Propagation of external regulation and asynchronous dynamics in random Boolean networks

Mahmoudi, Hamed; Pagnani, Andrea; Weigt, Martin; Zecchina, Riccardo

doi:10.1063/1.2742931

Cited by 4 publications

(5 citation statements)

References 31 publications

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“…Besides, from a purely theoretical viewpoint, very often the problems thus defined present phase structures and algorithmic challenges that suffice by themselves to attract a considerable statistical mechanical effort (see e.g. [17,18]).…”

Section: Introductionmentioning

confidence: 99%

Boolean constraint satisfaction problems for reaction networks

2013

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We define and study a class of (random) Boolean constraint satisfaction problems representing minimal feasibility constraints for networks of chemical reactions. The constraints we consider encode, respectively, for hard mass-balance conditions (where the consumption and production fluxes of each chemical species are matched) and for soft mass-balance conditions (where a net production of compounds is in principle allowed). We solve these constraint satisfaction problems under the Bethe approximation and derive the corresponding Belief Propagation equations, that involve 8 different messages. The statistical properties of ensembles of random problems are studied via the population dynamics methods. By varying a chemical potential attached to the activity of reactions, we find first order transitions and strong hysteresis, suggesting a non-trivial structure in the space of feasible solutions. Contents

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Section: Introductionmentioning

confidence: 99%

Boolean constraint satisfaction problems for reaction networks

2013

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“…by the Markov property (7). Assuming that equation (18) holds with γ chosen as in (12), the estimation error in f (v; U ) is at most ǫ/2 by equation (20), and it holds that f (v; U ) < ǫ/2 for each U N (v).…”

Section: General Reconstructionmentioning

confidence: 99%

“…Thus all U N (v) are rejected. If U = N (v), then by the Markov property (7) and the conditions (16) and (17), for any i and W ⊂ V ,…”

Section: General Reconstructionmentioning

confidence: 99%

Reconstruction of Markov Random Fields from Samples: Some Observations and Algorithms

Bresler

Mossel

Sly

Lecture Notes in Computer Science

177

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Markov random fields are used to model high dimensional distributions in a number of applied areas. Much recent interest has been devoted to the reconstruction of the dependency structure from independent samples from the Markov random fields. We analyze a simple algorithm for reconstructing the underlying graph defining a Markov random field on n nodes and maximum degree d given observations. We show that under mild non-degeneracy conditions it reconstructs the generating graph with high probability using Θ(dǫ −2 δ −4 log n) samples where ǫ, δ depend on the local interactions. For most local interaction ǫ, δ are of order exp(−O(d)).Our results are optimal as a function of n up to a multiplicative constant depending on d and the strength of the local interactions. Our results seem to be the first results for general models that guarantee that the generating model is reconstructed. Furthermore, we provide explicit O(n d+2 ǫ −2 δ −4 log n) running time bound. In cases where the measure on the graph has correlation decay, the running time is O(n 2 log n) for all fixed d. We also discuss the effect of observing noisy samples and show that as long as the noise level is low, our algorithm is effective. On the other hand, we construct an example where large noise implies non-identifiability even for generic noise and interactions. Finally, we briefly show that in some simple cases, models with hidden nodes can also be recovered.

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“…It has also been used to characterize the behavior of random-update Boolean networks. 87 The reference models for such equilibrium studies are the so called ''spin models''. These are one of the most ''versatile'' models in Statistical Physics, and have been successfully applied in several contexts.…”

Section: Discrete Modelsmentioning

confidence: 99%

Functional models for large-scale gene regulation networks: realism and fiction

et al. 2009

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High-throughput experiments are shedding light on the topology of large regulatory networks and at the same time their functional states, namely the states of activation of the nodes (for example transcript or protein levels) in different conditions, times, environments. We now possess a certain amount of information about these two levels of description, stored in libraries, databases and ontologies. A current challenge is to bridge the gap between topology and function, i.e. developing quantitative models aimed at characterizing the expression patterns of large sets of genes. However, approaches that work well for small networks become impossible to master at large scales, mainly because parameters proliferate. In this review we discuss the state of the art of large-scale functional network models, addressing the issue of what can be considered as "realistic" and what the main limitations may be. We also show some directions for future work, trying to set the goals that future models should try to achieve. Finally, we will emphasize the possible benefits in the understanding of biological mechanisms underlying complex multifactorial diseases, and in the development of novel strategies for the description and the treatment of such pathologies.

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Propagation of external regulation and asynchronous dynamics in random Boolean networks

Cited by 4 publications

References 31 publications

Boolean constraint satisfaction problems for reaction networks

Boolean constraint satisfaction problems for reaction networks

Reconstruction of Markov Random Fields from Samples: Some Observations and Algorithms

Functional models for large-scale gene regulation networks: realism and fiction

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