Methods In this study, we apply a Markov chain Monte Carlo (MCMC)-like algorithm to probe the design space of three-node GRNs with the ability to generate a band-like expression pattern (target phenotype) in the middle of an arrangement of 30 cells, which resemble a simple (1-D) morphogenetic field in a developing embryo. Unlike most modeling studies published so far, here we explore the space of GRN topologies with nodes having the potential to perceive the same input signal differently. This allows for a lot more flexibility during the search space process, and thus enables us to identify a larger set of potentially interesting and realizable morphogen interpretation mechanisms.

Results Out of 2061 GRNs selected using the search space algorithm, we found 714 classes of network topologies that could correctly interpret the morphogen. Notably, the main network motif that generated the target phenotype in response to the input signal was the type 3 Incoherent Feed-Forward Loop (I3-FFL), which agrees with previous theoretical expectations and experimental observations. Particularly, compared to a previously reported pattern forming GRN topologies, we have uncovered a great variety of novel network designs, some of which might be worth inquiring through synthetic biology methodologies to test for the ability of network design with minimal regulatory complexity to interpret a developmental cue robustly.