Operating principles of circular toggle polygons

Abstract

Decoding the dynamics of cellular decision-making and cell differentiation is a central question in cell and developmental biology. A common network motif involved in many cell-fate decisions is a mutually inhibitory feedback loop between two self-activating 'master regulators' A and B, also called as toggle switch. Typically, it can allow for three stable states -(high A, low B), (low A, high B) and (medium A, medium B). A toggle triad -three mutually repressing regulators A, B and C, i.e. three toggle switches arranged circularly (between A and B, between B and C, and between A and C) -can allow for six stable states: three 'single positive' and three 'double positive' ones. However, the operating principles of larger toggle polygons, i.e. toggle switches arranged circularly to form a polygon, remain unclear. Here, we simulate using both discrete and continuous methods the dynamics of different sized toggle polygons. We observed a pattern in their steady state frequency depending on whether the polygon was an even or odd numbered one. The even-numbered toggle polygons result in two dominant states with consecutive components of the network expressing alternating high and low levels. The oddnumbered toggle polygons, on the other hand, enable more number of states, usually twice the number of components with the states that follow 'circular permutation' patterns in their composition. Incorporating self-activations preserved these trends while increasing the frequency of multistability in the corresponding network. Our results offer insights into design principles of circular arrangement of regulatory units involved in cell-fate decision making, and can offer design strategies for synthesizing genetic circuits.

Coupled Mutual Inhibition and Mutual Activation Motifs as Tools for Cell-Fate Control

“…One such architecture recently explored was a serial and parallel connection of positive feedback loops, where the authors showed that a parallel architecture might help in limiting cell-cell variability, and hence is a preferred architecture in differentiation networks (10) . In previous work, we had explored a variety of the serial connection, a cyclic chain of MI motifs labelled circular toggle polygons (29) . Given the additional feedback embedded in the circular/cyclic connection, it should be a better candidate for a synchronous expression of nodes potentially leading to the stabilization of cell-fates.…”