The Study Of Detecting Attractors Of Boolean Network

Boolean network which based on graph theory is a simple but very effective mathematical model. In Boolean networks, attractors are some special status and have important biological significance. Since the state space of Boolean network increases exponentially with the network size, requiring the use of more efficient algorithms to detect Boolean networks attractors. In this paper, starting from the characteristics of single attractor, defined the concept of conditional Boolean functions and proposed an algorithm based on function reduction for detecting attractors. In conditional Boolean functions, some variables are determined as 0 or 1. When the states of all the variables have been determined and there is only one input left in each conditional Boolean function, the state combined by each variable is a single attractor. There are two ways to determining the state of variables. First, if the variable in the current conditional Boolean function for all possible input or output are 0 or 1, then all Boolean functions with the variable state is determined as consistent state. Otherwise, both trying determining the variables as 0 and 1.Studies have shown that it is relevant genes which determine the states and structures of attractor of Boolean network. In this paper a simple method of calculating relevant gene was proposed and was used to improve the efficiency of the algorithm. In addition, this paper presented the concept of compound Boolean networks, introduced the calculation method of compound Boolean networks and formal proof of the variation of original Boolean network attractors in compound networks. By the use of compound network, the function reduction-based algorithm can compute small size attractors.Finally, this paper implemented a software follow the thought of function reduction-based algorithm combined with the concept of relevant gene and compound Boolean network. Enter the file name of text file which saved Boolean network data as required and the parameter p, the software will automatically reading the file and outputting all attractors not larger than p to another file. Another software was implemented for generating random Boolean networks. Both two softwares can handle or generate files at one time.