Boolean Networks and Their Dynamics: The Impact of Updates

Paulevé, Loı̈c; Sené, Sylvain

doi:10.1002/9781119716600.ch6

“…There is a vast zoo of update modes (Paulevé and Sené, 2022), but traditionally, two modes are usually considered in biological modeling: the synchronous (or parallel) deterministic mode, where the next configuration is given by its application to f (x is succeeded by f (x)), and the fully asynchronous (often denoted only asynchronous) where the next configuration results from the application of only one local function, chosen non-deterministically.…”

Section: Update Modesmentioning

confidence: 99%

Reprogramming of locally-monotone Boolean networks with BoNesis

Ivanov

¹

2023

PCI Math Comp Biol

0

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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. (Paulevé et al., 2020). The problems we tackle are related to marker reprogramming: the desired target attractors are specified by a set of markers, associating a subset of nodes of the network to fixed values (e.g., A = 1, C = 0). After reprogramming, all the configurations in all (reachable) attractors must be compatible with these markers. Importantly, the target attractors are not necessarily attractors of the original (wild-type) BN: the reprogramming can destroy and create new attractors. In particular, if there is no attractor in the original model matching with the marker, the reprogramming will identify perturbations that will create such an attractor and ensure its reachability. This is a substantial difference with many of the methods in the literature. Moreover, the approach we present here can return all the possible solutions, possibly up to a given maximum number of perturbations to apply, and possibly avoiding uncontrollable nodes.We address the following BN reprogramming problems in the scope of the MP update mode:• P1 : Marker reprogramming of fixed points: after reprogramming, all the fixed points of the BN match with the given markers; optionally, we can also ensure that at least one fixed point exists. • P2 : Source-marker reprogramming of fixed points: after reprogramming, all the fixed points that are reachable from the given initial configuration match with the given markers.• P3 : Marker reprogramming of attractors: after reprogramming, all the configurations of all the MP attractors (the minimal trap spaces) of the BN match with the given markers.• P4 : Source-marker reprogramming of attractors: after reprogramming, all the configurations of all the attractors that are reachable from the given initial configuration match with the given markers. MP fixed points match with the fixed points of the global Boolean map of the BN (and are thus identical to the fixed points of the...

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“…Given a BN f and a configuration x, the update mode specifies how to compute the next configuration. There is a vast zoo of update modes (Paulevé and Sené, 2022), but traditionally, two modes are usually considered in biological modeling: the synchronous (or parallel) deterministic mode, where the next configuration is given by its application to f (x is succeeded by f (x)), and the fully asynchronous (often denoted only asynchronous) where the next configuration results from the application of only one local function, chosen non-deterministically.…”

Section: Introductionmentioning

confidence: 99%

“…However, (a)synchronous update modes do not lead to a complete qualitative abstraction of quantitative systems and preclude the prediction of trajectories that are actually feasible when considering time scales or concentration scales. The Most Permissive (MP) (Paulevé, Kolčák, Chatain, and Haar, 2020;Paulevé and Sené, 2021) is a recently-introduced update mode which brings the formal guarantee to capture any trajectory that is feasible by any quantitative system compatible with the Boolean network (see (Paulevé et al, 2020) for details). The main idea behind the MP update mode is to systematically consider a potential delay when a component changes state, and consider any additional transitions that could occur if the changing component is in an intermediate state.…”

Section: Introductionmentioning

confidence: 99%

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

Paulevé¹

2023

Peer Community Journal

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2

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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.

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