scholarly journals From foodwebs to gene regulatory networks (GRNs) - weak repressions by microRNAs confer system stability

2017 ◽  
Author(s):  
Yuxin Chen ◽  
Yang Shen ◽  
Stefano Allesina ◽  
Chung-I Wu
Keyword(s):  
Regulatory Networks ◽  
Stability Control ◽  
System Stability ◽  
Yeast Cells ◽  
System Level ◽  
Main Function ◽  
Highly Expressed Genes ◽  
Gene Regulatory ◽  
Mechanistic Basis ◽  
The Stability

AbstractMore than 30% of mRNAs are repressed by microRNAs (miRNAs) but most repressions are too weak to have a phenotypic consequence. The diffuse actions have been a central conundrum in understanding the functions of miRNAs. By applying the May-Wigner theory used in foodweb studies, we show that i) weak repressions cumulatively enhance the stability of gene regulatory network (GRN), and ii) broad and weak repressions confer greater stability than a few strong ones. Transcriptome data show that yeast cells, which do not have miRNAs, use strong and non-specific mRNA degradation to stabilize their GRN; in contrast, human cells use miRNAs to increase degradation more modestly and selectively. Simulations indicate that miRNA repressions should be distributed broadly to >25% of mRNAs, in agreement with observations. As predicted, extremely highly expressed genes are avoided and transcription factors are preferred by miRNAs. In conclusion, the diffuse repression by miRNAs is likely a system-level strategy for enhancing GRN stability. This stability control may be the mechanistic basis of “canalization” (i.e., developmental homeostasis within each species), sometimes hypothesized to be a main function of miRNAs.

scholarly journals Gene regulatory network stabilized by pervasive weak repressions: microRNA functions revealed by the May–Wigner theory

2019 ◽  
Vol 6 (6) ◽  
pp. 1176-1188 ◽  
Author(s):  
Yuxin Chen ◽  
Yang Shen ◽  
Pei Lin ◽  
Ding Tong ◽  
Yixin Zhao ◽  
...  
Keyword(s):  
Gene Regulatory Networks ◽  
Biological Networks ◽  
Regulatory Network ◽  
Mammalian Cells ◽  
Regulatory Networks ◽  
Yeast Cells ◽  
Gene Products ◽  
Mathematical Solution ◽  
Gene Regulatory ◽  
The Stability

Abstract Food web and gene regulatory networks (GRNs) are large biological networks, both of which can be analyzed using the May–Wigner theory. According to the theory, networks as large as mammalian GRNs would require dedicated gene products for stabilization. We propose that microRNAs (miRNAs) are those products. More than 30% of genes are repressed by miRNAs, but most repressions are too weak to have a phenotypic consequence. The theory shows that (i) weak repressions cumulatively enhance the stability of GRNs, and (ii) broad and weak repressions confer greater stability than a few strong ones. Hence, the diffuse actions of miRNAs in mammalian cells appear to function mainly in stabilizing GRNs. The postulated link between mRNA repression and GRN stability can be seen in a different light in yeast, which do not have miRNAs. Yeast cells rely on non-specific RNA nucleases to strongly degrade mRNAs for GRN stability. The strategy is suited to GRNs of small and rapidly dividing yeast cells, but not the larger mammalian cells. In conclusion, the May–Wigner theory, supplanting the analysis of small motifs, provides a mathematical solution to GRN stability, thus linking miRNAs explicitly to ‘developmental canalization’.

Global stability analysis of fractional-order gene regulatory networks with time delay

2019 ◽  
Vol 12 (06) ◽  
pp. 1950067 ◽  
Author(s):  
Zhaohua Wu ◽  
Zhiming Wang ◽  
Tiejun Zhou
Keyword(s):  
Time Delay ◽  
Fractional Order ◽  
Gene Regulatory Networks ◽  
Existence And Uniqueness ◽  
Regulatory Networks ◽  
Lyapunov Method ◽  
Regulation Mechanism ◽  
Global Stability Analysis ◽  
Gene Regulatory ◽  
The Stability

Fractional-order gene regulatory networks with time delay (DFGRNs) have proven that they are more suitable to model gene regulation mechanism than integer-order. In this paper, a novel DFGRN is proposed. The existence and uniqueness of the equilibrium point for the DFGRN are proved under certain conditions. On this basis, the conditions on the global asymptotic stability are established by using the Lyapunov method and comparison theorem for the DFGRN, and the stability conditions are dependent on the fractional-order [Formula: see text]. Finally, numerical simulations show that the obtained results are reasonable.

The Impact of Process Architecture on Equilibrium Stability in Distributed Design

2011 ◽  
Vol 133 (10) ◽  
Author(s):  
Erich Devendorf ◽  
Kemper Lewis
Keyword(s):  
Solution Process ◽  
System Stability ◽  
System Level ◽  
Design System ◽  
Distributed Design ◽  
General Process ◽  
Architecture Model ◽  
The Stability ◽  
Process Architecture ◽  
The Impact

In distributed design processes, individual design subsystems have local control over design variables and seek to satisfy their own individual objectives, which may also be influenced by some system level objectives. The resulting network of coupled subsystems will either converge to a stable equilibrium or diverge in an unstable manner. In this paper, we study the dependence of system stability on the solution process architecture. The solution process architecture describes how the design subsystems are ordered and can be either sequential, parallel, or a hybrid that incorporates both parallel and sequential elements. In this paper, we demonstrate that the stability of a distributed design system does indeed depend on the solution process architecture chosen, and we create a general process architecture model based on linear systems theory. The model allows the stability of equilibrium solutions to be analyzed for distributed design systems by converting any process architecture into an equivalent parallel representation. Moreover, we show that this approach can accurately predict when the equilibrium is unstable and the system divergent when previous models suggest that the system is convergent.

scholarly journals Stability Analysis of an Inverted Pendulum on a Cart with the Presence of Restoring and Frictional Forces Disturbance using Observer Based and Full State Feedback H2 Controllers

2020 ◽  
Author(s):  
Mustefa Jibril ◽  
Messay Tadese ◽  
Fiseha Bogale
Keyword(s):  
State Feedback ◽  
Inverted Pendulum ◽  
Stability Control ◽  
System Stability ◽  
Lagrangian Equation ◽  
System Equation ◽  
Full State ◽  
Full State Feedback ◽  
Frictional Forces ◽  
The Stability

In this paper, the stability control of the inverted pendulum on a cart with a disturbance forces has been done using observer based and full state feedback H2 controllers. The Lagrangian equation has been used to model the system equation of motions and linearized the system to the unstable upward position. Comparison of the system stability has been simulated by comparing the proposed controllers using Matlab/Scripts and a promising results has been analyzed successfully.

Duffing Chaotic System Stability Control Based on Sliding Mode Control

2012 ◽  
Vol 605-607 ◽  
pp. 1639-1642
Author(s):  
Ding Ma
Keyword(s):  
Chaotic System ◽  
Control Method ◽  
Sliding Mode ◽  
Variable Structure ◽  
Stability Control ◽  
System Stability ◽  
Terminal Sliding Mode ◽  
Sliding Mode Variable Structure ◽  
The Stability ◽  
And Control

Considering the Duffing chaotic system, the problem of stability control based on the terminal sliding mode variable structure is studied. A new terminal sliding mode surface and control law are designed. On this basis, the stability of closed-loop system is analyzed. Simulation results show the effectiveness of the control method.

scholarly journals Global uniform asymptotical stability for fractional-order gene regulatory networks with time-varying delays and structured uncertainties

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Zhaohua Wu ◽  
Zhiming Wang ◽  
Tiejun Zhou
Keyword(s):  
Fractional Order ◽  
Gene Regulatory Networks ◽  
Regulatory Networks ◽  
Contraction Mapping ◽  
Contraction Mapping Principle ◽  
Time Varying ◽  
The Novel ◽  
Razumikhin Technique ◽  
Gene Regulatory ◽  
The Stability

AbstractIn this paper, we investigate a class of fractional-order gene regulatory networks with time-varying delays and structured uncertainties (UDFGRNs). First, we deduce the existence and uniqueness of the equilibrium for the UDFGRNs by using the contraction mapping principle. Next, we derive a novel global uniform asymptotic stability criterion of the UDFGRNs by using a Lyapunov function and the Razumikhin technique, and the conditions relating to the criterion depend on the fractional order of the UDFGRNs. Finally, we provide two numerical simulation examples to demonstrate the correctness and usefulness of the novel stability conditions. One of the most interesting findings is that the structured uncertainties indeed have an impact on the stability of the system.

scholarly journals The Dynamics of Canalizing Boolean Networks

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-14
Author(s):  
Elijah Paul ◽  
Gleb Pogudin ◽  
William Qin ◽  
Reinhard Laubenbacher
Keyword(s):  
Gene Regulatory Networks ◽  
Regulatory Networks ◽  
Boolean Network ◽  
Boolean Networks ◽  
Molecular Networks ◽  
Biological Applications ◽  
Expected Number ◽  
Modeling Framework ◽  
Gene Regulatory ◽  
The Stability

Boolean networks are a popular modeling framework in computational biology to capture the dynamics of molecular networks, such as gene regulatory networks. It has been observed that many published models of such networks are defined by regulatory rules driving the dynamics that have certain so-called canalizing properties. In this paper, we investigate the dynamics of a random Boolean network with such properties using analytical methods and simulations. From our simulations, we observe that Boolean networks with higher canalizing depth have generally fewer attractors, the attractors are smaller, and the basins are larger, with implications for the stability and robustness of the models. These properties are relevant to many biological applications. Moreover, our results show that, from the standpoint of the attractor structure, high canalizing depth, compared to relatively small positive canalizing depth, has a very modest impact on dynamics. Motivated by these observations, we conduct mathematical study of the attractor structure of a random Boolean network of canalizing depth one (i.e., the smallest positive depth). For every positive integer ℓ, we give an explicit formula for the limit of the expected number of attractors of length ℓ in an n-state random Boolean network as n goes to infinity.

Incorporating Process Architecture in the Evaluation of Stability in Distributed Design

2011 ◽  
Author(s):  
Erich Devendorf ◽  
Kemper Lewis
Keyword(s):  
Solution Process ◽  
System Stability ◽  
System Level ◽  
Design System ◽  
Distributed Design ◽  
Equilibrium Solutions ◽  
General Process ◽  
Architecture Model ◽  
The Stability ◽  
Process Architecture

In distributed design processes, individual design subsystems have local control over design variables and seek to satisfy their own individual objectives, which may also be influenced by some system level objectives. The resulting network of coupled subsystems will either converge to a stable equilibrium, or diverge in an unstable manner. In this paper, we study the dependence of system stability on the solution process architecture. The solution process architecture describes how the design subsystems are ordered and can be either sequential, parallel, or a hybrid that incorporates both parallel and sequential elements. In this paper we demonstrate that the stability of a distributed design system does indeed depend on the solution process architecture chosen and we create a general process architecture model based on linear systems theory. The model allows the stability of equilibrium solutions to be analyzed for distributed design systems by converting any process architecture into an equivalent parallel representation. Moreover, we show that this approach can accurately predict when the equilibrium is unstable and the system divergent when previous models suggest the system is convergent.

scholarly journals Stability of Imbalanced Triangles in Gene Regulatory Networks of Cancerous and Normal Cells

2021 ◽  
Vol 11 ◽  
Author(s):  
Abbas Karimi Rizi ◽  
Mina Zamani ◽  
Amirhossein Shirazi ◽  
G. Reza Jafari ◽  
János Kertész
Keyword(s):  
Gene Regulatory Networks ◽  
Collective Behavior ◽  
Regulatory Networks ◽  
Sequencing Data ◽  
Normal Cells ◽  
Gene Regulatory ◽  
Regulatory Effects ◽  
The Stability ◽  
Cancerous Cells ◽  
Inhibitory Interactions

Genes communicate with each other through different regulatory effects, which lead to the emergence of complex network structures in cells, and such structures are expected to be different for normal and cancerous cells. To study these differences, we have investigated the Gene Regulatory Network (GRN) of cells as inferred from RNA-sequencing data. The GRN is a signed weighted network corresponding to the inductive or inhibitory interactions. Here we focus on a particular of motifs in the GRN, the triangles, which are imbalanced if the number of negative interactions is odd. By studying the stability of imbalanced triangles in the GRN, we show that the network of cancerous cells has fewer imbalanced triangles compared to normal cells. Moreover, in the normal cells, imbalanced triangles are isolated from the main part of the network, while such motifs are part of the network's giant component in cancerous cells. Our result demonstrates that due to genes' collective behavior the structure of the complex networks is different in cancerous cells from those in normal ones.

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