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)

The scoring system The alignment algorithm Measuring alignment significance

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 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? 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 How do you determine scores? What is out there already for your use? DNA versus Amino Acids?

TTACGGAGCTTC CTGAGATCC

Multiple Sequence Alignment

Global versus Local Alignments Progressive alignment

Estimate guide tree Do pairwise alignment on subtrees

ClustalX

Improvements 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 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

Software Clustal T-Coffee MUSCLE (limited models) MAFFT (wide variety of models)

Comparisons Speed

Muscle>MAFFT>CLUSTALW>T-COFFEE

Accuracy MAFFT>Muscle>T-COFFEE>CLUSTALW

Lots more work to do here!

Why Genome Sequencing?

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)

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.

Sanger (1982) introduced chain-termination sequencing.

Automated Sequencing

Perkin-Elmer 3700:Can sequence ~500bp with 98.5% accuracy

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 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.

In a Perfect World

Difficulties? 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.

Phrap www.phrap.org

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.

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 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 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 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 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.

The Big Picture

HybridizationSuppose 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 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 Königsberg

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 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 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…

Sizes of genomes and numbers of genes

Sequencing parameters 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 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 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 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