Intervention and Control of Gene Regulatory Networks: Theoretical Framework and Application to Human Melanoma Gene Regulation

The cell maintains its function via an elaborate network of interconnecting positive and negative feedback loops of genes, RNAs, and proteins that send different signals to a large number of pathways and molecules. These structures are referred to as genetic regulatory networks, and their dynamics are used to understand the mechanisms and characteristics of biological cells as well as to search for possible remedy to various diseases such as cancer. In classical biological experiments, cell function is ascertained based on rough phenotypical and genetic behavior. On the other hand, the use of dynamical system models allows one to analytically explore biological hypotheses. Current research in cancer biology indicates that global, systemic molecular interactions are pivotal in understanding cellular dynamics and in designing intervention strategies to combat genetic diseases. In particular, most genetic ailments, such as cancer, are not caused by a single gene, but rather by the interaction of multiple genes. Global, holistic approaches to the study of biological systems reveal the dynamic nature of cellular networks, which provide an important framework for drug discovery and design. The massive amounts of information that omics (e.g., genomics, proteomics, metabolomics) high-throughput sequencing technology generate marked a great leap forward in computational methods for analyzing and interpreting biological data. However, it remains a major challenge to design optimal intervention strategies in order to affect the time evolution of gene activity in a desirable manner. One of the main aims of modern biological research is focused on intervening in biological cell dynamics in order to alter the gene regulatory network and avoid undesirable cellular states, for example, metastasis. The development of effective control approaches for therapeutic intervention within genetic regulatory networks requires new models and powerful tools for understanding and managing complex networks. This chapter is organized as follows. In Section 12.2, we review the main research streams in inference of genetic regulatory networks. In particular, we discuss the advantages and drawbacks of continuous and discrete-time stochastic models of genetic regulatory networks. In Section 12.3, we present a comprehensive review of the intervention strategies in regulatory networks proposed in the literature. The framework of optimal perturbation control is introduced in Section 12.4. In this section, we study the perturbation control feasibility, optimality, and robustness. Section 12.5 is devoted to simulation results on the control of the human melanoma genetic regulatory network. Finally, Section 12.6 presents a summary of the main results of the chapter and a discussion of future trends and directions in control of genetic regulatory networks. The ultimate goal is to develop engineering methods designed to intervene in the development of living organisms and transition cells from malignant states into benign forms. In this chapter, we consider real variables. We use ℝ to denote the set of real numbers. Scalars are denoted by lower case letters, for example, s, t. Vectors in ℝn are denoted by bold letters, numbers, or lower-case Greek letters, for example, 1, x, π, where 1 denotes a vector whose all components are equal to one. xt denotes the transpose of the vector x. The notation within x = (y,z) a shorthand for x is a linear combination of y and z. If the inner product $\langle$x, y$\rangle$ = 0, we write x $\bot$ y. Matrices in ℝm×n are denoted by capital letters or upper-case Greek letters, for example, within C, P, $\Lambda$. I stands for the identity matrix.