Landau theory for cellular patterns driven by lateral inhibition interaction

Mechanochemical feedback loops in contact-dependent fate patterning

To reliably form and maintain structures with specific functions, many multicellular systems evolved to leverage the interplay between biochemical signaling, mechanics, and morphology. We review mechanochemical feedback loops in cases where cell-cell contact-based Notch signaling drives fate decisions, and the corresponding differentiation process leads to contact remodeling. We compare different mechanisms for initial symmetry breaking and subsequent pattern refinement, as well as discuss how patterning outcomes depend on the relationship between biochemical and mechanical timescales. We conclude with an overview of new approaches, including the study of synthetic circuits, and give an outlook on future experimental and theoretical developments toward dissecting and harnessing mechanochemical feedback.

Contact-mediated signaling enables disorder-driven transitions in cellular assemblies

We show that, when cells communicate by contact-mediated interactions, heterogeneity in cell shapes and sizes leads to qualitatively distinct collective behavior in the tissue. For intercellular coupling that implements lateral inhibition, such disorder-driven transitions can substantially alter the asymptotic pattern of differentiated cells by modulating their fate choice through changes in the neighborhood geometry. In addition, when contact-induced signals influence inherent cellular oscillations, disorder leads to the emergence of functionally relevant partially-ordered dynamical states.

Stochastic fluctuations promote ordered pattern formation of cells in the Notch-Delta signaling pathway

The Notch-Delta signaling pathway mediates cell differentiation implicated in many regulatory processes including spatiotemporal patterning in tissues by promoting alternate cell fates between neighboring cells. At the multicellular level, this "lateral inhibition” principle leads to checkerboard patterns with alternation of Sender and Receiver cells. While it is well known that stochasticity modulates cell fate specification, little is known about how stochastic fluctuations at the cellular level propagate during multicell pattern formation. Here, we model stochastic fluctuations in the Notch-Delta pathway in the presence of two different noise types–shot and white–for a multicell system. Our results show that intermediate fluctuations reduce disorder and guide the multicell lattice toward checkerboard-like patterns. By further analyzing cell fate transition events, we demonstrate that intermediate noise amplitudes provide enough perturbation to facilitate “proofreading” of disordered patterns and cause cells to switch to the correct ordered state (Sender surrounded by Receivers, and vice versa). Conversely, high noise can override environmental signals coming from neighboring cells and lead to switching between ordered and disordered patterns. Therefore, in analogy with spin glass systems, intermediate noise levels allow the multicell Notch system to escape frustrated patterns and relax towards the lower energy checkerboard pattern while at large noise levels the system is unable to find this ordered base of attraction.

The Notch pathway is involved in many biological processes and is known to form precise spatial patterns alternating Sender and Receiver cell states. Quantifying the implications of stochastic fluctuations provided insight that patterns formed in Notch-mediated pathways must follow a predetermined path towards checkerboard or exist in a noisy environment which promotes order through error correction.

We model Notch pattern formation stochastically and analyze the spatiotemporal dynamics. Our results show multicellular systems equilibrate towards ordered systems, but mistakes in the initial lattice propagate causing the systems to relax into frustrated systems. Only through existing in a noisy environment are the systems able to relax into the checkerboard pattern. Analyzing the temporal dynamics confirms, in environments with intermediate noise, the “incorrect” cells (Sender in a Sender environment, and vice versa) can be flipped to the correct state (Sender in a Receiver environment, and vice versa). Comparing with the spin glass energy landscape, we suggest the multicellular model follows a rugged landscape to form patterns with stochastic fluctuations required to enforce order throughout the system.