Stochastic delay differential equations for genetic regulatory networks
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A general mathematical formalism via stochastic delay differential equations for describing time delays in genetic regulatory networks derived from the Langevin approach is introduced.About:
This article is published in Journal of Computational and Applied Mathematics.The article was published on 2007-08-20 and is currently open access. It has received 159 citations till now. The article focuses on the topics: Delay differential equation & Differential equation.read more
Citations
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Chatter detection in turning using persistent homology
TL;DR: In this article, a topological data analysis (TDA) approach is proposed for determining the stability of stochastic dynamical systems in their parameter space by examining their time series using TDA.
Book
Inference for Diffusion Processes: With Applications in Life Sciences
TL;DR: This work has shown that Markov Jump Processes by Diffusions are approximated by Stochastic Differential Equations and Diffusions in a Nutshell as well as Bayesian Inference for Diffusions with Low-frequency Observations.
Journal ArticleDOI
On Robust Stability of Stochastic Genetic Regulatory Networks With Time Delays: A Delay Fractioning Approach
TL;DR: This paper utilizes a new Lyapunov functional based on the idea of ¿delay fractioning¿ and employs the linear matrix inequality (LMI) technique to derive delay-dependent sufficient conditions ensuring the robust stability of the gene regulatory networks.
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Stochastic stability for uncertain genetic regulatory networks with interval time-varying delays
TL;DR: Some new delay-range-dependent and rate-dependent stability criteria are established in terms of linear matrix inequalities (LMIs) to guarantee the delayed genetic regulatory networks to be robustly asymptotically stable in the mean square.
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Transcriptional delay stabilizes bistable gene networks.
TL;DR: This work investigates several stochastic models of bistable gene networks and finds that increasing delay dramatically increases the mean residence times near stable states and introduces a non-Markovian, analytically tractable reduced model.
References
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Approximate accelerated stochastic simulation of chemically reacting systems
TL;DR: With further refinement, the τ-leap method should provide a viable way of segueing from the exact SSA to the approximate chemical Langevin equation, and thence to the conventional deterministic reaction rate equation, as the system size becomes larger.
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Intrinsic noise in gene regulatory networks
TL;DR: An analytic model is used to investigate the emergent noise properties of genetic systems and finds for a single gene that noise is essentially determined at the translational level, and that the mean and variance of protein concentration can be independently controlled.
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Autoinhibition with Transcriptional Delay: A Simple Mechanism for the Zebrafish Somitogenesis Oscillator
TL;DR: It is shown by mathematical simulation that direct autorepression of her1 and her7 by their own protein products provides a mechanism for the intracellular oscillator, and Such Notch-mediated synchronous oscillations are predicted even in the absence of direct her1/her7 autoregulation.
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Oscillatory expression of the bHLH factor Hes1 regulated by a negative feedback loop.
Hiromi Hirata,Shigeki Yoshiura,Toshiyuki Ohtsuka,Yasumasa Bessho,Takahiro Harada,Kenichi Yoshikawa,Ryoichiro Kageyama +6 more
TL;DR: It is shown that serum treatment of cultured cells induces cyclic expression of both mRNA and protein of the Notch effector Hes1, a basic helix-loop-helix (bHLH) factor, with 2-hour periodicity, which may regulate timing in many biological systems.
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Oscillatory Expression of Hes1, p53, and NF-κB Driven by Transcriptional Time Delays
TL;DR: Results provide direct evidence that transcriptional delays can drive oscillatory gene activity and highlight the importance of considering delays when analyzing genetic regulatory networks, particularly in processes such as developmental pattern formation, where short half-lives and feedback inhibition are common.