CS 5263 Bioinformatics Reverse-engineering Gene Regulatory Networks.
Transcript of CS 5263 Bioinformatics Reverse-engineering Gene Regulatory Networks.
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CS 5263 Bioinformatics
Reverse-engineering Gene Regulatory Networks
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Genes and Proteins
Transcriptional regulation
Translational regulation
Post-translational regulation
mRNA degradation
Gene (DNA)
mRNA
Protein
Transcription (also called expression)
Translation
(De)activation
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Gene Regulatory Networks
• Functioning of cell controlled by interactions between genes and proteins
• Genetic regulatory network: genes, proteins, and their mutual regulatory interactions
gene 1
gene 2 gene 3
activator
repressor
repressor
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Reverse-engineering GRNs
• GRNs are large, complex, and dynamic• Reconstruct the network from observed gene expression
behaviors– Experimental methods focus on a few genes only– Computer-assisted analysis: large scale
• Since 1960s– Theoretical study mostly
• Attracting much attention since the invent of Microarray technology
• Emerging advanced large-scale assay techniques are making it even more feasible (ChIP-chip, ChIP-seq, etc.)
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Problem Statement
• Assumption: expression value of a gene depends on the expression values of a set of other genes
• Given: a set of gene expression values under different conditions
• Goal: a function for each gene that predicts its expression value from expression of other genes– Probabilistically: Bayesian network– Boolean functions: Boolean network– Linear functions: linear model– Other possibilities such as decision trees, SVMs
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Characteristics
• Gene expression data is often noisy, with missing values
• Only measures mRNA level– Many genes regulated not only on the
transcriptional level
• # genes >> # experiments. Underdetermined problem!!!!
• Correlation causality• Good news: Network structure is
sparse (scale-free)
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Methods for GRN inference
• Directed and undirected graphs– E.g. KEGG, EcoCyc
• Boolean networks– Kauffman (1969), Liang et al (1999), Shmulevich et al (2002),
Lähdesmäki et al (2003)• Bayesian networks
– Friedman et al (2000), Murphy and Mian (1999), Hartmink et al (2002)
• Linear/non-linear regression models– D’Haeseleer et al (1999), Yeung et al (2002)
• Differential equations– Chen, He & Church (1999)
• Neural networks– Weaver, Workman and Stormo (1999)
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Boolean Networks
• Genes are either on or off (expressed or not expressed)
• State of gene Xi at time t is a Boolean function of the states of some other genes at time t-1
X Y Z
X’ Y’ Z’
X Y Z X’ Y’ Z’
0 0 0 0 0 0
0 0 1 0 0 0
0 1 0 1 0 1
0 1 1 0 0 1
1 0 0 0 1 0
1 0 1 0 1 0
1 1 0 1 1 1
1 1 1 0 1 1
X’ = Y and (not Z)
Y’ = X
Z’ = Y
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Learning Boolean Networks for Gene Expression
• Assumptions:– Deterministic (wiring does not change)– Synchronized update– All Boolean functions are probable
• Data needed: 2N for N genes. (In comparison, N needed for linear models)
• General techniques: limit the # of inputs per gene (k). Data required reduced to 2k log(N).
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Learning Boolean Networks
• Consistency Problem– Given: Examples S: {<In, Out>}, where
• In {0,1}k, output {0,1}– Goal: learn Boolean function f such that for every <In, Out>
S, f(In) = out.– Note:
• Given the same input, the output is unique.• For k input variables, there are at most 2k distinct input
configurations. – Example:
<001,1> <101,1> <110,1> <010,0> <011,0> <101,0> 1,1 5,1 6,1 2,0 3,0 5,0
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Learning Boolean Networks
<001,1><101,1> <110,1> <010,0> <101,1><101,0>
?100?*1?
no clash -> consistency.
Question marks -> undetermined elements
O (Mk), M is # of experiments
N genes, Choose k from N,
N * C(N, k) * O(MK)
Best-fit problem: Find a function f with minimum # of errors
Limited error-size problem: Find all functions with error-size within max
Lähdesmäki et al, Machine Learning 2003;52: 147-167.
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State space and attractor basins
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What are some biological interpretations of basins and attractors?
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Linear Models
• Expression level of gene at time t depends linearly on the expression levels of some genes at time t-1
X1
X2
X3
X1
X2
X3
t-1 tW11
W21W31
W33
W32
W31
o Basic model: Xi (t) = Σj Wij Xj(t-1)
o Xi’ (t) = Σj Aij Xj(t), where Xi(t) can be measured, Xi’ (t) can be estimated from Xi(t)
o In matrix form: X’NM = ANN XNM , where M is the number of time points, N is the number of genes
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Linear Models (cont’d)
• X’NM = ANN ·XNM
• ANN: connectivity matrix, Aij describes the type and strength of the influence of the jth gene on the ith gene.
• To solve A, need to solve MN linear equations
• In general N2 >> MN, therefore under-determined => infinity number of solutions
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Get Around The Curse of Dimensionality
• Non-linear interpolation to increase # of time points
• Cluster genes to reduce # of genes• Singular Value Decomposition (SVD)
– A = A0 + CNN · VTNN, where cij = 0 if j > M
– Take A0 as a solution, guaranteed smallest sum of squares.
• Robust regression– Minimize # of edges in the network– Biological networks are sparse (scale-free)
Cij 0
CNN
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0
1
2
3
4
5
6
0 2 4 6
Robust Regression
• A = A0 + CNN · VTNN,
• Minimizing # of non-zero entries in A by selecting C– Set A = 0, then C · VT
= -A0 , solve for C.
– Over-determined. (N2 equations, MN free variables).
• Robust regression– Fit a hyper-plane to a set of points
by passing as many points as possible
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Simulation Experiments
SVD + Robust Regression SVD alone
Yeung et al, PNAS. 2002;99:6163-8.
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Simulation Experiments (cont’d)Linear System
Nonlinear System close to steady state
Does not work for nonlinear system not close to steady state
Scale-free property does not hold on small networks
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Bayesian Networks• A DAG G (V, E), where
– Vertex: a random variable – Edge: conditional distribution for a
variable, given its parents in G.
• Markov assumption: i, I (Xi, non-descendent(Xi) | PaG(Xi))e.g. I(X3, X4 | X2), I(X1, X5 | X3)
X1
X5
X4X3
X2
Chain rule: P(X1, X2, …, Xn) = Πi P(Xi | PaG(Xi), i = 1..n
P (X1, X2, X3, X4, X5) = P(X1) P(X2) P(X3 | X1, X2) P (X4 | X2) P(X5 | X3)
Learning: argmaxG P (G | D) = P (D | G) * P (G) / C
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Bayesian Networks (Cont’d)
• Equivalence classes of Bayesian Networks– Same topology, different edge
directions– Can not be distinguished from
observation• Causality
– Bayesian network does not directly imply causality
– Can be inferred from observation with certain assumptions:
• no hidden common cause• ……
A B
C
A B
C
I (A, B | C)
A B
C Hidden variable
A B
CPDAG
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Bayesian Networks for Gene Expression
• Deals with noisy data well, reflects stochastic nature of gene expression
• Indication of causality• Practical issues:
– Learning is NP-hard– Over-fitting– Equivalent classes of
graphs• Solution:
– Heuristic search, sparse candidate
– Model averaging– Learning partial models
Gene E
Gene D Gene A
Gene C
Gene B
Other variables can be added, such as promoters sequences, experiment conditions and time.
(D | E):Multinomialor linear
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Learning Bayesian Nets
• Find G to maximize Score (G | D), where– Score(G | D) = Σi Score (Xi, PaG(Xi) | D)
• Hill-climbing– Edge addition, edge removal, edge reversal
• Divide-and-conquer– Solve for sub-graphs
• Sparse candidate algorithm– Limit the number of candidate parents for each
variables. (Biological implications – sparse graph)– Iteratively modifying the candidate set
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Partial Models (Features)
A BA B
C
orA and B in some joint biological interaction• Order relations
A B… A is a cause of B
• Model Averaging– Learn many models, common sub-graphs will be more
likely to be true– Confidence measure: # of times a sub-graph appeared– Method: bootstrap
• Markov relations– A is in B’s Markov blanket iff
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Experimental Results
• Real biological data set: Yeast cell cycle data
• 800 genes, 76 experiments, 200-fold bootstrap
• Test for significance and robustness– More higher scoring
features in real data than in randomized data
– Order relations are more robust than Markov relations with respect to local probability models.
Markov Relations
Friedman et al, J Comput Biol. 2000;7:601-20
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Transcriptional regulatory network
• Who regulates whom?• When?• Where?• How?
GenePromoter
TF
A B g1
RNA-Pol A and not B
A B g2
RNA-PolA and B
A B g3
RNA-Pol A or B
A B g4
RNA-Pol Not (A and B)
PNAS 2003;100(9):5136-41
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Data-driven vs. model-driven methods
clustering
MF
Learning
Post-processingBiological insights
Descriptive
Explanatory, predictive
model model
“A description of a process that could have generated the observed data”
gene
condition
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Data-driven approaches
• Assumption– Co-expressed genes are likely co-regulated: not necessarily true
• Limitations:– Clustering is subjective– Statistically over-represented but non-functional “junk” motifs– Hard to find combinatorial motifs
Clustering Motif finding
Hierarchical, K-means, …
MEME, Gibbs, AlignACE, …
Experiments
Gen
es
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Model-based approaches
• Intuition: find motifs that are not only statistically over-represented, but are also associated with the expression patterns– E.g., a motif appears in many up-regulated genes but
very few other genes => real motif?• Model: gene expression = f (TF binding motifs, TF
activities)• Goal: find the function that
– Can explain the observed data and predict future data
– Captures true relationships among motifs, TFs and expression of genes
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Transcription modeling
g1
g2
g3
g4
g5
g6
g7
g8
Motifs ExpressionPromoters
? Genelabels
Variables
e = f (m1, m2, m3, m4)
Assume that gene expression levels under a certain condition are a function of some TF binding motifs on their promoters.
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Different modeling approaches
• Many different models, each with its own limitations
• Classification models– Decision tree, support vector machine (SVM),
naïve bayes, …
• Regression models– Linear regression, regression tree, …
• Probabilistic models– Bayesian networks, probabilistic Boolean
networks, …
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Decision treem1
m2
yes
m4
yes
no
yesno no
A B C D
3, 641, 2, 57, 8
g1
g2
g3
g4
g5
g6
g7
g8
e
• Tree structure is learned from data– Only relevant variables (motifs) are used– Many possible trees, the smallest one is preferred
• Advantages: – Easy to interpret– Can represent complex logic relationships
e = f (m1, m2, m3, m4)
m1 m2 m3 m4
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A real example: transcriptional regulation of yeast stress response
• 52 genes up-regulated in heat-shock (postive)• 156 random irresponsive genes (negative)• 356 known motifs
Small tree: only used 4 motifs
All 4 motifs are well-known to be stress-related
RRPE-PAC combination well-known
RRPE
PACFHL1
RAP1 11 (+)1(-)
4 (-)3 (+)
23 (+)
151 (-)10 (+)
5 (+)
Yes
YesYes
Yes
No
NoNo
No
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Model network in Science, 2002;298(5594):799-804
Network by our methodRuan et. al., BMC Genomics, 2009
Application to yeast cell-cycle genes
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Regression tree
• Similar to decision tree
• Difference: each terminal node predicts a range of real values instead of a label
m1
m2
yes
m4
no
no
yesno yes
e20>e>2e20<e<2
g1
g2
g3
g4
g5
g6
g7
g8
em1 m2 m3 m4
e = f (m1, m2, m3, m4)
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Multivariate regression tree• Multivariate labels: use multiple experiments
simultaneously• Use motifs to classify genes into co-expressed groups• Does not need clustering in advance
e1 e2 e3e4e5
m1
m2
yes
m4yes
no
yesno no
g1g2g3g4g5g6g7g8
m1 m2 m3 m4
368
125
4
7
Phuong,T., et. al., Bioinformatics, 2004
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Modeling with TF activities
• Gene expression = f (binding motifs, TF activities)
tf1tf2tf3tf4
e1 e2 e3 e4 e5
g
tf1 tf2 tf3 tf4
e1 e2 e3 e4 e5
g
rotate
tf1
> 0 0
g0 g>0
g = f (tf1, tf2, tf3, tf4)
Soinov et al., Genome Biol, 2003
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A Decision Tree Model
Segal et al. Nat Genet. 2003,34(2):166-76.
gene
experiment
A decision tree model of gene expressions
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Algorithm BDTree
• Gene expression = f (binding motifs, TF activities)
• Ruan & Zhang, Bioinformatics 2006• Basic idea:
– Iteratively partition an expression matrix by splitting genes or experiments
– Split of genes is according to motif scores– Split of conditions is according to TF
expression levels– The algorithm decides the best motifs or TFs
to use
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Transcriptional regulation of yeast stress response
• 173 experiments under ~20 stress conditions
• 1411 differentially expressed genes• ~1200 putative binding motifs
– Combination of ChIP-chip data, PWMs, and over-represented k-mers (k = 5, 6, 7)
• 466 TFs
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Genes
Exp
erim
ent
s
…
Genes with motifs FHL1 but no RRPE are down-regulated when Ppt1 is down-regulated and Yfl052w is up-regulated
Genes with motifs RRPE & PAC are down-regulated when TFs Tpk1 & Kin82 are up-regulated
…
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Biological validation
• Most motifs and TFs selected by the tree are well-known to be stress-related– E.g., motifs RRPE, PAC, FHL1, TFs Tpk1 and
Ppt1
• 42 / 50 blocks are significantly enriched with some Gene Ontology (GO) functional terms
• 45 / 50 blocks are significantly enriched with some experimental conditions
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RRPE & PAC, ribosome biogenesis (60/94, p < e-65)
FHL1, protein biosynthesis (98/105, p<e-87)
STRE (agggg)carbohydrate metabolism p < e-20
RRPE only, ribosome biogenesis (28/99, p < e-18)
Nitrogen metabolism
PAC
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Relationship between methods
• A, C: from promoter to expression– A: single cond– C: multi conds
• B, D: from expression to expression– B: single gene– D: multi genes
g1g2g3g4g5g6g7g8
m1 m2 m3 m4
t1t2t3t4
c1 c2 c3 c4 c5
A
C
B
D