LOGOS: a modular Bayesian model for de novo motif...

LOGOS: a modular Bayesian model for

de novo motif detection

Eric Xing

�Wei Wu

�

Michael Jordan�

Richard Karp

�

�

University of California, Berkeley�

epxing,jordan,karp

�@cs.berkeley.edu

�

Lawrance Berkeley National [email protected]

13 Aug 2003

CSB2003

The cis-regulatory machinery of eukaryotic organisms

CSB2003 Eric Xing et al. — 1

A DNA motif (Gcn4)

Motif features:

� PSMD: position-specific multinomial distribution� PWM: position weight matrix


Meta-sequence features

� Shape bias: typical patterns of site-conservativeness due to binding surfaceconstraints.

� Spatial organization of motifs: dependencies between motif instances.

— Believed to be crucial in distinguishing biologically meaningful motifs from random

background or trivial recurring patterns.

Our goal: Build statistical models for motif-bearing sequences that:

� exploit the meta-sequence features and provide improved sensitivity tobiologically plausible motifs

� can generalize easily to various motifs and handle complex cis-regulatorystructures

� can make use of biologically identified motifs for de novo detection


Introduction

� Using a hierarchical Bayesian Markovian model to posit hiddendependency structures of motifs

� Exploit this model to predict locations of novel motifs

� Talk outline

� Modeling generation of motif instances with a hidden MarkovDirichlet-multinomial model� Modeling motif instance distribution with a hidden Markov grammar� The LOGOS motif model and a variational EM algorithm for motifdetection� Experiments� Future work


The Local Alignment Model— for multiple-aligned motif instances


Signature internal structures of motifs

Shape bias:

gal4:

0

1

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s

5′

1

C2

G3

CG

4CGA

5TA

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G3′

gal4-permute:

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pho4:

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pho4-permute:

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Two yeast motifs and their column-permuted versions.

� The conservativeness of sites in the motif may be spatially dependent.

� The conserved sites are more likely to occur consecutively and possibly followed (or

preceded) by heterogeneous sites that are also consecutive.� The “shape” is only associated with the conservativeness pattern of a motif PWM, but

not with any specific consensus sequence of the motif.


A standard motif alignment model

The Product Multinomial (PM) Model:

A 1 A 2 A M...={ }

1: AAAAGAGTCA2: AAATGACTCA. AAATGAGTCA . GAATGAGTCAM: AAAAGAGTCA

A=

θLθ2θ1

M M M

...A Am,2 Am,Lm,1

� The nucleotide distributions at different sites within the motif are assumedto be independent.

� Limitation:

� Unable to capture site dependence and shape preference in motifs


The PSMD simplex and the Dirichlet Distribution

Each possible position-specific nucleotide distribution corresponds to a point in the simplex.


A Markov model for PSMD-simplex sequence

α 1 α 3

α 2

α 4

The PSMD-simplex sequence defines a structural prior for the PWM.


Hidden Markov Dirichlet-multinomial model (HMDM)

I

s s

θ θ θ

M M M

1 2 L

1 2 L

...

...

s

A Am,2 Am,Lm,1

α

� Parameters (for all motifs):� �

sets of 4-dimensional Dirichlet parameter � � � � ��

.� Initial probability � and transition probability

�

of an HMM.

� Random variables (for each motif site):� The site prototype indicator indexing different distributions on thePSMD simplex is represented by a multinomial r.v. �� .� The PSMD associated with the site is represented by a Dirichlet r.v.

�� .� The nucleotide content of the site is represented as a multinomial r.v.�� .


The Global Distribution Model— for patterns of motif occurrences in genomic

sequences


Global organization of motif instances

cis-regulatory modules (Davidson [2001]):

� There exist instance (resp. cluster)-level dependencies between motifs(resp. modules).


A conventional global model

The uniform and independent (UI) start-position model:

� The locations of motif instances are assumed to be independently sampledfrom a uniform distribution over possible positions.

� Limitations:

� instances can overlap� does not capture inter-instance, inter-motif dependences


A hidden Markov model for motif occurrences

The state-transition grammar of the global HMM:

b(1)

(1) (1) (1)...1 2 L

(1’)... 1L(1’) 2 (1’)

β1

11/2

1/2

1

1

1

1

β1,i

β i,1

1,0

1

1

β

b(0)

0,0

αi,0β0,i αk,0 α1,0β0,1

β0,k

β

b(k)

(k) (k) (k)...1 2 L

(k’)...L(k’) 2 (k’) 1

k

k

1/2

1/2

1

1

1

1

βk,i

β i,k

k,0

1

1

...

� Latent states:

� all possible sites within motifs on the forward and reverse complementary strand� intra-cluster backgrounds� inter-cluster (global) background

� Observed output: unannotated sequence of nucleotides.

� Parameters: HMM parameters

��

; motif PWMs

�

; background frequencies

�! .


A modular motif model for de novo motif detection

� The integrated LOcal and GlObal motif Sequence model

� The occurrences of motifs in a DNA sequence, as indicated by ", aregoverned by a global distribution model # � $ " %& ' ( .� For each type of motif, the nucleotide sequence pattern shared by all itsinstances admits a local alignment model #*) $+ $ " , ( % " & � (

.� Assume that the background non-motif sequences are modeled by asimple conditional model, # $ ,.- + $ , " ( % " �0/ (

.

� The likelihood of a regulatory sequence , is:

# $ , %& ( �1

# � $ " % & ' ( #) $ , % " & � (

�1

# � $ " %& ' ( #) $+ % " & � ( # $ ,- + % " �/ (


Inference and parameter estimation

� The inference and learning problems:

� Maximum a posteriori (MAP) prediction of motif locations� Bayesian estimation of motif PWMs

A variational EM algorithm for LOGOS

Variational “E” step: Compute the

23 4, the expected count of each

nucleotide, for each motif and each site within it, via inference in theglobal motif model given

2576 � 4and sequence ,.

Variational “M” step: Compute the Bayesian estimation of the PWM, innatural parameter form

2 56 � 4, via inference in the local motif alignment

model given

23 4

.


Experiments:

� Semi-synthetic sequence: random background (300 8600bp) with genuinemotif instance(s) planted at known positions.

� Real genomic sequences: 500-5000 bp fragments in the genomicsequences flanking the motif instances.


Detecting a single motif using HMDM model

0 20 40 600

1

2

abf1 (21)

0 20 40 600

1

2

gal4 (14)

0 20 40 600

1

2

gcn4 (24)

0 20 40 600

1

2

gcr1 (17)

0 20 40 600

1

2

mat−a2 (12)

0 20 40 600

1

2

mcb (16)

0 20 40 600

1

2

mig1 (11)

0 20 40 600

1

2

crp (24)

abf1 gal4 gcn4 gcr1 mat mcb mig1 crpHMDM(f) 0.81 0.82 0.71 0.65 0 0 0.73 0.58HMDM(e) 0.77 0.89 0.63 0.12 0.67 0 1.00 0.54HMDM(b) 0.12 0 0 0.59 0.92 0.72 0.91 0.04

PM 0.14 0 0 0.41 0.79 0.13 0.64 0.04

� Result: different HMDMs can be used for different “classes” of motifs.

� can use #-value to identify best-performing model.


Detecting multiple motif instances using LOGOS

� We compare three variants of LOGOS, ordered with decreasing modelexpressiveness,

� HMDM+HMM (LOGOS 9 9)� PM+HMM (LOGOS : 9)� PM+UI (LOGOS :; )

motif LOGOS < < LOGOS = < LOGOS =>

name FP FN FP FN FP FNabf1 0.31 0.21 0.68 0.20 0.79 0.91gal4 0.16 0.16 0.19 0.15 0.29 0.79gcn4 0.18 0.24 0.61 0.28 0 0.96gcr1 0.20 0.21 0.34 0.20 0.33 0.94mat 0.07 0.03 0.36 0 0.50 0.96mcb 0.37 0.09 0.36 0.08 0.33 0.94mig1 0.08 0 0.09 0 0.98 0.10crp 0.38 0.34 0.27 0.53 0 0.95


Analyzing Yeast promoter sequences using LOGOS

set LOGOS MEME AlignACE seqname FP FN FP FN FP FN no.abf1 0.79 0.65 1.00 1.00 0.53 0.61 20csre 0.44 0.17 0.78 0.50 0.80 0.50 4gal4 0.13 0.07 0.17 0.29 0.33 0.14 6gcn4 0.35 0.18 1.00 1.00 0.33 0.56 9gcr1 0.29 0.61 1.00 1.00 0.45 0.46 6hstf 0.86 0.55 0.60 0.56 0.85 0.67 6mat 0.42 0 0.38 0.56 0.25 0.25 7mcb 0.47 0.25 0.20 0.33 0.25 0.25 6mig1 0.81 0.28 1.00 1.00 0.83 0.79 22pho2 0.90 0.50 1.00 1.00 1.00 1.00 3swi5 0.76 0.50 1.00 1.00 0.94 0.75 2uash 0.83 0.68 1.00 1.00 0.92 0.95 18


Analyzing Drosophila promoter sequences

� Motif patterns derived from biologically identified motif instances (Berman et al. [2002]).

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bcd cad hb kni kr

� Motif patterns detected by LOGOS in the promoter regions (600-5000bp) of 9 Drosophilagenes.

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� Motif patterns detected using conventional models.

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Future work

� Background model: higher order HMM

� Incorporating expression, binding, comparative genomic data

� Analyzing eucaryotic cis-regulatory networks


LOGOS: a modular Bayesian model for de novo motif...

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