Designing Genetic Regulatory Networks Using Fuzzy Petri Nets Approach

In this paper, we have successfully presented a fuzzy Petri net （FPN） model to design the genetic regulatory network. Based on the FPN model, an efficient algorithm is proposed to automatically reason about imprecise and fuzzy information. By using the reasoning algorithm for the FPN, we present an alternative approach that is more promising than the fuzzy logic. The proposed FPN approach offers more flexible reasoning capability because it is able to obtain results with fuzzy intervals rather than point values. In this paper, a novel model with a new concept of hidden fuzzy transition （HFT） to design the genetic regulatory network is developed. We have built the FPN model and classified the input data in terms of time point and obtained the output data, so the system can be viewed as the two-input and one output system. This method eliminates possible false predictions from the classical fuzzy model thereby allowing a wider search space for inferring regulatory relationship. The experimental results show the proposed approach is feasible and acceptable to design the genetic regulatory network and investigate the dynamical behaviors of gene network.

Stability of piecewise-linear models of genetic regulatory networks

This paper investigates the stability of the equilibria of the piecewise-linear models of genetic regulatory networks on the intersection of the thresholds of all variables. It first studies circling trajectories and derives some stability conditions by quantitative analysis in the state transition graph. Then it proposes a common Lyapunov function for convergence analysis of the piecewise-linear models and gives a simple sign condition. All the obtained conditions are only related to the constant terms on the right-hand side of the differential equation after bringing the equilibrium to zero.

Oscillatory and anti-oscillatory motifs in genetic regulatory networks

Recently, self-sustained oscillatory genetic regulatory networks （GRNs） have attracted significant attention in the biological field. Given a GRN, it is important to anticipate whether the network could generate oscillation with proper parameters, and what the key ingredients for the oscillation are. In this paper the ranges of some function-related parameters which are favorable to sustained oscillations are considered. In particular, some oscillatory motifs appearing with high-frequency in most of the oscillatory GRNs are observed. Moreover, there are some anti-oscillatory motifs which have a strong oscillation repressing effect. Some conclusions analyzing these motif effects and constructing oscillatory GRNs are provided.

MODELING GENETIC REGULATORY NETWORKS:A DELAY DISCRETE DYNAMICAL MODEL APPROACH

Modeling genetic regulatory networks is an important research topic in genomic research and computationM systems biology. This paper considers the problem of constructing a genetic regula- tory network （GRN） using the discrete dynamic system （DDS） model approach. Although considerable research has been devoted to building GRNs, many of the works did not consider the time-delay effect. Here, the authors propose a time-delay DDS model composed of linear difference equations to represent temporal interactions among significantly expressed genes. The authors also introduce interpolation scheme and re-sampling method for equalizing the non-uniformity of sampling time points. Statistical significance plays an active role in obtaining the optimal interaction matrix of GRNs. The constructed genetic network using linear multiple regression matches with the original data very well. Simulation results are given to demonstrate the effectiveness of the proposed method and model.

Bifurcation and Turing instability for genetic regulatory networks with diffusion

In this paper,a diffusive genetic regulatory network under Neumann boundary conditions is considered.First,the criteria for the local stability and diffusion-driven instability of the positive stationary solution without and with diffusion are investigated,respectively.Moreover,Turing regions and pattern formation are obtained in the plane of diffusion coeficients.Second,the existence and multiplicity of spatially homogeneous/nonhomogeneous non-constant steady-states are studied by using the Lyapunov-Schmidt reduction.Finally,some numerical simulations are carried out to illustrate the theoretical results.

Existence and exponential stability of weighted pseudo-almost periodic solutions for genetic regulatory networks with time-varying delays

The importance of prediction for genetic regulatory network(GRNs)makes mathematical modeling a prominent tool.In this paper,we consider weighted pseudo-almost periodic solutions for a class of GRNs with time-varying delays.We establish the existence,uniqueness,and global exponential stability by employing the theory of dichotomy,the fixed point theorem,and differential inequality.A numerical example along with a graphical illustration are presented to support our main results.Our results extend existing GRNs models using almost periodic functions to support a wider range of regulatory processes.

Delayed fuzzy genetic regulatory networks:Novel results

In this manuscript, we studied a class of delayed Fuzzy Genetic Regulatory Networks (FGRNs) with Stepanov-like weighted pseudo almost automorphic coefficients. New criteria for the existence, uniqueness and global exponential stability of its weighted pseudo almost automorphic solution are established. Our approach is based on Banach fixed point theorem and novel analysis techniques. Moreover, a numerical example is given to illustrate the validity of the obtained results.

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.

Structure and Dynamics of Artificial Regulatory Networks Evolved by Segmental Duplication and Divergence Model

Based on a model of network encoding and dynamics called the artificial genome, we propose a segmental duplication and divergence model for evolving artificial regulatory networks. We find that this class of networks share structural properties with natural transcriptional regulatory networks. Specifically, these networks can display scale-free and small-world structures. We also find that these networks have a higher probability to operate in the ordered regimen, and a lower probability to operate in the chaotic regimen. That is, the dynamics of these networks is similar to that of natural networks. The results show that the structure and dynamics inherent in natural networks may be in part due to their method of generation rather than being exclusively shaped by subsequent evolution under natural selection.

Computing a Predictor Set Influence Zone through a Multi-Layer Genetic Network to Explore the Role of Estrogen in Breast Cancer

Modeling inter-relationships of genes over a specific genetic network is one of the most challenging studies in systems biology. Among the families of models proposed one commonly used is the discrete stochastic, based on conditionally independent Markov chains. In practice, this model is estimated from time sequential sampling, usually obtained by microarray experiments. In order to improve the accuracy of the estimation method, we can use biological knowledge. In this paper, we decided to apply this idea to study the role of estrogen in breast cancer proliferation. The n-influence zone of a set S of genes in a given multi-layer genetic network is a set L of genes regulated, directly or indirectly, by genes in S, after at most n-1 layers. In this manuscript we describe a new approach for computing the n-influence zone of S through the estimation of a multi-layer genetic network from gene expression time series, measured by microarrays, and biological knowledge. Using seed genes related to cell proliferation, our method was able to add to the third layer of the network other genes related to this biological function and validated in the literature. Using a set of genes directly influenced by estrogen, we could find a new role for cell adhesion genes estrogen dependent. Our pipeline is user-friendly and does not have high system requirements. We believe this paper could contribute to improve the data mining for biologists in microarray time series.