Synchronism versus asynchronism in monotonic Boolean automata networks

Noual, Mathilde; Sené, Sylvain

doi:10.1007/s11047-016-9608-8

Cited by 24 publications

(18 citation statements)

References 33 publications

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“…Moreover, we show that when instantiated on RPNs encoding of BNs (according to Sect. 4.1), the general characterization of synchronism sensitivity in RPNs allows to recover the results of synchronism sensitivity in BNs with respect to their influence graph [30], with a slight generalization relaxing the local monotonicity constraints of BNs.…”

Section: Synchronism Sensitivitymentioning

confidence: 99%

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Concurrency in Boolean networks

et al. 2019

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Boolean networks (BNs) are widely used to model the qualitative dynamics of biological systems. Besides the logical rules determining the evolution of each component with respect to the state of its regulators, the scheduling of component updates can have a dramatic impact on the predicted behaviours. In this paper, we explore the use of Read (contextual) Petri Nets (RPNs) to study dynamics of BNs from a concurrency theory perspective. After showing bi-directional translations between RPNs and BNs and analogies between results on synchronism sensitivity, we illustrate that usual updating modes for BNs can miss plausible behaviours, i.e., incorrectly conclude on the absence/impossibility of reaching specific configurations. We propose an encoding of BNs capitalizing on the RPN semantics enabling more behaviour than the generalized asynchronous updating mode. The proposed encoding ensures a correct abstraction of any multivalued refinement, as one may ex-

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Section: Synchronism Sensitivitymentioning

confidence: 99%

“…[30], Prop. 1) A critical cycle must be NOPE: negative with odd length or positive with even length.…”

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confidence: 99%

Concurrency in Boolean networks

et al. 2019

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“…All results given here can thus be applied to the widespread Thomas’ modeling [ 42 ] in the asynchronous scheme and to the Kauffman modeling in the synchronous scheme [ 43 ]. In addition, this framework can encompass any update rules, such as the ones represented in [ 44 , 45 ].…”

Section: Conclusion and Future Directionmentioning

confidence: 99%

ASP-based method for the enumeration of attractors in non-deterministic synchronous and asynchronous multi-valued networks

Abdallah

Folschette

Roux

et al. 2017

Algorithms Mol Biol

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BackgroundThis paper addresses the problem of finding attractors in biological regulatory networks. We focus here on non-deterministic synchronous and asynchronous multi-valued networks, modeled using automata networks (AN). AN is a general and well-suited formalism to study complex interactions between different components (genes, proteins,...). An attractor is a minimal trap domain, that is, a part of the state-transition graph that cannot be escaped. Such structures are terminal components of the dynamics and take the form of steady states (singleton) or complex compositions of cycles (non-singleton). Studying the effect of a disease or a mutation on an organism requires finding the attractors in the model to understand the long-term behaviors.ResultsWe present a computational logical method based on answer set programming (ASP) to identify all attractors. Performed without any network reduction, the method can be applied on any dynamical semantics. In this paper, we present the two most widespread non-deterministic semantics: the asynchronous and the synchronous updating modes. The logical approach goes through a complete enumeration of the states of the network in order to find the attractors without the necessity to construct the whole state-transition graph. We realize extensive computational experiments which show good performance and fit the expected theoretical results in the literature.ConclusionThe originality of our approach lies on the exhaustive enumeration of all possible (sets of) states verifying the properties of an attractor thanks to the use of ASP. Our method is applied to non-deterministic semantics in two different schemes (asynchronous and synchronous). The merits of our methods are illustrated by applying them to biological examples of various sizes and comparing the results with some existing approaches. It turns out that our approach succeeds to exhaustively enumerate on a desktop computer, in a large model (100 components), all existing attractors up to a given size (20 states). This size is only limited by memory and computation time.

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“…One major question is to study the behaviour of a given automata network under different update schedules. A lot is known about the relation between synchronous and asynchronous dynamics of finite or infinite interaction networks (see [3,4] and references therein). In particular, there is a stream of work that focuses on networks with the most "asynchronous power," i.e.…”

Section: Introductionmentioning

confidence: 99%

Commutative Automata Networks

Bridoux

Gadouleau

Theyssier

2020

Lecture Notes in Computer Science

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Automata networks are mappings of the form f : Q Z → Q Z , where Q is a finite alphabet and Z is a set of entities; they generalise Cellular Automata and Boolean networks. An update schedule dictates when each entity updates its state according to its local function fi : Q Z → Q. One major question is to study the behaviour of a given automata networks under different update schedules. In this paper, we study automata networks that are invariant under many different update schedules. This gives rise to two definitions, locally commutative and globally commutative networks. We investigate the relation between commutativity and different forms of locality of update functions; one main conclusion is that globally commutative networks have strong dynamical properties, while locally commutative networks are much less constrained. We also give a complete classification of all globally commutative Boolean networks.

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Synchronism versus asynchronism in monotonic Boolean automata networks

Cited by 24 publications

References 33 publications

Concurrency in Boolean networks

Concurrency in Boolean networks

ASP-based method for the enumeration of attractors in non-deterministic synchronous and asynchronous multi-valued networks

Commutative Automata Networks

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