Cellular Sensory Mechanisms for Detecting Specific Fold-Changes in Extracellular Cues

Cellular sensory systems often respond not to the absolute levels of inputs but to the fold-changes in inputs. Such a property is called fold-change detection (FCD) and is important for accurately sensing dynamic changes in environmental signals in the presence of fluctuations in their absolute levels. Previous studies defined FCD as input-scale invariance and proposed several biochemical models that achieve such a condition. Here, we prove that the previous FCD models can be approximated by a log-differentiator. Although the log-differentiator satisfies the input-scale invariance requirement, its response amplitude and response duration strongly depend on the input timescale. This creates limitations in the specificity and repeatability of detecting fold-changes in inputs. Nevertheless, FCD with specificity and repeatability by cells has been reported in the context of Drosophila wing development. Motivated by this fact and by extending previous FCD models, we here propose two possible mechanisms to achieve FCD with specificity and repeatability. One is the integrate-and-fire type: a system integrates the rate of temporal change in input and makes a response when the integrated value reaches a constant threshold, and this is followed by the reset of the integrated value. The other is the dynamic threshold type: a system response occurs when the input level reaches a threshold, whose value is multiplied by a certain constant after each response. These two mechanisms can be implemented biochemically by appropriately combining feed-forward and feedback loops. The main difference between the two models is their memory of input history; we discuss possible ways to distinguish between the two models experimentally.