Applying reduction mappings in designing genomic regulatory networks

Probabilistic Boolean Networks (PBNs) represent a class of nonlinear models of genetic regulatory networks incorporating the indeterminacy owing to latent variables external to the model that have biological interaction with genes in the model. Besides being used to model biological phenomena, such as cellular state dynamics and the switch-like behavior of certain genes, PBNs have served as the main model for the application of intervention methods, including optimal control strategies, to favorably effect system dynamics. An obstacle in applying PBNs to large-scale networks is the computational complexity of the model. It is sometimes necessary to construct computationally tractable sub-networks while still carrying sufficient structure for the application at hand. Hence, there is a need for size reducing mappings. Such mappings can be used not only to render computationally manageable sub-networks but they can also play an important role in the process of designing PBNs from microarray data. The process of inferring PBNs from data is known to be a one-to-many mapping, and one needs a biologically sound constraints when selecting the PBN that is optimal with respect the given data. This paper proposes such a constraint based on the recently introduced DIRE reduction algorithm.