Feedback Regulation and Its Efficiency in Biochemical Networks

Intracellular biochemical networks fluctuate dynamically due to various internal and external sources of fluctuation. Dissecting the fluctuation into biologically relevant components is important for understanding how a cell controls and harnesses noise and how information is transferred over apparently noisy intracellular networks. While substantial theoretical and experimental advancement on the decomposition of fluctuation was achieved for feedforward networks without any loop, we still lack a theoretical basis that can consistently extend such advancement to feedback networks. The main obstacle that hampers is the circulative propagation of fluctuation by feedback loops. In order to define the relevant quantity for the impact of feedback loops for fluctuation, disentanglement of the causally interlocked influences between the components is required. In addition, we also lack an approach that enables us to infer non-perturbatively the influence of the feedback to fluctuation in the same way as the dual reporter system does in the feedforward networks. In this work, we address these problems by extending the work on the fluctuation decomposition and the dual reporter system. For a single-loop feedback network with two components, we define feedback loop gain as the feedback efficiency that is consistent with the fluctuation decomposition for feedforward networks. Then, we clarify the relation of the feedback efficiency with the fluctuation propagation in an open-looped FF network. Finally, by extending the dual reporter system, we propose a conjugate feedback and feedforward system for estimating the feedback efficiency non-perturbatively only from the statistics of the system.