CisModule: De novo discovery of cis-regulatory modules by hierarchical mixture modeling

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CisModule De novo discovery of cis-regulatory
modules by hierarchical mixture modeling

• Qing Zhou and Wing Wong
• Slides by Qiaozhu Mei and
• Hong Cheng
• Presented by Saurabh Sinha

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Existing Methods

• Existing motif discovery methods
• Experimental methods
• DNase footprinting and gel-mobility shift assay
• Computational methods
• EM algorithm
• Gibbs sampler
• Word enumeration
• Dictionary model
• A good number of useful TF motifs found, but
  still many important TF motifs unexplored.

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Cis-regulatory Modules (CRMs)

• Observation Most eukaryotic genes are controlled
  by cis-regulatory modules (CRMs) each consisting
  of multiple TF-binding sites (TFBSs).
• When no prior knowledge on TFs is available, we
  must resort to de novo motif discovery algorithm.

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CRMs Discovery and Motif Estimation

• Greater sensitivity and specificity can be
  achieved for motif discovery by considering the
  colocalization of different TFBSs
• search for modules and motifs simultaneously.
• Module discovery and motif estimation is tightly
  coupled
• Motif patterns and binding sites are essential
  for predicting regulatory modules
• Discovery of modules will greatly improve the
  performance of motif detection.

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Method

• Goal search for binding sites for K different
  TFs within the CRMs of a given set of sequences
• A Hierarchical Mixture (HMx) model to generate
  the sequence
• 1st level the sequences are viewed as a mixture
  of CRMs, each of length l, and pure background
  sequences outside the modules
• 2nd level each module is modeled as a mixture of
  motifs and within-module background.
• Bayesian inference to estimate locations of
  modules, TFBSs and motif patterns based on the
  joint posterior distribution.

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HMx Model as a Stochastic Process

• Treat HMx model as a stochastic machinery to
  generate sequences.
• From the first sequence position, make a series
  of random decisions of whether to initiate a
  module of length l or generate a letter from the
  background model.
• Inside a module, If a site for the kth motif was
  initiated at position n, then generate wk letters
  from its PWM and place them at n, nwk-1,
  otherwise generate a letter from the background.
• After reaching the end of the current module,
  decide whether sampling from the background or
  initiating a new module.

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HMx Illustration
(A) Unaligned motif sites (Consider motifs
independently)
(B) Aligned motif sites represented by a
multinomial model (representation of a motif)
(C) Cis-regulatory regions of coregulated genes
(consider modules and motifs in a hierarchical
manner)
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Inside the Model

• Data Observed S
• S Set of sequences
• Model variables ?
• ?0 - first-order Markov Chain to generate
  background
• ?k - product multinomial parameters (PWM) for a
  motif k
• ? (?0, ?1, ?2,, ?K)
• r - probability of a module start
• qk - probability of starting a site for motif k
• q (q0,q1,,qK)
• wk - width of motif k
• W (w1,w2,,wK)
• Hidden variables (missing data) M A
• M - indicators for a module start
• S(M) sequence of modules S(Mc) sequence of
  background outside modules
• Ak - indicators for start positions for sites
  of motif k
• A (A0,A1,,Ak)
• Model parameters
• l - length of modules
• K - number of motifs

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Inside the Model (cont.)

• Under the HMx model, the complete sequence
  likelihood with M and A given is
• The joint posterior distribution is
• Priors
• ?(? wk) a Dirichlet distribution with
  parameter ?k
• ?(q) a Dirichlet distribution with parameter ?
• ?(wk) Poisson(w0)
• ?(r) Beta(a, b)

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Bayesian Inference

• Problem how to estimate ? (?, q, W, r)
• Regarded M and A as missing data and used the
  Gibbs sampler to perform Bayesian inference.
• With a random initialization, the algorithm
  CisModule iteratively cycles through the steps of
  parameter update and module-motif detection.
• Given current modules and motif sites (M and A),
  update all the parameters sample ? from
  conditional prob. ? M, A, S
• Given current values of the parameters, sample
  modules and motif sites from the conditional
  distribution

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Sampling ? given M and A

• ? (?, q, r, W) parameters of model
• Align binding sites of each motif, calculate PWM
  from these to get samples of ?
• q (motif transition probabilities) derived from
  total number of sites of each motif
• r (module probability) derived from number of
  modules prescribed by M
• W (motif widths) sampled by Metropolis strategy

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Sampling M and A given ?

• Need to pick (M,A) with Pr(M,A ?,S)
• Use forward summation to compute
• Then use backward sampling to generate the
  module indicators (i.e., M) and the site
  indicators (i.e., A)

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Forward Summation

• Forward Summation
• where is the probability of observing
  
• given that it is within a module.

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Backward Sampling

• Starting from n L.
• At position n, decide whether
• (i) is at the last position of a module,
  or
• (ii) is from the background.
• Probabilities of these events are proportional to
  An(?) and Bn(?) respectively
• Depending on choosing event (i) or (ii), move to
  position n-l or n-1.
• Repeat the binary decision process.
• In this way, generate all the module indicators.
• Then, generate motif indicators in a similar
  manner

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Algorithm Illustration
sample M, A from conditional prob. M,A ?, S -
Given ?, how to decode the sequence? Two-phase
Sampling..
sample ? from conditional prob. ? M, A, S -
Given M, A, how to estimate ?? Alignments!
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Parameter selection

• In the previous discussion, module length l and
  TF number K are left as user-input parameters.
• How to determine them when no prior knowledge
  provided?
• For l An extra conditional sampling by a
  Metropolis update can be performed to determine
  the most likely module length.
• Metropolis ration

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Strategies on l and K

• About the TF number K.
• Formulated as a Bayesian model selection problem.
• Then run CisModule with K1,..,Km, where with Km
  the algorithm stops detecting new motifs. Treat
  the K in 1,, Km-1 that maximize the posterior
  odds as the estimated K.

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Results

• Simulation Studies
• Motif E2F, YY1 and c_MYC
• Background sequences are generated by a
  first-order Markov chain .
• Module Predictions
• Total length, 2,009 and 4,108 bp on average,
  excess rates 0.5 and 2.7
• Coverage of true sites, 84.3 and 94.0
• Motif discovery
• Comparison with MEME and BioProspector
• Improvement over MEME and BP

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Output Result

• By using the samples from the joint posterior
  distribution, and can be estimated.
• The top -mers that are most frequently
  sampled as sites for the kth motif are aligned as
  output sites.
• The modules are inferred by the marginal
  posterior probability of each sequence position
  being sampled as within modules.
• The positions where this probability gt0.5 are
  output as modules.

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Simulation Results
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Homotypic Regulatory Modules in Drosophila

• Motif
• Bicoid (Bcd),Hunchback(Hb) and Kruppel (Kr)
• Results

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Muscle-Specific Regulatory Regions

• Motif
• Mef-2, TEF and SRF
• Results

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Discussion

• HMx model
• Capture the spatial correlation between different
  binding sites
• CisModule
• A Bayesian module sampler to infer the motif
  modules and the binding sites for a set of TFs
• May be trapped in local modes.
• Need multiple trials.
• Can use available prior informatioin

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Future Work

• Incorporate the information from comparative
  genomics into CisModule.
• Greater prior probabilities for modules and sites
  can be assigned to the regions that are highly
  conserved across species of appropriate
  evolutionary distances.
• The HMx model captures the colocalization
  tendency of cooperating TFBSs but not their order
  or precise spacing.
• Additional refinements to the model may improve.