(665f) Modeling Supercoiling-Dependent Feedback As a Transcriptional Coordinator to Understand and Engineer Biological Circuits.

Cells coordinate complex behaviors through precise spatiotemporal control of gene expression and a myriad of interwoven control circuits. Gene- and cell-based therapies require synthetic circuits to similarly coordinate dynamic patterns of gene expression across a large population of cells. However, stable, robust expression of synthetic circuits in mammalian cells is challenging due to significant extrinsic and intrinsic expression noise. In particular, the stochastic nature of transcription makes coordinating expression across multiple genetic elements challenging. Spatial variation in the nucleus and biochemical dynamics in transcriptional condensates may contribute to bursting but provide limited parameters for tuning transcriptional noise.

Mechanical sources of gene regulation, such as the waves of positive and negative supercoiling induced by the motion of RNA polymerases, can be a powerful force driving expression changes at the kilobase scale. In yeast and human cells, transcriptionally-induced supercoiling demarks bounds of gene activity. In particular, transcriptional activity dictates the strength of contact domains such as gene-to-gene interactions, indicating a role for transcription in forming and maintaining interactions at the kilobase scale.

By modeling the underlying biophysical interactions that drive RNA polymerase activity--including the motion and stalling of polymerases acting under the influence of supercoiling and the supercoiling-dependent initiation process--a context-dependent understanding of biological circuit behavior emerges. In addition to being sensitive to the surrounding boundary conditions, the relative placement, orientation, and promoter strength of genes affect the simulated behavior. Applying the resulting stochastic-differential equation model to the behavior of simple two-gene genetic circuits, we identify that supercoiling-mediated feedback drives differences in gene expression via changes in polymerase stalling and transcriptional burst frequency. By further simulating the behavior of mutually-inhibitory toggle switches, we find that supercoiling-dependent feedback provides an additional, tunable source of control that can be layered on traditional synthetic regulatory schemes.

Applying our model of supercoiling-dependent feedback to native systems, we find that accumulated supercoiling well explains the observed behavior of the *her1-her7* segmentation gene network in zebrafish, with supercoiling-dependent polymerase initiation predicted to play a key role in establishing robust, periodic oscillations.
In sum, our model both predicts design rules for creating synthetic regulatory circuits and and provides explanatory power into the context-dependent mechanical regulation of native circuits. With these tools, we may be able to design robust sensors and actuators of cell state.