GTCAGATGAGCAAAGTAGACACTCCAGTAACGCGGTGAGTACATTAA exon intron intergene Find Gene Structures in DNA Intergene State First Exon State Intron State.

GTCAGATGAGCAAAGTAGACACTCCAGTAACGCGGTGAGTACATTAA

exon exon exonintronintronintergene intergene

Find Gene Structures in DNA

Intergene State

First Exon State

IntronState

Hidden Markov Model for Gene Finding

• Intron, Exon, Intergenic states

• Exon frame is encoded in the architecture by defining more states

• Exon states have explicit duration density

• Intron states have geometric duration

• Parameters are trained separately in different levels of GC content (correlated with amount of genes, and length of exons & introns)

Comparison-based Methods

Cross-species gene finding

5’ 3’

Exon1 Exon2 Exon3Intron1 Intron2

[human]

[mouse]

GGTTTT--ATGAGTAAAGTAGACACTCCAGTAACGCGGTGAGTAC----ATTAA | ||||| ||||| ||| ||||| ||||||||||||| | |C-TCAGGAATGAGCAAAGTCGAC---CCAGTAACGCGGTAAGTACATTAACGA-

Comparison of 1196 orthologous genes(Makalowski et al., 1996)

• Sequence identity between genes in human/mouse– exons: 84.6%– protein: 85.4%– introns: 35%– 5’ UTRs: 67%– 3’ UTRs: 69%

• 27 proteins were 100% identical.

Human Mouse

Human-mouse homology

Not always: HoxA human-mouse

Twinscan

• Twinscan is an augmented version of the Gencscan HMM.

E I

transitions

duration

emissionsACUAUACAGACAUAUAUCAU

Twinscan Algorithm

1. Align the two sequences (eg. from human and mouse)

2. Mark each human base as gap ( - ), mismatch ( : ), match ( | )

New “alphabet”: 4 x 3 = 12 letters

= { A-, A:, A|, C-, C:, C|, G-, G:, G|, U-, U:, U| }

Twinscan Algorithm

3. Run Viterbi using emissions ek(b) where b { A-, A:, A|, …, T| }

Note:

Emission distributions ek(b) estimated from real genes from human/mouse

eI(x|) < eE(x|): matches favored in exons

eI(x-) > eE(x-): gaps (and mismatches) favored in introns

Example

Human: ACGGCGACGUGCACGU

Mouse: ACUGUGACGUGCACUU

Alignment: ||:|:|||||||||:|

Input to Twinscan HMM:A| C| G: G| C: G| A| C| G| U| G| C| A| C| G: U|

Recall, eE(A|) > eI(A|)

eE(A-) < eI(A-)

Likely exon

HMMs for simultaneous alignment and gene finding:

Generalized Pair HMMs

A Pair HMM for alignments

MP(xi, yj)

IP(xi)

JP(yj)

1 - 2

1- - 2

1- - 2

BEGIN

END

M JI

Generalized Pair HMMs

Exon GPHMM

d

e

1.Choose exon lengths (d,e).2.Generate alignment of length d+e.

Cross-species gene finding

5’ 3’

Exon1 Exon2 Exon3Intron1 Intron2

CNS CNS CNS

[human]

[mouse]

The SLAM hidden Markov model

Model Time Space

HMM N2T NTPHMM N2TU NTUGHMM D2N 2T NTGPHMM D4N 2TU NTU

N no. states

Dmax durationT length

seq1U length seq2

Computational complexity

Approximate alignment

Reduces

TU -factor

to

hT

Measuring Performance

Example: HoxA2 and HoxA3

SLAM

SGP-2

TwinscanGenscan

TBLASTXSLAM CNS

VISTARefSeq

Suffix Trees

(a short break from biology)

Suffix Trees

• Suffix trees are a method to find all maximal matches between two strings (and much more)

Example: x = dabdac d a b d a c

ca

bd

acc

cca

db

1

4

25

63

Definition of a Suffix Tree

Definition:

For string x = x1…xm, a suffix tree is:

A rooted tree with m leaves

Leaf i: xi…xm

Each edge is a substring

No two edges out of a node, start with same letter

It follows, every substring corresponds to

an initial part of a path from root to a leaf

Naïve Algorithm to Construct a Suffix Tree

1. Initialize tree T: a single root node r

2. Insert special symbol $ at end of x

3. For j = 1 to m

• Find longest match of xi…xm to T, starting from r

• Split edge where match stops: new node w

• Create edge (w, j), and label with unmatched portion of xi…xm

Example of Suffix Tree Construction

1

x = d a b d a $

d a b d a $

1. Insert d a b d a $

a

bd

a$

2

2. Insert a b d a $

$a

db

3

3. Insert b d a $

$

4

4. Insert d a $

$

5

5. Insert a $

$

6

6. Insert $

Memory to Store Suffix Tree

• Can store in O( N ) memory!

• Every edge is labeled with (i, j):

(i,j) denotes xi…xj

• Tree has O( N ) nodes

Proof:1. # leafs # nodes – 1

2. # leafs = |x|

Faster Construction

Several algorithms

O( N ) time,

O( N ) memory with a big constant ~15 bytes/char

Technical but not deep, outside the scope of this course

Optional: Gusfield, chapter 6

Application: find all matches between x, y

1. Build suffix tree for x, mark nodes with x

2. Insert y in suffix tree, mark all nodes y “passes from” with y

The path label of every node marked both 0 and 1, is a common substring

1

x = d a b d a $y = a b a d a $

d a b d a $1. Construct tree for x

a

bd

a$2

$a

db

3

$

4

$

5

$6

xx

x

6. Insert a $

5

6

6. Insert $

4. Insert a d a $

da$

3

5. Insert d a $

y

4

2. Insert a b a d a $

a

y

da

$

1

y

yx

3. Insert b a d a $ ady

2

a$

x

Example of Suffix Tree construction

Application: common substrings of k strings

To find the longest common substring of s1, s2, …sn

1. Build suffix tree for s1,…, sn

2. All nodes labeled {si1, …, sik} represent a match between si1, …, sik

Suffix Arrays

ABRACADABRA$

11 $10 A$ 7 ABRA$ 0

ABRACADABRA$ 3 ACADABRA$ 5 ADABRA$ 8 BRA$ 1 BRACADABRA$ 4 CADABRA$ 6 DABRA$ 9 RA$ 2 RACADABRA#$

• Fast O(log n) search for every specific string

• Used for data compression such as bzip2

• Can be built in O(n) time by first building suffix tree and then get ordered suffixes by in-order traversal Too much memory— ~15n bytes Difficult to implement

• Theoretical build in O(n log n) using O(n/ sqrt(log n)) extra memory

• Hot topic how to build fast in practice