Switching dynamics in reaction networks induced by molecular discreteness

Togashi, Yuichi; Kaneko, Kunihiko

doi:10.1088/0953-8984/19/6/065150

Cited by 9 publications

(8 citation statements)

References 31 publications

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“…The situation in this stochastic synchronization is analogous to discreteness-induced transitions, previously reported by one of the authors [10,21]. No matter how fast the positive feedback reaction progresses, it completely stalls when the relevant molecules vanish.…”

Section: Intermolecular Fluctuationssupporting

confidence: 75%

“…No matter how fast the positive feedback reaction progresses, it completely stalls when the relevant molecules vanish. In the previously reported case [10,21], for the transitions to occur, decay of a certain chemical species had to be faster than the interval of molecular inflow of the chemical; however, in the present case, decay must be sufficiently faster than the turnover time, although the threshold is also affected by β.…”

Section: Intermolecular Fluctuationsmentioning

confidence: 58%

“…Substituting equations (10), (14), (19), and (20) to equation (26), we obtain the explicit form of Λ. Here, λ is one of the eigenvalues of Λ, i.e., satisfying Λ λ | − | = I 0 (see equations (21) and (25) Im ( ) (2 ) i i represent the growth rate (i.e., the instability of the steady state) and frequency of the oscillatory mode, respectively. If μ i is positive, the mode can grow when perturbation is applied to the steady state.…”

Section: Stability Analysis Considering Intramolecular Fluctuationsmentioning

confidence: 99%

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Spatiotemporal patterns enhanced by intra- and inter-molecular fluctuations in arrays of allosterically regulated enzymes

Togashi

Casagrande

2015

New J. Phys.

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Enzymatic reactions often involve slow conformational changes, with reaction cycles that sometimes require milliseconds or seconds to complete. The dynamics are strongly affected by fluctuations at the nanoscale. However, such enzymes often occur in small numbers in a cell; hence, the fluctuations caused by finite numbers of molecules should also be substantial. Because of these factors, the behavior of the system is likely to deviate from that of classical reaction-diffusion equations, in which immediate reaction events are assumed to occur without memory and between a huge number of molecules. In this work, we model each enzyme as a unit represented by a phase variable to investigate the effects of fluctuations in arrays of enzymes. Using an analysis based on partial differential equations and stochastic simulations, we show that fluctuations arising from internal states of enzymes (intramolecular fluctuations) and those arising from the stochastic nature of interactions between molecules (intermolecular fluctuations) have distinctive effects on spatiotemporal patterns; the former generally disturb synchronization at high frequencies, whereas the latter can enhance synchronization. The balance of the two types of fluctuations may determine the spatiotemporal behavior of biochemical processes.

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Section: Intermolecular Fluctuationssupporting

confidence: 75%

Section: Intermolecular Fluctuationsmentioning

confidence: 58%

Section: Stability Analysis Considering Intramolecular Fluctuationsmentioning

confidence: 99%

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Spatiotemporal patterns enhanced by intra- and inter-molecular fluctuations in arrays of allosterically regulated enzymes

Togashi

Casagrande

2015

New J. Phys.

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“…Noise may even be exploited by the network to generate desired variability (phenotypic and cell‐type diversification) 2, 27–30. Noise from gene expression can induce new dynamics including signal amplification,31 enhanced sensitivity (stochastic focusing),24, 32 bistability (switching between states) and oscillations,33–37 stabilization of a deterministically unstable state,38 and even discreteness‐induced switching of catalytic reaction networks 39. These are both quantitatively and qualitatively different from what is predicted or possible deterministically.…”

Section: Why Stochastic Modeling?mentioning

confidence: 99%

Stochastic approaches in systems biology

Ullah

Wolkenhauer

2010

WIREs Mechanisms of Disease

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The discrete and random occurrence of chemical reactions far from thermodynamic equilibrium, and low copy numbers of chemical species, in systems biology necessitate stochastic approaches. This review is an effort to give the reader a flavor of the most important stochastic approaches relevant to systems biology. Notions of biochemical reaction systems and the relevant concepts of probability theory are introduced side by side. This leads to an intuitive and easy-to-follow presentation of a stochastic framework for modeling subcellular biochemical systems. In particular, we make an effort to show how the notion of propensity, the chemical master equation (CME), and the stochastic simulation algorithm arise as consequences of the Markov property. Most stochastic modeling reviews focus on stochastic simulation approaches--the exact stochastic simulation algorithm and its various improvements and approximations. We complement this with an outline of an analytical approximation. The most common formulation of stochastic models for biochemical networks is the CME. Although stochastic simulations are a practical way to realize the CME, analytical approximations offer more insight into the influence of randomness on system's behavior. Toward that end, we cover the chemical Langevin equation and the related Fokker-Planck equation and the two-moment approximation (2MA). Throughout the text, two pedagogical examples are used to key illustrate ideas. With extensive references to the literature, our goal is to clarify key concepts and thereby prepare the reader for more advanced texts.

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confidence: 99%

Investigating the Gap between Discrete and Continuous Models of Chemically Reacting Systems

Haruna

2010

J. Comput. Chem. Jpn.

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Molecular discreteness would be important in intracellular chemical reactions since the number of copies of molecules included in the reactions is small compared to in vitro situations [1][2][3][4][5]. Recently an experimental evidence for the significance of the molecular discreteness was found [6]. For a theoretical study, Togashi and Kaneko [3] reported a new transition phenomenon in a small autocatalytic system by a discrete stochastic simulation of the system. It cannot be observed in a model based on the classical reaction rate equation. However, Ohkubo et al. [7] found that the transition phenomenon reported However, we use CLE as a reference model in order to investigate the discrete nature of chemically reacting systems J. Comput. Chem. Jpn., Vol. 9, No. 3, pp.135-142 (2010) © The aim of this paper is to investigate the discrete nature of chemically reacting systems. In order to achieve our purpose we propose a systematic method to compare the discrete stochastic model of chemically reacting systems with the continuous stochastic model. We adopt the chemical master equation ( well-known idea of approximating diffusion processes by birth-death processes, we construct a family of master equations parameterized by the degree of discreteness. This family of master equations bridges CME and CFPE.With full degree of discreteness we obtain CME and as decreasing discreteness the family of master equations converges to CFPE. Our strategy is not to study CME directly but to distinguish the properties of CME by putting CME into the family of master equations bridging CME and CFPE. We examine the usefulness of our construction by two simple examples.

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Switching dynamics in reaction networks induced by molecular discreteness

Cited by 9 publications

References 31 publications

Spatiotemporal patterns enhanced by intra- and inter-molecular fluctuations in arrays of allosterically regulated enzymes

Spatiotemporal patterns enhanced by intra- and inter-molecular fluctuations in arrays of allosterically regulated enzymes

Stochastic approaches in systems biology

Investigating the Gap between Discrete and Continuous Models of Chemically Reacting Systems

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