标题： 抑制子格子：反馈、共容性和动力学挫折 显示英文标题

标题： The Repressor-Lattice: Feed-Back, Commensurability, and Dynamical Frustration

摘要： 一个阻遏振荡器由三个抑制相互作用的基因组成的环构成。 我们在每个三角形上构建一个六边形晶格，并将其作为多个相互作用反馈环的模型系统。 通过对称性论证和稳定性分析，我们认为阻遏剂晶格可以处于一种非矛盾的振荡状态，仅有三种不同的相位。 如果系统尺寸与三不一致，可能存在几种不同相位的振荡解。 随着节点之间相互作用强度的增加，系统经历多次转变，破坏了多种对称性。 最终出现动态矛盾状态，其中时间演化是混沌的，尽管没有内置的矛盾。 讨论了阻遏剂晶格在真实生物系统中的应用，例如组织或生物膜。 显示英文摘要

摘要： A repressilator consists of a loop made up of three repressively interacting genes. We construct a hexagonal lattice with repressilators on each triangle, and use this as a model system for multiple interacting feedback loops. Using symmetry arguments and stability analysis we argue that the repressor-lattice can be in a non-frustrated oscillating state with only three distinct phases. If the system size is not commensurate with three, oscillating solutions of several different phases are possible. As the strength of the interactions between the nodes increases, the system undergoes many transitions, breaking several symmetries. Eventually dynamical frustrated states appear, where the temporal evolution is chaotic, even though there are no built-in frustrations. Applications of the repressor-lattice to real biological systems, such as tissues or biofilms, are discussed.