4,295 research outputs found
On the attenuation and amplification of molecular noise in genetic regulatory networks
BACKGROUND: Noise has many important roles in cellular genetic regulatory functions at the nanomolar scale. At present, no good theory exists for identifying all possible mechanisms of genetic regulatory networks to attenuate the molecular noise to achieve regulatory ability or to amplify the molecular noise to randomize outcomes to the advantage of diversity. Therefore, the noise filtering of genetic regulatory network is an important topic for gene networks under intrinsic fluctuation and extrinsic noise. RESULTS: Based on stochastic dynamic regulation equation, the intrinsic fluctuation in reaction rates is modeled as a state-dependent stochastic process, which will influence the stability of gene regulatory network, especially, with low concentrations of reacting species. Then the mechanisms of genetic regulatory network to attenuate or amplify extrinsic fluctuation are revealed from the nonlinear stochastic filtering point of view. Furthermore, a simple measure of attenuation level or amplification level of extrinsic noise for genetic regulatory networks is also introduced by nonlinear robust filtering method. Based on the global linearization scheme, a convenient method is introduced to measure noise attenuation or amplification for each gene of the nonlinear stochastic regulatory network by solving a set of filtering problems, which correspond to a set of linearized stochastic regulatory networks. Finally, by the proposed methods, several simulation examples of genetic regulatory networks are given to measure their robust stability under intrinsic fluctuations, and to estimate the genes' attenuation and amplification levels under extrinsic noises. CONCLUSION: In this study, a stochastic nonlinear dynamic model is developed for genetic regulatory networks under intrinsic fluctuation and extrinsic noise. By the method we proposed, we could determine the robust stability under intrinsic fluctuations and identify the genes that are significantly affected by extrinsic noises, which we call the weak structure of the network. This method will be potential for robust gene circuit design in future, on which a drug design could be based
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Filtering for nonlinear genetic regulatory networks with stochastic disturbances
In this paper, the filtering problem is investigated for nonlinear genetic regulatory networks with stochastic disturbances and time delays, where the nonlinear function describing the feedback regulation is assumed to satisfy the sector condition, the stochastic perturbation is in the form of a scalar Brownian motion, and the time delays exist in both the translation process and the feedback regulation process. The purpose of the addressed filtering problem is to estimate the true concentrations of the mRNA and protein. Specifically, we are interested in designing a linear filter such that, in the presence of time delays, stochastic disturbances as well as sector nonlinearities, the filtering dynamics of state estimation for the stochastic genetic regulatory network is exponentially mean square stable with a prescribed decay rate lower bound beta. By using the linear matrix inequality (LMI) technique, sufficient conditions are first derived for ensuring the desired filtering performance for the gene regulatory model, and the filter gain is then characterized in terms of the solution to an LMI, which can be easily solved by using standard software packages. A simulation example is exploited in order to illustrate the effectiveness of the proposed design procedures
Disturbance analysis of nonlinear differential equation models of genetic SUM regulatory networks
Noise disturbances and time delays are frequently met in cellular genetic regulatory systems. This paper is concerned with the disturbance analysis of a class of genetic regulatory networks described by nonlinear differential equation models. The mechanisms of genetic regulatory networks to amplify (attenuate) external disturbance are explored, and a simple measure of the amplification (attenuation) level is developed from a nonlinear robust control point of view. It should be noted that the conditions used to measure the disturbance level are delay-independent or delay-dependent, and are expressed within the framework of linear matrix inequalities, which can be characterized as convex optimization, and computed by the interior-point algorithm easily. Finally, by the proposed method, a numerical example is provided to illustrate how to measure the attenuation of proteins in the presence of external disturbances. © 2011 IEEE.published_or_final_versio
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Network Topologies That Can Achieve Dual Function of Adaptation and Noise Attenuation.
Many signaling systems execute adaptation under circumstances that require noise attenuation. Here, we identify an intrinsic trade-off existing between sensitivity and noise attenuation in the three-node networks. We demonstrate that although fine-tuning timescales in three-node adaptive networks can partially mediate this trade-off in this context, it prolongs adaptation time and imposes unrealistic parameter constraints. By contrast, four-node networks can effectively decouple adaptation and noise attenuation to achieve dual function without a trade-off, provided that these functions are executed sequentially. We illustrate ideas in seven biological examples, including Dictyostelium discoideum chemotaxis and the p53 signaling network and find that adaptive networks are often associated with a noise attenuation module. Our approach may be applicable to finding network design principles for other dual and multiple functions
Complete integrability of information processing by biochemical reactions
Statistical mechanics provides an effective framework to investigate
information processing in biochemical reactions. Within such framework
far-reaching analogies are established among (anti-) cooperative collective
behaviors in chemical kinetics, (anti-)ferromagnetic spin models in statistical
mechanics and operational amplifiers/flip-flops in cybernetics. The underlying
modeling -- based on spin systems -- has been proved to be accurate for a wide
class of systems matching classical (e.g. Michaelis--Menten, Hill, Adair)
scenarios in the infinite-size approximation. However, the current research in
biochemical information processing has been focusing on systems involving a
relatively small number of units, where this approximation is no longer valid.
Here we show that the whole statistical mechanical description of reaction
kinetics can be re-formulated via a mechanical analogy -- based on completely
integrable hydrodynamic-type systems of PDEs -- which provides explicit
finite-size solutions, matching recently investigated phenomena (e.g.
noise-induced cooperativity, stochastic bi-stability, quorum sensing). The
resulting picture, successfully tested against a broad spectrum of data,
constitutes a neat rationale for a numerically effective and theoretically
consistent description of collective behaviors in biochemical reactions.Comment: 24 pages, 10 figures; accepted for publication in Scientific Report
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Robust filtering for stochastic genetic regulatory networks with time-varying delay
This is the post print version of the article. The official published version can be obtained from the link - Copyright 2009 Elsevier LtdThis paper addresses the robust filtering problem for a class of linear genetic regulatory networks (GRNs) with stochastic disturbances, parameter uncertainties and time delays. The parameter uncertainties are assumed to reside in a polytopic region, the stochastic disturbance is state-dependent described by a scalar Brownian motion, and the time-varying delays enter into both the translation process and the feedback regulation process. We aim to estimate the true concentrations of mRNA and protein by designing a linear filter such that, for all admissible time delays, stochastic disturbances as well as polytopic uncertainties, the augmented state estimation dynamics is exponentially mean square stable with an expected decay rate. A delay-dependent linear matrix inequality (LMI) approach is first developed to derive sufficient conditions that guarantee the exponential stability of the augmented dynamics, and then the filter gains are parameterized in terms of the solution to a set of LMIs. Note that LMIs can be easily solved by using standard software packages. A simulation example is exploited in order to illustrate the effectiveness of the proposed design procedures.This work was supported in part by the Biotechnology and Biological Sciences Research Council (BBSRC) of the U.K. under Grants BB/C506264/1 and 100/EGM17735, an International Joint Project sponsored by the Royal Society of the U.K., the Research Grants Council of Hong Kong under Grant HKU 7031/06P, the National Natural Science Foundation of China under Grant 60804028, and the Alexander von Humboldt Foundation of Germany
Feedback Regulation and its Efficiency in Biochemical Networks
Intracellular biochemical networks fluctuate dynamically due to various
internal and external sources of fluctuation. Dissecting the fluctuation into
biologically relevant components is important for understanding how a cell
controls and harnesses noise and how information is transferred over apparently
noisy intracellular networks. While substantial theoretical and experimental
advancement on the decomposition of fluctuation was achieved for feedforward
networks without any loop, we still lack a theoretical basis that can
consistently extend such advancement to feedback networks. The main obstacle
that hampers is the circulative propagation of fluctuation by feedback loops.
In order to define the relevant quantity for the impact of feedback loops for
fluctuation, disentanglement of the causally interlocked influence between the
components is required. In addition, we also lack an approach that enables us
to infer non-perturbatively the influence of the feedback to fluctuation as the
dual reporter system does in the feedforward network. In this work, we resolve
these problems by extending the work on the fluctuation decomposition and the
dual reporter system. For a single-loop feedback network with two components,
we define feedback loop gain as the feedback efficiency that is consistent with
the fluctuation decomposition for feedforward networks. Then, we clarify the
relation of the feedback efficiency with the fluctuation propagation in an
open-looped FF network. Finally, by extending the dual reporter system, we
propose a conjugate feedback and feedforward system for estimating the feedback
efficiency only from the statistics of the system non-perturbatively
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