Analysis of Deterministic Cyclic Gene Regulatory Network Models with Delays

Ahsen, Mehmet Eren; Özbay, Hitay; Niculescu, Silviu–Iulian

doi:10.1007/978-3-319-15606-4

Cited by 8 publications

(12 citation statements)

References 51 publications

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“…As the number of fixed points of a function is directly related to its shape, a shape-indicator of F 1α (x), called "Schwarzian derivative" [1], is calculated.…”

Section: A Functions With Negative Schwarzian Derivativesmentioning

confidence: 99%

“…Proof: It is easy to show that F 1α (x) > 0 ∀ x ∈]0, +∞[, F 1α (0) = 0 from the properties of Hill functions, and F 1α (x) is bounded. It follows that there exists a > 0 such that F 1α (x) is strictly increasing ∀ x ∈]0, a[ and F 1α (x) is strictly decreasing ∀ x ∈]a, +∞[ (see [1] for the details). This is exactly the definition of a sigmoid function.…”

Section: Definitionmentioning

confidence: 99%

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Global asymptotic stability of a genetic negative feedback loop with an affine control

Chambon¹,

Gouzé²

2019

2019 IEEE 58th Conference on Decision and Control (CDC)

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Genetic negative feedback loops are essential and recurrent biological motifs. They are traditionally described with N-dimensional competitive dynamical systems, composed of highly non-linear Hill functions. The stability property of their unique steady state usually determines the global dynamical behavior: homeostasis under stability or emergence of oscillations. When homeostasis conditions are disrupted, undesired oscillations can emerge and may lead to various diseases. This paper presents a classical affine control strategy that is able to stabilize the unstable steady state of the disrupted system and suppress undesired oscillations. For biological purpose, this control is designed as simple as possible in order to reduce the use of devices and the complexity of the biological set-up. For this reason, the control law only depends on the measurement of a unique gene and only acts on its own expression. Due to the complexity of this controlled dynamical system, a new methodology, based on the construction of successive hyperrectangles of the state space that act as Lyapunov function level-sets, is proposed in order to prove global convergence and global stability results. Despite its apparent simplicity, this affine control law is shown to globally stabilize the disrupted system and recover homeostasis.

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“…As the number of fixed points of a function is directly related to its shape, a shape-indicator of F 1α (x), called "Schwarzian derivative" [1], is calculated.…”

Section: A Functions With Negative Schwarzian Derivativesmentioning

confidence: 99%

Section: Definitionmentioning

confidence: 99%

Global asymptotic stability of a genetic negative feedback loop with an affine control

Chambon¹,

Gouzé²

2019

2019 IEEE 58th Conference on Decision and Control (CDC)

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“…In fact, the Hill functions in (1), that belong to the family of functions with negative Schwarzian derivatives (see [5], Chap. 3) are commonly encountered in many real-life problems.…”

Section: The Coupling Form Between Ordinary and Mutated Cellsmentioning

confidence: 99%

Control in dormancy or eradication of cancer stem cells: Mathematical modeling and stability issues

Djema

Bonnet

Mazenc

et al. 2018

Journal of Theoretical Biology

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We propose a biologically based model endowed with rich dynamics. It incorporates a new parameter representing immunoediting processes, including the case where proliferation of cancer cells is locally kept under check by the immune cells. It also considers the overproliferation of cancer stem cells, modeled as a subpopulation of mutated cells that is constantly active in cell division. The analysis that we perform here reveals the conditions of existence of several steady states, including the case of cancer dormancy, in the coupled model of interest. Our study suggests that cancer dormancy may result from a plastic sensitivity of mutated cells to their shared environment, different from that - fixed - of healthy cells, and this is related to an action (or lack of action) of the immune system. Next, the stability analysis that we perform is essentially oriented towards the determination of sufficient conditions, depending on all the model parameters, that ensure either a regionally (i.e., locally) stable dormancy steady state or eradication of unhealthy cells. Finally, we discuss some biological interpretations, with regards to our findings, in light of current and emerging therapeutics. These final insights are particularly formulated in the paradigmatic case of hematopoiesis and acute leukemia, which is one of the best known malignancies for which it is always hard, in presence of a clinical and histological remission, to decide between cure and dormancy of a tumoral clone.

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“…There are a lot of gene network models [1][2][3][4][5][6][7]. As a relatively simple model, in this section, an ordinary differential equation (ODE) gene network model of circadian rhythm [7] is focused on.…”

Section: Ode Gene Network Modelmentioning

confidence: 99%

“…There exist a variety of gene network models [1][2][3][4][5][6][7]. Among them, in this paper, a gene network model of circadian rhythm [7] is focused on since the circadian rhythm is one of the most fundamental gene-oriented phenomena.…”

Section: Introductionmentioning

confidence: 99%

A novel hardware-efficient gene network model based on asynchronous cellular automaton dynamics

Yoshimoto

Torikai

2017

NOLTA

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Abstract:The gene affects various behaviors of animals such as circadian rhythm, courtship behavior, motor behavior, visual behavior, and learning. The circadian rhythm is a biological rhythm having a period of almost 24 hours, which is sometimes called internal clock or biological clock. In this paper, a novel asynchronous cellular automaton model of a gene network is proposed, where its vector field is designed based on an ordinary differential equation gene network model. It is shown that the proposed model can reproduce typical phenomena (e.g., oscillations, mutual synchronization, locking to light stimulation, and related bifurcations) observed in the differential equation gene network model. It is also shown that the proposed model can be implemented on an FPGA by using much less hardware resource compared to the differential equation model

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Analysis of Deterministic Cyclic Gene Regulatory Network Models with Delays

Cited by 8 publications

References 51 publications

Global asymptotic stability of a genetic negative feedback loop with an affine control

Global asymptotic stability of a genetic negative feedback loop with an affine control

Control in dormancy or eradication of cancer stem cells: Mathematical modeling and stability issues

A novel hardware-efficient gene network model based on asynchronous cellular automaton dynamics

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