Current Bioinformatics, 2006, 1, 167-184 167 1574-8936/06 $50.00+.00 © 2006 Bentham Science Publishers Ltd. Intervention in Probabilistic Gene Regulatory Networks Aniruddha Datta *,1 , Ranadip Pal 1 and Edward R. Dougherty 1,2 1 Department of Electrical Engineering and Genomic Signal Processing Laboratory, Texas A&M University, College Station, TX 77843-3128, USA 2 Computational Biology Division, Translational Genomics Research Institute, Phoenix, AZ 85004, USA Abstract: In recent years, there has been a considerable amount of interest in the area of Genomic Signal Processing, which is the engineering discipline that studies the processing of genomic signals. Since regulatory decisions within the cell utilize numerous inputs, analytical tools are necessary to model the multivariate influences on decision-making produced by complex genetic networks. Signal processing approaches such as detection, prediction and classification have been used in the recent past to construct genetic regulatory networks capable of modeling genetic behavior. To accommodate the large amount of uncertainty associated with this kind of modeling, many of the networks proposed are probabilistic. One of the objectives of network modeling is to use the network to design different intervention approaches for affecting the time evolution of the gene activity profile of the network. More specifically, one is interested in intervening to help the network avoid undesirable states such as those associated with a disease. This paper provides a tutorial survey of the intervention approaches developed so far in the literature for probabilistic gene networks (probabilistic Boolean networks) and outlines some of the open challenges that remain. Keywords: Gene regulatory network, markov chain, steady-state distribution, optimal control, dynamic programming, context sensitive networks. 1. INTRODUCTION From a translational perspective, the ultimate objective of genetic regulatory network modeling is to use the network to design different approaches for affecting network dynamics in such a way as to avoid undesirable phenotypes, for instance, cancer. In this paper we present a tutorial survey of the results obtained to date on intervention in the context of probabilistic gene regulatory networks, which, owing to their original binary formulation and their usual application using binary and ternary gene-expression quantization, are generically called probabilistic Boolean networks (PBNs) [1]. These are essentially probabilistic generalizations of the standard Boolean networks introduced by Kauffman [2-4] that allow the incorporation of uncertainty into the inter-gene relationships. Given a PBN, the transition from one state to the next takes place in accordance with certain transition probabilities and their dynamics, and hence intervention, can be studied in the context of homogeneous Markov chains with finite state spaces. A major goal of functional genomics is to screen for genes that determine specific cellular phenotypes (disease) and model their activity in such a way that normal and abnormal behavior can be differentiated. The pragmatic manifestation of this goal is the development of therapies based on the disruption or mitigation of aberrant gene function contributing to the pathology of a disease. Mitigation would be accomplished by the use of drugs to act on the gene products. Engineering therapeutic tools involves synthesizing nonlinear dynamical networks, analyzing these networks to characterize gene regulation, and developing *Address correspondence to this author at the Room No. 216N, Zachry Engineering Center, Tamu 3128, College Station, TX, 77843, USA; Tel: 979-845-5917; Fax: 979-845-6259; E-mail: datta@ee.tamu.edu intervention strategies to modify dynamical behavior. For instance, changes in network connectivity or functional relationships among the genes in a network, via mutations or re-arrangements, can lead to steady-state behavior associated with tumorigenesis, and this is likely to lead to a cancerous phenotype unless corrective therapeutic intervention is applied. To date, intervention studies have used three different approaches: (i) resetting the state of the PBN, as necessary, to a more desirable initial state and letting the network evolve from there [5]; (ii) changing the steady-state (long- run) behavior of the network by minimally altering its rule- based structure [6]; and (iii) manipulating external (control) variables that alter the transition probabilities of the network and can, therefore, be used to desirably affect its dynamic evolution [7]. The control-theoretic approach has subsequently been extended. First, the optimal intervention algorithm has been modified to accommodate the case where the entire state vector, or gene activity profile (GAP) as it is known, is not available for measurement [8]. Second, whereas the original control-theoretic approach has been developed in the framework of instantaneously random PBNs, the intervention results have been extended to context-sensitive PBNs (terminology to be defined shortly) [9]. The paper is organized in the following manner: Section 2 reviews the necessary essentials of PBNs; Section 3 discusses intervention limited to a one-time flipping of the expression status of a single gene; Section 4 considers intervention to alter the steady-state behavior of the network; Section 5 formulates the intervention problem in probabilistic gene regulatory networks as an optimal control problem that is then solved using the standard approach of dynamic programming; Section 6 extends the results of Section 5 to the imperfect information case; Section 7