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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?
individual genome
alignments, darker
= higher scoring
known gap in
assembly
sequence
present but
unalignable
UCSC Browser track
averaged
conservation for
17 genomes
alignment discontinuity
(e.g. translocation break
point)
questionable
alignment
segment
GQSQVGQGPPCPHHRCTTCCPDGCHFEPQVCMCDWESCCEEG
GQSEVRQGPQCPYHKCIKCQPDGCHYEPTVCICREKPCDEKG
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)
Making large searches faster
• 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).
BLAST searches (cont.)
• For example, the search sequence word “WVH” might score
above threshold with these indexed sequences:
Indexed word
WVH
WIH
WVY
WIY
Score
23
22
17
16
• Target sequences around each indexed word hit are retrieved
and the initial match is extended in both directions:
...VFEWVHLLP...
WIY
your sequence
database (many sites)
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..
Match
Score:
Total
Score:
16
16
-3
13
-2
11
-1
10
[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).
Dynamic programming after BLAST matching
genome A
BLAST
matches
DP alignment region
M x N manageable
genome B
Defining what a “tree” means
rooted tree (all real trees are rooted):
unrooted tree (used when
the root isn’t known):
sequences
(leaves or tips)
branch
points
root
ancestral
sequence
branches
time vaguely radiates out from
somewhere near the center
time
…divergence time is the sum of (horizontal) branch lengths
A tree has topology and distances
Are these different trees?
The number of tree topologies grows extremely fast
3 leaves
3 branches
1 internal node
1 topology
(3 insertions)
In general, an unrooted tree
with N leaves has:
2N – 3 branches
N – 2 internal nodes
~ O(N!) topologies 3  5  7  ...   2 N  5
4 leaves
5 branches
2 internal nodes
3 topologies (x3)
(5 insertions)
5 leaves
7 branches
3 internal nodes
15 topologies (x5)
(7 insertions)
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