About block-parallel Boolean networks: a position paper

Demongeot, Jacques; Sené, Sylvain

doi:10.1007/s11047-019-09779-x

Cited by 18 publications

(8 citation statements)

References 38 publications

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“…As a consequence, further studies need to be done on the scheduling of updates over time. A first avenue is to focus for instance on more likely updating modes, in agreement with the discussion of what is claimed in [DS20].…”

Section: Discussionsupporting

confidence: 61%

Boolean automata isolated cycles and tangential double-cycles dynamics

Demongeot,

Melliti,

Noual

et al. 2022

Preprint

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Our daily social and political life is more and more impacted by social networks. The functioning of our living bodies is deeply dependent on biological regulation networks such as neural, genetic, and protein networks. And the physical world in which we evolve, is also structured by systems of interacting particles. Interaction networks can be seen in all spheres of existence that concern us, and yet, our understanding of interaction networks remains severely limited by our present lack of both theoretical and applied insight into their clockworks. In the past, efforts at understanding interaction networks have mostly been directed towards applications. This has happened at the expense of developing understanding of the generic and fundamental aspects of interaction networks (properties and behaviours due primarily to the fact that a system is an interaction network, as opposed to properties and behaviours rather due to the fact a system is a genetic interaction network for instance). Intrinsic properties of interaction networks (e.g., the ways in which they transmit information along entities, their ability to produce this or that kind of global dynamical behaviour depending on local interactions) are thus still not well understood. Lack of fundamental knowledge tends to limit the innovating power of applications. Without more theoretical fundamental knowledge, applications cannot evolve deeply and become more impacting. Hence, it is necessary to better apprehend and comprehend the intrinsic properties of interaction networks, notably the relations between their architecture and their dynamics and how they are affected by and set in time. In this chapter, we use the elementary mathematical model of Boolean automata networks as a formal archetype of interaction networks. We survey results concerning the role of feedback cycles and the role of intersections between feedback cycles, in shaping the asymptotic dynamical behaviours of interaction networks. We pay special attention to the impact of the automata updating modes.

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Section: Discussionsupporting

confidence: 61%

Boolean automata isolated cycles and tangential double-cycles dynamics

Demongeot,

Melliti,

Noual

et al. 2022

Preprint

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“…Between these two extreme schedules, the updating modes are called block-sequential, i.e., they are parallel in a block, the blocks being updated sequentially. A more realistic schedule in genetic and metabolic networks is called block parallel [ 50 ]: These networks are composed of blocks made of genes sequentially updated, these blocks being updated in parallel ( Figure 2 Top middle). Some interactions between these blocks can exist (i.e., there are w ij ≠ 0, with i and j belonging to 2 different blocks), but because the block sizes are different, the time at which the first attractor state is reached in a block is not necessarily synchronized with the corresponding times in other blocks: the synchronization expected as asymptotic behavior of the dynamics depends on the intra-block as well as on the inter-block interactions, which explains that states of genes in a block serving as the clock for the network are highly dependent on states of genes in other blocks connected to them (e.g., acting as transcription factors of the clock genes).…”

Section: Methodsmentioning

confidence: 99%

“…In the present paper, we will focus on the study of robustness of genetic regulatory networks driven by Hopfield’ stochastic rule [ 35 ], by using the Kolmogorov-Sinaï entropy of the Markov process underlying the state transition dynamics [ 36 , 37 , 38 , 39 , 40 , 41 , 42 , 43 , 44 , 45 , 46 , 47 , 48 , 49 , 50 ]. In Section 2 , we define the concepts underlying the relationships between complexity, stability and robustness in the Markov framework of genetic threshold Boolean random regulatory networks.…”

Section: Introductionmentioning

confidence: 99%

Entropy as a Robustness Marker in Genetic Regulatory Networks

Rachdi

Waku

Hazgui

et al. 2020

Entropy

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Genetic regulatory networks have evolved by complexifying their control systems with numerous effectors (inhibitors and activators). That is, for example, the case for the double inhibition by microRNAs and circular RNAs, which introduce a ubiquitous double brake control reducing in general the number of attractors of the complex genetic networks (e.g., by destroying positive regulation circuits), in which complexity indices are the number of nodes, their connectivity, the number of strong connected components and the size of their interaction graph. The stability and robustness of the networks correspond to their ability to respectively recover from dynamical and structural disturbances the same asymptotic trajectories, and hence the same number and nature of their attractors. The complexity of the dynamics is quantified here using the notion of attractor entropy: it describes the way the invariant measure of the dynamics is spread over the state space. The stability (robustness) is characterized by the rate at which the system returns to its equilibrium trajectories (invariant measure) after a dynamical (structural) perturbation. The mathematical relationships between the indices of complexity, stability and robustness are presented in case of Markov chains related to threshold Boolean random regulatory networks updated with a Hopfield-like rule. The entropy of the invariant measure of a network as well as the Kolmogorov-Sinaï entropy of the Markov transition matrix ruling its random dynamics can be considered complexity, stability and robustness indices; and it is possible to exploit the links between these notions to characterize the resilience of a biological system with respect to endogenous or exogenous perturbations. The example of the genetic network controlling the kinin-kallikrein system involved in a pathology called angioedema shows the practical interest of the present approach of the complexity and robustness in two cases, its physiological normal and pathological, abnormal, dynamical behaviors.

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“…Different automata may have different transition tables and state sets. To update a node v of the network, first collect the states of its inbound neighbors into a tuple, and then feed that tuple as an input symbol to the update function of v. Globally speaking, all nodes are updated synchronously (though an extensive literature has explored other update modes [25]), so that the state of v at time t + 1 only depends on the states of its neighbors at time t.…”

Section: Introductionmentioning

confidence: 99%

Hardness of monadic second-order formulae over succinct graphs

Gamard,

Guillon,

Perrot

et al. 2023

Preprint

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Our main result is a succinct counterpoint to Courcelle's meta-theorem as follows: every arborescent monadic second-order (MSO) property is either NP-hard or coNPhard over graphs given by succinct representations. Succint representations are Boolean circuits computing the adjacency relation. Arborescent properties are those which have infinitely many models and countermodels with bounded treewidth.We actually prove this result in the terminology of automata network, which is a generalization of finite cellular automata over arbitrary graphs. This model arose from the biological modelization of neural networks and gene regulation networks. Our result states that every arborescent MSO property on the transition graph of automata networks is either NP-hard or coNP-hard.Moreover, we explore what happens when the arborescence condition is dropped and show that, under a reasonable complexity assumption, the previous dichotomy fails, even for questions expressible in first-order logic.

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About block-parallel Boolean networks: a position paper

Cited by 18 publications

References 38 publications

Boolean automata isolated cycles and tangential double-cycles dynamics

Boolean automata isolated cycles and tangential double-cycles dynamics

Entropy as a Robustness Marker in Genetic Regulatory Networks

Hardness of monadic second-order formulae over succinct graphs

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