Using Sub-Network Combinations to Scale Up an Enumeration Method for Determining the Network Structures of Biological Functions

Deduction of biological regulatory networks from their functions is one of the focus areas of systems biology. Among the different techniques used in this reverse-engineering task, one powerful method is to enumerate all candidate network structures to find suitable ones. However, this method is severely limited by calculation capability: due to the brute-force approach, it is infeasible for networks with large number of nodes to be studied using traditional enumeration method because of the combinatorial explosion. In this study, we propose a new reverse-engineering technique based on the enumerating method: sub-network combinations. First, a complex biological function is divided into several sub-functions. Next, the three-node-network enumerating method is applied to search for sub-networks that are able to realize each of the sub-functions. Finally, complex whole networks are constructed by enumerating all possible combinations of sub-networks. The optimal ones are selected and analyzed. To demonstrate the effectiveness of this new method, we used it to deduct the network structures of a Pavlovian-like function. The whole Pavlovian-like network was successfully constructed by combining robust sub-networks, and the results were analyzed. With sub-network combination, the complexity has been largely reduced. Our method also provides a functional modular view of biological systems.