Multi-Stability, Limit Cycles, and Period-Doubling Bifurcation with Reaction Systems

Azimi, Sepinoud; Panchal, Charmi; Mizera, Andrzej; Petre, Ion

doi:10.1142/s0129054117500368

Cited by 8 publications

(6 citation statements)

References 29 publications

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“…Model checking for reaction systems has been considered in a number of different setups, based on, e.g. temporal logic ( [26][27][28]), and computational complexity ( [1,2,5]). We recall here the result on the reachability problem [13].…”

Section: Definitionmentioning

confidence: 99%

“…Since their introduction in 2007, two major research directions on reaction systems have been established. The first direction focuses on their formal properties as a dynamical system: sequences of states [31,32], power of small systems for various size measures [17,[34][35][36]38], cycles and attractors [5,14,16], connections to propositional logic [33], etc. The second major direction of research on reaction systems consists in exploring their potential as a modelling framework, in particular for biological applications [3,4,10].…”

Section: Introductionmentioning

confidence: 99%

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Controllability of reaction systems

Ivanov

Petre

2020

J Membr Comput

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Controlling a dynamical system is the ability of changing its configuration arbitrarily through a suitable choice of inputs. It is a very well-studied concept in control theory, with wide-ranging applications in medicine, biology, social sciences and engineering. We introduce in this article the concept of controllability of reaction systems as the ability of transitioning between any two states through a suitable choice of context sequences. We show that the problem is PSPACE-hard. We also introduce a model of oncogenic signalling based on reaction systems and use it to illustrate the intricacies of the controllability of reaction systems. This study opens up a new line of research on the dynamic properties of reaction systems and it introduces a new, intricate biomedical model based on reaction systems.

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Section: Definitionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Controllability of reaction systems

Ivanov

Petre

2020

J Membr Comput

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“…Model checking for reaction systems has been considered in a number of different setups, based on, e.g., temporal logic ( [30], [28], [29]), and computational complexity ( [2], [1], [5]). We recall here the result on the reachability problem [13].…”

Section: Reaction Systemsmentioning

confidence: 99%

“…Since their introduction in 2007, two major research directions on reaction systems have been established. The first direction focuses on their formal properties as a dynamical systems: sequences of states [32], [33], power of small systems for various size measures [18], [35], [36], [37], [39], cycles and attractors [5], [14], [17], connections to propositional logic [34], etc. The second major direction of research on reaction systems consists in exploring their potential as a modelling framework, in particular for biological applications [3], [4], [10].…”

Section: Introductionmentioning

confidence: 99%

Controllability of reaction systems

Ivanov¹,

Petre²

2020

Preprint

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Controlling a dynamical system is the ability of changing its configuration arbitrarily through a suitable choice of inputs. It is a very well studied concept in control theory, with wide ranging applications in medicine, biology, social sciences, engineering. We introduce in this article the concept of controllability of reaction systems as the ability of transitioning between any two states through a suitable choice of context sequences. We show that the problem is PSPACE-hard. We also introduce a model of oncogenic signalling based on reaction systems and use it to illustrate the intricacies of the controllability of reaction systems.

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“…On the one hand, reaction systems have been investigated for their mathematical and computational properties as a model for interactive biocomputation, on topics such as minimal systems [5,6], functions and state sequences [7,8], timed versions [9,10,11,12], modular decompositions [13], equivalence properties [14,15,16]. On the other hand, reaction systems have been studied a modeling framework for capturing realistic biological processes and for enhancing their analytic capabilities; topics include model checking properties [17,18,19], modeling of the heat shock response [20], of the self-assembly of intermediate filaments [21], and of the ErbB signaling pathway [22], bifurcation and multi-stability properties [23].…”

Section: Introductionmentioning

confidence: 99%

Reaction Systems and Synchronous Digital Circuits

et al. 2019

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A reaction system is a modeling framework for investigating the functioning of the living cell, focused on capturing cause–effect relationships in biochemical environments. Biochemical processes in this framework are seen to interact with each other by producing the ingredients enabling and/or inhibiting other reactions. They can also be influenced by the environment seen as a systematic driver of the processes through the ingredients brought into the cellular environment. In this paper, the first attempt is made to implement reaction systems in the hardware. We first show a tight relation between reaction systems and synchronous digital circuits, generally used for digital electronics design. We describe the algorithms allowing us to translate one model to the other one, while keeping the same behavior and similar size. We also develop a compiler translating a reaction systems description into hardware circuit description using field-programming gate arrays (FPGA) technology, leading to high performance, hardware-based simulations of reaction systems. This work also opens a novel interesting perspective of analyzing the behavior of biological systems using established industrial tools from electronic circuits design.

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Multi-Stability, Limit Cycles, and Period-Doubling Bifurcation with Reaction Systems

Cited by 8 publications

References 29 publications

Controllability of reaction systems

Controllability of reaction systems

Controllability of reaction systems

Reaction Systems and Synchronous Digital Circuits

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