Gene Networks

Hans J. Bohnert

Shisong Ma (present address: Yale University)

Introduction

High­throughput transcript profiling platforms – microarrays in a variety of forms ­

make use of the increasing amount of genomic DNA and EST sequences and

generate a flood of data. Tools are urgently needed that allow for analyses that

convert these data into models for the structures of any underlying pathways and

causal networks (Brazhnik et al., 2002). From an organism’s response to various

developmental or externally manipulated conditions at the transcript level it

should be possible to infer functional relations between genes based on co­

expression pattern, essentially by assuming “guilt by association”. However, the

use of these data in interpreting how genes respond to external or internal, i.e.,

hormonal or biochemical, stimuli has been fraught with uncertainties. Statistical

models abound, yet there is no consensus about how biological context and

significance are to be merged in these models. Common are notions that

generate “relevance networks” by determining Pearson correlation coefficients

(Markowetz and Spang, 2007), which indeed associate many genes with similar

expression patterns. However, the method is encumbered by several problems

because it cannot separate indirect from direct interactions and tends to recover

far too many interactions, which then frustrate interpretation (Schäfer and

Strimmer, 2005a). Also, results are dominated by a few heavily connected

1 pathways, for example genes associated with functions of the ribosome, while

the effects of environmental factors are less faithfully represented.

We have chosen the graphical Gaussian model, GGM, as a method for representing

correlation. GGM is based on partial correlation (Schäfer and Strimmer, 2005a,

b; Opgen­Rhein and Strimmer, 2007), placing the relationship between gene

pairs in the context of the entire transcriptome, while the Pearson correlation

approach considers each pair of genes separate. The partial correlation

approach has superior ability in separating direct from indirect interactions.

However, GGM is impeded by what may be called the problem of “large p, small

n”. This describes the fact that the number of microarray slides (n) in a dataset is

invariably much smaller than the number of genes (p) in a genome. For the

model plant Arabidopsis thaliana, whose genome is well known, some 3,000

microarray experiments with the Affymetrix ATH1 platform on which >22,000

gene probes are printed represent ~150 experimental conditions. A “shrinkage”

method (Schäfer and Strimmer, 2005a, b) makes it possible to infer partial

correlations from among 2,000 genes from this dataset. We then proposed and

implemented an iterative sampling routine, coupled with the shrinkage approach,

thus expanding the partial correlation analysis to establish network coverage of

the whole genome (Ma et al., 2007).

Subsequent analyses revealed that GGM recovers interactions between seemingly

unrelated biological pathways (developmental and biochemical) that cover

diverse aspects, which provided particular advantages for the analysis of

responses to external factors. Depending on the stringency of the settings,

which may be adjusted based on biological knowledge, it is possible to recover

2 genome­wide networks of moderate sizes that cover many pathways, and which

can be controlled by the degree with which they recount known gene

interactions. Although this represents a heuristic, experimental approach many

interactions with biological significance have been recovered (Ma et al., 2007; Ma

and Bohnert, 2008; Li et al., 2008). Further meaningful enhancement of the

GGM can be obtained using clustering methods (Gasch and Eisen, 2002; Ma et

al., 2006; Ma and Bohnert, 2007).

It seems that modified GGM approaches can provide novel understanding of

transcript profiles, that the process can identify genes in biochemical pathways,

in explaining hormonal, biotic and abiotic stress­relevant responses, and in

placing genes into developmental pathways. The chosen model is particularly

suitable placing various isoforms of genes in families into different context, and

by assigning genes of unknown functions into networks that can then be

experimentally interrogated. GGM would profit from increased experimentation,

especially if the number of experimental conditions and the number of time

course experiments were increased, and if more wild type to (knockout) mutant

comparisons were included. The numbers of stringently controlled and

annotated experiments is not yet sufficient to provide a sufficiently complex and

nearly scale­free model of the Arabidopsis transcriptome. Also, we are still far

from being able to integrate into an improved GGM and to see in context data

established by different microarray platforms, or to profit from diverse datasets as

they are provided by protein interaction or metabolite dynamics studies, via, e.g.,

Bayesian network approaches (Lee et al, 2004b), although robust models about

3 how to reconcile data from different microarray platforms are still to be in

developed.

Another plant database exists that organizes a network based on the Pearson

correlation coefficient (Obayashi et al, 2007). For non­plant organisms, a co­

expression network based on 1st order partial correlation exists for yeast

(Magwene and Kim, 2004). Other networks, for yeast, C. elegans, or human

tissues, typically combine co­expression data with other types of data, such as

protein­protein interactions, CHIP­experimental data or across­species gene

conservation studies (Ramani et al., 2008; Lee et al., 2008; Lee et al., 2004a;

Lee et al., 2007). Owing to the fact that more protein interaction studies have

been conducted for important other models, human cell cultures or yeast in

particular, less emphasis has been placed in these models on gene networks,

while integration of different datasets has been emphasized. A similar trajectory

can be expected for plant datasets in the future to become incorporated into the

TAIR database that strives o incorporate all information on Arabidopsis genetics,

biochemistry and genomics (Rhee et al., 2003).

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Selected Links

TAIR: http://www.arabidopsis.org

Genevestigator: http://www.genevestigator.ethz.ch

Bohnert Lab: http://www.life.uiuc.edu/bohnert

ATTED­II: http://www.atted.bio.titech.ac.jp/

GGM (Strimmer lab): http://strimmerlab.org/notes/ggm.html

NASC: http://arabidopsis.info

Society Computational Biology: http://www.iscb.org

Society Molecular Biology: http://www.iscb.org/ismb2008/index.php

Keywords

Gene network, microarray, transcript profiling, gene expression, biochemical pathways,

signaling cascades, environmental control, graphical Gaussian model, scale­free

networks, Pearson correlation

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