Logical modeling is a powerful tool in biology, offering a system-level understanding of the complex interactions that govern biological processes. A gap that hinders the scalability of logical models is the need to specify the update function of every vertex in the network depending on the status of its predecessors. To address this, we introduce in this paper the concept of strong regulation, where a vertex is only updated to active/inactive if all its predecessors agree in their influences; otherwise, it is set to ambiguous. We explore the interplay between active, inactive, and ambiguous influences in a network. We discuss the existence of phenotype attractors in such networks, where the status of some of the variables is fixed to active/inactive, while the others can have an arbitrary status, including ambiguous.

翻译：逻辑建模是生物学中的一种强大工具，能够提供对调控生物过程的复杂相互作用的系统级理解。阻碍逻辑模型可扩展性的一个关键缺口在于，需要根据网络中每个顶点的前驱状态来指定其更新函数。为解决这一问题，本文引入了强调控的概念，即仅当一个顶点的所有前驱在其调控影响上达成一致时，该顶点才会被更新为激活/抑制状态；否则，它将被设置为模糊状态。我们探讨了网络中激活、抑制与模糊影响之间的相互作用。我们讨论了此类网络中表型吸引子的存在性，其中部分变量的状态被固定为激活/抑制，而其他变量可以具有任意状态（包括模糊状态）。