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.
Highlights
The ultimate objective of gene-regulatory-network modeling and analysis is to design effective intervention strategies so that the dynamics of the network evolves toward desirable cellular states
The optimal structural intervention is to determine which perturbation on the truth table governing a Boolean network with perturbation p (BNp) or Probabilistic Boolean networks (PBNs) would result in the maximal long-term effect on the dynamic behavior of the network
We propose an algorithm that quickly determines the size of the basin of attraction (BOA) after a one-bit perturbation based on the basin of states (BOS) for each state
Summary
The ultimate objective of gene-regulatory-network modeling and analysis is to design effective intervention strategies so that the dynamics of the network evolves toward desirable cellular states. External intervention changes the SSD only when the control policies are performed From this point of view, structural intervention has a greater potential impact on the dynamic behavior of networks than external intervention, and gene therapies are more likely to be developed by applying drug or genetic manipulation to alter extant cell behavior. Xiao et al proposed several algorithms to determine the optimal perturbation function based on the change in the size of the BOA9. Their algorithms are very cumbersome and require closely observing the state transition changes before and after a perturbation.
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