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### Genome evolution:

Lecture 12: Evolution of regulatory sequences

Beyond Protein Coding Sequences

Non coding fraction of the genome:

- E. coli : 12%
- Yeast : 27%
- Fly : 76%
- Human : 97.6%

How biological functions of non-coding sequence can be defined?

Sequence specific transcription factors

- Sequence specific transcription factors (TFs) are a critical part of any gene activation or gene repression machinery
- TFs include a DNA binding domain that recognize specifically “regulatory elements” in the genome.
- The TF-DNA duplex is then used to target larger transcriptional structure to the genomic locus.

Lactose Repressor

Sequence specificity is represented using consensus sequences or weight matrices

- The specificity of the TF binding is central to the understanding of the regulatory relations it can form.
- We are therefore interested in defining the DNA motifs that can be recognize by each TF.
- A simple representation of the binding motif is the consensus site, usually derived by studying a set of confirmed TF targets and identifying a (partial) consensus. Degeneracy can be introduced into the consensus by using N letters (matching any nucleotide) or IUPAC characters (representing pairs of nucleotides, for examlpe W=[A|T], S=[C|G]
- A more flexible representation is using weight matrices (PWM/PSSM):
- PWMs are frequently plotted using motif logos, in which the height of the character correspond to its probability, scaled by the position entropy

ACGCGT

ACGCGA

ACGCAT

TCGCGA

TAGCGT

In vitro TF binding energy is approximated by weight matrices

We can interpret weight matrices as energy functions:

This linear approximation is reasonable for most TFs.

Yeast Leu3 data

(Liu and Clarke, JMB 2002)

In-vivo TF binding affinity is approximated by weight matrices

- s

- s

Chromatin ImmunoPrecipitation (ChIP)

Ume6

11.5

Cross-link and sheer

Average PWM energy

Stronger prediction

ImmunoPrecipitation

5.5

ChIP ranges

Stronger binding

Tanay. Genome Res 2006

TF binding affinity is kinetically important, with possible functional implications

Kalir et al. Science 2001

TFs are present at only a fraction of their optimal sequence targets. Binding is regulated by co-factors, nucleosomes and histone modifications

Heinzman et al. Nature Genetics, 2007)

TFs are present at only a fraction of their optimal sequence targets. Binding is regulated by co-factors, nucleosomes and histone modifications

Heinzman et al. Nature Genetics, 2007)

Specific proteins are identifying enhancersHere are studies of p300 binding in the developing mouse brain

(visel et al. Nature 2009)

TFBSs are clustered in promoters or in “sequence modules”

- The distribution of binding sites in the genome is non uniform
- In small genomes, most sites are in promoters, and there is a bias toward nucleosome free region near the TSS
- In larger genomes (fly) we observe CRM (cis-regulatory-modules) which are frequently away from the TSS. These represent enhancers.
- A single binding site, without the context of other co-sites, is unlikely to represent a functional loci

Discriminative scores for motifs

- So far we used a generative probabilistic model to learn PWMs
- The model was designed to generate the data from parameters
- We assumed that TFBSs are distributed differently than some fixed background model
- If our background model is wrong, we will get the wrong motifs..
- A different scoring approach try to maximize the discriminative power of the motif model.
- We will not go here into the details of discriminative vs. generative models, but we shall exemplify the discriminative approach for PWMs.

High specificity discriminator

High sensitivity discriminator

Lousy discriminator

Hypergeometric scores and thresholding PWMs

Hyper geometric probability

(sum for j>=k is the hg p-value)

Positive

Number of sequences

True positive

PWM score threshold

For a discriminative score, we need to decide on both the PWM model and the threshold.

Constructing a weight matrix from aligned TFBSs is trivial

- This is done by counting (or “voting”)
- Several databases (e.g., TRANSFAC, JASPAR) contain matrices that were constructed from a set of curated and validated binding site
- Validated site: usually using “promoter bashing” – testing reported constructs with and without the putative site

Transfac 7.0/11.3 have 400/830 different PWMs, based on more than 11,000 papers

However, there are no real different 830 matrices out there – the real binding repertoire in nature is still somewhat unclear

High density arrays quantify TF binding preferences and identify binding sites in high throughput

- Using microarrays (high resolution tiling arrays) we can now map binding sites in a genome-wide fashion for any genome
- The problem is shifting from identifying binding sites to understanding their function and determining how sequences define them

Harbison et al., Nature 2004

Direct measurements of the in-vitro binding affinity of 8-mers and DNA binding domains (here just a library of homeodomains, from Berger et al. 2008)

Profiling binding affinity to the entire k-mer spectrum provide direct quantification of in-vitro affinity (Badis et al., 2009)

104 TFs

Heatmap of 2D hierarchical agglomerative clustering analysis of 4740 ungapped 8-mers over 104 nonredundant TFs, with both 8- mers and proteins clustered using averaged E-score from the

two different array designs.

8-mers

What kind of biological function is naturally selected?

Discrete and deterministic “binding sites” in yeast as identified by Young, Fraenkel and colleuges

In fact, binding is rarely deterministic and discrete, and simple wiring is something you should treat with extreme caution.

The Halpern-Bruno model for selection on affinity

We work on deriving the substitution rate at each position of the binding site, given its observed stationary frequency. We are assuming that the fitness of the site is defined by multiplying the fitness values of all loci. This means fitness is generally linear in the binding energy!

According to Kimura’s theory, an allele with fitness s and a homogeneous population would fixate with probability:

Assuming slow mutation rate (which allow us to assume a homogenous population) and motifs a and b with relative fitness s the fixation probabilities (chance of fixation given that mutation occurred!) are:

If p represent the mutation probability, and p the stationary distribution, and if we assume the process as a whole is reversible then:

(Halpern and Bruno, MBE 1998)

The Halpern-Bruno model for selection on affinity

The HB model is limited for the study of general sequences.

When restricting the analysis to relatively specific sites, HB is not completely off

Moses et al., 2003

Testing the general binding energy – fitness correspondence

Expected and observed energy distribution in E.Coli CRP sites (left) and background (right)

- While E(S) is approximated by a PWM, F(E) is unlikely to be linear
- Assume that the background probability of a motif a is P0(a). In detailed balance, and assuming the fitness of a at functional sites is F(a), the stationary distribution at sites can be shown to be:

- If we collapse all sites with binding energy E (and hence the same F(a)=F(E(a))

- The entire genome should behave like a mixture of background sequance and functional loci:
- So we can try and recover Q(E) and therefore F(E) from the maximum likelihood parameters fitting an empirical W(E)

Comparison of CRP energies in E.coli and S. typhimurium

Inferred F(E), is shown in Orange

(Hwa and Gerland, 2000-)

Mustonen and Lassig, PNAS 2005

Altered affinity

CACGCGTT

CACACGTT

Rate?

Selection?

TFBS evolution: purifying selection and conservationTF1

TF1

Similar function

Disrupted function

CACGCGTT

CACGCGTA

CACGCGTT

CACGAGTT

Neutral evolution

Low rate

purifying selection

TF1

TF2

Altered function

CACGCGTT

CACACGTT

Low rate

purifying selection

Kellis et al., 2003

Binding sites conservation: heuristic motif identification

Kellis et al., 2003

Analyzing k-mer evolutionary dynamics

- Instead of trying to identify conserved motifs try to infer the evolutionary rate of substitution between pairs of k-mers
- Start from a multiple alignment and reconstruct ancestral sequences (assuming site independence, or even max parsimony)
- Now estimate the number of substitution between pairs of 8-mers, compare this number to the number expected by the background model
- Do it for a lot of sequence, so that statistics on the difference between observed and expected substitutions can be derived

the Reb1 cluster: selection hints

toward multi modality of Reb1

Saccharomyces TFBS Selection NetworkNodes: octamers

node

conservation

conserved @ 2SD

conserved @ 3SD

otherwise

Arcs: 1nt substitution

arc

Rate

Selection

Normal

neutral

Low

negative

not enough stat

Tanay et al., 2004

high affinity to high

affinity motifs

0.3

0.2

0.1

0

-5

-4

-3

-2

-1

0

1

2

3

log delta affinity

High Affinity

(Kd < 60)

Substitution changing

high affinity to low

affinity motifs

High rate subs.

Meidum Affinity

(400 > Kd > 60)

Leu3 selection networkSubstitution rate

TF4

AAATTT

AATTTT

AAAATT

ACGCGT

TCGCGT

ACGCGT

TF3

TF1

GATGAG

GATGCG

GATGAT

CACGTG

CACTTG

All the rest

TF2

TGACTG

TGAGTG

TGACTT

A simple transcriptional code and its evolutionary implicationsThe Halpren-Bruno model for selection on affinity

The basic notion here is of the relations between sequence, binding and function/fitness

Sequence

Binding energy

Function

We argued that E(S) can be approximated by a PWM

F(E) is a completely different story, for example:

Is there any function at all to low affinity binding sites?

Is there a difference between very high affinity and plain strong binding sites?

Are all appearances of the site subject to the same fitness landscape?

More tests for possible conservation of low binding energy sites

Simulation

(Neutral, context aware)

S. mikitae

S. cerevisiae

High affinity

ΔE

ΔE

..

..

ΔE

ΔE

..

..

Low affinity

S

S

Binding site conservation

Conservation of total

energy

More tests for possible conservation of low binding energy sitesReb1

Conservation score

binding energy percentile

Gcn4

Ume6

Cbf1

Mbp1

Conservation score

binding energy percentile

binding energy percentile

binding energy percentile

binding energy percentile

Tanay, GR 2006

Evolutionary dynamics of transcription factor binding (mammals)

Shared binding loci: 4%

Schimdt et al. Science 2010

Evolutionary dynamics of transcription factor binding (flies) – correlates with the sequence

Bradley et al. PLoS biology 2010

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