Programmable pattern formation in cellular systems with local signaling

Abstract

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.

The French flag problem revisited: Creating robust and tunable axial patterns without global signaling

“…Although we have limited our analysis to one-dimensional models here, extending the analysis of axial patterning in two- or three-dimensional systems would not pose conceptual challenges. Additional lateral signaling in two- or three-dimensional systems could also be leveraged to increase the robustness of the patterning process to noise, via a positive reinforcement or majority voting scheme ( Ramalho et al, 2021 ).…”

“…Given our focus on axial patterns, it is sufficient to consider one-dimensional CA composed of a line of cells. Axial patterning in two-dimensional systems can use the same strategies as in one dimension, while an additional lateral coupling between adjacent lines of cells could increase the robustness of the patterning process ( Ramalho et al, 2021 ). The cells in a one-dimensional CA of size L are labelled by a position index i = 1 … L .…”

“…By focusing on logical rules for local signaling and the dynamics of a small number of discrete cell states, CA provide a suitable level of description for our study. CA have previously been used to explore patterning principles for cellular systems ( Deutsch and Dormann, 2005 ; Basanta et al, 2008 ; Ramalho et al, 2021 ; Bojer et al, 2022 ), and to construct specific solutions for different “Flag problems” ( Herman and Liu, 1973 ; Rohlf and Bornholdt, 2005, 2009 ; Nichele et al, 2017 ). Clearly, modeling frameworks other than CA are available, such as message passing models, which have been used to construct solutions to the French flag problem based on the communication and computation abilities of digital electronic devices ( Ancona et al, 2019 ).…”

From the origin of life to pandemics: emergent phenomena in complex systems

“…Moreover, even the inverse problem is an open challenge: predicting the macroscopic outcome(s) of a process, given the microscopic rules governing a system's units might lead to the discovery of a new kind of universality class. Recent advances in the latter are related to programmable pattern formation, for which there are interesting applications to the case of cellular systems with local signalling [180].…”