Emergent bimodality and switch induced by time delays and noises in a synthetic gene circuit

Zhang, Chun; Du, Liping; Xie, Qingshuang; Wang, Tonghuan; Zeng, Chunhua; Nie, Linru; Duan, Wei-Long; Jia, Zheng; Wang, Can-Jun

doi:10.1016/j.physa.2017.04.052

Cited by 16 publications

(5 citation statements)

References 69 publications

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“…76), we can construct path integral descriptions of systems with strong and state-dependent/multiplicative noise. Although Gillespie showed [27] some time ago that chemical Langevin equations generically have multiplicative noise terms, the qualitative impact of these terms (and of intrinsic noise more generally) on gene regulation models [99][100][101][102][103][104][105] is only recently being appreciated.…”

Section: Discussionmentioning

confidence: 99%

Stochastic path integrals can be derived like quantum mechanical path integrals

Vastola¹,

Holmes²

2019

Preprint

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Stochastic mechanics-the study of classical stochastic systems governed by things like master equations and Fokker-Planck equations-exhibits striking mathematical parallels to quantum mechanics. In this article, we make those parallels more transparent by presenting a quantum mechanics-like formalism for deriving a path integral description of systems described by stochastic differential equations. Our formalism expediently recovers the usual path integrals (the Martin-Siggia-Rose-Janssen-De Dominicis and Onsager-Machlup forms) and is flexible enough to account for different variable domains (e.g. real line versus compact interval), stochastic interpretations, arbitrary numbers of variables, explicit time-dependence, dimensionful control parameters, and more.We discuss the implications of our formalism for stochastic biology.

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Section: Discussionmentioning

confidence: 99%

Stochastic path integrals can be derived like quantum mechanical path integrals

Vastola¹,

Holmes²

2019

Preprint

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“…, m is a positive integer. 24 No interference is considered Based on the model of equation 8, when the torque amplitude of the driving gear T inp and the torque fluctuation frequency O of the input stage change, the influence on the amplitude gain Q is shown in Figure 9, where T outq = 0:002, v 3 = 25, v 1 = 2, v 2 = 1.6, v 11 = 20, and v 22 = 25. The mass and moment of inertia of each gear in Figure 9(a) are shown in Table 1, and Figure 9(b) as the corresponding Figure 9(a) projection drawing.…”

Section: Vibration Resonance Analysis Of Two-stage Braided Gear Systemmentioning

confidence: 99%

“…In equation (12), B s = 2 mT ∫ 0 mT x true¯ 2 ( t ) sin ( ω 3 t ) dt , B c = 2 mT ∫ 0 mT x true¯ 2 ( t ) cos ( ω 3 t ) dt , m is a positive integer. 24…”

Section: Vibration Resonance Analysis Of Two-stage Braided Gear Systemmentioning

confidence: 99%

Response analysis of 3D braided two-stage gear system excited by different frequency signals

Zhang

Tang

et al. 2021

Advances in Mechanical Engineering

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The knitting principle of 3D braided gear was studied, and the dynamic model of the two-stage gear system was established. The fourth-order Runge-Kutta method was used to numerically simulate the dynamic characteristics of common gear and 3D braided gear. The results showed that the fundamental frequency ω1 of the static transmission error excitation had the greatest effect on the speed and frequency characteristics of the first-stage gear along the meshing line. The research on frequency characteristics of common gear and 3D braided gear shows that the fundamental frequency ω1 of the static transmission error excitation has a large effect on the speed and frequency characteristics of the first-stage gear along the meshing line. With the reduction of the gear mass and moment of inertia, the amplitude in the low-frequency band increases. The vibration resonance of the system is studied by defining the amplitude gain of the response of the system output at the low-frequency signal ω3. The results show that with the reduction of gear mass and moment of inertia, when the input stage torque fluctuation frequency is Ω > 5, the fluctuation of amplitude gain Q disappears, which indicates that the vibration resistance of the 3D braided gear to high-frequency input stage torque fluctuation frequency is greatly improved.

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“…On the other hand, the time delay [ 24 , 25 , 26 ] is one of the essential aspects featured in GRNs [ 7 , 8 , 13 , 27 ]. Time delays describe the propagation phenomena, material transfer in intercommoned systems, and data transmission in communicating systems in many natural and physical setups [ 28 ].…”

Section: Introductionmentioning

confidence: 99%

Effects of noise and time delay on E2F's expression level in a bistable Rb‐E2F gene’s regulatory network

Kirunda

Yang

Liu

et al. 2021

IET Systems Biology

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The bistable Rb-E2F gene regulatory network plays a central role in regulating cellular proliferation-quiescence transition. Based on Gillespie's chemical Langevin method, the stochastic bistable Rb-E2F gene's regulatory network with time delays is proposed. It is found that under the moderate intensity of internal noise, delay in the Cyclin E synthesis rate can greatly increase the average concentration value of E2F. When the delay is considered in both E2F-related positive feedback loops, within a specific range of delay (3-13)hr, the average expression of E2F is significantly increased. Also, this range is in the scope with that experimentally given by Dong et al. [65]. By analysing the quasi-potential curves at different delay times, simulation results show that delay regulates the dynamic behaviour of the system in the following way: small delay stabilises the bistable system; the medium delay is conducive to a high steady-state, making the system fluctuate near the high steady-state; large delay induces approximately periodic transitions between high and low steady-state. Therefore, by regulating noise and time delay, the cell itself can control the expression level of E2F to respond to different situations. These findings may provide an explanation of some experimental result intricacies related to the cell cycle.This is an open access article under the terms of the Creative Commons Attribution-NonCommercial License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited and is not used for commercial purposes.

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Emergent bimodality and switch induced by time delays and noises in a synthetic gene circuit

Cited by 16 publications

References 69 publications

Stochastic path integrals can be derived like quantum mechanical path integrals

Stochastic path integrals can be derived like quantum mechanical path integrals

Response analysis of 3D braided two-stage gear system excited by different frequency signals

Effects of noise and time delay on E2F's expression level in a bistable Rb‐E2F gene’s regulatory network

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