Hugh Shanahan Association Talk

Associative
methods in
Systems
Biology

Hugh
Shanahan
Associative methods in Systems Biology
Outline

Gene
Ontologies
Hugh Shanahan Over-representation
Semantic similarity

Associative
Measures
Department of Computer Science Hypotheses
Royal Holloway, University of London Linear Correlation
Partial Correlation
Non-linear measures

September 22, 2009 Validation
DREAM

Hugh Shanahan Associative methods in Systems Biology

Outline

Associative
methods in
1 Outline Systems
Biology

2 Gene Ontologies Hugh
Shanahan
Over-representation
Outline
Semantic similarity
Gene
Ontologies
3 Associative Measures Over-representation
Semantic similarity

Hypotheses Associative
Linear Correlation Measures
Hypotheses

Partial Correlation Linear Correlation
Partial Correlation

Non-linear measures Non-linear measures

Validation
DREAM
4 Validation
DREAM


Gene Ontologies

Associative
methods in
Systems
Biology

Hugh
Before ﬁnding interactions, need to be able Shanahan

to systematically annotate all genes Outline

Gene
to determine which functional groupings are Ontologies
Over-representation
over-represented Semantic similarity

measure objectively the “functional similarity” of two Associative
Measures
genes. Hypotheses
Linear Correlation
Partial Correlation
Gene Ontology (GO) is a means to do this. Non-linear measures

Validation
DREAM


Ontologies

Associative
methods in
Systems
Biology
Abstract method for expressing structured data. Hugh
Shanahan
Annotation of any gene can be expressed in terms of
Outline
incresingly accurate description, e.g.
Gene
This gene is involved in transport. Ontologies
Over-representation

This gene is involved in vesicle mediated Semantic similarity

Associative
transport. Measures
Hypotheses
This gene is involved in vesicle fusion. Linear Correlation
Partial Correlation

Genes may not have an accurate annotation, so Non-linear measures

Validation
deﬁnition can stop higher up in this hierarchy. DREAM


More complexity required

Associative
methods in
Systems
Biology
Annotation is not a simple chain.
Hugh
A single gene can have have a very speciﬁc annotation, Shanahan

which comes from two (or more) more general Outline
descriptions. Gene
Ontologies
Different types of annotation as well: location, Over-representation
Semantic similarity

biochemistry, part of organism expressed in, and so on. Associative
Measures
An Ontology is a Directed Acyclic Graph (DAG), not a Hypotheses
Linear Correlation
Tree (this means a lot to Graph Theorists). Partial Correlation
Non-linear measures

Each node in the DAG is an annotation term. Validation
DREAM
Each “child” node can more than one “parent” nodes.


GO’s visualised

Associative
IEWS methods in
Systems
Biology

a b c Hugh
Biological
process (root) Shanahan

Outline
Transport Membrane organization
and biogenesis Gene
asing
ficity Ontologies
is_a is_a
or
Over-representation
larity
Vesicle-mediated Semantic similarity
Membrane fusion
transport
Associative
part_of is_a
Measures
Hypotheses
Vesicle fusion
Linear Correlation
Partial Correlation
Figure 1 | Simple trees versus directed acyclic graphs. Boxes represent nodes and arrows represent edges. a | An
Nature Reviews | Genetics
example of a simple tree, in which each child has only one parent and the edges are directed, that is, there is a source Non-linear measures

(parent) and a destination (child) for each edge. b | A directed acyclic graph (DAG), in which each child can have one or
Validation
Rhee et al., Nature Reviews Genetics, (2008)
more parents. The node with multiple parents is coloured red and the additional edge is coloured grey.c | An example of
a node, vesicle fusion, in the biological process ontology with multiple parentage. The dashed edges indicate that there DREAM
are other nodes not shown between the nodes and the root node (biological process). A root is a node with no incoming
edges, and at least one leaf (also called a sink). A leaf node is a node with no outgoing edges, that is, a terminal node with
no children (vesicle fusion). Similar to a simple tree, A DAG has directed edges and does not have cycles, that is, no path
starts and ends at the same node, and will always have at least one root node. The depth of a node is the length of the
longest path from the root to that node, whereas the height is the length of the longest path from that node to a leaf41.
is_a and part_of are types of relationships that link the terms in the GO ontology. More information about the
relationships between GO terms are found online (An Introduction to the Gene Ontology).

GO’s visualised

Associative
methods in
Systems
Biology

Hugh
Shanahan

Outline

Gene
Ontologies
Over-representation
Semantic similarity

Associative
Measures
Hypotheses
Linear Correlation
Partial Correlation
http://amigo.geneontology.org/ Non-linear measures

Validation
DREAM


Different types of Annotation

Associative
methods in
Systems
Biology

Hugh
Typically, there are three distinct ontologies Shanahan

(overwhelmingly used). Outline

Cellular Compartment Gene
Ontologies
Over-representation
Biological Process Semantic similarity

Molecular Function Associative
Measures
Hypotheses
Many other ontologies have been constructed, e.g. Linear Correlation
Partial Correlation
Plant Organ for Arabidopsis. Non-linear measures

Validation
DREAM


Caveat

Associative
methods in
Systems
Biology
The annotation of most genes (90%) have been carried out Hugh
Shanahan
computationally. The annotations usually work pretty well,
though they have a tendency not to be as accurate as those Outline

obtained by direct assay. Gene
Ontologies
All annotated genes have an evidence code (IED) Over-representation
Semantic similarity
associated with them in order to demonstrate how much we Associative
can rely on it. Measures
Hypotheses

Increasingly, co-expression is being used as a means to Linear Correlation
Partial Correlation

annotate genes, so one should be careful in not using this Non-linear measures

information in constructing annotations ! Validation
DREAM


Over-representation

Associative
methods in
Systems
One of the most useful tools to hand when one analyses Biology
micro-array data is to ask what functional groupings occur Hugh
Shanahan
more often than one expects.
Outline
Notation
Gene
N number of genes in the genome. Ontologies
Over-representation
Semantic similarity
n number of genes which have been found to be
Associative
differentially expressed. Measures
Hypotheses

m number of genes in the genome with a speciﬁc Linear Correlation
Partial Correlation

annotation. Non-linear measures

Validation
k number of genes which are differentially expressed DREAM

with the same annotation.


Probabilities

Associative
methods in
Systems
One can derive the probability Pk that k genes would be Biology

found by chance amongst n genes using the Hugh
Shanahan
hypergeometric probability distribution and the above
Outline
parameters.
Gene
For the record Ontologies
Over-representation
Semantic similarity

Associative
m C N−m C Measures
k n−k
Pk = NC
, (1) Hypotheses
Linear Correlation
n Partial Correlation

N N! Non-linear measures

Cm = . (2) Validation
(N − n)!n! DREAM


Difficulties

Associative
methods in
Systems
Biology
There are thousand’s of possible GO terms and one Hugh
should adjust the probabilities to deal with multiple Shanahan

hypotheses. Outline

Applying Bonferroni correction using all GO terms gives Gene
Ontologies
a p-value of 10−7 equivalent to 1% significence. Over-representation
Semantic similarity

Because of the structure of the GO terms these Associative
Measures
probabilities are highly correlated with each other. Hypotheses
Linear Correlation

In all these cases focussing on as short a list of Partial Correlation
Non-linear measures

possible biological processes as possible will minimise Validation
the above difficulties. DREAM


What genes match

In benchmarking methods to infer interactions between Associative
methods in
gene products, we expect genes that interact to have similar Systems
Biology
GO terms, though perhaps not entirely the same. Hugh
Semantic Similarity is a means to measure how similar the Shanahan

annotations of two genes are (0 being no similarity, 1 Outline

meaning total similarity). Gene
Ontologies
GO provides us with a means to do this in a quantitative Over-representation
Semantic similarity
fashion.
Associative
Measures
Hypotheses
Linear Correlation
Partial Correlation
Non-linear measures

Validation
DREAM


Simple implementation

Determine the ratio of the number of nodes two genes share Associative
methods in
with the total number of nodes they have between them. Systems
Biology

Hugh
#{N(G1 ) ∩ N(G2 )} Shanahan
GOsimUI = (3)
#{N(G1 ) ∪ N(G2 )} Outline
N(G1 ) being the set of nodes associated with G1 ’s Gene
Ontologies
annotation. Over-representation
Semantic similarity

Associative
Measures
Hypotheses
Linear Correlation
Partial Correlation
Non-linear measures

Validation
DREAM

More elaborate methods are available.

Motivation

Associative
methods in
Systems
Yesterday, encountered clustering. Biology

Hugh
Hypothesis 1 (weak) :- coexpression implies involvment Shanahan
in the same process.
Outline
Expand to many different experiments. Gene
Ontologies
Hypothesis 2 (strong) :- greater a level of association, Over-representation
Semantic similarity
greater the chance of interaction.
Associative
Measures
Hypothesis 2 is often referred to as “guilt by Hypotheses

association”. Linear Correlation
Partial Correlation
Non-linear measures
Association may tell us about interactions between
Validation
gene products. It does not tell us anything about the DREAM

regulation mechanism.


Associative
methods in
Systems
Biology

Hugh
Shanahan

Outline

Gene
Ontologies
Over-representation
Semantic similarity

Associative
Measures
Hypotheses
Linear Correlation
http://www.arabidopsis.leeds.ac.uk/act/index.php Partial Correlation
Non-linear measures

266841_at AT2G26150 Validation
heat shock transcription factor family protein contains Pfam profile: DREAM
PF00447 HSF-type DNA-binding domain
260978_at AT1G53540

17.6 kDa class I small heat shock protein


What do we mean by association ?

Associative
methods in
Systems
Knowing something about the expression level of one gene Biology
(over many different experiments) means we know Hugh
Shanahan
something about the expression level of the other.
Replotting the above Outline

Gene
Ontologies
Over-representation
Semantic similarity

Associative
Measures
Hypotheses
Linear Correlation
Partial Correlation
Non-linear measures

Validation
DREAM


Linear Correlation
coexpression

Associative
methods in
Simplest form of association. Systems
Biology
Assume that there is a linear relationship between Hugh
Shanahan
genes.
Outline
Formally :-
Gene
y1 = a12 + c12 y2 + η12 , (4) Ontologies
Over-representation
Semantic similarity

Associative
y1 , y2 are (log) expression levels Measures
η12 noise term. Hypotheses
Linear Correlation
a12 , c12 parameters to be determined. Partial Correlation
Non-linear measures

But we’re not interested in that ! Validation
DREAM
We are interested in asking how good a model is this
for this pair of genes ?


Covariance

Associative
methods in
Can estimate how good the linear model is by computing Systems
Biology

E((y1 − y 1 )(y2 − y 2 )) , Hugh
Shanahan

where y 1 , y 2 = E(y1 ), E(y2 ) are the means of y1 and y2 . Outline

Gene
E means the expectation value of the above (think of it Ontologies
Over-representation
for now as taking the average over all the points in the Semantic similarity

previous ﬁgure). Associative
Measures
Can prove to oneself (exercise) that the magnitude of Hypotheses
Linear Correlation

the covariance is largest when y1 can be perfectly Partial Correlation
Non-linear measures

expressed as a linear function of y2 . Validation
DREAM
The covariance is zero when there is no relationship at
all between y1 and y2 .


Associative
methods in
Systems
Biology

Hugh
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Shanahan
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Non-linear measures

Maximum covariance Zero covariance Validation
DREAM


Correlation

Associative
methods in
Systems
Biology

Hugh
We want to compare every possible pair of genes, so using Shanahan

the covariance is not very practical since the maximum Outline
covariance will vary from pair of gene to pair of gene. Gene
However, Ontologies
Over-representation
Semantic similarity

E((y1 − y 1 )(y2 − y 2 )) Associative
ρ12 = , (5) Measures
E((y1 − y 1 )2 )E((y2 − y 2 )2 ) Hypotheses
Linear Correlation
Partial Correlation

is bounded: −1 ≤ ρ12 ≤ 1. Non-linear measures

Validation
DREAM


How well does it work ?

Associative
methods in
Systems
Number of examples of improved functional annotation. Biology

Unannotated gene which is highly correlated with gene Hugh
Shanahan
in a known response implies it is likely to be in the
same response. Outline

Gene
Ontologies
Over-representation
Semantic similarity

Associative
Measures
Hypotheses
Linear Correlation
Partial Correlation
Non-linear measures

Validation
DREAM


Associative
methods in
Systems
Biology

Hugh
Shanahan
Difﬁculty : genes correlate with many other genes, not
Outline
just a few.
Gene
Why ? Ontologies
Over-representation

Suggestion : correlations do not distinguish between Semantic similarity

Associative
potential direct interactions and indirect interactions Measures
Hypotheses
between gene products. Linear Correlation
Partial Correlation
Non-linear measures

Validation
DREAM


Example

Associative
methods in
Other interactions Systems
A Biology

Hugh
Shanahan
B
F Outline

Gene
Ontologies
D Over-representation

C Semantic similarity

Associative
Measures
E Hypotheses
Linear Correlation
Partial Correlation
Non-linear measures

B directly interacts with three other genes, but could be Validation
highly correlated with others. DREAM

C and D would be highly correlated with each other
even though they are not directly interacting.

Associative
methods in
Artiﬁcial example: create randomised data to represent Systems
Biology
expression of B.
Hugh
Generate two other sets of data (C and D) that are by Shanahan

construction highly correlated to the original data set, but Outline
are not set out to have a relationship with each other. Gene
Ontologies
Over-representation
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Validation

−4
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−4 −2 0 2 −4 −2 0 2 −4 −3 −2 −1 0 1 2 3
DREAM
B B C

ρ = 0.98 ρ = 0.98 ρ = 0.96 (!!!)


Extending correlations :- partial correlations

Associative
methods in
Systems
Correlations only take pairs of genes into consideration. Biology

Hugh
Partial correlations extends the initial pairwise Shanahan
regression model introduced in equation 4.
Outline

Gene
y1 = a1 + b12 y2 + b13 y3 + · · · + b1n yp + η1 . (6) Ontologies
Over-representation
Semantic similarity
Again, we are not interested in solving this explicitely. Associative
Measures
We want to understand the correlation that each one of Hypotheses

the genes y2 . . . yp has on y1 once we have removed Linear Correlation
Partial Correlation

the effect of all the other genes. Non-linear measures

Validation
We will use the notation PCij to refer to this partial DREAM

correlation.


Derivation

Associative
Computed easily once you have all the correlations methods in
Systems
between all the genes. Biology

Hugh
Shanahan
 
1 ρ12 ρ13 . . .
 ρ12 1 ρ23 . . .  Outline
R= ρ  , (7)
 
 13 ρ23 1 . . . 
Gene
Ontologies
.
. .
. .
. .. Over-representation
. . . . Semantic similarity

Associative
Measures
Covariance matrix C is deﬁned similarly. Hypotheses
Linear Correlation

ρij is the correlation between gene i and gene j. Partial Correlation
Non-linear measures

Validation
−1
Rij DREAM

PCij = − (8)
−1 −1
Rii Rjj


Questions

Associative
methods in
Systems
Biology

Hugh
Shanahan

Outline
ρij = ρji - why ? Gene
Ontologies
Diagonals are 1 - why ? Over-representation
Semantic similarity

Exercise :- compute PC using the covariance matrix. Associative
Measures
Hypotheses
Linear Correlation
Partial Correlation
Non-linear measures

Validation
DREAM


Artiﬁcial example

Associative
methods in
Systems
Biology

Hugh
Shanahan
 
1.0 0.96 0.98 Outline

RBCD =  0.96 1.0 0.98  , (9) Gene
Ontologies
0.98 0.98 1.0 Over-representation
Semantic similarity
 
−1.0 −0.01 0.70 Associative
Measures
PCBCD =  −0.01 −1.0 0.70  . (10) Hypotheses
Linear Correlation
0.70 0.70 −1.0 Partial Correlation
Non-linear measures

Validation
DREAM


Disadvantages of using Partial correlations

Associative
methods in
Systems
Biology

Hugh
High partial correlations no longer tend to go to 1 (or Shanahan
-1).
Outline
Dependent on ranking. Gene
Ontologies
How large should/can p (the number of genes Over-representation
Semantic similarity
examined) be ? Associative
Measures
Taking inverses of matrices should make us jumpy - Hypotheses

especially when there is limited data. Linear Correlation
Partial Correlation
Non-linear measures
Problem also dates to computing correlations. Validation
DREAM


“Large p, small n”

Notation Associative
methods in
Systems
p :- number of variables (in this case, expression of a Biology

gene) Hugh
Shanahan
n :- number of measurements (total number of affy
Outline
slides)
Gene
Ontologies

R has of the order p2 (p(p − 1)/2 to be exact) Over-representation
Semantic similarity

potentially interesting correlations. Associative
Measures
Could be dealing with of the order 10, 0002 variables. Hypotheses
Linear Correlation

Have at best a few thousand measurements per gene :- Partial Correlation
Non-linear measures

n ∼ 1000. Validation
DREAM
If p n, then the deﬁnition of equation (5) gives a
robust estimate of all those correlations, but that is not
where we are !

Artiﬁcial example

p/n = 0.1 p/n = 0.5 Associative
methods in

600

600
Systems
400 Biology

400
eigenvalue

eigenvalue
!
!
!
!!
!!!
!
!
!!
!
!
Hugh
! !
!
! !
Shanahan
200

200
!!
! !
!
!!
! !!
!!
!!! !!
! !
!!
!! !!
!!
!!
!! !!
!!
!!
!! !!
!!
!!
!! !!
!!!
!!
!! !!!
!!!
!!! !!!
!!!
!!!
!!! !!!!
!!!!
!!!
!!! !!!!!
!!!!!!!
!!!!
!!!! !!!!!!!!!!!!
!!!!!!!!!!!!!!
!!!!!!
!!!!!! !!!!!!!!
!!
!!!!!!!!!!!
!!!!!!!!!!!
Outline
0

0
0 20 40 60 80 100 0 20 40 60 80 100
Gene
Ontologies
Over-representation
Semantic similarity
p/n = 2 p/n = 10
Associative
1500

1500
Measures
Hypotheses
1000

1000
eigenvalue

eigenvalue

Linear Correlation
! Partial Correlation
500

500

!
! Non-linear measures
!
! !
!!
!! !!
!! !
!!
!! !
!!!
!!! !!!
!!!!
!!!!!
!!!!!!!!
!!!!!!!!!!!!!!!!!!!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!!!!!!!!!!!!!!!!!
!!
!!!!!
!!!!!!!
!!!!!!!!!
!!!!!!!!!!!!!
!!!!!!!!!!!!!!!
!!!!!!!!!!!!!
!!!!!!!!!!!!
!!!!!!!!!!
!!!!
Validation
0

0

DREAM
0 20 40 60 80 100 0 20 40 60 80 100

Schäfer and Strimmer, Statistical Applications in Genetics
Figure 1: Ordered eigenvalues of the sample covariance matrix S (thin black line) and
that of an alternative estimator 4, 1, (2005)
and Molecular Biology, S (fat green line, for deﬁnition see Tab. 1), calculated from
simulated data with underlying p-variate normal distribution, for p = 100 and various ratios Biology
Hugh Shanahan Associative methods in Systems

Explanation

Associative
methods in
Systems
Biology

Spectrum of eigen-values. Hugh
Shanahan
Any eigen-value equal to zero means matrix is
Outline
non-invertible.
Gene
Dashed lines - actual eigenvalues. Ontologies
Over-representation

Thin black lines - estimated eigenvalues using equation Semantic similarity

Associative
(5). Measures
Hypotheses

Green line - improved estimator. Linear Correlation
Partial Correlation

In general, if n < p then the correlation/covariance Non-linear measures

Validation
matrix is non-invertible. DREAM


Strategies

Associative
methods in
Systems
Biology

Hugh
Shanahan
Reduce p - cluster data initially, then perform analysis
on each cluster. (Toh and Harimoto, 2002). Outline

Gene
Compute lower order partial correlations - compute ﬁrst Ontologies
order partial correlations (Magwene and Kim, 2004). Over-representation
Semantic similarity

Employ improved estimator of correlations (Schäffer Associative
Measures
and Strimmer, 2005). Hypotheses
Linear Correlation

These options are not necessarily exclusive. Partial Correlation
Non-linear measures

Validation
DREAM


Shrinkage estimate - wordy explanation

Associative
methods in
Systems
What is computed in equation (5) is an estimate of the Biology

correlation based on the available data, not the actual Hugh
Shanahan
correlation if we knew the underlying multi-variate
distribution. They would coincide if we had much greater Outline

Gene
statistics. That said, we can use other estimators of Ontologies
correlation. Statisticians have pointed out that many other Over-representation
Semantic similarity

possible estimators can be used which work better in the Associative
Measures
regime we lie (large p, small n). Hypotheses

Shrinkage estimates attempt to combine different naive Linear Correlation
Partial Correlation

estimates to get an improved estimate. The principal has Non-linear measures

Validation
been around for some time (Stein, 1956) though its use has DREAM

increased signiﬁcantly in the last ten years.


Shrinkage estimates - the details

Associative
methods in
Systems
Biology
Notation:
Hugh
Shanahan
C is the actual covariance matrix.
ˆ
C is an estimate of the covariance matrix. Outline

Gene
ˆ
In computing C we could either attempt to compute it Ontologies
Over-representation

using the standard deﬁnition (“full”) or assume (for Semantic similarity

example) that all the off-diagonal entries are zero Associative
Measures
(“reduced”). Hypotheses
Linear Correlation

ˆ
CF for the “full” estimate of covariance matrix. Partial Correlation
Non-linear measures

ˆ
CR for the “reduced” estimate of covariance matrix. Validation
DREAM


Mean Square Error

Associative
methods in
Systems
Deﬁning Biology

Hugh
Shanahan
ˆ
MSE(C) = ˆ
E((C − C)2 ) , (11)
= ˆ ˆ
Var (C) + Bias2 (C) . (12)
Outline

Gene
ˆ
Var (C) = ˆ ˆ
E((C − E(C))2 ) , (13) Ontologies
Over-representation

ˆ
Bias(C) = ˆ
E(C) − C . (14)
Semantic similarity

Associative
Measures
(Expectation operator is over the data that we have). Hypotheses
Linear Correlation
Partial Correlation
ˆ ˆ
Bias(CF ) is small but Var (CF ) will be large. Non-linear measures

Validation
ˆ ˆ
Var (CR ) will be small but Bias(CR ) will be large. DREAM


The problem

Associative
methods in
Systems
Biology

Hugh
Depending on the assumptions we use to estimate the Shanahan

correlation/covariance matrix Outline

we can either compute a very poor estimate of the Gene
Ontologies
parameters in a very accurate model, Over-representation
Semantic similarity

or compute a good estimate of the parameters for a Associative
Measures
very inaccurate model (!) Hypotheses
Linear Correlation

But maybe we can reconcile the two... Partial Correlation
Non-linear measures

Validation
DREAM


Combining the two

Associative
methods in
One can combine these two estimates: Systems
Biology

Hugh
Shanahan
C ∗ ˆ ˆ
= λCR + (1 − λ)CF , (15)
Outline
0 ≤ λ ≤ 1 , (16) Gene
Ontologies
Over-representation

choosing a λ such that MSE(C∗ ) is minimised. Semantic similarity

Associative
Computing λ is normally very expensive. Measures
Hypotheses

Ledoit and Wolf (2003) came up with a short analytical Linear Correlation
Partial Correlation

way of computing λ; Schäffer and Strimmer modiﬁed Non-linear measures

Validation
this for genomic data. DREAM

We have an R package to do this.


Final Note

Associative
methods in
Systems
Biology

Hugh
Shanahan

The Schäffer and Strimmer estimate uses the Outline
“zero-covariance” low dimensional model for their estimate, Gene
but this isn’t necessarily the best choice. Ontologies
Over-representation

Notably, while shrinkage estimates make much of Semantic similarity

incorporating information, they don’t explicitely include Associative
Measures
Biological information. Hypotheses
Linear Correlation
Partial Correlation
Non-linear measures

Validation
DREAM


b1057 pckA
nuoI
pspB
ompT
resultsyecO
ompC ompF
nuoF
artQ
glnH glnP
hupB
yfiA Associative
methods in
Using E. coli time series data (8 time slices), Schäffer and Systems
GM network Biology
Strimmer examined 102 genes using correlations and Schäfer and Strimmer: Large-Scale Covariance Matrix Estimation
Hugh
partial correlations. Shanahan
yjbO yjbE ybjZ sucC pyrI
yhgI hns
yfiA yfaD yedE pspD manX
sucA sodA nuoM nmpC nuoA atpG flgD atpH
grpE gltA gatC glnP gatA yhfV
Outline
fixC dnaJ ibpA nuoL manZ hupA manY flgC
ilvC lacA cspA cyoD dnaJ
lacY aldA atpB yjcH
manY artJ sucD b0725 nuoH
ptsG
b0725 yjbE gltA yhdM ygbD
hisJ Gene
yrfH cchB ynaF
pyrI aceB
manZ
ompF cchB mopB yhfV sodA atpF Ontologies
yfaD
pyrB ompC atpF ibpB nmpC ahpC nuoB Over-representation
ompT degS cstA ftsJ sucA
sucC yecO tnaA ycgX gatB
ibpB icdA pspC Semantic similarity
dnaK pckA ybjZ ygcE
atpE nuoI fixC gatZ atpE
yjcH artJ b1057 cyoD yceP eutG aceB
gatC b1191
ibpA
cstA
flgC
nuoC atpD
dnaG
folK aldA
pyrB
Associative
nuoH nuoL nuoM
lacZ manX mopB asnA yjbO yheI pspD Measures
nuoB ptsG
gatB
ahpC flgD aceA eutG yrfH b1963 pspA lpdA
ycgX b1583 lacY dnaK atpB Hypotheses
hisJ atpH asnA yedE
atpD artQ b1057 pckA Linear Correlation
atpG icdA grpE cspG nuoI
gatD b1191 lacA pspB Partial Correlation
tnaA sucD b1583 lacZ ompT
nuoF cspG b1963 nuoA gatD nuoC
yecO nuoF
folK dnaG cspA ompC ompF Non-linear measures
ynaF hns hupA gatZ ftsJ glnH artQ
lpdA hupB degS gatA
pspA pspB
ygbD ygcE yaeM pspC yceP ilvC glnH glnP
yhgI yhdM yheI aceA yaeM yfiA
hupB Validation
DREAM
(a) Shrinkage GGM network
(c) Relevance network
Correlations Partial Correlations (Graphical gatD gatB
aceB nuoL

(Relevance Network)
yjbO

Gaussian Network)
manY
yjbO
ahpC
sucA yfiA yfaD sodA yedE pspD
asnA ygcE nuoM nmpC

coli data by (a) the shrinkage GGM ap- sodA
atpB

ynaF
icdA
cspA

yfiA
gatZ artJ

pckA
cstA

ilvC
grpE
lacA
gltA

lacY
gatC
cspA

ptsG
glnP

aldA
fixC

b0725
dnaJ
atpB
gatA

manY
yhfV

yjbE
nmpC yrfH

asso GGM approach by Meinshausen and
yrfH b1583 hupA
manX pyrI aceB ompF cchB mopB
gatC hupB manZ
flgC ybjZ ibpB
hns pyrB ompC atpF ibpB
yjbE ompF pyrI nuoH yecO
ompT degS yecO
ibpA degS
fixC cchB sucC
cspG pckA ybjZ

k with abs(r) > 0.8. Black and grey edges Shanahan
manZ pyrB dnaK
ompC gltA sucC
nuoB yaeM atpE nuoI
folK atpD b1963 yjcH b1057 cyoD
b1057 glnH yjcH ygbD artJ
atpF
sucD ibpA nuoC
atpH cstA
flgD
nuoL flgC
Hugh
atpE

Associative methods in Systems Biology
ptsG pspC ilvC yhfV nuoH
aceA nuoF hisJ
tnaA
b1191 lacZ nuoB manX
cyoD
ompT
pspD glnP nuoC dnaJ
gatB
dnaK eutG aceA eutG
ahpC flgD

Results of comparison

Associative
methods in
Systems
Biology

Hugh
Shanahan

Outline
Recover centrality of sucA gene. Gene
Ontologies
lacA, lacZ and lacY genes have the largest absolute Over-representation
Semantic similarity
partial correlations. Associative
Measures
Hypotheses
Linear Correlation
Partial Correlation
Non-linear measures

Validation
DREAM


Associative
methods in
Systems
Biology
So far, we have concerned outselves with linear
Hugh
relationships. Shanahan

However, such an approximation may not be valid. Outline

Naively, one expects a more non-linear relatiopnship Gene
Ontologies
between gene products. Over-representation
Semantic similarity

For example, typically Transcription Factor - target Associative
Measures
interactions are modelled using Michaelis-Menton Hypotheses
Linear Correlation
kinetics. Partial Correlation
Non-linear measures

Furthermore expression levels are derived after a Validation
number of transformations. DREAM


One approach: Spearman correlation

Associative
methods in
Systems
Biology

Hugh
Shanahan
Basic idea: use ranks rather than raw data.
Outline
Use nearly the same deﬁnition of linear (Pearson) Gene
Ontologies
correlation. Over-representation
Semantic similarity
Must be careful about ties, i.e. raw data having Associative
precisely the same value (unlikely for ﬂoating point Measures
Hypotheses
data). Linear Correlation
Partial Correlation
Non-linear measures

Validation
DREAM


Comparison

Associative
methods in
Systems
Biology

Hugh
Shanahan

Outline

Gene
Ontologies
Over-representation
Semantic similarity

Associative
Measures
Hypotheses
Linear Correlation
Partial Correlation
Non-linear measures

Comparison of different measures. Validation
DREAM
Many other methods for non-linear measures are possible,
the best known being Mutual Information.


Modelling of gene interactions

Associative
We have only just touched upon methods for inferring methods in
Systems
interactions between gene products using transcriptomic Biology
data. Some of the others include the use of Hugh
Shanahan
Mutual Information/Spearman Correlations - addresses
Outline
non-linearities.
Gene
Kinetic models - attempt to infer interactions. Ontologies
Over-representation

Boolean Networks - model interactions as circuitry. Semantic similarity

Associative
Petri Nets - Prof. Ming Chen. Measures
Hypotheses

Bayesian Networks - Dr. Chris Needham. Linear Correlation
Partial Correlation
Non-linear measures
Machine Learning methods - Validation
Unsupervised/semi-supervised/supervised learning. DREAM

Integration of other data sources.
...

Explosion of methods
160 Annals of the New York Academy of Sciences
Associative
methods in
Systems
Biology

Hugh
Shanahan

Outline

Gene
Ontologies
Over-representation
Semantic similarity

Associative
Measures
Hypotheses
Linear Correlation
Partial Correlation
Non-linear measures

FIGURE 1. The number of publications retrieved from a PubMed search of “Pathway Validation
Inference” or “Reverse Engineering.” On average, this number has been doubling every two DREAM
years since about 1995. (Color is shown in online version.)

reverse-engineering methods was going to be that computational methods can, in the blink of
a key prerequisite to their increasing value to an eye, generate large numbers of predictions,
Stolovitzsky et al., Ann.the ﬁeld of re- from a few (2009) hundreds of thousands,
biology. Indeed, at that time, N.Y. Acad. Sci. hundred to
verse engineering biological networks was be- most (if not all) of which usually go untested.
ginning to experience considerable expansion, Even worse, and this would be a best case sce-

Validation - DREAM

Associative
methods in
While there are a colossal number of methods out there, the Systems
Biology
validation of them is very much in its infancy.
Hugh
DREAM (Dialogue for Reverse Engineering Assessments Shanahan

and Methods) is an attempt to deal with this question. Outline
Features: Unseen experimental data of (for example) Gene
Ontologies
Transcription Factor bindings sites, Over-representation
Semantic similarity

artiﬁcial data (in silico), Associative
Measures
genome-wide interactions, Hypotheses
Linear Correlation
Partial Correlation
is gathered and groups are invited to reproduce the Non-linear measures

interactions. Different groups results are then compared Validation
DREAM

against data to determine how well they did. New
challenges are presented on an annual basis.


Some Results from DREAM 2 (2007)

Associative
methods in
Systems
Biology

Hugh
Challenge 1: Shanahan

Identify targets of transcription factor BCL6. Outline

53 genuine targets of BCL6 inferred from unpublished Gene
Ontologies
ChP-chip data. Over-representation
Semantic similarity

147 decoys addes. Associative
Measures
Task : identify the genuine targets from decoys by Hypotheses
Linear Correlation

picking genes with similar expression patterns to BCL6. Partial Correlation
Non-linear measures

Validation
DREAM


Results

Associative
methods in
Systems
Biology

Best approaches were selective in the data sets Hugh
Shanahan
employed. (Data sets where BCL6 was highly
expressed or not expressed at all were used.) Outline

Gene
Semi-supervised learning was employed - using known Ontologies
Over-representation
targets of BCL6 to train best method. Semantic similarity

Used correlations. Associative
Measures
Hypotheses
1st-order Partial correlations did badly. Linear Correlation
Partial Correlation

Basic correlations were approaching most Non-linear measures

sophisticated approaches. Validation
DREAM


More results from DREAM

Associative
methods in
Systems
Challenge 2: E. Coli network. Biology

Hugh
From RegulonDB good evidence for targets to assorted Shanahan
Transcription Factors.
Outline
Task : identify targets.
Gene
Results Ontologies
Over-representation
Semantic similarity
Best method used Mutual Information and ideas behind
Associative
1st order partial correlation. Measures
Hypotheses

Correlations and Partial Correlations were not too far Linear Correlation
Partial Correlation

behind. Non-linear measures

Validation
Level of identiﬁcation of targets was low - perhaps 5%. DREAM


Conclusions

Associative
GO terms allow us to handle large amounts of methods in
Systems
annotation in a structured fashion. Biology

Hugh
Associative measures are a ﬁrst attempt at using the Shanahan

huge amounts of expression data that is out there.
Outline
Very simple ideas such as correlation work surprisingly Gene
Ontologies
well (or rather more complicated methods of Over-representation

association don’t give orders of magnitude better Semantic similarity

Associative
performance). Measures
Hypotheses

A long way to go nonetheless. Linear Correlation
Partial Correlation

The type of expression data we select; Non-linear measures

Validation
a clear understanding of what microarray/RNA-seq/... DREAM

technology;
may be even more important.

Hugh Shanahan Association Talk

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