Magnetic induction inspires a schematic theory for crosstalk-driven relaxation dynamics in cells

Establishing formal mathematical analogies between disparate physical systems can be a powerful tool, allowing for the well studied behavior of one system to be directly translated into predictions about the behavior of another that may be harder to probe. In this paper we lay the foundation for such an analogy between the macroscale electrodynamics of simple magnetic circuits and the microscale chemical kinetics of transcriptional regulation in cells. By artificially allowing the inductor coils of the former to elastically expand under the action of their Lorentz pressure, we introduce nonlinearities into the system that we interpret through the lens of our analogy as a schematic model for the impact of crosstalk on the rates of gene expression near steady state. Synthetic plasmids introduced into a cell must compete for a finite pool of metabolic and enzymatic resources against a maelstrom of crisscrossing biological processes, and our theory makes sensible predictions about how this noisy background might impact the expression profiles of synthetic constructs without explicitly modeling the kinetics of numerous interconnected regulatory interactions. We conclude the paper with a discussion of how our theory might be expanded to a broader class of plasmid circuits and how our predictions might be tested experimentally.