Abstract
BackgroundNumerous cellular differentiation processes can be captured using discrete qualitative models of biological regulatory networks. These models describe the temporal evolution of the state of the network subject to different competing transitions, potentially leading the system to different attractors. This paper focusses on the formal identification of states and transitions that are crucial for preserving or pre-empting the reachability of a given behaviour.MethodsIn the context of non-deterministic automata networks, we propose a static identification of so-called bifurcations, i.e., transitions after which a given goal is no longer reachable. Such transitions are naturally good candidates for controlling the occurrence of the goal, notably by modulating their propensity. Our method combines Answer-Set Programming with static analysis of reachability properties to provide an under-approximation of all the existing bifurcations.ResultsWe illustrate our discrete bifurcation analysis on several models of biological systems, for which we identify transitions which impact the reachability of given long-term behaviour. In particular, we apply our implementation on a regulatory network among hundreds of biological species, supporting the scalability of our approach.ConclusionsOur method allows a formal and scalable identification of transitions which are responsible for the lost of capability to reach a given state. It can be applied to any asynchronous automata networks, which encompass Boolean and multi-valued models. An implementation is provided as part of the Pint software, available at http://loicpauleve.name/pint.
Highlights
The emerging complexity of dynamics of biological networks, and in particular of signalling and gene regulatory networks, is mainly driven by the interactions between the species, and the numerous feedback circuits they generate [1,2,3,4]
We formally introduce the notion of bifurcation transitions in discrete dynamics of automata networks (ANs) and we provide a scalable method for their identification that relies on declarative programming with Answer-Set Programming (ASP) [10]
Bifurcations Given an initial state s0 and a goal local state, a bifurcation transition is a transition from a state where the goal a1, b0, c1
Summary
The emerging complexity of dynamics of biological networks, and in particular of signalling and gene regulatory networks, is mainly driven by the interactions between the species, and the numerous feedback circuits they generate [1,2,3,4]. One of the prominent and fascinating features of cells is their capability to differentiate: starting from a multi-potent state (for instance, a stem cell), cellular processes progressively confine the cell dynamics in a narrow state space, an attractor. Deciphering those decision processes is a tremendous challenge, with important. Numerous cellular differentiation processes can be captured using discrete qualitative models of biological regulatory networks These models describe the temporal evolution of the state of the network subject to different competing transitions, potentially leading the system to different attractors.
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