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Incoming links: Sequence alignment
BLOSUM62 2026-10-20
David J. Lipman Created 2026-10-20 Updated 2026-10-24
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Portrait of David J. Lipman
. Brian Glanz / Open Science Federation; White House Open Science Champions of Change (2013); existing Commons crop. CC BY 2.0, via Wikimedia Commons. Source..jpg){kind=link}
DNA sequencing Created 2026-10-13 Updated 2026-10-18
DNA sequencing determines the order of nucleotide bases in DNA. Sequence data can test molecular rearrangements, as in the functional plastid-to-nucleus gene transfer experiment, or support phylogenetics after a suitable sequence alignment.
An ordered nucleotide sequence answers a different question from fragment size. The eight-nucleotide strands ACGTTAGC and AACCGGTT have equal lengths and identical counts of adenine, cytosine, guanine and thymine, yet different orders. A length-compatible gel band therefore cannot identify either strand by itself. Sanger sequencing makes length informative by deliberately coupling each stopping position to the identity of its last added nucleotide.
That coupling is the beautiful experimental idea: convert an invisible order into a collection of ordered endpoints. Sanger ladder reading recovers the newly synthesized strand; base pairing and the reverse complement then connect that readout to the original template. The distinction also matters when checking a mutation: a reliable local nucleotide sequence supports a particular molecular change, while its effect on a phenotype requires additional evidence.
Resemblance is a clue, not sufficient evidence of common descent. A small size, two surrounding membranes, division, retained DNA or bacterial-looking ribosomes does not uniquely identify an ancestor. Internal membranes exist outside these organelles, and a similar function can favor similar structures. The stronger question is whether independently examined molecular characters support the same historical relationship.
A concrete genomic observation is the mitochondrial sequence reported in 1997 for Reclinomonas americana: base pairs containing 97 identified genes, including four for a bacterial-type multisubunit RNA polymerase. This is a reported genome inventory, not a calculation from the pictured shape of a mitochondrion. Retention of such bacterial features strengthens the ancestry argument; a living Reclinomonas americana is not itself an ancestral eukaryote. The inspected abstract supplies these observations but not the detailed sequencing protocol or contamination controls, so those details are not attributed to this report here. [ref]
An ancestral mitochondrial DNA resembling a eubacterial genome in miniature by B. Franz Lang and others. Abstract, Nature 387 (1997), pp. 493–497: genome length, gene inventory and bacterial-type RNA polymerase
A sequence-based investigation obtains nucleotide sequences by DNA sequencing, identifies comparable genes, makes a sequence alignment and uses phylogenetics to infer relationships. The readout is a proposed relationship with support and uncertainty, not a photograph of an ancient encounter. Comparisons of plastid sequences with bacterial sequences support cyanobacterial ancestry, while the exact closest sampled cyanobacterial group has depended on the chosen data and inference. A bacterial affinity in one gene is weaker than coherent evidence across several genes and cellular systems. [ref]
Origin and Evolution of Plastids and Photosynthesis in Eukaryotes by Geoffrey I. McFadden. “The endosymbiont: when and who?”: alternative phylogenetic placements and lateral gene transfer
For such an analysis, useful checks include distinguishing organelle DNA from bacterial contamination, verifying sequence quality, comparing corresponding rather than unrelated genes, sampling several bacterial groups and testing sensitivity to the sequence alignment and evolutionary mathematical model. These are methodological requirements, not a claim that this article has rerun a particular published analysis. Horizontal gene transfer, gene loss and unequal evolutionary change can make an individual gene's history differ from a whole organism's history. A supported bacterial origin therefore need not identify an extant donor species, an exact date or the original mode of entry. [ref]
Origin and Evolution of Plastids and Photosynthesis in Eukaryotes by Geoffrey I. McFadden. “The endosymbiont: when and who?”: ancient origin and confounding lateral transfer
Gap penalty 2026-10-20
Jorja G. Henikoff Created 2026-10-20 Updated 2026-10-24
Model organism evidence transfer 2026-10-13
Evidence transfers at a stated level. Sequence alignment can suggest a candidate relationship between genes; functional complementation tests whether a candidate can supply a particular function in a chosen recipient. Neither alone establishes identical native gene expression, identical signal transduction, or identical consequences in every species. The yeast cross-species complementation experiment is especially useful because it tests a conserved function by intervention rather than assuming it from resemblance. [ref]
Pathways over Time: Functional Genomics Research in an Introductory Laboratory Course by Todd D. Reeves and others. Reeves et al. (2018), project design, pp. 3–4, and Course Activities, pp. 5–6
Even successful functional complementation occurs within a specific genetic background, nutrient supply and imposed gene expression. The enzyme may work with the recipient’s available substrates and partner proteins at an experimentally imposed abundance. Establishing the same role in the donor species calls for experiments there; establishing behavior under another condition calls for experiments under that condition. A conserved component can therefore coexist with context-dependent behavior of an entire pathway. This separation makes model organisms powerful: an accessible experiment supplies a precise mechanistic foothold and a better question for the next system.
Read the ten residue–residue columns from the BLOSUM62 substitution matrix. In their order in the supplied sequence alignment, their contributions areThere are three gap positions, each incurring the stated linear gap penalty of four, including the leading gap. Therefore the alignment score is .
An affine gap penalty charges a larger opening cost than extension cost, reflecting that a single insertion or deletion event can span several residues. For a gap of length , explicitly chooseThe supplied sequence alignment has two gap runs, of lengths one and two. Its residue–residue score remains , so this choice givesMore generally, this affine gap penalty convention gives . There is no unique numerical rescore until opening and extension costs are chosen. A concave length-dependent gap penalty can make very long gaps progressively cheaper per added residue; distinct terminal gap penalties can accommodate incomplete sequence ends. Each choice encodes a different assumption about insertions, deletions or sequence completeness.
Use local sequence alignment, such as the Smith-Waterman algorithm, to compare the globin fragment with the matching region of each full-length target. A global sequence alignment would penalize long target flanks absent from the fragment. For a linear gap penalty the dynamic programming recurrence includes a restart option:Initialize boundary entries to zero, start traceback at the largest entry anywhere, and stop at zero. If the entire query is known to be valid and must be retained, fitting sequence alignment is a suitable refinement: align the whole fragment while leaving target flanks unpenalized.
First check the sequence alphabet: the prompt calls the targets “genes”. If the FASTA format file contains DNA rather than protein, translate the relevant coding sequences into amino acids before a protein-to-protein sequence alignment. If coding frames are unknown, search translated frames. A file in FASTA format specifies storage syntax, not whether the contents are nucleotides or residues.
The gain comes from avoiding a full dynamic programming table for every target. BLAST searches for short, sufficiently high-scoring word matches between query and database, then extends promising seeds. Modern versions reserve expensive gapped refinement for candidates passing earlier filters. FASTA sequence search similarly starts from short word matches, collects promising runs along alignment diagonals, and refines or joins selected regions. Word lookup and database indexing make candidate discovery inexpensive compared with considering every pair of positions.[ref]
Basic local alignment search tool by Stephen F. Altschul and others. pp. 403–406, word matches and hit extension
[ref]Improved tools for biological sequence comparison by William R. Pearson and David J. Lipman. pp. 2444–2446, FASTA search stages
These are heuristic algorithms: a good local sequence alignment can be missed if it has no acceptable seed, contains many interruptions, or is filtered before extension. Longer words and higher seed-score thresholds usually speed the search but reduce sensitivity; shorter words and looser thresholds recover weaker similarities at greater cost. Repetitive or compositionally biased regions can create many uninformative hits and erode both speed and specificity. No guarantee remains of finding the optimal sequence alignment for the chosen scoring scheme.
Use the supplied BLOSUM62 entry for every diagonal move in the Smith-Waterman algorithm, while retaining the stipulated linear gap penalty of . If and are the current amino acids, the dynamic programming recurrence isThe zero option permits a new local start. The following original implementation also records the traceback coordinates needed in part (c); its tie ordering is left, up, diagonal, and an equal overall maximum replaces the previous best cell, as in the supplied convention:
def local_alignment(query,reference,alphabet,scores,gap=-1):
lookup={aa:i for i,aa in enumerate(alphabet)}
table=np.asarray(scores,dtype=int)
height,width=len(query)+1,len(reference)+1
H=np.zeros((height,width),dtype=int)
back=np.zeros((height,width),dtype=np.int8)
best=(0,0,0)
for i,a in enumerate(query,1):
for j,b in enumerate(reference,1):
# Order implements the printed LEFT, UP, DIAGONAL tie priority.
candidates=(0,H[i,j-1]+gap,H[i-1,j]+gap,
H[i-1,j-1]+int(table[lookup[a],lookup[b]]))
value=max(candidates);H[i,j]=value
back[i,j]=0 if value==0 else candidates.index(value)
if value>=best[0]:best=(value,i,j)
score,i,j=best;query_end,ref_end=i,j
aq=[];ar=[]
while H[i,j]>0:
step=back[i,j]
if step==1:aq.append('-');ar.append(reference[j-1]);j-=1
elif step==2:aq.append(query[i-1]);ar.append('-');i-=1
elif step==3:aq.append(query[i-1]);ar.append(reference[j-1]);i-=1;j-=1
qa=''.join(reversed(aq));ra=''.join(reversed(ar));length=len(qa)
identities=sum(a==b and a!='-' for a,b in zip(qa,ra))
similarities=sum(a!='-' and b!='-' and table[lookup[a],lookup[b]]>0 for a,b in zip(qa,ra))
gaps=sum(a=='-' or b=='-' for a,b in zip(qa,ra))
return dict(query=qa,reference=ra,score=int(score),query_start=i+1,query_end=query_end,
reference_start=j+1,reference_end=ref_end,query_length=len(query),reference_length=len(reference),
alignment_length=length,identities=int(identities),similarities=int(similarities),gaps=int(gaps),
identity_percent=100*identities/length if length else 0.,
similarity_percent=100*similarities/length if length else 0.,gap_percent=100*gaps/length if length else 0.)
queries = {"baboon": baboon, "squirrel_monkey": squirrel_monkey,
"dingo": dingo, "goldfish": goldfish}
alignments = {
name: local_alignment(seq, reference_epo_receptor_human, amino_acids, bmat)
for name, seq in queries.items()
}
for name, result in alignments.items():
print(name, "score", result["score"])
print(result["query"])
print(result["reference"])The resulting local sequence alignments, with the query above the reference, are:
baboon; score 314
SLLTPSDLDPLILTLSLILVLIVVLLTVLALLSHRRALKQKIWPGIPSPESEFEGLFTTHKG-FQL
SLLTPSDLDPLILTLSLILVVILVLLTVLALLSHRRALKQKIWPGIPSPESEFEGLFTTHKGNFQLsquirrel monkey; score 278
VCFWEEAASAGMGPDNYSFSYQL-DNEPWKR-CRLHQTPTARGVVRFWCSLPRADTSS
VCFWEEAASAGVGPGNYSFSYQLED-EPWK-LCRLHQAPTARGAVRFWCSLPTADTSSdingo; score 301
MNHLW--THLWPG-VGSLCLLLAGAAWASLPKP-L-DPKFESKAALLAARAPEELLCFTERLEDLVCFWEE
MDHL-GAS-LWP-QVGSLCLLLAGAAWAP-P-PNLPDPKFESKAALLAARGPEELLCFTERLEDLVCFWEEgoldfish; score 190
L--LVLSIGLILC--L-LSLTVI-L-SHQKFLLK-KLWPDIPTPEHKFPGLFTVYKGDFKE-WMSH-NNGSM
LDPLILTLSLILVVILVL-LTVLALLSHRR-ALKQKIWPGIPSPESEFEGLFTTHKGNF-QLWL-YQNDGCLThe several short gaps are a consequence of the specified inexpensive linear gap penalty; substituting a different default or an affine gap penalty would solve a different scoring problem.
Let be the time since the two sampled mitochondrial genomes shared their ancestor. Under the stipulated one-change-per-difference approximation, both descendant lineages contribute, giving a total evolutionary duration . Therefore the per-site, per-lineage mutation rate estimate isThis is not a whole-genome event rate; multiplying by the number of usable sites would give that rate. Without equal lineage rates, the pairwise data identify their sum rather than either rate separately.
The calculation assumes an accurate sequence alignment of corresponding ancestral sites, negligible errors in DNA sequencing, and an appropriate divergence-time calibration for the sampled mitochondrial genomes. It assumes a constant molecular clock on each lineage, comparable rates across sites for this simple average, and no extra differences introduced by incorrectly aligned insertions or deletions. It treats observed nucleotide substitutions as a record of mutations; interpreting a substitution-based rate as the underlying mutation rate additionally requires a suitable neutral model rather than strong filtering by natural selection. Independence between sites is useful for a simple sampling model and uncertainty calculation. The supplied time must refer to the common ancestor of these sequences: a species split need not coincide exactly with a sampled gene's ancestral split.
Past exam of the plant Sciences course of the University of Cambridge 2025 Paper plm3 2 Solution 2026-10-20
Maximum likelihood and Bayesian phylogenetics can use the same model of sequence evolution, but they answer different inferential questions: optimization of the likelihood versus a posterior distribution over trees and other unknowns. Let be a sequence alignment, a phylogenetic tree topology, its branch lengths in expected substitutions per site, and the parameters of a nucleotide substitution model. Both methods can useThe likelihood function sums over unobserved ancestral states, rather than choosing one ancestral sequence and treating it as observed. For conditionally independent sites it is a product of site likelihoods; transitions along a branch can be described by the matrix exponential of a continuous-time Markov chain rate matrix . The phylogenetic pruning algorithm computes the ancestral sums efficiently.[ref]
Evolutionary trees from DNA sequences: a maximum likelihood approach by Joseph Felsenstein. Journal of Molecular Evolution 17, pp. 368–376; likelihood calculation by summing over ancestral states
With maximum likelihood estimation, one seeksIn practice, the enormous discrete tree space requires searches and repeated optimization of continuous parameters; heuristic failure to find the best tree is a computational error distinct from statistical uncertainty. A tree's optimized likelihood is not the probability that it is correct. bootstrap analyses resample alignment columns and repeat inference to assess support under the resampling procedure; their frequencies are not automatically posterior probabilities. Independence assumptions matter, because linked sites and heterogeneous loci can make simple column resampling an imperfect representation of replication.
In Bayesian phylogenetic inference,The prior distribution supplies weights on topologies, branch lengths and model parameters. Integrating over nuisance parameters givesThus a very narrow likelihood peak can lose posterior support to a broader region with a slightly lower maximum. maximum a posteriori estimation is another optimization and does not replace this integration. Markov chain Monte Carlo provides dependent samples approximating the posterior distribution; a clade's posterior probability is the posterior mass of trees containing that clade. The early likelihood-based Bayesian formulation explicitly distinguished these probabilities from bootstrap support.[ref]
Probability distribution of molecular evolutionary trees: a new method of phylogenetic inference by Bruce Rannala and Ziheng Yang. Journal of Molecular Evolution 43, pp. 304–311; posterior probabilities of trees and comparison with bootstrap proportions
Neither approach is protected against systematic error. Poor sequence alignment, incorrect orthology assignments, compositionally heterogeneous sequences, and an inadequate substitution process can support a wrong tree with high apparent confidence. A gene tree can differ from a species tree because of incomplete lineage sorting or introgression; extra sequence from that gene does not automatically fix the mismatch. Model comparison, biological examination of the data and sensitivity to locus sampling are needed in both approaches. In Bayesian analyses, agreement among short chains is not proof of convergence: independent runs, adequate mixing between topologies and an appropriate effective sample size of a Markov chain should be checked. A credible interval and a confidence interval also have different interpretations even if their numerical endpoints happen to resemble one another.
Time inference adds a particularly strong role for assumptions. If a branch spans , with mean rate , its expected length is . Without an external absolute-time anchor, scaling every time by and every rate by leaves the sequence likelihood unchanged. Even a very long alignment can identify branch lengths accurately without identifying an absolute calendar scale. For example, a lineage length substitutions per site is compatible with per site per million years and million years, or twice that rate and half that duration. This is an identifiability issue, not merely a shortage of sampled bases.
In Bayesian divergence-time inference, a schematic joint analysis iswhere is fossil information already used to construct the conditional prior. An alternative generative analysis includes a fossil-sampling likelihood explicitly; the same fossil evidence must not be counted twice. A strict molecular clock equates rates across branches; a relaxed molecular clock allows variation, whose distribution and correlations also require specification. A narrow rate prior favors particular absolute ages, and a strong rate-smoothing assumption can redistribute inferred time among branches. A birth-death process prior on the tree encodes assumptions about lineage origination, extinction and sampling; it is not a neutral choice just because it is mathematically convenient.
fossil calibration must separate a fossil's geological age from the age of the lineage split it constrains. A confidently placed crown fossil gives a minimum age for the relevant crown, whereas a stem fossil does not automatically set that crown minimum. Uncertain placement and the incompleteness of the record complicate upper bounds. hard calibration bounds assign zero probability outside the permitted range; enough sequence cannot overcome a zero prior. soft calibration bounds allow small tail probabilities, exposing rather than eliminating the possibility of conflict. Multiple-calibration analyses demonstrate that changing the treatment of bounds changes inferred times and uncertainty.[ref]
Bayesian estimation of species divergence times under a molecular clock using multiple fossil calibrations with soft bounds by Ziheng Yang and Bruce Rannala. Molecular Biology and Evolution 23, pp. 212–226; hard versus soft bounds and the divergence-time prior
Furthermore, separately specified calibration densities are not necessarily the marginal priors the program uses. The rule that an ancestor must be older than its descendant truncates their joint possibilities. If two ages are initially independent uniform variables on , conditioning on gives marginal densities and , respectively. Neither remains uniform. Combining tree-process priors, calibration densities and ordering constraints can therefore introduce substantial information unintentionally.[ref]
Conceptual issues in Bayesian divergence time estimation by Bruce Rannala. Sections on node ordering and the realized joint prior; recommendation to sample the prior with a fixed likelihood
The practical response is to run the analysis without sequence information to inspect the effective prior distribution, then compare it with the posterior distribution. Repeat under defensible calibration tails, rate models, tree priors and fossil placements; report which ages change and whether the data sharpen relative ages more than absolute ages. Examine prior predictive checks and posterior predictive checks, and keep numerical mixing diagnostics separate from biological model adequacy. Priors can legitimately supply the time information missing from sequences, but narrow posterior ages are persuasive only when that information and its sensitivity are explicit.
Central hypothesis and objectives. PUF50 participates in one or more protein assemblies whose composition or activity affects Wnt signalling. The proposal should distinguish membership, direct binding and causal pathway regulation. The three aims are to nominate plausible partners, identify reproducible cellular complexes, and test whether a supported interaction explains the phenotype.
Computational starting point. Inspect the verified PUF50 sequence for protein domains, localization signals, conserved residues and predicted disordered regions. Use sequence alignment and orthology to compare well-annotated homologues, recording uncertainty in functional transfer. Public interaction and expression resources can nominate partners expressed in the experimental cell line. Structural predictions can prioritize testable interfaces, but a confident fold alone does not establish a cellular interaction or tumour-suppressor function.
Discovery proteomics. Use affinity purification-mass spectrometry to compare PUF50-associated material with matched negative controls across independent biological replicates. An endogenous or functionally validated tagged preparation is preferable to assuming that strong overexpression preserves normal localization and complex stoichiometry. Tag-only controls, input abundance measurements and an unrelated bait help distinguish reproducible association from abundant or sticky contaminants. Quantitative enrichment should be evaluated together with replicate consistency and a controlled false discovery rate.
Complexes may vary with pathway state. Compare a relevant baseline and a defined Wnt-responsive state, checking that changes in recovered partner abundance are not explained solely by input abundance, cell number or viability. If transient or compartmentalized partners are missed, proximity labeling can provide complementary neighbourhood evidence. Its hits should be labelled as proximity associations rather than automatically promoted to direct complex subunits.
Independent validation and mechanism. Validate leading associations by reciprocal co-immunoprecipitation and localization evidence. Where a direct interaction is important to the proposed mechanism, test it with an independent assay suited to the relevant protein domains. A genetic perturbation and rescue comparison can ask whether loss of PUF50 changes pathway output and whether restoring PUF50 restores it. Compare pathway-proximal measurements with downstream transcription and longer-term growth phenotypes, because a growth defect alone is not specific to Wnt regulation.
A separation-of-function comparison is especially informative: a PUF50 variant that retains abundance and localization but loses a supported partner association could help connect the interaction to function. This interpretation requires checking folding and stability, since an inactive misfolded protein does not isolate one interface's role. Genetic interaction analysis can then place PUF50 relative to known pathway components without treating every correlated expression change as a direct target.
Analysis, deliverables and alternatives. Integrate quantitative interaction evidence, localization and perturbation responses into an annotated protein interaction network, retaining evidence type on each edge. Report effect sizes and uncertainty, include unsuccessful validation, and release analysis code with processed data. A negative stable-complex result would motivate a transient or condition-specific interaction hypothesis rather than proving that PUF50 acts alone. The principal deliverable is a ranked, experimentally qualified set of complexes and a causal test of the most supported pathway mechanism.
Profile hidden Markov model 2026-10-20
Sequence alignment 2026-10-13
A sequence alignment places nucleotide sequences or protein sequences in correspondence for comparison. The choice of corresponding positions affects evolutionary inference; matching a short stretch alone does not establish common descent of entire organisms.
Splice-aware sequence alignment 2026-10-20
A sequence alignment that permits gaps corresponding to removed introns when matching processed RNA reads to a genome. Short microexons require particular care because their supporting aligned segments can be very small.
Stephen Altschul 2026-10-24