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Probabilistic methods (weight matrix)

Probabilistic methods

Probabilistic methods

- Introduction Multiple Alignments
- Multiple alignment based on HMM
- Motif Finding
- Motif representation
- Algorithm
- Search Space
- Word counting methods
- Probabilistic methods

- Profile Searches
- Introduction

- Exercises

http://www.esat.kuleuven.ac.be/~kmarchal/

- Global multiple alignment (ClustalW)
- Proteins, nucleotides
- Long stretches of conservation essential
- Identification of protein family profiles
- Score gaps

- Local multiple alignments (motif detection)
- Proteins, nucleotides
- Short stretches of conservation (12 NT, 6 AA)
- Identification of regulatory motifs (DNA, protein)
- No explicit gap scoring
- Explicit use of a profile

- Introduction Multiple Alignments
- Multiple alignment based on HMM
- Motif Finding
- Motif representation
- Algorithm
- Search Space
- Word counting methods
- Probabilistic methods

- Profile Searches
- Introduction

- Exercises

- Introduction Multiple Alignments
- Multiple alignment based on HMM
- Motif Finding
- Motif representation
- Algorithm
- Search Space
- Word counting methods
- Probabilistic methods

- Profile Searches
- Introduction

- Exercises

http://www.esat.kuleuven.ac.be/~kmarchal/

cell

chromosome

sigma

motif

Gene 1

Gene 2

Gene 3

Gene 4

gene

transcription

?

mRNA

translation

protein

Transcriptional regulation

Consensus sequence:

- reductionistic representation of a motif
- Most frequent instance is used as a representative
- Loss of information
Regular expression:

- More complex representation allowing motif degeneracy
Position specific scoring matrix (PSSM):

- Probabilistic representation

Consensus

CTTAATATTAACTTAAT

Regular expression

CTTAAKRTTMAYTTAAT

PSSM (motif logo)

Search for motifs that are present more frequently in a set of sequences than in a set of unrelated sequences

- Methods based on word counting (regular expression)
- NP problems, heuristic methods clever algorithms
- motif w=8; combinations=8!
- Jensen & Knudsen, 2000; van Helden, 2000; Vanet, 2000

- NP problems, heuristic methods clever algorithms

- Multiple alignment by locally aligning small conserved regions in a set of unaligned sequences.
- Motif model represented by a probability matrix
- EM, Gibbs sampler (optimization algorithms)
- AlignACE http://atlas.med.harvard.edu/
- BioProspector: http://bioprospector.stanford.edu/
- Motif Sampler http://www.esat.kuleuven.ac.be/~dna/BioI/Software.html

- When are motifs overrepresented statistically?
- Set of coexpressed (coregulated sequences)
- Literature searches
- Microarrays, expression profiling

- Set of orthologous sequences (phylogenetic footprinting)
- Comparative genomics
- Orthologous sequences similar ancestral origin => similar mechanism of transcriptional regulation

coexpression

Search space

Preprocessing of the data

cDNA arrays

Clustering

Upstream regions

Gibbs

sampling

EMBL

BLAST

Phylogenetic footprinting PhoPQ is autoregulated

Search space

- PhoPQ ubiquitous system
- Salmonella
- Escherichia
- Yersinia
- Vibrio
- Pseudomonas
- Providencia
- Pectobacterium

- Methods based on word counting
- NP problems, heuristic methods clever algorithms
- motif w=8; combinations=8!
- Jensen & Knudsen, 2000; van Helden, 2000; Vanet, 2000

- NP problems, heuristic methods clever algorithms

- Optimisation problems, self learning, AI
- Motif model represented by a probability matrix
- Bayesian, Gibbs sampler
- AlignACE http://atlas.med.harvard.edu/
- BioProspector: http://bioprospector.stanford.edu/
- Motif Sampler http://www.esat.kuleuven.ac.be/~dna/BioI/Software.html

Monad frequencies: single word counts:

(RSA tools) (J. Vanhelden et al., 1998 J. Mol. Biol.)

- Enumerate all oligonucleotides
- count the number of occurrences of all oligonucleotides of selected size in a set of coregulated genes
- compare the number of occurrences with its expected value in the background

http://bio.cigb.edu.cu/jvanheld/rsa-tools/RSA_home.shtml

Relevance of the motifs detected

p-Value and Sig score (string based methods)

- Expected number of occurrences in background

- Statistical significance

- Methods based on word counting
- NP problems, heuristic methods clever algorithms
- motif w=8; combinations=8!
- Jensen & Knudsen, 2000; van Helden, 2000; Vanet, 2000

- NP problems, heuristic methods clever algorithms

- Optimisation problems, self learning, AI
- Motif model represented by a probability matrix
- Bayesian, Gibbs sampler
- AlignACE http://atlas.med.harvard.edu/
- BioProspector: http://bioprospector.stanford.edu/
- Motif Sampler http://www.esat.kuleuven.ac.be/~dna/BioI/Software.html

Find common motifs, that represent regulatory elements, in the region upstream of translation start in a set of co-expressed DNA sequences

- Motifs are hidden in background sequence

- Motif Representation: Probability matrix (PSSM)

- Background model
- Single nucleotide frequencies
- Described by an mth order Markov process, that can be represented by a transition matrix

Step 1:Initialization of alignment vectorA (predictive update)

j

1

i

n

Step 2: Calculate motif model for all sequences except one

G A A T T

C A T G T

C A C T T

C A T T G

Probabilistic Algorithms

- Step 3 (expectation):
- Select remaining sequence
- For each window (site) calculate the probability that the sequence in the window is generated by the motif model versus the probability that it is generated by the background model

1

i

n

P(S|M) = 0.0098 x 0.0097 x 0.495 x 0.0098 x 0.245

P(S|B) =

- Assign weight based on this score to this site

Probabilistic Algorithms

Step 4 (Maximization):

- Re-estimate new positions based on the weights calculated in step 3
- Go to step 1

j

j

1

1

i

i

n

n

- Re-iterate until stable motifs are found

- local optima
- EM update alignment vector:
- Select positions with highest score
- Deterministic output but local minimum

- EM update alignment vector:
- global optimum
- Gibbs sampling
- Select positions according to probability distribution
- Stochastic output:
- i.e. result differs each time the algorithm runs
- allows to detect stable motifs
- statistical analysis describes quality of the motif detected

- Gibbs sampling

- Influence of the background model:e.g. p(ATCGT|Bm)=p(AT)p(C|AT)p(G|TC)p(T|CG)
- Compensates for motifs that occur frequently because of the general background composition
- Makes the outcome of the algorithm more robust

Two organisms with similar background model

Two organisms with different background model

Motif scores for probabilistic motif finding algorithms

- Information content (Consensus score)

- Entropy

- Relative entropy (Information content)

- Log likelihood

Result: bacterial O2 responsive element FNR

Probabilistic Algorithms

Does only take into account the degree of conservation

Takes into account the background model

Tradeoff between the degree of conservation and the number of occurrences

- Introduction Multiple Alignments
- Multiple alignment based on HMM
- Motif Finding
- Motif representation
- Algorithm
- Search Space
- Word counting methods
- Probabilistic methods

- Profile Searches
- Introduction

- Exercises

- GENOMICS
- Genomic sequence data

EXPERIMENTAL

High throughput measurements

Literature

- 1. Microarray Datamining
- Preprocessing
- Clustering

- 3. Comparative Genomics
- Genomewide Screening
- Phylogenetic Footprinting

Clusters of coexpressed genes

Novel targets

Novel Conditions

- 2. Sequence Datamining
- Motif Detection

Summarized information

Target Identification

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