Whole genome alignments

Genome 559: Introduction to Statistical and Computational Genomics

Prof. James H. Thomas

Review

• What a score matrix is and how to calculate and use one.

• Why an affine gap penalty is desirable.

• How to align sequences using dynamic programming.

• How to calculate and interpret p-values and E-values for pair alignments and database searches.

Whole genome alignments

Why?

known gap in

assembly

averaged conservation

for 17 genomes

individual genome

alignments, darker = higher

scoring

alignment discontinuity (e.g. translocation

break point)

questionable

alignment segment

sequence present but unalignable

UCSC Browser track

GQSQVGQGPPCPHHRCTTCCPDGCHFEPQVCMCDWESCCEEGGQSEVRQGPQCPYHKCIKCQPDGCHYEPTVCICREKPCDEKG

How are genome-wide alignments made?

• mouse and human genomes are each about 3x109 nucleotides.

• how many calculations would a dynamic programming alignment have to make?

• at a minimum - 3 integer additions and 3 inequality tests for each DP matrix position

(by the way, there are other problems too, including assuming colinearity)

• Most common method is the BLAST search (Basic Local Alignment Search Tool). Only the initial step is substantially different from dynamic alignment.

• Search sequence is broken into small words (usually 3 residues long for proteins). 20 * 20 * 20 = 8,000 words. These act as seeds for searches.

• The target dataset is pre-indexed to indicate the positions in the database sequences that match each search word above some score threshold (using a global score matrix such as BLOSUM62).

Making large searches faster

...VFEWVHLLP... WIY

• Target sequences around each indexed word hit are retrieved and the initial match is extended in both directions:

your sequencedatabase (many sites)

• For example, the search sequence word “WVH” might score above threshold with these indexed sequences:

Indexed word Score WVH 23 WIH 22 WVY 17 WIY 16

BLAST searches (cont.)

Schematic of indexed matches

Result – instead of aligning these 3 amino acids to everything, they are aligned only with the tiny fraction of sequence regions that are good candidates for a valid alignment.

(note- blast actually looks for two such matches close to each other)

Extension and scoring

...QSVFEWVHLLPGA... ..WIY..

...QSVFEWVHLLPGA... ..WIYQ..

...QSVFEWVHLLPGA... ..WIYQK..

...QSVFEWVHLLPGA... ..WIYQKA..

Total Score:

16

13

11

10

Match Score:

16

-3

-2

-1

[mention gap variant]

Extension termination

• Extension is continued until the cumulative score drops below some threshold (usually 0).

• This permits the match to cross a region of marginal similarity or frank mismatching (e.g. a small intron in tblastn) if it flanks a region of high similarity.

• Extensions whose maximal cumulative score is above some threshold are kept for reporting to user.

• For web interfaces, various formatting, links, and overviews are added and reported according to user settings (it is also fairly easy to download and run your own blast).

Key to speed: word matching and prior indexing

• Though gapped blast local alignment is slow (like dynamic programming), only a very small part of total search space is analyzed.

• Because the positions of all database word matches are indexed and stored prior to the blast search, the relevant parts of search space are reached quickly.

• Tradeoff is in accuracy and certainty – occasionally matches will be missed (when they are distant enough and dispersed enough that no local word pairs match well enough).

genome A

genome BDP alignment region

M x N manageable

BLAST matches

Dynamic programming after BLAST matching

Defining what a “tree” means

rooted tree (all real trees are rooted):unrooted tree (used when the root isn’t known):

time

ancestral sequence

time vaguely radiates out from somewhere near the center

…divergence time is the sum of (horizontal) branch lengths

sequences(leaves or tips)branch

points

branches

root

A tree has topology and distances

Are these different trees?

The number of tree topologies grows extremely fast

3 leaves3 branches1 internal node1 topology(3 insertions)

4 leaves5 branches2 internal nodes3 topologies (x3)(5 insertions)

5 leaves7 branches3 internal nodes15 topologies (x5)(7 insertions)

In general, an unrooted tree with N leaves has:2N – 3 branchesN – 2 internal nodes~ O(N!) topologies 3 5 7 ... 2 5N

There are many rooted trees for each unrooted tree

For each unrooted tree, there are 2N - 3 times as many rooted trees, where N is the number of leaves (# internal branches = 2N – 3).

20 leaves - 564,480,989,588,730,591,336,960,000,000 topologies