On the complexity of acyclic modules in automata networks

Modules were introduced as an extension of Boolean automata networks. They have inputs which are used in the computation said modules perform, and can be used to wire modules with each other. In the present paper we extend this new formalism and study the specific case of acyclic modules. These modules prove to be well described in their limit behavior by functions called output functions. We provide other results that offer an upper bound on the number of attractors in an acyclic module when wired recursively into an automata network, alongside a diversity of complexity results around the difficulty of deciding the existence of cycles depending on the number of inputs and the size of said cycle.Comment: 21 page

Behaviour Preservation of a Biological Regulatory Network when Embedded into a Larger Network

International audienceThe main contribution of this work is a mathematical theorem which establishes a necessary and sufficient condition to preserve the behaviour of a genetic regulatory network when it is embedded into a larger network. We adopt the modelling approach of René Thomas, which provides a discrete representation of biological regulatory networks. This framework is entirely formalized using labelled graphs with semantics defined in terms of state graphs with transitions. Our theorem offers the possibility to automatically verify whether a subnetwork has autonomous behaviour. It will allow biologists to better identify relevant sets of genes which should be studied together

Embedding of biological regulatory networks and property preservation

Abstract. In the course of understanding biological regulatory networks (BRN), scientists usually start by studying small BRNs that they believe to be of particular importance to represent a biological function, and then, embed them in a larger network. Such a reduction can lead to neglect relevant regulations and to study a network whose properties can be very different from the properties of this network viewed as a part of the whole. In this paper we study, from a logical point of view, on which conditions concerning both networks, properties can be inherited by BRNs from sub-BRNs. We give some conditions on the nature of the network embeddings ensuring that dynamic properties on the embedded sub-BRNs are preserved at the level of the whole BRN