Presentation Information
[SS06-03]Attractor-based Analysis of Boolean Networks
*Tatsuya Akutsu1 (1. Kyoto University (Japan))
Keywords:
Boolean networks,Attractors,Multilayer networks
Boolean networks (BNs) have been used as a discrete model of biological networks including genetic networks and neural networks, where each node corresponds toa gene (or neuron) and each edge represents a directed regulatory relation between two genes. Each node takes 0 (active) or 1 (inactive), where its state is updated at each time step according to a regulation rule given as a Boolean function. The state of the whole network eventually falls into a statically steady state (point attractor) or a periodically steady state (periodic attractor). Here, we present two of our recent results on theoretical analyses of attractors and their applications to BN models of real biological systems [1,2].
Although attractors play important roles in analysis of BNs, detection of attractors from a given network is computationally difficult (NP-hard). Specifically, detection of a long periodic attractor is quite difficult for which no algorithm theoretically faster than the naive method is known. In order to cope with this difficulty, we developed a novel method to compute attractors based on a priori information (state probability of each node), which works much and provably faster than the naive method. We applied the method to analysis of two large-scale BN models of real biological systems, one for the effect of the microenvironment during angiogenesis and the other for a cell cycle control network in Saccharomyces cerevisiae with 3158 nodes. The results suggest that long periodic attractors can be found for large BNs if a priori information is available.
Another issue on attractor analysis is that BN structure may differ from individual to individual. In order to cope with this issue, we studied common attractors and similar attractors in multiple BNs to uncover hidden similarities and differences among BNs. We theoretically analyzed the expected number of common and similar attractors for random BNs, and developed to find such attractors. We applied one of the methods to analysis of a BN model of the TGF-beta signaling pathway, where the result suggests that common attractors and similar attractors are useful for exploring tumor heterogeneity and homogeneity in eight cancers.
[1] U. Munzner et al.: Identification of periodic attractors in Boolean networks using a priori information, PLoS Comp. Biol., 18:1009702, 2022.
[2] Y. Cao et al.: Common attractors in multiple Boolean networks, IEEE/ACM Trans. Comp. Biol. & Bioinform., 20:2862-2873, 2023.
Although attractors play important roles in analysis of BNs, detection of attractors from a given network is computationally difficult (NP-hard). Specifically, detection of a long periodic attractor is quite difficult for which no algorithm theoretically faster than the naive method is known. In order to cope with this difficulty, we developed a novel method to compute attractors based on a priori information (state probability of each node), which works much and provably faster than the naive method. We applied the method to analysis of two large-scale BN models of real biological systems, one for the effect of the microenvironment during angiogenesis and the other for a cell cycle control network in Saccharomyces cerevisiae with 3158 nodes. The results suggest that long periodic attractors can be found for large BNs if a priori information is available.
Another issue on attractor analysis is that BN structure may differ from individual to individual. In order to cope with this issue, we studied common attractors and similar attractors in multiple BNs to uncover hidden similarities and differences among BNs. We theoretically analyzed the expected number of common and similar attractors for random BNs, and developed to find such attractors. We applied one of the methods to analysis of a BN model of the TGF-beta signaling pathway, where the result suggests that common attractors and similar attractors are useful for exploring tumor heterogeneity and homogeneity in eight cancers.
[1] U. Munzner et al.: Identification of periodic attractors in Boolean networks using a priori information, PLoS Comp. Biol., 18:1009702, 2022.
[2] Y. Cao et al.: Common attractors in multiple Boolean networks, IEEE/ACM Trans. Comp. Biol. & Bioinform., 20:2862-2873, 2023.