Abstract
The property termed scale-invariance, or fold-change detection, represents a phenomenon that is observed in a variety of biological systems, ranging from bacterial to eukaryotic signaling pathways. Mathematically, it represents invariance of the complete output trajectory with respect to a rescaling of input magnitudes. In the systems biology literature, an often-discussed motif for approximate fold-change detection is based on a time-scale separation in which output variables respond faster than internal components do. This paper shows that there is a lower bound on the scaling error for systems based on this property, independently of the magnitude of the time-scale separation. Furthermore, the paper discusses how adaptation and scale invariance properties often fail to hold when the effect of molecular noise is taken into account.
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