Noise response in monomolecular closed systems

One of the primary interests in understanding biological systems is the interaction between noise and cellular regulation. Noise levels can be altered by rate constant perturbations, which may result in an imbalance of important biological functions. Although the theory of noise localization can estimate noise perturbation response, it is currently limited to open systems, where the majority of biological networks belong. However, during their lifetime, some components of biological systems participate in reactions that can be categorized under a closed system. Therefore, a counterpart theory for closed systems is desirable. In this work, steady-state perturbations of monomolecular closed systems and ways to estimate the response of noise as (co)variances are explored. We extend the structural sensitivity analysis for analyzing noise response patterns by using additional clues derived from multinomial assumptions. We identified scenarios in which this combination might fail in noise prediction, which we call noise flip, arising from the nonlinear dependence of variance upon composition. Nevertheless, theoretical intuition and simulation show that noise flip diminishes with increasing system size. This work provides an efficient and scalable means to estimate noise responses with potential applications in model discrimination, network-wide response scanning, and reconstruction.