Chaotic motifs in gene regulatory networks

Chaos should occur often in gene regulatory networks (GRNs) which have been widely described by nonlinear coupled ordinary differential equations, if their dimensions are no less than 3. It is therefore puzzling that chaos has never been reported in GRNs in nature and is also extremely rare in models of GRNs. On the other hand, the topic of motifs has attracted great attention in studying biological networks, and network motifs are suggested to be elementary building blocks that carry out some key functions in the network. In this paper, chaotic motifs (subnetworks with chaos) in GRNs are systematically investigated. The conclusion is that: (i) chaos can only appear through competitions between different oscillatory modes with rivaling intensities. Conditions required for chaotic GRNs are found to be very strict, which make chaotic GRNs extremely rare. (ii) Chaotic motifs are explored as the simplest few-node structures capable of producing chaos, and serve as the intrinsic source of chaos of random few-node GRNs. Several optimal motifs causing chaos with atypically high probability are figured out. (iii) Moreover, we discovered that a number of special oscillators can never produce chaos. These structures bring some advantages on rhythmic functions and may help us understand the robustness of diverse biological rhythms. (iv) The methods of dominant phase-advanced driving (DPAD) and DPAD time fraction are proposed to quantitatively identify chaotic motifs and to explain the origin of chaotic behaviors in GRNs.     

Cardiac gene regulatory networks in Drosophila

The Drosophila system has proven a powerful tool to help unlock the regulatory processes that occur during specification and differentiation of the embryonic heart. In this review, we focus upon a temporal analysis of the molecular events that result in heart formation in Drosophila, with a particular emphasis upon how genomic and other cutting-edge approaches are being brought to bear upon the subject. We anticipate that systems-level approaches will contribute greatly to our comprehension of heart development and disease in the animal kingdom.     

Evolution of evolvability in gene regulatory networks

Gene regulatory networks are perhaps the most important organizational level in the cell where signals from the cell state and the outside environment are integrated in terms of activation and inhibition of genes. For the last decade, the study of such networks has been fueled by large-scale experiments and renewed attention from the theoretical field. Different models have been proposed to, for instance, investigate expression dynamics, explain the network topology we observe in bacteria and yeast, and for the analysis of evolvability and robustness of such networks. Yet how these gene regulatory networks evolve and become evolvable remains an open question.     

Probabilistic representation of gene regulatory networks

MOTIVATION: Recent experiments have established unambiguously that biological systems can have significant cell-to-cell variations in gene expression levels even in isogenic populations. Computational approaches to studying gene expression in cellular systems should capture such biological variations for a more realistic representation. RESULTS: In this paper, we present a new fully probabilistic approach to the modeling of gene regulatory networks that allows for fluctuations in the gene expression levels. The new algorithm uses a very simple representation for the genes, and accounts for the repression or induction of the genes and for the biological variations among isogenic populations simultaneously. Because of its simplicity, introduced algorithm is a very promising approach to model large-scale gene regulatory networks. We have tested the new algorithm on the synthetic gene network library bioengineered recently. The good agreement between the computed and the experimental results for this library of networks, and additional tests, demonstrate that the new algorithm is robust and very successful in explaining the experimental data. AVAILABILITY: The simulation software is available upon request. SUPPLEMENTARY INFORMATION: Supplementary material will be made available on the OUP server.     

MicroRNAs: key participants in gene regulatory networks

microRNAs (miRNAs) are a newly identified and surprisingly large class of endogenous tiny regulatory RNAs. They exhibit various expressional patterns and are highly conserved across species. Recently, several regulatory targets of miRNAs have been predicted. Functional analysis of the potential targets indicated that miRNAs may be involved in a wide range of pivotally biological events. The nature of miRNAs and their intersection with small interfering RNAs endow them with many regulatory advantages over proteins and make them a potent and novel means to regulate gene expression at almost all levels. Here we argue that miRNAs are key participants in gene regulatory network.     

Signal propagation in nonlinear stochastic gene regulatory networks

The ability to build genetic circuits with a reproducible response to external stimuli depends on the experimental and theoretical methods used in the process. A theoretical formalism that describes the response of a nonlinear stochastic genetic network to the external stimuli (input signals), is proposed. Two applications are studied in detail: the design of a logic pulse and the interference of three signal generators in the E2F1 regulatory element. The gene interactions are presented using molecular diagrams that have a precise mathematical structure and retain the biological meaning of the processes.     

Perturbation avalanches and criticality in gene regulatory networks

Boolean networks are simplified models of gene regulatory networks. We derive an approximation of the size distribution of perturbation avalanches in Boolean networks based on known results in the theory of branching processes. We show numerically that the approximation works well for different kinds of Boolean networks. It has been suggested that gene regulatory networks may be dynamically critical. To study this, as an application of the presented theory we present a novel method for estimating an order parameter from microarray data. According to the available data and our method, we find that gene regulatory networks appear to be stable and reside near the phase transition between order and chaos.     

Modeling stochasticity and variability in gene regulatory networks

Modeling stochasticity in gene regulatory networks is an important and complex problem in molecular systems biology. To elucidate intrinsic noise, several modeling strategies such as the Gillespie algorithm have been used successfully. This article contributes an approach as an alternative to these classical settings. Within the discrete paradigm, where genes, proteins, and other molecular components of gene regulatory networks are modeled as discrete variables and are assigned as logical rules describing their regulation through interactions with other components. Stochasticity is modeled at the biological function level under the assumption that even if the expression levels of the input nodes of an update rule guarantee activation or degradation there is a probability that the process will not occur due to stochastic effects. This approach allows a finer analysis of discrete models and provides a natural setup for cell population simulations to study cell-to-cell variability. We applied our methods to two of the most studied regulatory networks, the outcome of lambda phage infection of bacteria and the p53-mdm2 complex.     

Learning about gene regulatory networks from gene deletion experiments

Gene regulatory networks are a major focus of interest in molecular biology. A crucial question is how complex regulatory systems are encoded and controlled by the genome. Three recent publications have raised the question of what can be learned about gene regulatory networks from microarray experiments on gene deletion mutants. Using this indirect approach, topological features such as connectivity and modularity have been studied.