Topoisomerase Based Control of Cellular Transcription and Growth

Global cellular transcription and growth are tightly coupled to the supercoiling state of a cells genomic DNA. Direct processes that modulate the supercoiling state of genomic DNA thus provide a novel mechanistic route for biological control of cellular dynamics. In this work, we develop a stochastic model of genome-wide transcriptional responses to local DNA supercoiling and show that, despite heterogeneity in the transcription of each individual gene, the overall system converges to a unique stationary distribution. From the stochastic system, we derive a corresponding nonlinear population model with both local and global supercoiling states, demonstrate that the proposed model exhibits a unique, globally stable equilibrium point, and identify key parameters through sensitivity analysis. We further extend the model by considering the temperature-sensitive gyrase mutant E. coli strain nalA43 and illustrate how shifting the gyrase-topoisomerase balance via temperature acts as an effective control knob on the population, from which we derive a control law. Numerical simulations confirm the effectiveness of the derived control law and provide insight into the dynamics of the system. These results help establish a theoretical foundation for understanding the crucial equilibrium dynamics of topoisomerase enzymes and their implications for cell function.