Fold-change detection and scalar symmetry of sensory input fields

Oren Shoval, Lea Goentoro, Yuval Hart, Avi Mayo, Eduardo Sontag, Uri Alon*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

172 Scopus citations


Recent studies suggest that certain cellular sensory systems display fold-change detection (FCD): a response whose entire shape, including amplitude and duration, depends only on fold changes in input and not on absolute levels. Thus, a step change in input from, for example, level 1 to 2 gives precisely the same dynamical output as a step from level 2 to 4, because the steps have the same fold change. We ask what the benefit of FCD is and show that FCD is necessary and sufficient for sensory search to be independent of multiplying the input field by a scalar. Thus, the FCD search pattern depends only on the spatial profile of the input and not on its amplitude. Such scalar symmetry occurs in a wide range of sensory inputs, such as source strength multiplying diffusing/convecting chemical fields sensed in chemotaxis, ambient light multiplying the contrast field in vision, and protein concentrations multiplying the output in cellular signaling systems. Furthermore,weshowthatFCD entailstwofeatures found across sensory systems, exact adaptation and Weber's law, but that these two features are not sufficient for FCD. Finally, we present a wide class of mechanisms that have FCD, including certain nonlinear feedback and feed-forward loops. We find that bacterial chemotaxis displays feedback within the present class and hence, is expected to show FCD. This can explain experiments in which chemotaxis searches are insensitive to attractant source levels. This study, thus, suggests a connection between properties of biological sensory systems and scalar symmetry stemming from physical properties of their input fields.

Original languageAmerican English
Pages (from-to)15995-16000
Number of pages6
JournalProceedings of the National Academy of Sciences of the United States of America
Issue number36
StatePublished - 7 Sep 2010
Externally publishedYes


  • Adaptation
  • Sensory response
  • Spatial search


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