Marker and source-marker reprogramming of Most Permissive Boolean networks and ensembles with BoNesis

Boolean networks (BNs) are discrete dynamical systems with applications to the modeling of cellular behaviors. In this paper, we demonstrate how the software BoNesis can be employed to exhaustively identify combinations of perturbations which enforce properties on their fixed points and attractors. We consider marker properties, which specify that some components are fixed to a specific value. We study 4 variants of the marker reprogramming problem: the reprogramming of fixed points, of minimal trap spaces, and of fixed points and minimal trap spaces reachable from a given initial configuration with the most permissive update mode. The perturbations consist of fixing a set of components to a fixed value. They can destroy and create new attractors. In each case, we give an upper bound on their theoretical computational complexity, and give an implementation of the resolution using the BoNesis Python framework. Finally, we lift the reprogramming problems to ensembles of BNs, as supported by BoNesis, bringing insight on possible and universal reprogramming strategies. This paper can be executed and modified interactively.Comment: Notebook available at https://nbviewer.org/github/bnediction/reprogramming-with-bonesis/blob/release/paper.ipyn

Under-approximating Cut Sets for Reachability in Large Scale Automata Networks

In the scope of discrete finite-state models of interacting components, we present a novel algorithm for identifying sets of local states of components whose activity is necessary for the reachability of a given local state. If all the local states from such a set are disabled in the model, the concerned reachability is impossible. Those sets are referred to as cut sets and are computed from a particular abstract causality structure, so-called Graph of Local Causality, inspired from previous work and generalised here to finite automata networks. The extracted sets of local states form an under-approximation of the complete minimal cut sets of the dynamics: there may exist smaller or additional cut sets for the given reachability. Applied to qualitative models of biological systems, such cut sets provide potential therapeutic targets that are proven to prevent molecules of interest to become active, up to the correctness of the model. Our new method makes tractable the formal analysis of very large scale networks, as illustrated by the computation of cut sets within a Boolean model of biological pathways interactions gathering more than 9000 components

Attractor identification in asynchronous Boolean dynamics with network reduction

Identification of attractors, that is, stable states and sustained oscillations, is an important step in the analysis of Boolean models and exploration of potential variants. We describe an approach to the search for asynchronous cyclic attractors of Boolean networks that exploits, in a novel way, the established technique of elimination of components. Computation of attractors of simplified networks allows the identification of a limited number of candidate attractor states, which are then screened with techniques of reachability analysis combined with trap space computation. An implementation that brings together recently developed Boolean network analysis tools, tested on biological models and random benchmark networks, shows the potential to significantly reduce running times.Comment: 13 page

Computational Complexity of Minimal Trap Spaces in Boolean Networks

Trap spaces of a Boolean network (BN) are the sub-hypercubes closed by the function of the BN. A trap space is minimal if it does not contain any smaller trap space. Minimal trap spaces have applications for the analysis of dynamic attractors of BNs with various update modes. This paper establishes computational complexity results of three decision problems related to minimal trap spaces of BNs: the decision of the trap space property of a sub-hypercube, the decision of its minimality, and the decision of the belonging of a given configuration to a minimal trap space. Under several cases on Boolean function specifications, we investigate the computational complexity of each problem. In the general case, we demonstrate that the trap space property is coNP-complete, and the minimality and the belonging properties are $\Pi_2^{\text P}$-complete. The complexities drop by one level in the polynomial hierarchy whenever the local functions of the BN are either unate, or are specified using truth-table, binary decision diagrams, or double-DNF (Petri net encoding): the trap space property can be decided in P, whereas the minimality and the belonging are coNP-complete. When the BN is given as its functional graph, all these problems can be decided by deterministic polynomial time algorithms

Goal-Driven Unfolding of Petri Nets

International audienceUnfoldings provide an efficient way to avoid the state-space explosion due to interleavings of concurrent transitions when exploring the runs of a Petri net. The theory of adequate orders allows one to define finite prefixes of unfoldings which contain all the reachable markings. In this paper we are interested in reachability of a single given marking, called the goal. We propose an algorithm for computing a finite prefix of the unfolding of a 1-safe Petri net that preserves all minimal configurations reaching this goal. Our algorithm combines the unfolding technique with on-the-fly model reduction by static analysis aiming at avoiding the exploration of branches which are not needed for reaching the goal. We present some experimental results

Goal-Driven Unfolding of Petri Nets

International audienceUnfoldings provide an efficient way to avoid the state-space explosion due to interleavings of concurrent transitions when exploring the runs of a Petri net. The theory of adequate orders allows one to define finite prefixes of unfoldings which contain all the reachable markings. In this paper we are interested in reachability of a single given marking, called the goal. We propose an algorithm for computing a finite prefix of the unfolding of a 1-safe Petri net that preserves all minimal configurations reaching this goal. Our algorithm combines the unfolding technique with on-the-fly model reduction by static analysis aiming at avoiding the exploration of branches which are not needed for reaching the goal. We present some experimental results

Topological fixed points in Boolean networks

International audienceWe introduce the notion of a topological fixed point in Boolean Networks: a fixed point of Boolean network F is said to be topologic if it is a fixed point of every Boolean network with the same interaction graph as the one of F. Then, we characterize the number of topological fixed points of a Boolean network according to the structure of its interaction graph

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

International audienceBoolean 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

Necessary and sufficient conditions for protocell growth

International audienceWe consider a generic protocell model consisting of any conservative chemical reaction network embedded within a membrane. The membrane results from the self-assembly of a membrane precursor and is semi-permeable to some nutrients. Nutrients are metabolized into all other species including the membrane precursor, and the membrane grows in area and the protocell in volume. Faithful replication through cell growth and division requires a doubling of both cell volume and surface area every division time (thus leading to a periodic surface area-to-volume ratio) and also requires periodic concentrations of the cell constituents. Building upon these basic considerations, we prove necessary and sufficient conditions pertaining to the chemical reaction network for such a regime to be met. A simple necessary condition is that every moiety must be fed. A stronger necessary condition implies that every siphon must be either fed, or connected to species outside the siphon through a pass reaction capable of transferring net positive mass into the siphon. And in the case of nutrient uptake through passive diffusion and of constant surface area-to-volume ratio, a sufficient condition for the existence of a fixed point is that every siphon be fed. These necessary and sufficient conditions hold for any chemical reaction kinetics, membrane parameters or nutrient flux diffusion constants