Unconditional global exponential stability in Lagrange sense of genetic regulatory networks with SUM regulatory logic

Globally Asymptotic Stability Analysis for Genetic Regulatory Networks with Mixed Delays: An M-Matrix-Based Approach

This paper deals with the problem of globally asymptotic stability for nonnegative equilibrium points of genetic regulatory networks (GRNs) with mixed delays (i.e., time-varying discrete delays and constant distributed delays). Up to now, all existing stability criteria for equilibrium points of the kind of considered GRNs are in the form of the linear matrix inequalities (LMIs). In this paper, the Brouwer's fixed point theorem is employed to obtain sufficient conditions such that the kind of GRNs under consideration here has at least one nonnegative equilibrium point. Then, by using the nonsingular M-matrix theory and the functional differential equation theory, M-matrix-based sufficient conditions are proposed to guarantee that the kind of GRNs under consideration here has a unique nonnegative equilibrium point which is globally asymptotically stable. The M-matrix-based sufficient conditions derived here are to check whether a constant matrix is a nonsingular M-matrix, which can be easily verified, as there are many equivalent statements on the nonsingular M-matrices. So, in terms of computational complexity, the M-matrix-based stability criteria established in this paper are superior to the LMI-based ones in literature. To illustrate the effectiveness of the approach proposed in this paper, several numerical examples and their simulations are given.

Sufficient and necessary conditions for Lyapunov stability of genetic networks with SUM regulatory logic

In this paper, a nonlinear model for genetic regulator networks (GRNs) with SUM regulatory logic is presented. Four sufficient and necessary conditions of global asymptotical stability and global exponential stability for the equilibrium point of the GRNs are proposed, respectively. Specifically, three weak sufficient conditions and corresponding corollaries are derived by using comparing theorem and Dini derivative method. Then, a famous GRN model is used as the example to illustrate the effectiveness of our theoretical results. Comparing to the results in the previous literature, some novel ideas, study methods and interesting results are explored.

Stochastic S-system modeling of gene regulatory network

Microarray gene expression data can provide insights into biological processes at a system-wide level and is commonly used for reverse engineering gene regulatory networks (GRN). Due to the amalgamation of noise from different sources, microarray expression profiles become inherently noisy leading to significant impact on the GRN reconstruction process. Microarray replicates (both biological and technical), generated to increase the reliability of data obtained under noisy conditions, have limited influence in enhancing the accuracy of reconstruction . Therefore, instead of the conventional GRN modeling approaches which are deterministic, stochastic techniques are becoming increasingly necessary for inferring GRN from noisy microarray data. In this paper, we propose a new stochastic GRN model by investigating incorporation of various standard noise measurements in the deterministic S-system model. Experimental evaluations performed for varying sizes of synthetic network, representing different stochastic processes, demonstrate the effect of noise on the accuracy of genetic network modeling and the significance of stochastic modeling for GRN reconstruction . The proposed stochastic model is subsequently applied to infer the regulations among genes in two real life networks: (1) the well-studied IRMA network, a real-life in-vivo synthetic network constructed within the Saccharomyces cerevisiae yeast, and (2) the SOS DNA repair network in Escherichia coli.

Evaluating influence of microRNA in reconstructing gene regulatory networks

Gene regulatory network (GRN) consists of interactions between transcription factors (TFs) and target genes (TGs). Recently, it has been observed that micro RNAs (miRNAs) play a significant part in genetic interactions. However, current microarray technologies do not capture miRNA expression levels. To overcome this, we propose a new technique to reverse engineer GRN from the available partial microarray data which contains expression levels of TFs and TGs only. Using S-System model, the approach is adapted to cope with the unavailability of information about the expression levels of miRNAs. The versatile Differential Evolutionary algorithm is used for optimization and parameter estimation. Experimental studies on four in silico networks, and a real network of Saccharomyces cerevisiae called IRMA network, show significant improvement compared to traditional S-System approach.