Do Funnels Exist

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Do Funnels Exist ?
First Rotation Group Meeting Noa
Rappaport 23/1/04
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Lecture Outline

• What is a funnel Challenges and ideas
• Analysis Methods
• Analysis Performed
• Simulation
• Signal Smoothing
• Cebp Promoter Funnel
• Plans for the future

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DNA Binding Transcriptional Regulators

• Bind DNA in order to influence mRNA
  transcription.
• They control cell growth, cell development and
  differentiation.
• Function by binding to specific DNA sequences
  located upstream to the gene and induce or
  repress gene expression.
• These sequence are usually short (5-15bp) and
  frequently degenerate -gt which confers different
  levels of activity upon different promoters
  (Bulyk et. al)

4
DNA Binding Transcriptional Regulators

• Grouped into families according to sequence and
  structural homologies, such as
• Helix Turn Helix -Zinc-Finger
• Helix-Loop-Helix -Betta Ribon

5
DNA Binding Transcriptional Regulators

• Protein DNA interactions are governed by
• Amino acid base pair interaction
• Van der Waals interactions
• Water mediated protein-DNA hydrogen bonds
• Binding of small ligands
• Homo and hetero protein dimerization
• Binding of an associated transcription factor
• Translational modifications.
• (Marmorstein et al.)

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DNA Binding Transcriptional Regulators
(Jacobson, 1997)
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What is a Funnel ?
funnel
funnel
DNA strand
?G
AGGTTGCAATTTCTTTTTCTATTAGTAGCTAAAAATGGGTCACGTGATCT
ATATTCGAAAGGGGCGGTTGCCTCAGGAA
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Challenges and ideas

• Creating the energy layout of the sequence
• Understanding the hopping\sliding mechanism
• Smoothing of energy signal
• Funnel Qualification
• Multiplicity of Sites
• Same motif different promoters
• Conservation of funnel
• Adi Shamirs problem
• Simulations

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Funnel - Expected Features
Finding time ?t(finding)
Escape time ?t(escape)
DNA strand
Orthologs/Paralogs
Touch down
?
?
Noise Problems
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First Evidences of Funnel

• In the literature, one negative evidence

(Gerland et. al, 2002)
Recent suspect for a funnel for the TF cebp
in the IL18BP promoter
Some qualitative observations in Yeast.
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Some Problems

• Very few TFs have experimentally verified binding
  sites.
• Binding sites are usually predited by points who
  have the greatest score, while this doesnt
  necessarily has to be so.
• Very few (100) structure of DNA protein were
  solved by crystallography and NMR.
• Much information exists regarding PSSMs, but it
  has errors and their correction is a theory on
  its own (pseudo counts).

Analysis has to be performed on predicted sites
and predicted affinity signal.
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Methods of Producing the Affinity Signal

• Exact CalculationPossible, but limited due to
  small DB of solved protein DNA structures
  (proNIT).

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Methods of Producing the Affinity Signal
PSSM Scoring
AGGTTGCAATTTCTTTTTCTATTAGTAGCTAAAAATGGGTCACGTGATCT
ATATTCGA
Score -log(0.50.20.250.70.10.250.1)
Score -log(0.050.20.250.70.20.250.5)
Score -log(0.050.30.250.10.60.250.5)
Scores Vector
4.36
4.98
4.56
And we can keep going
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Methods of Producing the Affinity Signal
PSSM Scoring

• Assumes positions are independent doesnt
  allow for logic.

• Might be problematic for values which are zero.

• Some PSSMs are defective.

• multiplication of the probabilities correlates
  with the thermodynamic constant K.

• Taking the log correlate with calculation of ?G.

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Methods of Producing the Affinity Signal
Bayesian Network Models
(Barash et. al, 2003)
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Possible Approaches
Given a relatively reliable affinity signal,
there could be a few approaches to attack the
problem

• Simulations Giving the kinetic aspect
• Working on real\smoothed signals.
• Scan the space of possible theoretical funnels
  for our 4 demands.

• Analytical Calculations
• Working on real\smoothed signals.
• Scan the space of possible theoretical funnels
  for our 4 demands.

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Monte Carlo Modeling

• Any method which solves a problem by generating
  suitable random numbers and observing that
  fraction of the numbers obeying some property or
  properties.

• The method is useful for obtaining numerical
  solutions to problems which are too complicated
  to solve analytically.

• The name Monte Carlo'' was given by Metropolis
  during the Manhattan Project of World War II,
  because the capital of Monaco was a center for
  gambling.

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Monte Carlo Modeling

• The only requirement is that the physical (or
  mathematical) system can be described by
  probability density functions (pdf's).

• Once the pdf's are known, the Monte Carlo
  simulation can proceed by random sampling from
  the pdf's.

• Many simulations are then performed, and the
  desired result is taken as an average over the
  number of observations.

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Analysis Methods - Simulation

• Represent the space by a discrete lattice.
• Represent the DNA energy layout as a topographic
  terrain.
• Represent the TF as a moving particle.
• Take discrete points of time
• The Lattice represent the cell, and the
  possibility of attaching other exposed sites on
  the DNA.

(Halford et. al 2002)
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Analysis Methods - Simulation
T 0
T 1
T 2
Eureka !
T 3
T 4
TF
site
T 5
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Probability distribution functions
Intermediate State

• Treat the DNA-TF interactions as a set of second
  order elementary reactions.

?G
ka
A B ? A-B complex
kd
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Probability distribution functions

• We have three possible transitions

• Sliding on the DNA Linear diffusion

-10 -5
-5 -10

• Dessociation- Reassociation

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Probability distribution functions

• In the first stage we can assume that the energy
  barrier when moving from the higher energy state
  to the intermediate state is uniform.

• Sliding on the DNA Linear diffusion

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Parameters checked with the simulation
Touch down
Real Promoter vs. Shuffled
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Problems with the simulation

• Activation Energy for
• Sliding
• Attachment-Detachment from the DNA
• Lattice Movement
• Lattice Size
• Lattice Energy

• Assumption on second order elementary reactions.

(Ferreiro et. al 2003)
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Simulation - Results
Coordinates on the DNA
The energy terrain
Number of time steps
PSSM score
Coordinate on the DNA
The energy terrain
Number of time steps
PSSM score
Coordinate on the DNA
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Artificial Funnel - Results
Step function terrain
Step function in comparison to funnel
Funnel terrain
Number of time steps
200 initial points
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Multi-Width-Depth Anal.
200 Initial Positions Stop at endpoint
Funnel width
Distracter depth
Compare
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Two Parabolas Analysis - Results
Width Funnel- 0.1 Width Distracter 0.1 Depth F.
7 Depth D. - 5
Number of time steps
kinetic verification
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Effect of Funnels Width on Finding Time
1000 initial points
Average of time steps
Funnel Width
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Effect of Distracter Depth on Finding Time
Funnel Width 0.1 100 initial points.
Average of time steps
Distracters Depth
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Step Function Terrain
100 initial points Finding time mean
2.9736e004 Finding time std 3.3282e004 Error
in mean finding time 3.3282e003
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Verifying exponential search time in a flat
surface
Step function terrain
Average of time steps
Average of time steps
Distance from end point
Log(Distance) from end point
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Verifying linear search time in an all-funnel
surface
Funnel terrain
Average of time steps
Distance from end point
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Distribution of Finding Times starting from the
same IP
The simulation was run over the following
terrain Three initial points were tested, each
repeated 200 times.
Funnel Edge
right
Left
Finding Time Distribution
Finding Time Distribution
Finding Time Distribution
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Does Funnel Improve Capturing of the TF in its
Vicinity ?

• This question can be regarded by the simulation.
  The TF was put at time zero at the funnels
  minima and a few factors were checked1. The
  first time the TF escaped the funnels
  vicinity.2. The max distance from the funnels
  minima the TF got to.
• Those factors were checked for a set of
  combinations of different widths and depths of
  the funnel. Each time the simulation was let to
  run 100000 time steps, and each such run was
  repeated 100 times.

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Results First Escape Time
Escape time was found to increase with funnels
depth as expected. It can be seen as well that
for increasing funnel width the first escape time
increases for the same distracter depth.
Average of time steps
Distracters Depth
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Results First Escape Time

• The Number of time steps until the first escape
  was compared to the number on a stair-step
  terrain. The following graph was received.
• The number drops on deeper funnels.
• The vicinity was taken to be all the area
  contained between the right and left borders,
  including the lattice.

Mean F.E.T funnel/Mean F.E.T flat
Funnels Depth
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Results Max Distance

• The Maximal distance the TF got to on the DNA was
  measured for a few funnel depths and widths.

Max Distance
Funnels Depth
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Yeast Analysis

• The non coding region of the Yeast genome is
  relatively compact, complete genome available,
  well characterized phylogeny.

• Working on a dataset containing sequences of 4483
  promoter sequences in yeast. For each TF it is
  possible to get a prediction of the promoters it
  is likely to be found on by ScanAce. Then, we can
  generate a score of each point of the promoter.

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Gal4 Analysis

• One of the binding sites of Gal4 was taken. It is
  found in the promoter of the Gelatos permease.
  The area around it was expanded

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Gal4 Transcription Factor

• Zink Finger transcription factor
• Bind as a homodimer to the DNA
• Recognizes inverted CGG half sites repeats with
  11 base pairs spacer

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Gal4 Binding Site
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Finding Time Analysis
kT4
kT4
kT6
kT5
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Finding Time Analysis
kT7
kT8
kT15
kT20
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Vicinity Analysis
Mean FT promoter/Mean FT shuffled
kT
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Same IP analysiskT 4
Original
rand
Original
rand
Window on the Edge of the Funnel (680-700)
Window at the far end (100-120)
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Same IP analysisDistribution
Original promoter - close
Shuffled promoter - close
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Same IP analysisDistribution
Original promoter - far
Shuffled promoter - far
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Using Fourier transform for signal smoothing

• The fast discrete Fourier transform was used to
  transform between the spatial domain and the
  frequency domain.

• In the frequency domain, high frequencies were
  zeroed.

• Transforming back to the spatial domain resulted
  in a smoother signal.

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Using Fourier transform for signal smoothing -
Example
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IL18BP - Promoter
Scanned with cebpß PSSM
Smoothed Signal
Real Signal Smoothed Signal
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Conservation map for cebp signal
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An Unexpected Result
Alignment of Mouse and Human Promoters
Calculate Similarity Percent
Produce random sequences for which the similarity
is in the same percent
Generate scores vector for each random sequence

• Took the mouse and human promoters. Check the
  similarity in sequence. Produce random sequences
  for which the similarity is in the same percent
  (by randomly changing the same X percent of their
  positions). Generate scores vector for each
  random sequence. Check the correlation for each
  of the random sequences with the human funnel.
  Generate distribution of the correlation
  coefficient as a function of the number of
  sequences that have it. Check where the
  mouse-human coefficient is situated on the
  distribution. If it is on this side it means
  that the conservation in the funnel is more than
  due to sequence similarity but more due to funnel
  similarity.
• Results
• Comparison between the conservation pattern
  between the human and mouse promoter and between
  the human promoter and my random promoter

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An Unexpected Result
Generate scores vector for each random sequence
Smooth it by Fourier
Check the correlation for each of the random
sequences with the human funnel
Generate scores vector for each random sequence
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An Unexpected Result
Check where the mouse-human correlation
coefficient is situated on the distribution
Expectation it will be localized in the right
hand side of the distribution, having high
p-value, meaning the reason for the funnels
similarity is sequence similarity.

• Result

The p-value for the mouse-human signals is zero.
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Scanning human promoters with cebp PSSM
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Scanning IL18BP promoter with human PSSMs
Original Promoter
Shuffled Promoter
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Scanning IL18BP promoter with Statx and IRF PSSMs
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Methods of Producing the Affinity Signal
MatInspector Algorithm
On the Motif
Employ an alignment algorithm
Calculate the nucleotide distribution matrix
Calculate ci value for each position
Define a core region
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Methods of Producing the Affinity Signal
MatInspector Algorithm
Scanning
Calculate the core similarity for each position
of the sequence
Calculate the matrix similarity if core
similarity reaches threshold
Binding Sites - the sequences that reach the
minimum core and matrix similarity thresholds.
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For the Future

• Add hopping

• Large Scale Analysis for all yeast promoters

• Analytical Calculation for hopefully reducing
  run-time

• Optimization of the scoring method

• Use of DB of known binding sites verified
  experimentally with high credibility.

• Analysis over the parameters space

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For the Future

• Develop a method for MFA

• Check for all the criterions with other methods
  of shuffling e.g. k-mer preserving.

• Analytical calculation for specific protein and
  DNA interaction.

• Use Gillespie algorithm

• If funnels exists, check for common features of
  promoters containing them.

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Acknowledgments
Thanks to Tzachi, Ran, , Reut, Arren and
everyone else !
Igor
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PSSM
PSSM Position Specific Scoring Matrix.
A
T
C
G
66
ScanAce

• ScanACE (Scans for Nucleic Acid Conserved
  Elements) is a program which scans DNA sequence
  for elements which match a DNA motif.

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Simulations Methods
Gillsepie Algorithm

• An algorithm for simulating system with multiple
  reaction channels and multiple chemical species.

• Consider a system of r chemical reactions

• For each time step, the system is exactly at one
  state.

• A transition occurs when executing a reaction,
  and then the state changes.

• Gillespies direct method calculates which
  reaction occurs next and when it occurs.

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Simulations Methods
Gillsepie Algorithm

• The probability for reaction channel µ to be the
  next reaction

• Derive from the probability distribution
  for times

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Monte Carlo Modeling

• Probability distribution functions (pdf's) - the
  physical (or mathematical) system must be
  described by a set of pdf's.

• Random number generator - a source of random
  numbers uniformly distributed on the unit
  interval must be available.

• Sampling rule - a prescription for sampling from
  the specified pdf's, assuming the availability of
  random numbers on the unit interval, must be
  given.

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Monte Carlo Modeling

• Scoring (or tallying) - the outcomes must be
  accumulated into overall tallies or scores for
  the quantities of interest.

• Error estimation - an estimate of the statistical
  error (variance) as a function of the number of
  trials and other quantities must be determined.

• Variance reduction techniques - methods for
  reducing the variance in the estimated solution
  to reduce the computational time for Monte Carlo
  simulation

• Parallelization and vectorization - algorithms to
  allow Monte Carlo methods to be implemented
  efficiently on advanced computer architectures.

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Probability distribution functions
Intermediate State
?G
ka
A B ? A-B -gt C complex
kd