Robust stability of stochastic delayed genetic regulatory networks.
Ontology highlight
ABSTRACT:
SUBMITTER: Wang Z
PROVIDER: S-EPMC2727162 | biostudies-other | 2009 Sep
REPOSITORIES: biostudies-other
Similar Datasets
Project description:This paper investigates robust stability of genetic regulatory networks with distributed delay. Different from other papers, distributed delay is induced. It says that the concentration of macromolecule depends on an integral of the regulatory function of over a specified range of previous time, which is more realistic. Based on Lyapunov stability theory and linear matrix inequality (LMI), sufficient conditions for genetic regulatory networks to be global asymptotic stability and robust stability are derived in terms of LMI. Two numerical examples are given to illustrate the effectiveness of our theoretical results.
| S-EPMC2585616 | biostudies-other
Project description:Bistability arises within a wide range of biological systems from the lambda phage switch in bacteria to cellular signal transduction pathways in mammalian cells. Changes in regulatory mechanisms may result in genetic switching in a bistable system. Recently, more and more experimental evidence in the form of bimodal population distributions indicates that noise plays a very important role in the switching of bistable systems. Although deterministic models have been used for studying the existence of bistability properties under various system conditions, these models cannot realize cell-to-cell fluctuations in genetic switching. However, there is a lag in the development of stochastic models for studying the impact of noise in bistable systems because of the lack of detailed knowledge of biochemical reactions, kinetic rates, and molecular numbers. In this work, we develop a previously undescribed general technique for developing quantitative stochastic models for large-scale genetic regulatory networks by introducing Poisson random variables into deterministic models described by ordinary differential equations. Two stochastic models have been proposed for the genetic toggle switch interfaced with either the SOS signaling pathway or a quorum-sensing signaling pathway, and we have successfully realized experimental results showing bimodal population distributions. Because the introduced stochastic models are based on widely used ordinary differential equation models, the success of this work suggests that this approach is a very promising one for studying noise in large-scale genetic regulatory networks.
| S-EPMC1482501 | biostudies-literature
Project description:Finite-state automata (FSA) are simple computational devices that can nevertheless illustrate interesting behaviours. We propose that FSA can be employed as control circuits for engineered stochastic biological and biomolecular systems. We present an implementation of FSA using counts of chemical species in the range of hundreds to thousands, which is relevant for the counts of many key molecules such as mRNAs in prokaryotic cells. The challenge here is to ensure a robust representation of the current state in the face of stochastic noise. We achieve this by using a multistable approximate majority algorithm to stabilize and store the current state of the system. Arbitrary finite state machines can thus be compiled into robust stochastic chemical automata. We present two variants: one that consumes its input signals to initiate state transitions and one that does not. We characterize the state change dynamics of these systems and demonstrate their application to solve the four-bit binary square root problem. Our work lays the foundation for the use of chemical automata as control circuits in bioengineered systems and biorobotics.
| S-EPMC8692961 | biostudies-literature
Project description:Design and implementation of robust network modules is essential for construction of complex biological systems through hierarchical assembly of 'parts' and 'devices'. The robustness of gene regulatory networks (GRNs) is ascribed chiefly to the underlying topology. The automatic designing capability of GRN topology that can exhibit robust behavior can dramatically change the current practice in synthetic biology. A recent study shows that Darwinian evolution can gradually develop higher topological robustness. Subsequently, this work presents an evolutionary algorithm that simulates natural evolution in silico, for identifying network topologies that are robust to perturbations. We present a Monte Carlo based method for quantifying topological robustness and designed a fitness approximation approach for efficient calculation of topological robustness which is computationally very intensive. The proposed framework was verified using two classic GRN behaviors: oscillation and bistability, although the framework is generalized for evolving other types of responses. The algorithm identified robust GRN architectures which were verified using different analysis and comparison. Analysis of the results also shed light on the relationship among robustness, cooperativity and complexity. This study also shows that nature has already evolved very robust architectures for its crucial systems; hence simulation of this natural process can be very valuable for designing robust biological systems.
| S-EPMC4304830 | biostudies-literature
Project description:BACKGROUND: Various computational models have been of interest due to their use in the modelling of gene regulatory networks (GRNs). As a logical model, probabilistic Boolean networks (PBNs) consider molecular and genetic noise, so the study of PBNs provides significant insights into the understanding of the dynamics of GRNs. This will ultimately lead to advances in developing therapeutic methods that intervene in the process of disease development and progression. The applications of PBNs, however, are hindered by the complexities involved in the computation of the state transition matrix and the steady-state distribution of a PBN. For a PBN with n genes and N Boolean networks, the complexity to compute the state transition matrix is O(nN22n) or O(nN2n) for a sparse matrix. RESULTS: This paper presents a novel implementation of PBNs based on the notions of stochastic logic and stochastic computation. This stochastic implementation of a PBN is referred to as a stochastic Boolean network (SBN). An SBN provides an accurate and efficient simulation of a PBN without and with random gene perturbation. The state transition matrix is computed in an SBN with a complexity of O(nL2n), where L is a factor related to the stochastic sequence length. Since the minimum sequence length required for obtaining an evaluation accuracy approximately increases in a polynomial order with the number of genes, n, and the number of Boolean networks, N, usually increases exponentially with n, L is typically smaller than N, especially in a network with a large number of genes. Hence, the computational efficiency of an SBN is primarily limited by the number of genes, but not directly by the total possible number of Boolean networks. Furthermore, a time-frame expanded SBN enables an efficient analysis of the steady-state distribution of a PBN. These findings are supported by the simulation results of a simplified p53 network, several randomly generated networks and a network inferred from a T cell immune response dataset. An SBN can also implement the function of an asynchronous PBN and is potentially useful in a hybrid approach in combination with a continuous or single-molecule level stochastic model. CONCLUSIONS: Stochastic Boolean networks (SBNs) are proposed as an efficient approach to modelling gene regulatory networks (GRNs). The SBN approach is able to recover biologically-proven regulatory behaviours, such as the oscillatory dynamics of the p53-Mdm2 network and the dynamic attractors in a T cell immune response network. The proposed approach can further predict the network dynamics when the genes are under perturbation, thus providing biologically meaningful insights for a better understanding of the dynamics of GRNs. The algorithms and methods described in this paper have been implemented in Matlab packages, which are attached as Additional files.
| S-EPMC3532238 | biostudies-literature
Project description:BackgroundThis work explores the quantitative characteristics of the local transcriptional regulatory network based on the availability of time dependent gene expression data sets. The dynamics of the gene expression level are fitted via a stochastic differential equation model, yielding a set of specific regulators and their contribution.ResultsWe show that a beta sigmoid function that keeps track of temporal parameters is a novel prototype of a regulatory function, with the effect of improving the performance of the profile prediction. The stochastic differential equation model follows well the dynamic of the gene expression levels.ConclusionWhen adapted to biological hypotheses and combined with a promoter analysis, the method proposed here leads to improved models of the transcriptional regulatory networks.
| S-EPMC1892092 | biostudies-literature
Project description:The presence of protein-DNA binding reactions often leads to analytically intractable models of stochastic gene expression. Here we present the linear-mapping approximation that maps systems with protein-promoter interactions onto approximately equivalent systems with no binding reactions. This is achieved by the marriage of conditional mean-field approximation and the Magnus expansion, leading to analytic or semi-analytic expressions for the approximate time-dependent and steady-state protein number distributions. Stochastic simulations verify the method's accuracy in capturing the changes in the protein number distributions with time for a wide variety of networks displaying auto- and mutual-regulation of gene expression and independently of the ratios of the timescales governing the dynamics. The method is also used to study the first-passage time distribution of promoter switching, the sensitivity of the size of protein number fluctuations to parameter perturbation and the stochastic bifurcation diagram characterizing the onset of multimodality in protein number distributions.
| S-EPMC6098115 | biostudies-literature
Project description:In this article, the controllability of asynchronous Boolean multiplex control networks (ABMCNs) with time delay is studied. Firstly, dynamical model of Boolean multiplex control networks is constructed, which is assumed to be under Harvey' asynchronous update and time delay is introduced both in states and controls. By using of semi-tensor product (STP) approach, the logical dynamics is converted into an equivalent algebraic form by obtaining the control-depending network transition matrices of delayed system. Secondly, a necessary and sufficient condition is proved that only control-depending fixed points of the studied dynamics can be controlled with probability one. Thirdly, respectively for two types of controls, the controllability of dynamical control system is investigated. When initial states and time delay are given, formulae are obtained to show a) the reachable set at time s under specified controls; b) the reachable set at time s under arbitrary controls; c) the reachable probabilities to different destination states. Furthermore, an approach is discussed to find a precise control sequence which can steer dynamical system into a specified target with the maximum reachable probability. Examples are shown to illustrate the feasibility of the proposed scheme.
| S-EPMC4268650 | biostudies-other
Project description:This work mainly studies the robust stability analysis and design of a controller for uncertain neutral stochastic nonlinear systems with time-delay. Using a modified Lyapunov–Krasovskii functional and the free-weighting matrices technique, we establish some new delay-dependent criteria in terms of linear matrix inequality (LMI). The innovative point of this work is that we generalize the robust stability analysis of nonlinear stochastic time-delay systems to the uncertain neutral stochastic systems. Due to the added derivative term of time-delay, the proposed scheme can be applied more widely. Finally, numerical examples are provided to validate the derived results.
| S-EPMC6208627 | biostudies-other
Project description:The stochastic block model is able to generate random graphs with different types of network partitions, ranging from the traditional assortative structures to the disassortative structures. Since the stochastic block model does not specify which mixing pattern is desired, the inference algorithms discover the locally most likely nodes' partition, regardless of its type. Here we introduce a new model constraining nodes' internal degree ratios in the objective function to guide the inference algorithms to converge to the desired type of structure in the observed network data. We show experimentally that given the regularized model, the inference algorithms, such as Markov chain Monte Carlo, reliably and quickly find the assortative or disassortative structure as directed by the value of a single parameter. In contrast, when the sought-after assortative community structure is not strong in the observed network, the traditional inference algorithms using the degree-corrected stochastic block model tend to converge to undesired disassortative partitions.
| S-EPMC6744415 | biostudies-literature