Algorithms for the Sequential Reprogramming of Boolean Networks

Abstract

Cellular reprogramming, a technique that opens huge opportunities in modern and regenerative medicine, heavily relies on identifying key genes to perturb. Most of the existing computational methods for controlling which attractor (steady state) the cell will reach focus on finding mutations to apply to the initial state. However, it has been shown, and is proved in this article, that waiting between perturbations so that the update dynamics of the system prepares the ground, allows for new reprogramming strategies. To identify such sequential perturbations, we consider a qualitative model of regulatory networks, and rely on Binary Decision Diagrams to model their dynamics and the putative perturbations. Our method establishes a set identification of sequential perturbations, whether permanent (mutations) or only temporary, to achieve the existential or inevitable reachability of an arbitrary state of the system. We apply an implementation for temporary perturbations on models from the literature, illustrating that we are able to derive sequential perturbations to achieve trans-differentiation. !

Drawing the Line: Basin Boundaries in Safe Petri Nets

“…We have developped Petri net-represented structures that allow to identify completely the strong basins of attraction for all attractors present in a finite safe Petri net. Future work will investigate further the different types of boundaries encountered here, and aim at refining and evaluating robustness of attractors and reprogramming strategies [17,16] in the context of concurrency. Finally, in regard to benchmarks in prior work relying on Petri net unfoldings [2,4], the time and space consumption of the proposed algorithms allows to envisage their application to networks with two-digit numbers of nodes.…”

Scalable Control of Asynchronous Boolean Networks

“…To cope with this problem, we employ the 'divide and conquer' strategy to explore both the structural and dynamical properties of a BN. As shown in Table 1, we have developed efficient methods to solve the minimal one-step source-target control with instantaneous, temporary and permanent perturbations [8,9,11], the minimal sequential source-target control with instantaneous perturbations [4,5], as well as the target control with instantaneous perturbations [1]. Among these methods, sequential source-target control identifies a sequence of intermediate states and the associated perturbations.…”

Sequential Temporary and Permanent Control of Boolean Networks

“…We have developed efficient methods to tackle the minimal OI, OT and OP control [21,22,26], as well as ASI control [11,12]. Considering the advantages of sequential control and temporary and permanent perturbations, in this paper, we shall develop methods to solve the AST and ASP control problems based on the methods for the minimal OT and OP control.…”

“…AST and ASP integrate promising factors: attractorbased sequential control and temporary/permanent control. Attractor-based sequential control is more practical than the general sequential control [12], where any state can play the role of intermediate states. Moreover, temporary and permanent controls have proved their potential in reducing the number of perturbations [26].…”