Abstract

Biology emerges from interactions between molecules, which are challenging to elucidate with current techniques. An orthogonal approach is to probe for 'response signatures' that identify specific circuit motifs. For example, bistability, hysteresis, or irreversibility are used to detect positive feedback loops. For adapting systems, such signatures are not known. Only two circuit motifs generate adaptation: negative feedback loops (NFLs) and incoherent feed-forward loops (IFFLs). On the basis of computational testing and mathematical proofs, we propose differential signatures: in response to oscillatory stimulation, NFLs but not IFFLs show refractory–period stabilization (robustness to changes in stimulus duration) or period skipping. Applying this approach to yeast, we identified the circuit dominating cell cycle timing. In Caenorhabditis elegans AWA neurons, which are crucial for chemotaxis, we uncovered a Ca2+ NFL leading to adaptation that would be difficult to find by other means. These response signatures allow direct access to the outlines of the wiring diagrams of adapting systems.

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Acknowledgements

We thank C.I. Bargmann for mentorship, support, and comments on the manuscript. We thank E. Siggia for fruitful discussions. The work was supported by US National Institutes of Health grant 5RO1-GM078153-07 (F.R.C.), NRSA Training Grant CA009673-36A1 (S.J.R.), a Merck Postdoctoral Fellowship at The Rockefeller University (S.J.R.), and the Simons Foundation (S.J.R.). J.L. was supported by a fellowship from the Boehringer Ingelheim Fonds. E.D.S. was partially supported by the US Office of Naval Research (ONR N00014-13-1-0074) and the US Air Force Office of Scientific Research (AFOSR FA9550-14-1-0060).

Author information

Affiliations

  1. Laboratory of Cell Cycle Genetics, The Rockefeller University, New York, New York, USA.

    • Sahand Jamal Rahi
    • , Kresti Pecani
    •  & Frederick R Cross
  2. Center for Studies in Physics and Biology, The Rockefeller University, New York, New York, USA.

    • Sahand Jamal Rahi
  3. Howard Hughes Medical Institute, Lulu and Anthony Wang Laboratory of Neural Circuits and Behavior, The Rockefeller University, New York, New York, USA.

    • Johannes Larsch
    •  & Alexander Y Katsov
  4. Department of Genes–Circuits–Behavior, Max Planck Institute of Neurobiology, Martinsried, Germany.

    • Johannes Larsch
  5. Division of Pulmonary and Critical Care Medicine, Brigham and Women's Hospital, Boston, Massachusetts, USA.

    • Nahal Mansouri
  6. Department of Mathematics, College of Engineering, Mathematics and Physical Sciences and EPSRC Centre for Predictive Modelling in Healthcare, University of Exeter, Exeter, UK.

    • Krasimira Tsaneva-Atanasova
  7. Department of Mathematics and Center for Quantitative Biology, Rutgers, The State University of New Jersey, Piscataway, New Jersey, USA.

    • Eduardo D Sontag

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Contributions

Conceptualization and writing: S.J.R., J.L., K.P., A.Y.K., N.M., K.T.-A., E.S., and F.R.C. Experiments and data analysis: S.J.R., J.L., and K.P. Mathematical proofs: S.J.R. and E.D.S.

Competing interests

The authors declare no competing financial interests.

Corresponding author

Correspondence to Sahand Jamal Rahi.

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DOI

https://doi.org/10.1038/nmeth.4408

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