Aggregation Algorithm Towards Large-Scale Boolean Network Analysis

Abstract

Abstract-The analysis of large-scale Boolean network dynamics is of great importance in understanding complex phenomena where systems are characterized by a large number of components. The computational cost to reveal the number of attractors and the period of each attractor increases exponentially as the number of nodes in the networks increases. This paper presents an efficient algorithm to find attractors for medium to large scale networks. This is achieved by analyzing subnetworks within the network in a way that allows to reveal the attractors of the full network with little computational cost. In particular, for each subnetwork modeled as a Boolean control network, the input-state cycles are found and they are composed to reveal the attractors of the full network. The proposed algorithm reduces the computational cost significantly, especially in finding attractors of short period, or any periods if the aggregation network is acyclic. Also, this paper shows that finding the best acyclic aggregation is equivalent to finding the strongly connected components of the network graph. Finally, the efficiency of the algorithm is demonstrated on two biological systems, namely a Tcell receptor network and an early flower development network.

Optimization-Based Approaches to Control of Probabilistic Boolean Networks

“…Developing scalable control methods is important. Then, decomposition of networks is important (see, e.g., [50,51]). For BNs, we consider only one network structure (directed graph) such as Figure 1.…”

Improving BDD-based Attractor Detection for Synchronous Boolean Networks

“…proposed an aggregation algorithm to deal with large BNs. Their idea is to decompose a large BN into several sub-networks and detect attractors of each sub-network [26]. By merging the attractors of all the sub-networks, their algorithm can reveal the attractors of the original BN.…”

“…The attractor detection in each sub-network is performed one by one according to their credits. Unlike the algorithm in [26], when detecting attractors of a sub-network, the method of Guo et al considers the attractor information of other sub-networks whose credits are smaller. In this way, it reveals the attractors of the original BN by detecting attractors of the last sub-network.…”

“…In this way, it reveals the attractors of the original BN by detecting attractors of the last sub-network. In our work, we are inspired by the ideas in [9,26] to explore the structure of large BNs to accelerate the attractor detection process. Our main idea is to use all attractor information of small sub-networks, to which efficient attractor detection algorithms for small BNs can be applied, to reduce the set of initial states of the original BN and thus speed up the attractor detection of the original but large network.…”

Output tracking control of Boolean control networks via state feedback: Constant reference signal case

“…Then, one can analyze Boolean (control) networks by using the classical control theory. Up to now, there have been many interesting works on the control of BCNs via this novel method, which include controllability and observability (Chen & Sun, 2014;Cheng, Li, & Qi, 2010;Cheng & Qi, 2009Feng, Yao, & Cui, 2012;Fornasini & Valcher, 2013a;Laschov & Margaliot, 2012;Li & Sun, 2011a,b;Li & Wang, 2012;Zhao, Cheng, & Qi, 2010), disturbance decoupling (Cheng, 2011;, optimal control (Fornasini & Valcher, 2014;Laschov & Margaliot, 2011;Zhao, Li, & Cheng, 2011), stability and stabilization (Cheng, Qi, Li, & Liu, 2011;Li & Wang, 2013;, and other control problems (Cheng & Xu, 2013;Fornasini & Valcher, 2013b;Li & Chu, 2012;Wang, Zhang, & Liu, 2012;Xu & Hong, 2013;Zhang, 2012;Zhang & Feng, 2013;Zhao, Kim, & Filippone, 2013;Zou & Zhu, 2014).…”