci help test consistency; a single gene tree can disagree with the species history through duplication, incomplete lineage sorting, or horizontal transfer.
A molecular clock converts branch change to time through an evolutionary rate. For two equally evolving lineages, an expected distance and rate give a divergence time , but sequence information alone usually identifies a rate-time product, not its two factors separately. A fossil securely assigned to a descendant clade supplies a dated constraint: the ancestral split must be at least as old as that fossil. The oldest known fossil is normally a minimum age, not proof that the lineage originated exactly then.
Several independent fossil constraints, their dating and placement uncertainty, and a relaxed molecular clock permit rates to vary while estimating divergence times with uncertainty intervals. Geological absence alone is a weak upper bound when preservation or sampling is poor. Conflicting loci, uncertain alignments, saturation, model misspecification, and uncertain fossil assignments should be investigated rather than hidden by a precise-looking time axis. The resulting phylogenetic tree is a joint inference from sequences, evolutionary assumptions, and geological evidence.
Convert the supplied multiple sequence alignment to an ordinary array so that reducing over rows returns one value per column. With nine sequences, fewer than 30% gaps means at most two gaps in a column:
from collections import Counter
A = np.asarray(msa_matrix)
gap_fraction = np.mean(A == ".", axis=0)
match_mask = gap_fraction < .30
match_columns = np.flatnonzero(match_mask)
print(match_columns + 1) # human-readable, one-based alignment columnsThere are 72 match states: alignment columns 1–21 and 29–79, using one-based numbering. The seven remaining columns, 22–28, form one contiguous insertion region. The strict inequality is applied to the actual fraction, rather than to rounded percentages.
For each match state, count the nongap amino acids and divide by the number of nongap observations in that column. A gap is not one of the twenty emitted amino acids; including it in the denominator would make the emission probabilities sum to less than one:
def emission_counts(column):
counts = Counter(str(x) for x in column if x != ".")
n = sum(counts.values())
if n == 0:
raise ValueError("an all-gap column has no empirical emission distribution")
return counts, n
match_emissions = {}
for state, j in enumerate(match_columns, 1):
counts, n = emission_counts(A[:, j])
match_emissions[state] = {aa: count/n for aa, count in counts.items()}
print(state, j+1, match_emissions[state])The table gives an exact compact representation of every emission probability: divide each displayed count by the denominator in its row; all unlisted amino acids have probability zero. The state number follows the order of match states, while the column refers to the original multiple sequence alignment.
| State | Alignment column | Nongap counts | |
|---|---|---|---|
| 1 | 1 | 9 | I:1, K:1, R:1, S:2, V:3, Y:1 |
| 2 | 2 | 9 | D:1, E:2, G:1, I:1, L:1, Q:2, S:1 |
| 3 | 3 | 9 | E:2, I:1, K:1, Q:1, R:3, T:1 |
| 4 | 4 | 9 | L:8, M:1 |
| 5 | 5 | 9 | E:3, G:1, L:2, N:1, Q:1, S:1 |
| 6 | 6 | 9 | A:1, D:2, G:1, K:1, N:1, S:2, T:1 |
| 7 | 7 | 9 | A:1, E:3, I:2, L:1, M:1, V:1 |
| 8 | 8 | 9 | I:2, L:7 |
| 9 | 9 | 9 | D:3, E:1, K:1, L:2, N:1, Q:1 |
| 10 | 10 | 9 | D:1, E:3, G:1, N:1, P:1, S:2 |
| 11 | 11 | 9 | A:5, D:1, G:1, P:1, T:1 |
| 12 | 12 | 9 | I:1, L:7, Y:1 |
| 13 | 13 | 9 | E:1, F:1, G:1, H:2, M:1, Q:2, T:1 |
| 14 | 14 | 9 | F:9 |
| 15 | 15 | 9 | F:1, L:8 |
| 16 | 16 | 9 | E:1, I:1, L:1, N:3, Q:1, R:1, Y:1 |
| 17 | 17 | 9 | D:6, E:2, S:1 |
| 18 | 18 | 9 | C:7, F:1, S:1 |
| 19 | 19 | 9 | K:1, N:6, R:2 |
| 20 | 20 | 9 | E:1, F:1, I:5, L:1, V:1 |
| 21 | 21 | 9 | K:3, P:1, Q:1, S:4 |
| 22 | 29 | 7 | K:4, P:1, R:1, S:1 |
| 23 | 30 | 7 | E:2, F:1, G:1, I:1, K:1, V:1 |
| 24 | 31 | 7 | D:3, E:1, G:1, K:1, S:1 |
| 25 | 32 | 8 | D:1, E:1, G:1, K:1, N:1, R:3 |
| 26 | 33 | 8 | D:7, N:1 |
| 27 | 34 | 8 | A:1, P:6, S:1 |
| 28 | 35 | 9 | C:1, H:1, I:1, K:1, M:1, R:1, T:3 |
| 29 | 36 | 9 | E:1, F:1, G:1, L:1, Q:3, W:1, Y:1 |
| 30 | 37 | 9 | I:5, L:1, T:2, Y:1 |
| 31 | 38 | 9 | A:1, G:1, P:3, S:4 |
| 32 | 39 | 9 | I:1, K:6, L:1, R:1 |
| 33 | 40 | 9 | F:1, N:1, Q:4, T:2, V:1 |
| 34 | 41 | 9 | A:1, F:1, I:1, V:6 |
| 35 | 42 | 9 | I:1, L:7, V:1 |
| 36 | 43 | 9 | A:1, C:1, E:1, N:1, R:1, S:3, V:1 |
| 37 | 44 | 9 | D:3, E:5, Q:1 |
| 38 | 45 | 9 | A:1, C:7, I:1 |
| 39 | 46 | 9 | K:2, L:3, R:4 |
| 40 | 47 | 9 | A:3, E:1, L:1, N:3, T:1 |
| 41 | 48 | 9 | I:4, L:1, T:1, V:3 |
| 42 | 49 | 9 | L:9 |
| 43 | 50 | 9 | D:1, E:1, H:1, Q:1, S:1, T:1, V:1, Y:2 |
| 44 | 51 | 9 | E:1, K:1, Q:2, R:1, V:4 |
| 45 | 52 | 9 | L:9 |
| 46 | 53 | 9 | G:9 |
| 47 | 54 | 9 | P:8, T:1 |
| 48 | 55 | 9 | W:9 |
| 49 | 56 | 9 | A:2, C:7 |
| 50 | 57 | 9 | A:6, C:1, L:1, T:1 |
| 51 | 58 | 9 | A:1, D:3, F:1, S:2, V:1, Y:1 |
| 52 | 59 | 9 | K:4, R:2, S:3 |
| 53 | 60 | 9 | A:2, F:1, I:2, L:2, V:2 |
| 54 | 61 | 9 | A:7, G:1, Y:1 |
| 55 | 62 | 9 | E:3, G:3, Q:3 |
| 56 | 63 | 9 | I:3, M:3, T:1, Y:2 |
| 57 | 64 | 9 | F:3, L:2, M:3, N:1 |
| 58 | 65 | 9 | H:1, I:3, L:1, V:4 |
| 59 | 66 | 9 | K:1, M:1, P:1, R:4, S:1, T:1 |
| 60 | 67 | 9 | D:1, E:3, Q:4, Y:1 |
| 61 | 68 | 9 | I:1, L:7, M:1 |
| 62 | 69 | 9 | D:1, E:4, Q:4 |
| 63 | 70 | 9 | K:7, R:2 |
| 64 | 71 | 9 | A:1, I:2, M:1, N:1, R:1, Y:3 |
| 65 | 72 | 9 | A:1, C:1, D:1, E:2, I:2, V:2 |
| 66 | 73 | 9 | K:9 |
| 67 | 74 | 9 | H:4, L:1, Q:2, S:1, V:1 |
| 68 | 75 | 9 | E:8, Q:1 |
| 69 | 76 | 9 | Q:3, R:1, S:2, T:3 |
| 70 | 77 | 9 | C:2, E:3, G:1, R:1, S:1, V:1 |
| 71 | 78 | 9 | A:1, D:2, E:3, I:1, K:1, Y:1 |
| 72 | 79 | 9 | I:2, L:3, M:1, N:1, Q:1, V:1 |
These are unregularized maximum-likelihood estimates of the emission probabilities. No additional artificial observations are added. Although only emissions are requested here, a full profile hidden Markov model would also require transitions and deletion mechanisms to represent the gaps that remain in some match columns.