Fractional Dynamics of Globally Slow Transcription and Its Impact on Deterministic Genetic Oscillation

Wei, Kun; Gao, Shilong; Zhong, Shun; Ma, Hong

doi:10.1371/journal.pone.0038383

Cited by 8 publications

(6 citation statements)

References 34 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Note that even if an ODE describes an instantaneous process, the notion of instant depends on the time scale considered, whereas FDEs have the property of fading memory and depend on the range of α (0 < α < 1). Such memories can describe current events with the collective information from preceding events, while events in the far past can often be neglected compared to contributions from the near past [60]. Volterra defined the notion of fading memory as ''the principle of dissipation of hereditary action'' [61].…”

Section: Capture Of This Ubiquitous Dynamic Behavior Involved In Poe mentioning

confidence: 99%

Paradox of enrichment: A fractional differential approach with memory

Rana

Bhattacharya

Pal

et al. 2013

Physica A: Statistical Mechanics and its Applications

View full text Add to dashboard Cite

h i g h l i g h t s• We formulate the fractional counterpart of the Rosenzweig model. • We analyze the stability of this fractional order model. • We identify a threshold for the memory effect parameter. • Below this threshold value the system is always stable independent of enrichment.• Fractional differential equations may be an important tool for resolving the paradox of enrichment. a b s t r a c tThe paradox of enrichment (PoE) proposed by Rosenzweig [M. Rosenzweig, The paradox of enrichment, Science 171 (1971) 385-387] is still a fundamental problem in ecology. Most of the solutions have been proposed at an individual species level of organization and solutions at community level are lacking. Knowledge of how learning and memory modify behavioral responses to species is a key factor in making a crucial link between species and community levels. PoE resolution via these two organizational levels can be interpreted as a microscopic-and macroscopic-level solution. Fractional derivatives provide an excellent tool for describing this memory and the hereditary properties of various materials and processes. The derivatives can be physically interpreted via two time scales that are considered simultaneously: the ideal, equably flowing homogeneous local time, and the cosmic (inhomogeneous) non-local time. Several mechanisms and theories have been proposed to resolve the PoE problem, but a universally accepted theory is still lacking because most studies have focused on local effects and ignored non-local effects, which capture memory. Here we formulate the fractional counterpart of the Rosenzweig model and analyze the stability behavior of a system. We conclude that there is a threshold for the memory effect parameter beyond which the Rosenzweig model is stable and may be used as a potential agent to resolve PoE from a new perspective via fractional differential equations.

show abstract

Section: Capture Of This Ubiquitous Dynamic Behavior Involved In Poe mentioning

confidence: 99%

Paradox of enrichment: A fractional differential approach with memory

Rana

Bhattacharya

Pal

et al. 2013

Physica A: Statistical Mechanics and its Applications

View full text Add to dashboard Cite

show abstract

“…Instead, fractional differentials can reflect the memory properties of biochemical phenomena. It has also been shown that transcription dynamics are slow and fractional order systems are very suitable for modelling this dynamics [14]. The fractional order system also provides a large degree of freedom, thus dealing with the nonlinear effects of GRNs.…”

Section: Introductionmentioning

confidence: 99%

GENAVOS: A New Tool for Modelling and Analyzing Cancer Gene Regulatory Networks Using Delayed Nonlinear Variable Order Fractional System

Yaghoobi¹,

Maghooli²,

Asadi-Khiavi³

et al. 2020

Preprint

View full text Add to dashboard Cite

Complex diseases such as cancer are caused by changes in the Gene Regulatory Networks. Systems that model the complex dynamics of these networks along with adapting to real gene expression data are closer to reality and can help understand the creation and treatment of cancer. In this paper, for the first time, modelling of gene regulatory networks is performed using delayed nonlinear variable order fractional systems in the state space by a new tool called GENAVOS. This tool uses gene expression time series data to identify and optimize system parameters. This software has several tools for analyzing system dynamics. The results show that the nonlinear variable order fractional systems have very good flexibility in adapting to real data. We found that regulatory networks in cancer cells actually have a larger delay parameter than in normal cells. It is also possible to create chaos, periodic and quasi-periodic oscillations by changing the delay, degradation and synthesis rates. Our findings indicate a profound effect of time-varying order on these networks, which may be related to a type of cellular memory due to epigenetic and environmental factors. We showed that by changing the delay parameter and the variable order function for a normal cell system, its behavior changes and becomes quite similar to the behavior of a cancer cell. This work also confirms the effective role of the miR-17-92 cluster in the cancer cell cycle. GENAVOS is available at https://github.com/hanif-y/GENAVOS with its user guide and MATLAB codes.

show abstract

“…In the last decades, dynamic systems have been intensively studied the fields of natural science and engineering technology. Especially the fractional-order dynamic systems described by the fractional-order derivative have received widespread concern because they are more accurate expressions of real systems with memory and inherited features where such characteristics are neglected or difficult to express with integer-order systems [1][2][3][4][5][6][7][8].…”

Section: Introductionmentioning

confidence: 99%

Robust Synchronization of Fractional-Order Uncertain Chaotic Systems Based on Output Feedback Sliding Mode Control

et al. 2019

View full text Add to dashboard Cite

This paper mainly focuses on the robust synchronization issue for drive-response fractional-order chaotic systems (FOCS) when they have unknown parameters and external disturbances. In order to achieve the goal, the sliding mode control scheme only using output information is designed, and at the same time, the structures of a sliding mode surface and a sliding mode controller are also constructed. A sufficient criterion is presented to ensure the robust synchronization of FOCS according to the stability theory of the fractional calculus and sliding mode control technique. In addition, the result can be applied to identical or non-identical chaotic systems with fractional-order. In the end, we build two practical examples to illustrate the feasibility of our theoretical results.

show abstract

Fractional Dynamics of Globally Slow Transcription and Its Impact on Deterministic Genetic Oscillation

Cited by 8 publications

References 34 publications

Paradox of enrichment: A fractional differential approach with memory

Paradox of enrichment: A fractional differential approach with memory

GENAVOS: A New Tool for Modelling and Analyzing Cancer Gene Regulatory Networks Using Delayed Nonlinear Variable Order Fractional System

Robust Synchronization of Fractional-Order Uncertain Chaotic Systems Based on Output Feedback Sliding Mode Control

Contact Info

Product

Resources

About