Finding All Steady States in Biological Regulatory Networks

Abstract

Motivation. Computing the long term behavior of regulatory and signaling networks is critical in understanding how biological functions take place in organisms. Steady states of these networks determine the activity levels of individual entities in the long run. Identifying all the steady states of these networks is difficult as it suffers from the state space explosion problem. Results. In this paper, we propose a method for identifying all the steady states of regulatory and signaling networks accurately and efficiently. We build a mathematical model that allows pruning a large portion of the state space quickly without causing any false dismissals. For the remaining state space, which is typically very small compared to the whole state space, we develop a randomized algorithm that extracts the steady states. This algorithm estimates the number of steady states, and the expected behaviors of individual genes and gene pairs in steady states in an online fashion. Also, we formulate a stopping criteria that terminates the randomized algorithm as soon as user supplied percentage of the results are returned with high confidence. Finally, in order to maintain the scalability of our algorithm to very large networks, we develop a partitioning-based estimation strategy. We show that our algorithm can identify all the steady states accurately. Furthermore, our experiments demonstrate that our method is scalable to virtually any large real biological network.