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Probabilistic Graphical Modeling in Systems Biology: A Framework for Integrative Approaches

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Systems Biology

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Abstract

Systems biology may be defined as a discipline aiming at integrating various sources of heterogeneous data, with the objective to describe and predict the function of biological systems. The purpose is to cross many (possibly weak) evidences from several data types that describe different biological features of genes or proteins. Probabilistic graphical models offer an appealing framework for this objective. Through the thorough review of five selected examples, this chapter highlights how probabilistic graphical models can contribute to build the bridge between biology and computational modeling. In this methodological framework, the five cases illustrate three features of these models, which we discuss: flexibility, scalability and ability to combine heterogeneous sources of data. The applications covered address genetic association studies, identification of protein–protein interactions, identification of the target genes of transcription factors, inference of causal phenotype networks and protein function prediction.

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Notes

  1. 1.

    Depending on the context, the conditional probability of \(D_1\) given \(D_2\), \({\mathbb {P}} (D_1 \mid D_2)\), is also called the posterior probability of \(D_1\) conditional on \(D_2\).

  2. 2.

    \({\mathbb {P}} (M \mid D)\ {\mathbb {P}} (D) = {\mathbb {P}} (D \mid M)\ {\mathbb {P}} (M)\).

  3. 3.

    Gene fusion is likely to detect a PPI since two proteins interacting in the genome of one species are more likely to be fused into one single protein in the genome of another species.

  4. 4.

    A mixture model is a probabilistic model that represents a population of \(k\) groups, with random proportions \(\pi _1,\ \ldots ,\ \pi _k\).

  5. 5.
    $$\begin{aligned} {\mathbb {P}} _{(1)}(\varphi _1,\ \varphi _2,\ \varphi _3) = {\mathbb {P}} (\varphi _1)\ {\mathbb {P}} (\varphi _2 \mid \varphi _1)\ {\mathbb {P}} (\varphi _3 \mid \varphi _2)\ \text{ and }\ {\mathbb {P}} _{(2)}(\varphi _1,\ \varphi _2,\ \varphi _3) = {\mathbb {P}} (\varphi _2)\ {\mathbb {P}} (\varphi _1 \mid \varphi _2)\ {\mathbb {P}} (\varphi _3 \mid \varphi _2). \end{aligned}$$

    Equality is assessed from the Bayes theorem.

  6. 6.

    If \(X = y + E\), with \(E \sim \fancyscript{N}(0,\sigma ^2)\), then \(X \sim \fancyscript{N}(y,\sigma ^2)\).

Abbreviations

BN:

Bayesian network

ChIP-chip:

Chromatin immunoprecipitation on chip

ChIP-seq:

Chromatin immunoprecipitation followed by sequencing

CPN:

Causal phenotype network

DDI:

Domain-domain interaction

DNA:

Deoxyribonucleic acid

GA:

Genetic architecture

GO:

Gene ontology

GOS:

GO sub-ontology

GWAS:

Genome wide association study

MCMC:

Monte Carlo Markov chain

MRF:

Markov random field

MRF-MJM:

MRF mixture joint model

PGM:

Probabilistic graphical model

PPI:

Protein–protein interaction

QTL:

Quantitative trait loci

RNA:

Ribonucleic acid

RNAi:

RNA interference

ROC curve:

Receiver operating characteristic curve

SMM:

Standard mixture model

TF:

Transcription factor

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Acknowledgments

The author wishes to thank the anonymous reviewer for constructive comments on her manuscript, and feedback most helpful to produce the final version.

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Authors and Affiliations

  1. LINA, UMR CNRS 6241, Université de Nantes, 2 rue de la Houssinière, BP 92208, 44322, Nantes Cedex, France

    Christine Sinoquet

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  1. Christine Sinoquet
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Correspondence to Christine Sinoquet .

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Editors and Affiliations

  1. Chemical and Biological Engineering, Vanderbilt University, Nashville, TN, USA

    Aleš Prokop

  2. Research Group on Process Network Engineering, Kaposvár University, Kaposvár, Hungary

    Béla Csukás

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Sinoquet, C. (2013). Probabilistic Graphical Modeling in Systems Biology: A Framework for Integrative Approaches. In: Prokop, A., Csukás, B. (eds) Systems Biology. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-6803-1_8

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