Many feedforward mechanism. In Goentoro et al. (2009)

Many sensory systems show a response that is proportional to the fold-change in the stimulus relative to the background.

Fold-change (FC), is defined as a measure describing how much a quantity changes going from an initial to a final value. For instance, a step change in input from level 1 to 2 gives precisely the same output as a step from level 2 to 4, because the two steps have the same fold change (Shoval et al., 2010). Alon et al. defines fold-change detection (FCD) as response whose entire shape, including amplitude and duration, depends only on fold changes in input, and not on absolute changes (Shoval et al., 2010).

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Recent studies of suggest that the FCD response can be found in certain mammalian signaling systems. For example, ERK2 activation in EGF-stimulated carcinoma cells, and Wnt signaling in cell lines and embryos (J. Kim et al., 2014; Shoval et al., 2010). Two common features found in sensory systems are present in FCD.

First is Weber’s law, which state that the maximal response to a change in signal is inversely proportional to the background signal. Second is exact adaption, where the output to a change in input gradually returns to a level independent of the input. Shoval et al. (2010) have proven in their study, that FCD entails exact adaptation and Weber’s law, however both are not sufficient for FCD. FCD 10 entails exact adaptation by definition, because for any two constant inputs the steady-state output must be the same. And FCD also generally entails Weber’s law. In recent studies it has been proposed that adopting FCD may be beneficial to chemotactic bacteria (J.

Kim et al., 2014; Shoval et al., 2010). The main reason for this is that the process of a sensory search whereby cells move through their environment is independent of the source strength of the attractant (Shoval et al., 2010). However, this was proven for a specific feedback and not feedforward mechanism.

In Goentoro et al. (2009) different network motifs were studied for the presence of FCD. Among all the examined network motifs it was shown that only IFFL possesses the function of FCD, assuming that the activator in IFFL operates in linear regime and repressor saturates the promoter of target gene g. Shoval et al. (2010) theorized, that FCD can be generated by IFFL within a certain range of parameters, for example, when the intermediate species is a strong repressor of output. However, yet to be experimentally prove.

In the study of Takeda et al. (2012) the following features were found in FCD generated by IFFL after a step change in the input signal. The strength of the response increased with the fold change in signal, and the return time to steady state has decreased with the fold change in signal.