Models Of Genetic Regulatory Networks Research Articles

Exponential convergence in the mean-square sense of nonlocal stochastic almost automorphic genetic regulatory lattice networks

This paper first establishes the lattice model for nonlocal stochastic genetic regulatory networks with reaction diffusions by employing a mix of the finite difference and Mittag–Leffler time Euler difference techniques. Second, the existence of a unique bounded almost automorphic sequence in distribution and global mean-square exponential convergence to the achieved difference model are investigated. An illustrative example is used to show the feasible of the works of the current paper.

Mathematical Modeling of Four-dimensional Genetic Regulatory Networks Using a Logistic Function

Mathematical modeling is a universal tool for the study of complex systems. In this paper formulas for characteristic numbers of critical points for the systems of order four (4D) are considered. We show how an unstable focus-focus can appear in a four-dimensional system. Projections of 4D trajectories on two-dimensional and threedimensional subspaces are shown. In the considered four-dimensional system the logistic function is used. The research aims to investigate the four-dimensional system, find critical points of the system, calculate the characteristic numbers, and calculate Lyapunov exponents.

Novel adaptive strategies for synchronization control mechanism in nonlinear dynamic fuzzy modeling of fractional-order genetic regulatory networks

The synchronization problem for a nonlinear dynamic fuzzy modeling of fractional-order genetic regulatory networks with adaptive feedback controllers is addressed in this article. To address such a problem, a fuzzy feedback MAX template and a fuzzy feedback MIN template of fuzzy modeling are introduced. We developed adaptive based criteria to ensure the asymptotic and finite-time stability of the error system by constructing a suitable Lyapunov functional with linear matrix inequality (LMI) approach, which ensures the drive system synchronizes with the response system. Meanwhile, two distinct controllers, linear feedback and adaptive feedback control are being developed. It should be noted that the presented results are expressed in terms of LMI, which can be efficiently solved using Matlab LMI toolbox. Numerical simulations are carried out to illustrate the theoretical results.

Genetic engineering – construction of a network of four dimensions with a chaotic attractor

Systems of ordinary differential equations (ODE) of special form are considered in this paper. These systems appear in various models of genetic regulatory networks and telecommunication networks. The model of a genetic network with a chaotic attractor of dimension four is constructed. Geometrical considerations are used to study the properties of the systems. Computation of Lyapunov exponents is used to prove the existence of chaotic attractors. Problems of control and management of such regulatory systems are challenging issues in the theory of genetic networks.

Transcriptomic analysis of tuberous root in two sweet potato varieties reveals the important genes and regulatory pathways in tuberous root development

BackgroundTuberous root formation and development is a complex process in sweet potato, which is regulated by multiple genes and environmental factors. However, the regulatory mechanism of tuberous root development is unclear.ResultsIn this study, the transcriptome of fibrous roots (R0) and tuberous roots in three developmental stages (Rl, R2, R3) were analyzed in two sweet potato varieties, GJS-8 and XGH. A total of 22,914 and 24,446 differentially expressed genes (DEGs) were identified in GJS-8 and XGH respectively, 15,920 differential genes were shared by GJS-8 and XGH. KEGG pathway enrichment analysis showed that the DEGs shared by GJS-8 and XGH were mainly involved in “plant hormone signal transduction” “starch and sucrose metabolism” and “MAPK signal transduction”. Trihelix transcription factor (Tai6.25300) was found to be closely related to tuberous root enlargement by the comprehensive analysis of these DEGs and weighted gene co-expression network analysis (WGCNA).ConclusionA hypothetical model of genetic regulatory network for tuberous root development of sweet potato is proposed, which emphasizes that some specific signal transduction pathways like “plant hormone signal transduction” “Ca2+signal” “MAPK signal transduction” and metabolic processes including “starch and sucrose metabolism” and “cell cycle and cell wall metabolism” are related to tuberous root development in sweet potato. These results provide new insights into the molecular mechanism of tuberous root development in sweet potato.

Fixed-Time Synchronization Analysis of Genetic Regulatory Network Model with Time-Delay

The synchronous genetic regulatory networks model includes the drive system and response system, and the drive-response system is symmetric. From a biological point of view, this model illustrates the dynamic behaviors in gene-to-protein processes, in terms of transcription and translation. This paper introduces a model of genetic regulatory networks with time delay. The fixed-time synchronization control problem of the proposed model is studied based on fixed-time stability theory and the Lyapunov method. Concretely, the authors first propose a way to switch from the given model to matrix form. Then, two types of novel controllers are designed and the corresponding sufficient conditions are investigated respectively to ensure the fixed-time synchronization goal. Moreover, the settling times of fixed-time synchronization are estimated for the addressed discontinuous controllers, which are not dependent on the initial or delayed states of the model. Finally, numerical simulations are presented and compared to illustrate the benefits of the theoretical results.

Regulation and the Normativity Problem

ABSTRACT The concept of regulation pervades biology, for example in models of genetic regulatory networks and the endocrine system. Regulation has a normative opposite, dysregulation, which figures prominently in biomedical models of disease. The use of normative concepts in biology, however, has been thought to present some challenges for the physicalist view of the world, and various resolutions have been proposed. Up to now the problem of biological normativity has been debated largely in connection with the concept of biological information. In this paper we shift focus to the concept of biological regulation, proposing that it provides a promising new approach to these issues. Models of regulatory systems have several features: they are causal, but they do not deal with the energy exchanges and transformations covered by physics and chemistry; further, and entirely connected, regulatory systems can break down, and this is because they and their causal-regulatory properties are dependent on fragile molecular structures. Biological regulatory systems exhibit normativity, because they are not determined by physical and chemical laws, but their close relationship with physical laws and physicalist ontology is transparent.

Dynamics of fuzzy genetic regulatory networks with leakage and mixed delays in doubly-measure pseudo-almost periodic environment

The study of dynamics behaviors of genetic regulatory networks (GRNs) is essential for the understanding of living organisms at both molecular and cellular levels. This paper deals with a class of fuzzy genetic regulatory networks (FGRNs) with time varying-delays in leakage terms, time-varying discrete delays, unbounded distributed delays, and doubly-measure pseudo-almost periodic parameters. Based on the doubly-measure pseudo-almost periodic theory, exponential dichotomy, differential inequality, and the Banach fixed point theorem, we establish some sufficient conditions to support the existence and global exponential stability of doubly-measure pseudo-almost periodic solutions for the considered model. A numerical example along with a graphical illustration are presented to support our main results. The results of this paper are new and extend existing GRNs models using almost periodic and weighted pseudo-almost periodic functions to support a wider range of regulatory processes.

On convergence for hybrid models of gene regulatory networks under polytopic uncertainties: a Lyapunov approach

Hybrid models of genetic regulatory networks allow for a simpler analysis with respect to fully detailed quantitative models, still maintaining the main dynamical features of interest. In this paper we consider a piecewise affine model of a genetic regulatory network, in which the parameters describing the production function are affected by polytopic uncertainties. In the first part of the paper, after recalling how the problem of finding a Lyapunov function is solved in the nominal case, we present the considered polytopic uncertain system and then, after describing how to deal with sliding mode solutions, we prove a result of existence of a parameter dependent Lyapunov function subject to the solution of a feasibility linear matrix inequalities problem. In the second part of the paper, based on the previously described Lyapunov function, we are able to determine a set of domains where the system is guaranteed to converge, with the exception of a zero measure set of times, independently from the uncertainty realization. Finally a three nodes network example shows the validity of the results.

Mathematical Modelling of Leukemia Treatment

Leukemia is a cancer that can be treated in a variety of ways: chemotherapy, radiation therapy and stem cell transplant. Recovery rates for this disease are relatively high, the treatment itself has a painful effect on the body and is accompanied by numerous side effects that can persist years after the patient is cured. For this reason, efforts are underway worldwide to develop more selective therapies that will only affect leukemia cells and not healthy cells. Knowledge of developmental GRN is yet scarce, and it is early for a systematic comparative effort. We consider mathematical model of genetic regulatory networks. This model consists of a nonlinear system of ordinary differential equations. We describe the changes that system undergoes if the entries of the regulatory matrix are perturbed in some way. We discuss, how attractors for high-dimensional systems can be constructed, using known attractors of low-dimensional systems. Examples and visualizations are provided.

On Modelling of Genetic Regulatory Net Works

We consider mathematical model of genetic regulatory networks (GRN). This model consists of a nonlinear system of ordinary differential equations. The vector of solutions X(t) is interpreted as a current state of a network for a given value of time t: Evolution of a network and future states depend heavily on attractors of system of ODE. We discuss this issue for low dimensional networks and show how the results can be applied for the study of large size networks. Examples and visualizations are provided

State estimator design for genetic regulatory networks with leakage and discrete heterogeneous delays: A nonlinear model transformation approach

We address the state estimation problem for a class of genetic regulatory networks (GRNs) with leakage and discrete heterogeneous delays in this paper. In order to simplify the complexity of designing the state estimator for nonlinear delayed model of GRNs, a state estimate algorithm based on a model transformation method is presented, which goal is to get the entire system state. First, in light of the Lagrange’s mean-value theorem, the nonlinear model transformation method is applied to describe the nonlinear error system as a linear time-varying model. Second, by constructing the Lyapunov–Krasovskii functional dependent on the composite function variables of state estimate errors, a new technique lemma is provided and applied to the stability analysis. Third, the sufficient condition of state estimator design is obtained in term linear matrix inequalities, under which, the certification of the uniform asymptotic stability for state estimate error system is derived. Finally, a simulation example illustrates the rationality and effectiveness of the proposed theoretical results.

Logical matrix factorization towards topological structure and stability of probabilistic Boolean networks

Abstract The study of logical matrix factorization provides a new insight into the matrix dimension reduction problems of biological systems. This paper develops the logical matrix factorization technique for exploring the topological structure and stability of probabilistic Boolean networks (PBNs). Firstly, the union set of distinct indices in factorized structural matrices for different modes is obtained, based on which, a size-reduced system is constructed for the original PBN. Secondly, it is proved that the topological structure of original PBN is equivalent to that of the size-reduced system. Thirdly, the equivalence of finite-time stability and stability in distribution between the original PBN and the size-reduced system is further revealed. Finally, the effectiveness of the obtained new results are verified via several Boolean models of genetic regulatory networks (GRNs).

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.

Control in Inhibitory Genetic Regulatory Network Models

The system of two the first order ordinary differential equations arising in the gene regulatory networks theory is studied. The structure of attractors for this system is described for three important behavioral cases: activation, inhibition, mixed activation-inhibition. The geometrical approach combined with the vector field analysis allows treating the problem in full generality. A number of propositions are stated and the proof is geometrical, avoiding complex analytic. Although not all the possible cases are considered, the instructions are given what to do in any particular situation.

Robustness for Stability and Stabilization of Boolean Networks With Stochastic Function Perturbations

In genetic regulatory networks (GRNs), gene mutations often occur in a stochastic manner. As an important model of GRNs, gene mutations of Boolean networks are always described as function perturbations. This article studies the robust stability and stabilization of Boolean networks with stochastic function perturbations. A kind of parameterized set is constructed, and it is revealed that under the stochastic function perturbations, the property of finite-time stability remains unchanged when the perturbed set and the parameterized set are disjoint. In addition, it is proved that the finite-time stability is reduced to stability in distribution when the intersection of perturbed set and complement set of parameterized set is nonempty. As an application, the robust stabilization problem of Boolean control networks with stochastic function perturbations is discussed, and several necessary and sufficient conditions are presented for the robustness of feedback stabilizers. Finally, the obtained results are used to study the Drosophila melanogaster segmentation polarity gene network and the lac operon in the bacterium Escherichia coil.

Integrated mRNA and miRNA transcriptome analysis reveals a regulatory network for tuber expansion in Chinese yam (Dioscorea opposita)

BackgroundYam tuber is a storage organ, derived from the modified stem. Tuber expansion is a complex process, and depends on the expressions of genes that can be influenced by environmental and endogenous factors. However, little is known about the regulatory mechanism of tuber expansion. In order to identify the genes and miRNAs involved in tuber expansion, we examined the mRNAs and small RNAs in Dioscorea opposita (Chinese yam) cv. Guihuai 16 tuber during its initiation and expansion stages.ResultsA total of 14,238 differentially expressed genes in yam tuber at its expansion stage were identified by using RNA sequencing technology. Among them, 5723 genes were up-regulated, and 8515 genes were down-regulated. Functional analysis revealed the coordination of tuber plant involved in processes of cell events, metabolism, biosynthesis, and signal transduction pathways at transcriptional level, suggesting that these differentially expressed genes are somehow involved in response to tuber expansion, including CDPK, CaM, CDL, SAUR, DELLA, SuSy, and expansin. In addition, 541 transcription factor genes showed differential expression during the expansion stage at transcriptional level. MADS, bHLH, and GRAS were involved in cell differentiation, division, and expansion, which may relate to tuber expansion. Noteworthy, data analysis revealed that 22 known tuber miRNAs belong to 10 miRNA families, and 50 novel miRNAs were identified. The integrated analysis of miRNA-mRNA showed that 4 known miRNAs and 11 genes formed 14 miRNA-target mRNA pairs were co-expressed in expansion stage. miRNA160, miRNA396, miRNA535 and miRNA5021 may be involved in complex network to regulate cell division and differentiation in yam during its expansion stage.ConclusionThe mRNA and miRNA datasets presented here identified a subset of candidate genes and miRNAs that are putatively associated with tuber expansion in yam, a hypothetical model of genetic regulatory network associated with tuber expansion in yam was put forward, which may provide a foundation for molecular regulatory mechanism researching on tuber expansion in Dioscorea species.

Study of Piecewise Multi-affine models for Genetic Regulatory Networks via a Lyapunov approach: an LMI framework

In this work we study convergence properties of Piecewise Multi-Affine models of genetic regulatory networks, by means of a Lyapunov approach. These models, quantitatively more accurate than their Piecewise Affine counterpart, are obtained by a Piecewise Linear approximation of sigmoids regulation functions. In this work, using a linear matrix inequalities framework, we are able to find, if one exists subject to a box partitioning of the state space, a Piecewise Quadratic Lyapunov function, which is non-increasing along any system trajectory. In the first part of the paper we describe the considered model, defining and motivating the hyper-rectangular partition of the state space, while in the second part, using a result on the expression of multi-affine functions on an hyper-rectangle, we can define a set of linear matrix inequalities, whose solution gives the description of a piecewise quadratic Lyapunov function for the system. Convergence properties based on such functions are discussed and a numerical example will show the applicability of the results.

Distribution of fitness effects of mutations obtained from a simple genetic regulatory network model

Beneficial and deleterious mutations change an organism’s fitness but the distribution of these mutational effects on fitness are unknown. Several experimental, theoretical, and computational studies have explored this question but are limited because of experimental restrictions, or disconnect with physiology. Here we attempt to characterize the distribution of fitness effects (DFE) due to mutations in a cellular regulatory motif. We use a simple mathematical model to describe the dynamics of gene expression in the lactose utilization network, and use a cost-benefit framework to link the model output to fitness. We simulate mutations by changing model parameters and computing altered fitness to obtain the DFE. We find beneficial mutations distributed exponentially, but distribution of deleterious mutations seems far more complex. In addition, we find neither the starting fitness, nor the exact location on the fitness landscape, affecting these distributions qualitatively. Lastly, we quantify epistasis in our model and find that the distribution of epistatic effects remains qualitatively conserved across different locations on the fitness landscape. Overall, we present a first attempt at exploring the specific statistical features of the fitness landscape associated with a system, by using the specific mathematical model associated with it.

On the stability of multilayer Boolean networks under targeted immunization

In this paper, we study targeted immunization in a multilayer Boolean network model for genetic regulatory networks. Given a specific set of nodes immune to perturbations, we find that the stability of a multilayer Boolean network is determined by the largest eigenvalue of the weighted non-backtracking matrix of corresponding aggregated network. Aimed to minimize this largest eigenvalue, we developed the metric of multilayer collective influence (MCI) to quantify the impact of immunizing individual nodes on the stability of the system. Compared with other competing heuristics, immunizing nodes with high MCI scores can stabilize an unstable multilayer network with higher efficiency on both synthetic and real-world networks. Moreover, despite that coupling nodes can exert direct influence across multiple layers, they are found to exhibit less importance as measured by the MCI score. Our work reveals the mechanism of maintaining the stability of multilayer Boolean networks and provides an efficient targeted immunization strategy, which can be potentially applied to the location of pathogenesis of diseases and the development of targeted therapy.