Boolean modeling has been widely used to model biological systems lacking detailed kinetic information. Despite their simplicity, Boolean models can still capture some important features of biological systems such as steady states (i.e., attractors) and basins of attraction (i.e., basins). Thus, finding attractors and their basins are important problem in systems biology research. In Boolean modeling, an attractor is a set of states where state transitions converge, and basins to an attractor are a set of states that eventually converge to the attractor. Thus, in order to find attractors and basins, Boolean simulation must go through several state transitions. In the middle of simulation, however, a search space explosion may occur, and this greatly degrades the performance of simulation.
There are three main causes for a search space explosion: 1) explosively increasing state transitions with the number of initial states, 2) explosively increasing state transitions with the number of successor states and the length of state transitions, 3) explosively increasing duplicated searches of states in the middle of simulation. To tackle such a search space explosion, many approaches have been proposed in the past decade, but there is no generic method that can efficiently find every attractor and basin for large Boolean models so far. Recently, partition-based methods have been received wide attention since they can be orthogonally applied to other approaches. We thus concentrate on improving partition-based methods in this dissertation. Particularly, this dissertation addresses the major research question of partition-based methods: what is the best partition for minimizing explosive state transitions to efficiently detect attractors and basins?
In this dissertation, we claim that in order to alleviate explosive state transitions occurred in the middle of identifying attractors and basins of a Boolean model, total state transitions must be partitioned to minimize 1) the number of initial states, 2) the length of state transitions, and 3) duplicated searches of states. We propose partition-based algorithms for finding attractors and basins of a Boolean model. To analyze attractors for Boolean models with a single successor, we propose a novel scheme that partitions original network to several subnetworks so as subnetworks to have smaller number of initial states than the total initial states. In Boolean models with several successors, state transitions exponentially increase as a length of state transitions to an attractor increases. Thus, we divide long state transitions to a series of short state transitions. For basin analysis, we partition total search space based on attractors in a way to minimize duplicated searches of states. We show that the proposed partition-based approaches for finding attractors and basins mitigate a search space explosion by pruning a large amount of state transitions.