Synthesis of Boolean Networks from Biological Dynamical Constraints using Answer-Set Programming

Abstract

Boolean networks model finite discrete dynamical systems with complex behaviours. The state of each component is determined by a Boolean function of the state of (a subset of) the components of the network.This paper addresses the synthesis of these Boolean functions from constraints on their domain and emerging dynamical properties of the resulting network. The dynamical properties relate to the existence and absence of trajectories between partially observed configurations, and to the stable behaviours (fixpoints and cyclic attractors). The synthesis is expressed as a Boolean satisfiability problem relying on Answer-Set Programming with a parametrized complexity, and leads to a complete non-redundant characterization of the set of solutions.Considered constraints are particularly suited to address the synthesis of models of cellular differentiation processes, as illustrated on a case study. The scalability of the approach is demonstrated on random networks with scale-free structures up to 100 to 1,000 nodes depending on the type of constraints.

Synthesis and Simulation of Ensembles of Boolean Networks for Cell Fate Decision

“…With this approach, we leverage a priori knowledge and experimental data as constraints on the network architecture and the dynamical properties of the models under the MP semantics. Our method is based on [2], which implements constraints on existence and absence of trajectories between partially-specified configurations, existence of (reachable) fixed points and trap spaces. In biological applications, these constraints match well the observed properties of cell populations evolving towards mutually exclusive phenotypes.…”

“…In this paper, we extend [2] to support universal properties on (reachable) attractors. This enables specifying tight dynamical constraints.…”

“…mcfg(X,N,V) predicate template leads to the evaluation of the configuration X given the Boolean rules of the network [2]. The reachable values are then stored in the predicate eval(X,N,V).…”

“…Here, we extend prior work on BNs synthesis from reachability and attractor properties with Most Permissive semantics [2] to support universal properties on (reachable) fixed points and the specification of network perturbations. The synthesis is performed with the logic framework of Answer-Set Programming [1] (ASP).…”

“…In contrast, our approach is focused on ensembles of models which satisfy a set of constraints both on their architecture and on their dynamics. Synthesis of BNs from such constraints received a lot of interest in the literature [6,24,7,27,13,2], and methods like [6,27,13,2] allows reasoning implicitly on ensembles of models, notably by enabling checking for their emptiness.…”