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Alignment Problem. (Optimal) pairwise alignment consists of considering all possible alignments of two sequences and choosing the optimal one. Sub-optimal (heuristic) alignment algorithms are also very important: e.g. BLAST. Key Issues. Types of alignments (local vs. global)

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Alignment problem
Alignment Problem

  • (Optimal) pairwise alignment consists of considering all possible alignments of two sequences and choosing the optimal one.

  • Sub-optimal (heuristic) alignment algorithms are also very important: e.g. BLAST

Key issues
Key Issues

  • Types of alignments (local vs. global)

  • The scoring system

  • The alignment algorithm

  • Measuring alignment significance

Types of alignment
Types of Alignment

  • Global—sequences aligned from end-to-end.

  • Local—alignments may start in the middle of either sequence

  • Ungapped—no insertions or deletions are allowed

  • Other types: overlap alignments, repeated match alignments

Local vs global pairwise alignments
Local vs. Global Pairwise Alignments

  • A global alignment includes all elements of the sequences and includes gaps.

    • A global alignment may or may not include "end gap" penalties.

    • Global alignments are better indicators of homology and take longer to compute.

  • A local alignment includes only subsequences, and sometimes is computed without gaps.

    • Local alignments can find shared domains in divergent proteins and are fast to compute

How do you compare alignments
How do you compare alignments?

  • Scoring scheme

    • What events do we score?

      • Matches

      • Mismatches

      • Gaps

    • What scores will you give these events?

    • What assumptions are you making?

  • Score your alignment

Scoring matrices
Scoring Matrices

  • How do you determine scores?

  • What is out there already for your use?

  • DNA versus Amino Acids?



Multiple sequence alignment
Multiple Sequence Alignment

Global versus Local Alignments

  • Progressive alignment

    • Estimate guide tree

    • Do pairwise alignment on subtrees



  • Consistency-based Algorithms

    • T-Coffee - consistency-based objective function to minimize potential errors

      • Generates pair-wise global (Clustal)

      • Local (Lalign)

      • Then combine, reweight, progressive alignment

Iterative algorithms
Iterative Algorithms

  • Estimate draft progressive alignment (uncorrected distances)

  • Improved progressive (reestimate guide tree using Kimura 2-parameter)

  • Refinement - divide into 2 subtrees, estimate two profiles, then re-align 2 profiles

  • Continue refinement until convergence


  • Clustal

  • T-Coffee

  • MUSCLE (limited models)

  • MAFFT (wide variety of models)


  • Speed


  • Accuracy


  • Lots more work to do here!

Modern sequencing methods
Modern Sequencing Methods

  • Sanger (1982) introduced a sequencing method amenable to automation.

  • Whole-genome sequencing: Clone-By-Clone vs. Shotgun Assembly

  • Drosophila melongaster sequenced (Myers et al. 2000)

  • Homo sapien sequenced (Venter et al. 2001)

Alignment problem

Sanger (1982) introduced chain-termination sequencing.

Main idea: Obtain fragments of all possible lengths, ending in A, C, T, G.

Using gel electrophoresis, we can separate fragments of differing lengths, and then assemble them.

Automated sequencing
Automated Sequencing

Perkin-Elmer 3700:

Can sequence ~500bp with 98.5% accuracy

Reads and contigs
Reads and Contigs

Sequencing machines are limited to about ~500-750bp, so we must break up DNA into short and long fragments, with reads on either end.

Reads are then assembled into contigs, then scaffolds.

Clone by clone vs shotgun
Clone-by-Clone vs. Shotgun

  • Traditionally, long fragments are mapped, and then assembled by finding a minimum tiling path. Then, shotgun assembly is used to sequence long fragments.

  • Shotgun assembly is cheaper, but requires more computational resources.

  • Drosophila was successfully sequenced using shotgun assembly.


  • Good coverage does not guarantee that we can “see” repeats.

  • Read coverage is generally not “truly” random, due to complications in fragmentation and cloning.

  • Any automated approach requires extensive post-processing.


The fruit fly
The Fruit Fly

  • Drosophila melongaster was sequenced in 2000 using whole genome shotgun assembly.

  • Genome size is ~120Mbp for euchromatic (coding) portion, with roughly 13,600 genes.

  • The genome is still being refined.

Alignment problem

NIH used a Clone-By-Clone strategy; Celera used shotgun assembly.

Celera used 300 sequencing machines in parallel to obtain 175,000 reads per day.

Efforts were combined, resulting in 8x coverage of the human genome; consensus sequence is 2.91 billion base pairs.

Abstraction assembly.

  • The basic question is: given a set of fragments from a long string, can we reconstruct the string?

  • What is the shortest common superstring of the given fragments?

Overlap layout consensus
Overlap-Layout-Consensus assembly.

  • Construct a (directed) overlap graph, where nodes represent reads and edges represent overlap. Paths are contigs in this graph.

  • Problem: Find the consensus sequence by finding a path that visits all nodes in layout graph.

  • Note: This is an idealization, since we must handle errors!

Approximation algorithms
Approximation Algorithms assembly.

  • The shortest common superstring problem is NP-complete.

  • Greedily choosing edges is a 4-approximation, conjectured to be a 2-approximation.

  • Another idea: TSP has a 2-approximation if the edge weights are metric (Waterman et al. 1976 gives such metrics).

Handling repeats
Handling Repeats assembly.

  • We can estimate how much coverage a given set of overlapping reads should yield, based on coverage.

  • Repeats will “seem” to have unusually good coverage.

  • Celera’s algorithms are proprietary, but there is no explicit way to handle repeats in the overlap-layout-consensus paradigm.

Alignment problem

The Big Picture assembly.

Hybridization assembly.

Suppose we had a way to probe fragments of length k that were present in our sequence, from a hybridization assay.

Commercial products: Affymetrix GeneChip, Agilent, Amersham, etc.

Sequencing by hybridization
Sequencing-By-Hybridization assembly.

  • Then instead of reads, we have regularly sized fragments, k-mers.

  • Construct a multigraph G with (k-1)-mers as nodes, with edges representing k-mers. G is a de Bruijn graph.

  • Idea: An Eulerian path in G corresponds to the assembled sequence, and we don’t lose repeats (Pevzner 1989).

Bridges of k nigsberg
Bridges of Königsberg assembly.

Theorem (Euler 1736): A graph has a path visiting every edge exactly once if and only if it is connected and has 2 or fewer vertices of odd degree.

Pros and cons
Pros and Cons assembly.

  • An Eulerian path in a graph can be found in linear time, if one exists.

  • Errors in the hybridization experiments may prevent us from finding a solution.

  • Can we just use reads as “virtual” hybridization data?

Graph preprocessing
Graph Preprocessing assembly.

  • Read errors mean up to k missing/erroneous edges. But we cannot correct this until we are done assembling!

  • Greedily mutate reads to minimize size of set of k-mers.

  • We also need to deal with repeats, which requires contracting certain paths to single edges…

Sequencing parameters
Sequencing parameters assembly.

  • Difficulty and cost of large-scale sequencing projects depend on the following parameters:

    • Accuracy

      • How many errors are tolerated

    • Coverage

      • How many times the same region is sequenced

  • The two parameters are related

    • More coverage usually means higher accuracy

    • Accuracy is also dependent on the finishing effort

Sequence accuracy
Sequence accuracy assembly.

  • Highly accurate sequences are needed for the following:

    • Diagnostics

      • e.g., Forensics, identifying disease alleles in a patient

    • Protein coding prediction

      • One insertion or deletion changes the reading frame

  • Lower accuracy sufficient for homology searches

    • Differences in sequence are tolerated by search programs

Sequence accuracy and sequencing cost
Sequence accuracy and sequencing cost assembly.

  • Level of accuracy determines cost of project

    • Increasing accuracy from one error in 100 to one error in 10,000 increases costs three to fivefold

  • Need to determine appropriate level of accuracy for each project

    • If reference sequence already exists, then a lower level of accuracy should suffice

      • Can find genes in genome, but not their position

  • Sequencing coverage
    Sequencing coverage assembly.

    • Coverage is the number of times the same region is sequenced

      • Ideally, one wants an equal number of sequences in each direction

    • To obtain accuracy of one error in 10,000 bases, one needs the following:

      • 10x coverage

        • Stringent finishing

      • Complete sequence

        • Base-perfect sequencing

    Ncbi genome summary
    NCBI Genome Summary assembly.

    • NCBI

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