Programmable pattern formation in cellular systems with local signaling

Complex systems, ranging from developing embryos to systems of locally communicating agents, display an apparent capability of “programmable” pattern formation: They reproducibly form target patterns, but those targets can be readily changed. A distinguishing feature of such systems is that their subunits are capable of information processing. Here, we explore schemes for programmable pattern formation within a theoretical framework, in which subunits process local signals to update their discrete state following logical rules. We study systems with different update rules, topologies, and control schemes, assessing their capability of programmable pattern formation and their susceptibility to errors. Only a fraction permits local organizers to dictate any target pattern, by transcribing temporal patterns into spatial patterns, reminiscent of the principle underlying vertebrate somitogenesis. An alternative scheme employing variable rules cannot reach all patterns but is insensitive to the timing of organizer inputs. Our results establish a basis for designing synthetic systems and models of programmable pattern formation closer to real systems.