Abstract
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.
Highlights
This paper addresses the problem of finding attractors in biological regulatory networks
Conclusion and future direction In this paper, we presented a new logical approach to efficiently compute the list of all fixed points and attractors in biological regulatory networks
We designed a dedicated method for computing steady states and other programs for non-unitary attractors of a given length and a chosen update scheme
Summary
We exhibit several experiments conducted on biological networks. We first detail the results of our programs on the AN model of Fig. 1. We show the computation time for the enumeration of all results and the total number of returned answer sets yields 4 answers for the Trp-reg model and a cycle length of n = 4 with the asynchronous update scheme, and the computation takes 47 ms; this typically represents an attractor of size 4 where each answer set represents a cycle starting from a different initial state. For each model and for both update schemes (asynchronous and synchronous), the table shows, depending on the given path length n, the computation time for the first attractor found by the solver ( t), and the conclusion regarding the existence or not of at least one attractor (∃?A). Such pruning is not trivial in ASP and is the target of future works
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