Gene regulatory networks govern the function of key cellular processes, such as control of the cell cycle, response to stress, DNA repair mechanisms, and more. Boolean networks have been used successfully in modeling gene regulatory networks. In the Boolean network model, the transcriptional state of each gene is represented by 0 (inactive) or 1 (active), and the relationship among genes is represented by logical gates updated at discrete time points. However, the Boolean gene states are never observed directly, but only indirectly and incompletely through noisy measurements based on expression technologies such as cDNA microarrays, RNA-Seq, and cell imaging-based assays. Researchers from Texas A&M University show that the Partially-Observed Boolean Dynamical System (POBDS) signal model is distinct from other deterministic and stochastic Boolean network models in removing the requirement of a directly observable Boolean state vector and allowing uncertainty in the measurement process, addressing the scenario encountered in practice in transcriptomic analysis.
The p53-MDM2 Boolean gene regulatory network
The state of the system at time k is represented by a vector (ATM k ,p53 k ,WIP1 k ,MDM2 k ), where the subscript k indicates expression state at time k. The Boolean input u k =dna_dsb k at time k indicates the presence of DNA double strand breaks. Counter-clockwise from the top right: the activation/inhibition pathway diagram, transition diagrams corresponding to a constant inputs dna_dsb k ≡0 (no stress) and dna_dsb k ≡1 (DNA damage), and Boolean equations that describe the state transitions