Trade-offs between retroactivity and noise in connected transcriptional components

At the interconnection of two gene transcriptional components in a biomolecular network, the noise in the downstream component can be reduced by increasing its gene copy number. However, this method of reducing noise increases the load applied to the upstream system, called retroactivity, thereby causing a perturbation in the upstream system. In this work, we quantify the error in the system trajectories caused by perturbations due to retroactivity and noise, and analyze the trade-off between these two perturbations. We model the system as a set of nonlinear chemical Langevin equations and quantify the trade-off by employing contraction theory for stochastic systems.