Functional resilience of mutually repressing motifs embedded in larger regulatory networks

Elucidating the design principles of regulatory networks driving cellular decision-making has important implications in understanding cell differentiation and guiding the design of synthetic circuits. Mutually repressing feedback loops between master regulators of cell-fates can exhibit multistable dynamics, thus enabling multiple "single-positive" phenotypes: (high A, low B) and (low A, high B) for a toggle switch, and (high A, low B, low C), (low A, high B, low C) and (low A, low B, high C) for a toggle triad. However, the dynamics of these two network motifs has been interrogated in isolation in silico, but in vitro and in vivo, they often operate while embedded in larger regulatory networks. Here, we embed these network motifs in complex larger networks of varying sizes and connectivity and identify conditions under which these motifs maintain their canonical dynamical behavior, thus identifying hallmarks of their functional resilience. We show that an increased number of incoming edges onto a motif leads to a decay in their canonical stand-alone behaviors, as measured by multiple metrics based on pairwise correlation among nodes, bimodality of individual nodes, and the fraction of "single-positive" states. We also show that this decay can be exacerbated by adding self-inhibition, but not self-activation, loops on the master regulators. These observations offer insights into the design principles of biological networks containing these motifs, and can help devise optimal strategies for integration of these motifs into larger synthetic networks.