Dimension Reduction of Large Sparse AND-NOT Network Models

Abstract

In this manuscript we propose and implement a dimension reduction algorithm of AND-NOT networks for the purpose of steady state computation. Our method of network reduction consists in using “steady state approximations” that do not change the number of steady states. The algorithm is designed to work at the wiring diagram level without the need to evaluate or simplify Boolean functions. Also, our implementation of the algorithm takes advantage of the sparsity typical of discrete models of biological systems.The main features of our reduction algorithm are that it works at the wiring diagram level and it preserves the number of steady states. Furthermore, the steady states of the original network can be recovered from the steady states of the reduced network; thus, all steady states are found. Also, heuristic analysis and simulations show that it runs in polynomial time. We used our results to study AND-NOT network models of gene networks and showed that our algorithm greatly simplifies steady state analysis. Furthermore, our algorithm can handle sparse AND-NOT networks with up to 1,000,000 nodes.