Non-coding RNAs and a layered architecture of genetic networks

In eukaryotic cells, protein-coding sequences constitute a relatively small part of the genome. The rest of the genome is transcribed to non-coding RNAs (ncRNAs). Such RNAs form the cornerstone of a regulatory network that operates in parallel with the protein network. Their biological functions are based primarily on the ability to pair with and deactivate target messenger RNAs (mRNAs). To clarify the likely role of ncRNAs in complex genetic networks, we present and comprehensively analyze a kinetic model of one of the key counterparts of the network architectures. Specifically, the genes transcribed to ncRNAs are considered to interplay with a hierarchical two-layer set of genes transcribed to mRNAs. The genes forming the bottom layer are regulated from the top and negatively self-regulated. If the former regulation is positive, the dependence of the RNA populations on the governing parameters is found to be often non-monotonous. Specifically, the model predicts bistability. If the regulation is negative, the dependence of the RNA populations on the governing parameters is monotonous. In particular, the population of the mRNAs, corresponding to the genes forming the bottom layer, is nearly constant.     

ncRNA-mediated bistability in the synthesis of hundreds of distinct mRNAs and proteins

The kinetics of gene expression can be bistable due to the feedback between the mRNA and protein formation. In eukaryotic cells, the interplay between mRNAs and proteins can be influenced by non-coding RNAs. Some of these RNAs, e.g., microRNAs, may target hundreds of distinct mRNAs. The model presented here shows how a non-coding RNA can be used as a mediator in order to involve numerous mRNAs and proteins into a bistable network.     

Hierarchical genetic networks and noncoding RNAs

In eukaryotic cells, many genes are transcribed into noncoding RNAs. Such RNAs may associate with mRNAs and inhibit their translation and facilitate degradation. To clarify what may happen in this case, we propose a kinetic model describing the effect of noncoding RNAs on a mRNA-protein network with the hierarchical three-layer architecture. For positive regulation of the layers, our model predicts either bistability with a fairly narrow hysteresis loop or a unique steady state. For negative or mixed regulation, the steady state is found to be unique.     

Switches in gene expression including microRNA and a large number of distinct mRNAs

In eukaryotic cells, the kinetics of gene expression depends on the interplay of messenger RNAs (mRNAs), proteins, and nonprotein coding RNAs, or, more specifically, microRNAs. Some microRNAs may target hundreds of mRNAs. To describe this case, the author proposes a kinetic model implying that the microRNA synthesis is suppressed by the protein produced via the translation of one of the target mRNAs. With physically reasonable model parameters, the model predicts bistability or, in other words, switches in the expression of hundreds of genes. The text was submitted by the author in English.     

Dynamics and Mechanism of A Quorum Sensing Network Regulated by Small RNAs in Vibrio Harveyi

Bacterial quorum sensing (QS) has attracted much interests and it is an important process of cell communication. Recently, Bassler et al. studied the phenomena of QS regulated by small RNAs and the experimental data showed that small RNAs played important role in the QS of Vibrio harveyi and it can permit the fine-tuningof gene regulation and maintenance of homeostasis. According to Michaelis-Menten kinetics and mass action law in this paper, we construct a mathematical model to investigate the mechanism induced QS by coexist of small RNA and signal molecular (AI) and show that there are periodic oscillation when the time delay and Hill coefficient exceed a critical value and the periodic oscillation produces the change of concentration and induces QS. These results are fit to the experimental results. In the meanwhile, we also get some theoretical value of Hopf Bifurcation on time deday. In addition, we also find this network is robust against noise.     

Monostability,bistability, periodicity and chaos in gene regulatory network

This letter gives a general review on the monostability, bistability, periodicity and chaos in gene regulatory network. Some simple motifs that generate monostability, bistability, periodicity and chaos are analytically and numerically reported. Further research directions of the nonlinear dynamics of gene regulatory network are discussed.     

Drivers of structural features in gene regulatory networks: From biophysical constraints to biological function

Living cells can maintain their internal states, react to changing environments, grow, differentiate, divide, etc. All these processes are tightly controlled by what can be called a regulatory program. The logic of the underlying control can sometimes be guessed at by examining the network of influences amongst genetic components. Some associated gene regulatory networks have been studied in prokaryotes and eukaryotes, unveiling various structural features ranging from broad distributions of out-degrees to recurrent “motifs”, that is small subgraphs having a specific pattern of interactions. To understand what factors may be driving such structuring, a number of groups have introduced frameworks to model the dynamics of gene regulatory networks. In that context, we review here such in silico approaches and show how selection for phenotypes, i.e., network function, can shape network structure.     

Non-coding RNAs and complex distributed genetic networks

In eukaryotic cells, the mRNA-protein interplay can be dramatically influenced by non-coding RNAs (ncRNAs). Although this new paradigm is now widely accepted, an understanding of the effect of ncRNAs on complex genetic networks is lacking. To clarify what may happen in this case, we propose a mean-field kinetic model describing the influence of ncRNA on a complex genetic network with a distributed architecture including mutual protein-mediated regulation of many genes transcribed into mRNAs. ncRNA is considered to associate with mRNAs and inhibit their translation and/or facilitate degradation. Our results are indicative of the richness of the kinetics under consideration. The main complex features are found to be bistability and oscillations. One could expect to find kinetic chaos as well. The latter feature has however not been observed in our calculations. In addition, we illustrate the difference in the regulation of distributed networks by mRNA and ncRNA.     

Topological origin of global attractors in gene regulatory networks

Fixed-point attractors with global stability manifest themselves in a number of gene regulatory networks. This property indicates the stability of regulatory networks against small state perturbations and is closely related to other complex dynamics. In this paper, we aim to reveal the core modules in regulatory networks that determine their global attractors and the relationship between these core modules and other motifs. This work has been done via three steps. Firstly, inspired by the signal transmission in the regulation process, we extract the model of chain-like network from regulation networks. We propose a module of “ideal transmission chain(ITC)”, which is proved sufficient and necessary(under certain condition) to form a global fixed-point in the context of chain-like network. Secondly, by examining two well-studied regulatory networks(i.e., the cell-cycle regulatory networks of Budding yeast and Fission yeast), we identify the ideal modules in true regulation networks and demonstrate that the modules have a superior contribution to network stability(quantified by the relative size of the biggest attraction basin). Thirdly, in these two regulation networks, we find that the double negative feedback loops, which are the key motifs of forming bistability in regulation, are connected to these core modules with high network stability. These results have shed new light on the connection between the topological feature and the dynamic property of regulatory networks.     

Effects of nonlinear degradation of protein on the oscillatory dynamics in a simple gene regulatory network

Cooperative stability of protein is here defined as the tendency for the oligomers to be more stable than their monomeric components and to perform their physiological functions. In this paper, we incorporate nonlinear degradation of protein induced by cooperative stability into a simple model which has been previously presented in the biological literature. Linear analysis gives a critical time delay beyond which a periodic solution is born in a Hopf bifurcation. Lindstedt’s method is applied to the nonlinear system, resulting in closed form approximate expressions for the amplitude and frequency of oscillation. Our findings indicate that cooperative stability can cause periodic dynamics through reducing the critical time delay. In addition, we show that cooperative stability may increase the amplitude of oscillation. Our study contributes to the theoretical demonstration of the effect of cooperative stability in the simple gene regulatory network.     

Dynamics of network motifs in genetic regulatory networks

Network motifs hold a very important status in genetic regulatory networks. This paper aims to analyse the dynamical property of the network motifs in genetic regulatory networks. The main result we obtained is that the dynamical property of a single motif is very simple with only an asymptotically stable equilibrium point, but the combination of several motifs can make more complicated dynamical properties emerge such as limit cycles. The above-mentioned result shows that network motif is a stable substructure in genetic regulatory networks while their combinations make the genetic regulatory network more complicated.     

Coarse-grain reconstruction of genetic networks from expression levels

In the postgenome era many efforts have been dedicated to systematically elucidate the complex web of interacting genes and proteins. These efforts include experimental and computational methods. Microarray technology offers an opportunity for monitoring gene expression level at the genome scale. By recourse to information theory, this study proposes a mathematical approach to reconstruct gene regulatory networks at a coarse-grain level from high throughput gene expression data. The method provides the a posteriori probability that a given gene regulates positively, negatively or does not regulate each one of the network genes. This approach also allows the introduction of prior knowledge and the quantification of the information gain from experimental data used in the inference procedure. This information gain can be used to choose those genes that will be perturbed in subsequent experiments in order to refine our knowledge about the architecture of an underlying gene regulatory network. The performance of the proposed approach has been studied by in numero experiments. Our results suggest that the approach is suitable for focusing on size-limited problems, such as recovering a small subnetwork of interest by performing perturbation over selected genes.     

Power-law distribution of gene expression fluctuations

Large-scale genomic technologies has opened new possibilities to infer gene regulatory networks from time series data. Here, we investigate the relationship between the dynamic information of gene expression in time series and the underlying network structure. First, our results show that the distribution of gene expression fluctuations (i.e., standard deviation) follows a power-law. This finding indicates that while most genes exhibit a relatively low variation in expression level, a few genes are revealed as highly variable genes. Second, we propose a stochastic model that explains the emergence of this power-law behavior. The model derives a relationship that connects the standard deviation (variance) of each node to its degree. In particular, it allows us to identify a global property of the underlying genetic regulatory network, such as the degree exponent, by only computing dynamic information. This result not only offers an interesting link to explore the topology of real systems without knowing the real structure but also supports earlier findings showing that gene networks may follow a scale-free distribution.     

Statistical analysis of gene regulatory networks reconstructed from gene expression data of lung cancer

Recently, inferring gene regulatory network from large-scale gene expression data has been considered as an important effort to understand the life system in whole. In this paper, for the purpose of getting further information about lung cancer, a gene regulatory network of lung cancer is reconstructed from gene expression data. In this network, vertices represent genes and edges between any two vertices represent their co-regulatory relationships. It is found that this network has some characteristics which are shared by most cellular networks of health lives, such as power-law, small-world behaviors. On the other hand, it also presents some features which are obviously different from other networks, such as assortative mixing. In the last section of this paper, the significance of these findings in the context of biological processes of lung cancer is discussed.     

Evolution of canalizing Boolean networks

Boolean networks with canalizing functions are used to model gene regulatory networks. In order to learn how such networks may behave under evolutionary forces, we simulate the evolution of a single Boolean network by means of an adaptive walk, which allows us to explore the fitness landscape. Mutations change the connections and the functions of the nodes. Our fitness criterion is the robustness of the dynamical attractors against small perturbations. We find that with this fitness criterion the global maximum is always reached and that there is a huge neutral space of 100% fitness. Furthermore, in spite of having such a high degree of robustness, the evolved networks still share many features with “chaotic” networks.