Noise Propagation and Signaling Sensitivity in Biological Networks: A Role for Positive Feedback

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Abstract
Interactions between genes and proteins are crucial for efficient processing of internal or external signals, but this connectivity also amplifies stochastic fluctuations by propagating noise between components. Linear (unbranched) cascades were shown to exhibit an interplay between the sensitivity to changes in input signals and the ability to buffer noise. We searched for biological circuits that can maintain signaling sensitivity while minimizing noise propagation, focusing on cases where the noise is characterized by rapid fluctuations. Negative feedback can buffer this type of noise, but this buffering comes at the expense of an even greater reduction in signaling sensitivity. By systematically analyzing three-component circuits, we identify positive feedback as a central motif allowing for the buffering of propagated noise while maintaining sensitivity to long-term changes in input signals. We show analytically that noise reduction in the presence of positive feedback results from improved averaging of rapid fluctuations over time, and discuss in detail a particular implementation in the control of nutrient homeostasis in yeast. As the design of biological networks optimizes for multiple constraints, positive feedback can be used to improve sensitivity without a compromise in the ability to buffer propagated noise. Biological circuits need to be sensitive to changes in environmental signals but at the same time buffer rapid fluctuations (noise) that might be imposed on this input. In this paper, we analyze the interplay between sensitivity to signals and the ability to buffer noise. Previous studies reported that negative feedback attenuates noise. We show, however, that this ability comes at the expense of an even more dramatic reduction in sensitivity. In fact, when comparing systems of the same sensitivity, a system with negative feedback is more amenable to noise than a system without such feedback. We searched for small biological circuits that can buffer noise while maintaining high sensitivity, and found that positive feedback exhibits this property. This ability of positive feedback to buffer noise reflects its slowed-down dynamics. We discuss general requirements for the function of positive feedback as a noise-filtering device and describe a particular implementation that appears to function in yeast nutrient homeostasis. Our study emphasizes the need to consider multiple constraints when analyzing the design logic of biological networks.