1. B. de Freitas Magalhães, G. Fan, E.D. Sontag, K. Josic, and M.R. Bennett. Pattern formation and bistability in a synthetic intercellular genetic toggle. ACS Synthetic Biology, 13:2844-2860, 2024. [PDF] Keyword(s): synthetic biology, pattern formation, quorum sensing, systems biology, toggle switch. Abstract:

   Differentiation within multicellular organisms is a complex process that helps to establish spatial patterning and tissue formation within the body. Often, the differentiation of cells is governed by morphogens and intercellular signaling molecules that guide the fate of each cell, frequently using toggle-like regulatory components. Synthetic biologists have long sought to recapitulate patterned differentiation with engineered cellular communities, and various methods for differentiating bacteria have been invented. Here, we couple a synthetic corepressive toggle switch with intercellular signaling pathways to create a “quorum-sensing toggle�. We show that this circuit not only exhibits population-wide bistability in a well-mixed liquid environment but also generates patterns of differentiation in colonies grown on agar containing an externally supplied morphogen. If coupled to other metabolic processes, circuits such as the one described here would allow for the engineering of spatially patterned, differentiated bacteria for use in biomaterials and bioelectronics.

1. Y. Shafi, Z. Aminzare, M. Arcak, and E.D. Sontag. Spatial uniformity in diffusively-coupled systems using weighted L2 norm contractions. In Proc. American Control Conference, pages 5639-5644, 2013. [PDF] Keyword(s): contractions, contractive systems, matrix measures, logarithmic norms, Turing instabilities, diffusion, partial differential equations, synchronization. Abstract:

   We present conditions that guarantee spatial uniformity in diffusively-coupled systems. Diffusive coupling is a ubiquitous form of local interaction, arising in diverse areas including multiagent coordination and pattern formation in biochemical networks. The conditions we derive make use of the Jacobian matrix and Neumann eigenvalues of elliptic operators, and generalize and unify existing theory about asymptotic convergence of trajectories of reaction-diffusion partial differential equations as well as compartmental ordinary differential equations. We present numerical tests making use of linear matrix inequalities that may be used to certify these conditions. We discuss an example pertaining to electromechanical oscillators. The paper's main contributions are unified verifiable relaxed conditions that guarantee synchrony.

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