An efficient algorithm for identifying primary phenotype attractors of a large-scale Boolean network

Background: Boolean network modeling has been widely used to model large-scale biomolecular regulatory networks as it can describe the essential dynamical characteristics of complicated networks in a relatively simple way. When we analyze such Boolean network models, we often need to find out attractor states to investigate the converging state features that represent particular cell phenotypes. This is, however, very difficult (often impossible) for a large network due to computational complexity. Results: There have been some attempts to resolve this problem by partitioning the original network into smaller subnetworks and reconstructing the attractor states by integrating the local attractors obtained from each subnetwork. But, in many cases, the partitioned subnetworks are still too large and such an approach is no longer useful. So, we have investigated the fundamental reason underlying this problem and proposed a novel efficient way of hierarchically partitioning a given large network into smaller subnetworks by focusing on some attractors corresponding to a particular phenotype of interest instead of considering all attractors at the same time. Using the definition of attractors, we can have a simplified update rule with fixed state values for some nodes. The resulting subnetworks were small enough to find out the corresponding local attractors which can be integrated for reconstruction of the global attractor states of the original large network. Conclusions: The proposed approach can substantially extend the current limit of Boolean network modeling for converging state analysis of biological networks.