Dynamics analysis of gene regulatory networks

Pioneering theoretical work on gene regulatory networks (GRNs) has anticipated the emergence of postgenomic research and provided a mathematical framework for the current description and analysis of complex regulatory mechanisms. In biochemical networks, the rates of reaction of substrates, enzymes, factors or products have attracted considerable attention in correspondence with changes in concentrations. The dynamical behaviours of genes, proteins and metabolites can be modelled by a series of differential equations, in which the detailed understanding of different behaviours exhibited by a gene regulatory network could be explored. The GRN diagrams that resemble complex electrical circuits are generated by the connectivity of genes and proteins. Recently, applying control theory to study biology is fast becoming an interesting and exciting idea, although there exist large differences in culture, approach and the tools used in these two fields. The complexity of GRNs poses many challenges for scientists and engineers. In particular, the biological systems have apparently become dependent on the complex infrastructure of GRNs to such an extent that it is difficult to analyse and control these networks thoroughly with our current capabilities. Therefore, there is an urgent need for research into modelling, analysis of behaviours, systems theory, synchronisation and control in GRNs. Numerous fundamental questions have been addressed about the connections between GRN structure and dynamic properties including stability, bifurcations, controllability and other observable aspects. However, some major problems have not been fully investigated, such as the behaviour of stability, synchronisation and chaos control for GRNs, as well as their applications in, for example, systems biology and bioinformatics. GRNs have already become an ideal research area for control engineers, mathematicians, computer scientists and biologists to manage, analyse and interpret functional information from real-world networks. Sophisticated computer system theories and computing algorithms have emerged or been exploited in the general area of dynamic analysis of GRNs, such as analysis of algorithms, artificial intelligence, automata, computational complexity, computer security, concurrency and parallelism, data structures, knowledge discovery, DNA and quantum computing, randomisation, semantics, symbol manipulation, numerical analysis and mathematical software. In the past decade, a large amount of research results have been available in the literature on the topics that include, but are not limited to the following aspects of GRNs: (1) systems and control analysis of GRNs; (2) parameter identification of GRNs; (3) dynamic analysis of regulatory motifs such as repressors and circadian oscillators; (4) robustness and fragility analysis of GRNs; and (5) methods and algorithms for GRN analysis. This Special Issue aims to bring together the latest approaches to understanding gene regulatory networks from a dynamic system perspective. We have solicited submissions to this Special Issue from control engineers, mathematicians, biologists and computer scientists. After a rigorous peer review process, nine articles have been selected that provide overviews, solutions, or early promise, to manage, analyse and interpret functional information from gene regulatory networks. These articles have covered both the practical and theoretical aspects of gene regulatory networks in the broad areas of dynamical systems, artificial intelligence, mathematics, statistics, operational research and engineering. The modelling of gene regulatory networks is necessary to describe the manner in which cells execute and control normal function and how abnormal function results from a breakdown in regulation. Hence, gene regulatory networks are critical to translational genomics, whose aim is to develop therapies based on the disruption or mitigation of aberrant gene function contributing to the pathology of a disease. Two basic intervention approaches have been considered for gene regulatory networks in the context of probabilistic Boolean networks (PBNs), external control and structural intervention. In the article ‘Stationary and structural control in gene regulatory networks: basic concepts’ by Dougherty, Pal, Qian, Bittner and Datta, the fundamental aspects of stationary and structural intervention in Markovian gene regulatory networks, in particular, PBNs, are reviewed. Various issues regarding regulatory intervention are addressed. This review article mainly consists of five parts, i.e. the introduction of PBNs, the stationary control problem for PBNs, the