The Dynamics of Conjunctive and Disjunctive Boolean Network Models

作者：Jarrah Abdul Salam^*; Laubenbacher Reinhard; Veliz Cuba Alan

来源：Bulletin of Mathematical Biology, 2010, 72(6): 1425-1447.

DOI：10.1007/s11538-010-9501-z

• Gene regulatory network
• Conjunctive
• Disjunctive
• Boolean network model
• Feedback loop
• Network dynamics

For many biological networks, the topology of the network constrains its dynamics. In particular, feedback loops play a crucial role. The results in this paper quantify the constraints that (unsigned) feedback loops exert on the dynamics of a class of discrete models for gene regulatory networks. Conjunctive (resp. disjunctive) Boolean networks, obtained by using only the AND (resp. OR) operator, comprise a subclass of networks that consist of canalyzing functions, used to describe many published gene regulation mechanisms. For the study of feedback loops, it is common to decompose the wiring diagram into linked components each of which is strongly connected. It is shown that for conjunctive Boolean networks with strongly connected wiring diagram, the feedback loop structure completely determines the long-term dynamics of the network. A formula is established for the precise number of limit cycles of a given length, and it is determined which limit cycle lengths can appear. For general wiring diagrams, the situation is much more complicated, as feedback loops in one strongly connected component can influence the feedback loops in other components. This paper provides a sharp lower bound and an upper bound on the number of limit cycles of a given length, in terms of properties of the partially ordered set of strongly connected components.

• 出版日期2010-8
• 单位美国弗吉尼亚理工大学(Virginia Tech)