An efficient algorithm to identify the optimal one-bit perturbation based on the basin-of-state size of Boolean networks

Abstract

Boolean networks are widely used to model gene regulatory networks and to design therapeutic intervention strategies to affect the long-term behavior of systems. In this paper, we investigate the less-studied one-bit perturbation, which falls under the category of structural intervention. Previous works focused on finding the optimal one-bit perturbation to maximally alter the steady-state distribution (SSD) of undesirable states through matrix perturbation theory. However, the application of the SSD is limited to Boolean networks with about ten genes. In 2007, Xiao et al. proposed to search the optimal one-bit perturbation by altering the sizes of the basin of attractions (BOAs). However, their algorithm requires close observation of the state-transition diagram. In this paper, we propose an algorithm that efficiently determines the BOA size after a perturbation. Our idea is that, if we construct the basin of states for all states, then the size of the BOA of perturbed networks can be obtained just by updating the paths of the states whose transitions have been affected. Results from both synthetic and real biological networks show that the proposed algorithm performs better than the exhaustive SSD-based algorithm and can be applied to networks with about 25 genes.

RMut: R package for a Boolean sensitivity analysis against various types of mutations

“…Edge-reverse: This mutation represents a switch in both the type and outcome of a molecular interaction or relationship between two proteins or genes [ 58 ]. In other words, both the activation/inhibition relationship and the output value of an interaction are switched.…”

“…Edgetic mutations have been recently considered in experimental studies to better reveal genotype-to-phenotype relationships and drug discovery [ 15 , 16 ]. Some in silico studies have also been conducted [ 57 , 58 , 67 ]. For example, Li, Long [ 57 ] investigated the dynamic properties and stability of the yeast cell-cycle network by applying edge-removal, edge-addition, and edge-sign-switch mutations.…”

“…Previous studies have focused on the former [ 4 , 14 , 47 , 58 , 72 ] rather than the latter [ 57 ]. Specifically, edge-reverse mutations were implemented by flipping an output value of an input variable in a Boolean update rule [ 4 , 58 ]. Finally, the edge-attenuation mutation, which was not considered in any previous in silico studies, showed the smallest sensitivity values in all real networks.…”

A Boolean network control algorithm guided by forward dynamic programming

“…Authors found no exact algorithm for the same network control problem in more recent years. However, an algorithm for identification of the best one-bit perturbation is provided [35]. In this problem, a Boolean network is given and the problem is to find a gene that changing its initial state 1) does not change attractors of the network, 2) maximize the size of the basin of some desired attractors.…”

Algorithm to identify the optimal perturbation based on the net basin‐of‐state of perturbed states in Boolean network

“…The main obstacle for methods based on matrix perturbation theory is that operations on the probability transition matrix () are too time‐consuming, where n represents the gene number. In 2016, Hu et al [11] proposed an efficient algorithm which updated the state‐transition diagram based on the basin‐of‐states (BOS) of the perturbed states. The BOS of a state represents the number of states which can flow into it.…”