A unified approach to dissecting biphasic responses in cell signalling

  1. Vaidhiswaran Ramesh
  2. J Krishnan  Is a corresponding author
  1. Imperial College London, United Kingdom


Biphasic responses are encountered at all levels in biological systems. At the cellular level, biphasic dose-responses are widely encountered in cell signalling and post-translational modification systems and represent safeguards against over-activation or overexpression of species. In this paper we provide a unified theoretical synthesis of biphasic responses in cell signalling systems, by assessing signalling systems ranging from basic biochemical building blocks to canonical network structures to well-characterized exemplars on one hand, and examining different types of doses on the other. By using analytical and computational approaches applied to a range of systems across levels (described by broadly employed models) we reveal (i) design principles enabling the presence of biphasic responses, including in almost all instances, an explicit characterization of the parameter space (ii) structural factors which preclude the possibility of biphasic responses (iii) different combinations of the presence or absence of enzyme-biphasic and substrate-biphasic responses, representing safeguards against overactivation and overexpression respectively (iv) the possibility of broadly robust biphasic responses (v) the complete alteration of signalling behaviour in a network due to biphasic interactions between species (biphasic regulation) (vi) the propensity of different co-existing biphasic responses in the Erk signalling network. These results both individually and in totality have a number of important consequences for systems and synthetic biology.

Data availability

The current manuscript contains results which are computational and analytical (mathematical). These are all presented and discussed in the main text. Maple code was used for establishing the analytical results and this is uploaded as Source Code (Maple) and in pdf format as supplementary files (supplementary file 1 and supplementary file 2). The code for generating the computational results has been deposited at https://github.com/VaidhiswaranR/Work-in-progress--Biphasic2022

Article and author information

Author details

  1. Vaidhiswaran Ramesh

    Department of Chemical Engineerng, Imperial College London, London, United Kingdom
    Competing interests
    The authors declare that no competing interests exist.
  2. J Krishnan

    Department of Chemical Engineerng, Imperial College London, London, United Kingdom
    For correspondence
    Competing interests
    The authors declare that no competing interests exist.
    ORCID icon "This ORCID iD identifies the author of this article:" 0000-0001-6196-2033


No external funding was received for this work

Reviewing Editor

  1. Ahmad S Khalil, Boston University, United States

Version history

  1. Received: January 30, 2023
  2. Accepted: December 5, 2023
  3. Accepted Manuscript published: December 6, 2023 (version 1)


© 2023, Ramesh & Krishnan

This article is distributed under the terms of the Creative Commons Attribution License permitting unrestricted use and redistribution provided that the original author and source are credited.


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  1. Vaidhiswaran Ramesh
  2. J Krishnan
A unified approach to dissecting biphasic responses in cell signalling
eLife 12:e86520.

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