1. Some new sequencing technologies

2. Molecular Inversion Probes
The availability of large collections of single nucleotide polymorphisms (SNPs), along with the recent large-scale linkage disequilibrium mapping efforts, have brought the promise of whole genome association studies to the forefront of current thinking in human genetics.
ParAllele (now part of Affymetrix) has developed a novel technology based on the concept of Molecular Inversion Probes that enables up to 20,000 SNPs to be scored in a single assay. This unprecedented level of multiplexing is made possible through exquisite enzymological specificity using a unimolecular interaction that is insensitive to cross-reactivity among multiple probe molecules. The technology has been demonstrated to exhibit high accuracy while enabling a high rate of conversion of individual SNPs into working multiplexed assays. Molecular Inversion Probes
Molecular Inversion Probes are so named because the oligonucleotide probe central to the process undergoes a unimolecular rearrangement from a molecule that cannot be amplified (step 1), into a molecule that can be amplified (step 6). This rearrangement is mediated by hybridization to genomic DNA (step 2) and an enzymatic "gap fill" process that occurs in an allele-specific manner (step 3). The resulting circularized probe can be separated from cross-reacted or unreacted probes by a simple exonuclease reaction (step 4). Figure 1 shows these steps.
Applications of Molecular Inversion Probes
Molecular Inversion Probe technology is invaluable as a high-throughput SNP genotyping method for both targeted and whole genome SNP analysis projects as well as allele quantitation.

3. Single Molecule Array for Genotyping—Solexa
Genomic DNA is extracted from sample cells taken from an individual.
 In a single tube reaction, genomic DNA is processed into single-stranded oligonucleotide fragments. These are prepared for attachment to Solexa’s Single Molecule Arrays using proprietary primer and anchor molecules.
Hundreds of millions of molecules, representing the entire genome of the individual, are deposited and attached at discrete sites on a Single Molecule Array.
Fluorescently labelled nucleotides and a polymerase enzyme are added to the Single Molecule Array. Complementary nucleotides base-pair to the first base of each oligonucleotide fragment and are added to the primer by the enzyme. Remaining free nucleotides are removed.
Laser light of a specific wavelength for each base excites the label on the incorporated nucleotides, which fluoresce. This fluorescence is detected by a CCD camera that rapidly scans the entire array to identify the incorporated nucleotides on each fragment. Fluorescence is then removed.
The identity of the incorporated nucleotide reveals the identity of the base in the sample sequence to which it is paired. In this example, the first base is C (cytosine).
This cycle of incorporation, detection and identification is repeated approximately 25 times to determine the first 25 bases in each oligonucleotide fragment.
By simultaneously sequencing all molecules on the array the first 25 bases for the hundreds of millions of oligonucleotide fragments are determined.
These hundreds of millions of sequences are aligned and compared to the reference sequence using Solexa’s proprietary bioinformatics system. Known and unknown single nucleotide polymorphisms (SNP’s) together with other genetic variations can then be readily determined.

4. Nanopore Sequencing http://www.mcb.harvard.edu/branton/index.htm
Figure 1 . A nanopore sensor for sequencing DNA. A channel or nanopore in an insulating membrane separates two ionic solution-filled compartments. In response to a voltage bias (labeled “ - ” and “+”) across the membrane, ssDNA molecules (yellow) in the “-” compartment are driven, one at a time, into and through the channel. Embedded in the membrane, an electrically connected nanotube (orange) that abuts on the nanopore serves as a sensor to identify the nucleotides in the translocating DNA molecules. Elevated temperatures and denaturants maintain the DNA in an unstructured, single-stranded form.
The underlying principle of nanopore sequencing is that a single-stranded DNA or RNA molecule can be electrophoretically driven through a nano-scale pore in such a way that the molecule traverses the pore in strict linear sequence, as illustrated in Figure 1.  Because a translocating molecule partially obstructs or blocks the nanopore, it alters the pore's electrical properties 1 . 

5. Pyrosequencing
The Pyrosequencing™ technology is a relatively new DNA sequencing method. The technology has been commercialized and is today marketed by Biotage AB. The technique utilizes the cooperativity between four different enzymes and the phenomenon of bioluminescence to monitor the incorporation of nucleotides into the DNA. A short description of the steps in the Pyrosequencing process is given below.
Initial step
The reaction mixture consists of the four enzymes (DNA polymerase, ATP sulfurylase, luciferase and apyrase), different substrates needed for the reactions and the single stranded DNA to be sequenced. Step 1 - Polymerase
One of the four nucleotides dNTP (dATP, dCTP, dGTP, dTTP) is added to the reaction mixture. If the added nucleotide is complementary to the base in the DNA strand, it is incorporated and inorganic pyrophosphate (PPi) is released. Step 2 - ATP sulfurylase
The PPi is converted into ATP by the enzyme ATP sulfurylase. Step 3 - Luciferase
The luciferase catalyzes a reaction where ATP is used to generate light. The amount of light is proportional to the amount of ATP, and hence also proportional to the amount of incorporated nucleotides via the PPi. The light is then detected by a CCD camera. Step 4 - Apyrase
Remaining dNTP and ATP are degraded by the apyrase before the next nucleotide in the iterative cycle is added to the reaction mixture.

6. Pyrosequencing on a chip
Mostafa Ronaghi, Stanford Genome Technologies Center
454 Life Sciences

7. Polony Sequencing
"Polonies" are tiny colonies of DNA, about one micron in diameter, grown on a glass microscope slide (the word itself is a contraction of "polymerase colony"). To create them, researchers first pour a solution containing chopped-up DNA onto the slide. Adding an enzyme called polymerase causes each piece to copy itself repeatedly, creating millions of polonies, each dot containing only copies of the original piece of DNA. The polonies are then exposed to a series of chemically-labeled probes that light up when run through a scanning machine, identifying each nucleotide base in the strand of code, much as dusting with powder allows crime-scene investigators to bring up fingerprints on a surface.
Prior to sequencing, dsDNA is denatured and unbound copy strands are washed away.
- Covalently linked template strands allow for washing.

8. Some future directions for sequencing
Personalized genome sequencing
Find your ~1,000,000 single nucleotide polymorphisms (SNPs)
Find your rearrangements
Goals:
Link genome with phenotype
Provide personalized diet and medicine
(???) designer babies, big-brother insurance companies
Timeline:
Inexpensive sequencing:
Genotype–phenotype association: 2010-???
Personalized drugs: ???

9. Some future directions for sequencing
2. Environmental sequencing
Find your flora: organisms living in your body
External organs: skin, mucous membranes
Gut, mouth, etc.
Normal flora: >200 species, >trillions of individuals
Flora–disease, flora–non-optimal health associations
Timeline:
Inexpensive research sequencing: today
Research & associations within next 10 years
Personalized sequencing
Find diversity of organisms living in different environments
Hard to isolate
Assembly of all organisms at once

10. Some future directions for sequencing
Organism sequencing
Sequence a large fraction of all organisms
Deduce ancestors
Reconstruct ancestral genomes
Synthesize ancestral genomes
Clone—Jurassic park!
Study evolution of function
Find functional elements within a genome
How those evolved in different organisms
Find how modules/machines composed of many genes evolved

11. RNA Secondary Structure
aagacuucggaucuggcgacaccc
uacacuucggaugacaccaaagug
aggucuucggcacgggcaccauuc
ccaacuucggauuuugcuaccaua
aagccuucggagcgggcguaacuc

12. RNA and Translation

13. RNA and Splicing

14. Hairpin Loops
Interior loops
Stems
Multi-branched loop
Bulge loop

15. Tertiary Structure
Secondary Structure

18. Modeling RNA Secondary Structure: Context-Free Grammars

19. A Context Free Grammar S  AB Nonterminals: S, A, B
A  aAc | a Terminals: a, b, c, d
B  bBd | b Production Rules: 5 rules
Derivation:
Start from the S nonterminal;
Use any production rule replacing a nonterminal with a terminal, until no more nonterminals are present
S  AB  aAcB  …  aaaacccB  aaaacccbBd  …  aaaacccbbbbbdddd
Produces all strings ai+1cibj+1dj, for i, j  0

20. Example: modeling a stem loop
S  a W1 u
W1  c W2 g
W2  g W3 c
W3  g L c
L  agugc
What if the stem loop can have other letters in place of the ones shown? AG U CG
ACGG
UGCC

21. Example: modeling a stem loop
S  a W1 u | g W1 u
W1  c W2 g
W2  g W3 c | g W3 u
W3  g L c | a L u
L  agucg | agccg | cugugc
More general: Any 4-long stem, 3-5-long loop:
S  aW1u | gW1u | gW1c | cW1g | uW1g | uW1a
W1  aW2u | gW2u | gW2c | cW2g | uW2g | uW2a
W2  aW3u | gW3u | gW3c | cW3g | uW3g | uW3a
W3  aLu | gLu | gLc | cLg | uLg | uLa
L  aL1 | cL1 | gL1 | uL1
L1  aL2 | cL2 | gL2 | uL2
L2  a | c | g | u | aa | … | uu | aaa | … | uuu AG U CG
ACGG
UGCC AG C CG
GCGA
UGCU
CUG U CG
GCGA
UGUU

22. A parse tree: alignment of CFG to sequence
S  a W1 u
W1  c W2 g
W2  g W3 c
W3  g L c
L  agucg AG U CG
ACGG
UGCC S W1 W2 W3 L
A C G G A G U G C C C G U

23. Alignment scores for parses!
We can define each rule X  s, where s is a string,
to have a score.
Example:
W  g W’ c: 3 (forms 3 hydrogen bonds)
W  a W’ u: 2 (forms 2 hydrogen bonds)
W  g W’ u: 1 (forms 1 hydrogen bond)
W  x W’ z -1, when (x, z) is not an a/u, g/c, g/u pair
Questions:
How do we best align a CFG to a sequence? (DP)
How do we set the parameters? (Stochastic CFGs)

24. The Nussinov AlgorithmC C
Let’s forget CFGs for a moment
Problem:
Find the RNA structure with the maximum (weighted) number of nested pairings A G C C G G C A U A U U A A A C U G U G A C A C A A A A C U C G G C U G U G U C G G A G C C U U G A G G C G G A G C G A U G C A U C A A U U G A
ACCACGCUUAAGACACCUAGCUUGUGUCCUGGAGGUCUAUAAGUCAGACCGCGAGAGGGAAGACUCGUAUAAGCG

25. The Nussinov Algorithm
Given sequence X = x1…xN,
Define DP matrix:
F(i, j) = maximum number of weighted bonds if xi…xj folds optimally
Two cases, if i < j:
xi is paired with xj
F(i, j) = s(xi, xj) + F(i+1, j – 1)
xi is not paired with xj
F(i, j) = max{ k: i  k < j } F(i, k) + F(k+1, j) i j i j i k j

26. The Nussinov Algorithm
Initialization:
F(i, i-1) = 0; for i = 2 to N
F(i, i) = 0; for i = 1 to N
Iteration:
For l = 2 to N:
For i = 1 to N – l
j = i + l – 1
F(i+1, j – 1) + s(xi, xj)
F(i, j) = max
max{ i  k < j } F(i, k) + F(k+1, j)
Termination:
Best structure is given by F(1, N)
(Need to trace back; refer to the Durbin book)

27. The Nussinov Algorithm and CFGs
Define the following grammar, with scores:
S  g S c : 3 | c S g : 3
a S u : | u S a : 2
g S u : | u S g : 1
S S : 0 |
a S : 0 | c S : 0 | g S : 0 | u S : 0 |  : 0
Note:  is the “” string
Then, the Nussinov algorithm finds the optimal parse of a string with this grammar

28. The Nussinov Algorithm
Initialization:
F(i, i-1) = 0; for i = 2 to N
F(i, i) = 0; for i = 1 to N S  a | c | g | u
Iteration:
For l = 2 to N:
For i = 1 to N – l
j = i + l – 1
F(i+1, j – 1) + s(xi, xj) S  a S u | …
F(i, j) = max
max{ i  k < j } F(i, k) + F(k+1, j)
S  S S
Termination:
Best structure is given by F(1, N)

29. Stochastic Context Free Grammars
In an analogy to HMMs, we can assign probabilities to transitions:
Given grammar
X1  s11 | … | sin …
Xm  sm1 | … | smn
Can assign probability to each rule, s.t.
P(Xi  si1) + … + P(Xi  sin) = 1

30. Example S  a S b : ½ a : ¼ b : ¼
Probability distribution over all strings x:
x = anbn+1,
then P(x) = 2-n  ¼ = 2-(n+2)
x = an+1bn,
same
Otherwise: P(x) = 0

31. Computational Problems
Calculate an optimal alignment of a sequence and a SCFG
(DECODING)
Calculate Prob[ sequence | grammar ]
(EVALUATION)
Given a set of sequences, estimate parameters of a SCFG
(LEARNING)

32. Normal Forms for CFGs Chomsky Normal Form: X  YZ X  a
All productions are either to 2 nonterminals, or to 1 terminal
Theorem (technical)
Every CFG has an equivalent one in Chomsky Normal Form
(The grammar in normal form produces exactly the same set of strings)

33. Example of converting a CFG to C.N.F.S
S  ABC
A  Aa | a
B  Bb | b
C  CAc | c
Converting:
S  AS’
S’  BC
A  AA | a
B  BB | b
C  DC’ | c
C’  c
D  CA A B C A a B b C A c a B b c a b S A S’ A A B C a a B B D C’ B B b C A c b b c a

34. Another example Converting: S  ABC A  C | aA B  bB | b C  cCd | c
S  AS’
S’  BC
A  C’C’’ | c | A’A
A’  a
B  B’B | b
B’  b
C  C’C’’ | c
C’  c
C’’  CD
D  d

35. Decoding: the CYK algorithm
Given x = x1....xN, and a SCFG G,
Find the most likely parse of x
(the most likely alignment of G to x)
Dynamic programming variable:
(i, j, V): likelihood of the most likely parse of xi…xj,
rooted at nonterminal V
Then,
(1, N, S): likelihood of the most likely parse of x by the grammar

36. The CYK algorithm (Cocke-Younger-Kasami)
Initialization:
For i = 1 to N, any nonterminal V,
(i, i, V) = log P(V  xi)
Iteration:
For i = 1 to N – 1
For j = i+1 to N
For any nonterminal V,
(i, j, V) = maxXmaxYmaxik<j (i,k,X) + (k+1,j,Y) + log P(VXY)
Termination:
log P(x | , *) = (1, N, S)
Where * is the optimal parse tree (if traced back appropriately from above) i j V X Y

37. A SCFG for predicting RNA structure
S  a S | c S | g S | u S | 
 S a | S c | S g | S u
 a S u | c S g | g S u | u S g | g S c | u S a
 SS
Adjust the probability parameters to reflect bond strength etc
No distinction between non-paired bases, bulges, loops
Can modify to model these events
L: loop nonterminal
H: hairpin nonterminal
B: bulge nonterminal
etc

38. CYK for RNA folding Initialization: (i, i-1) = log P() Iteration:
For i = 1 to N
For j = i to N
(i+1, j–1) + log P(xi S xj)
(i, j–1) + log P(S xi)
(i, j) = max
(i+1, j) + log P(xi S)
maxi < k < j (i, k) + (k+1, j) + log P(S S)

39. Evaluation Recall HMMs: Forward: fl(i) = P(x1…xi, i = l)
Backward: bk(i) = P(xi+1…xN | i = k)
Then,
P(x) = k fk(N) ak0 = l a0l el(x1) bl(1)
Analogue in SCFGs:
Inside: a(i, j, V) = P(xi…xj is generated by nonterminal V)
Outside: b(i, j, V) = P(x, excluding xi…xj is generated by S and the excluded part is rooted at V)

40. The Inside Algorithm V X Y To compute
a(i, j, V) = P(xi…xj, produced by V)
a(i, j, v) = X Y k a(i, k, X) a(k+1, j, Y) P(V  XY) V X Y i k
k+1 j

41. Algorithm: Inside Initialization: For i = 1 to N, V a nonterminal,
a(i, i, V) = P(V  xi)
Iteration:
For i = 1 to N-1
For j = i+1 to N
For V a nonterminal
a(i, j, V) = X Y k a(i, k, X) a(k+1, j, X) P(V  XY)
Termination:
P(x | ) = a(1, N, S)

42. The Outside Algorithm Y V X
b(i, j, V) = Prob(x1…xi-1, xj+1…xN, where the “gap” is rooted at V)
Given that V is the right-hand-side nonterminal of a production,
b(i, j, V) = X Y k<i a(k, i-1, X) b(k, j, Y) P(Y  XV) Y V X k i j

43. Algorithm: Outside Initialization: b(1, N, S) = 1
For any other V, b(1, N, V) = 0
Iteration:
For i = 1 to N-1
For j = N down to i
For V a nonterminal
b(i, j, V) = X Y k<i a(k, i-1, X) b(k, j, Y) P(Y  XV) +
X Y k<i a(j+1, k, X) b(i, k, Y) P(Y  VX)
Termination:
It is true for any i, that:
P(x | ) = X b(i, i, X) P(X  xi)

44. Learning for SCFGs We can now estimate
c(V) = expected number of times V is used in the parse of x1….xN 1
c(V) = –––––––– 1iNijN a(i, j, V) b(i, j, v)
P(x | )
c(VXY) = –––––––– 1iNi<jN ik<j b(i,j,V) a(i,k,X) a(k+1,j,Y) P(VXY)

45. Learning for SCFGs
Then, we can re-estimate the parameters with EM, by:
c(VXY)
Pnew(VXY) = ––––––––––––
c(V)
c(V  a) i: xi = a b(i, i, V) P(V  a)
Pnew(V  a) = –––––––––– = ––––––––––––––––––––––––––––––––
c(V) 1iNi<jN a(i, j, V) b(i, j, V)

46. Summary: SCFG and HMM algorithms
GOAL HMM algorithm SCFG algorithm
Optimal parse Viterbi CYK
Estimation Forward Inside
Backward Outside
Learning EM: Fw/Bck EM: Ins/Outs
Memory Complexity O(N K) O(N2 K)
Time Complexity O(N K2) O(N3 K3)
Where K: # of states in the HMM
# of nonterminals in the SCFG

47. The Zuker algorithm – main ideas
Models energy of an RNA fold
Instead of base pairs, pairs of base pairs (more accurate)
Separate score for bulges
Separate score for different-size & composition loops
Separate score for interactions between stem & beginning of loop
Can also do all that with a SCFG, and train it on real data