Noise analysis of derivative-action biomolecular topologies
Temporal gradient sensing is a fundamental capability observed across diverse natural biological systems, contributing to the coordination of their functions. Harnessing this ability is also of significant interest in synthetic biology, particularly for sensing and control applications. In this work, we focus on a biomolecular topology that exemplifies a broader class of signal-differentiating architectures, while introducing a structural variant of it. We examine their behavior under both nominal and non-ideal conditions, accounting for stochastic noise arising from different sources. Our investigation includes scenarios where these topologies operate independently, as well as when embedded within minimal regulatory architectures based on negative as well as positive feedback. We analyze the stability of the resulting macroscopic dynamics--a prerequisite for practical deployment--and quantify stochastic fluctuations in system output, providing comparisons with the corresponding input/unregulated process. Importantly, our results demonstrate that signal differentiation can be effectively implemented in a biomolecular setting without incurring deleterious noise amplification--a major concern in the utilization of derivative action across disciplines.