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Analysis of Homeostatic Mechanisms in Biochemical Networks

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Abstract

Cell metabolism is an extremely complicated dynamical system that maintains important cellular functions despite large changes in inputs. This “homeostasis” does not mean that the dynamical system is rigid and fixed. Typically, large changes in external variables cause large changes in some internal variables so that, through various regulatory mechanisms, certain other internal variables (concentrations or velocities) remain approximately constant over a finite range of inputs. Outside that range, the mechanisms cease to function and concentrations change rapidly with changes in inputs. In this paper we analyze four different common biochemical homeostatic mechanisms: feedforward excitation, feedback inhibition, kinetic homeostasis, and parallel inhibition. We show that all four mechanisms can occur in a single biological network, using folate and methionine metabolism as an example. Golubitsky and Stewart have proposed a method to find homeostatic nodes in networks. We show that their method works for two of these mechanisms but not the other two. We discuss the many interesting mathematical and biological questions that emerge from this analysis, and we explain why understanding homeostatic control is crucial for precision medicine.

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Notes

  1. Golubitsky and Stewart, in preparation.

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Acknowledgements

The authors gratefully acknowledge support from the National Science Foundation and the National Institutes of Health.

Funding This research was supported by National Institutes of Health Grants 1R01MH106563-01A1 (JAB,MCR, HFN) and 1R21MH109959-01A1(JAB,MCR, HFN) and NSF Grants IOS-1562701 (HFN), EF-1038593, IOS-1557341(HFN,MCR) and DMS-1440386 to the Mathematical Biosciences Institute (MG).

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Authors and Affiliations

  1. Department of Mathematics, Duke University, Durham, NC, 27708, USA

    Michael Reed

  2. Department of Mathematics, The Ohio State University, Columbus, OH, 43210, USA

    Janet Best & Martin Golubitsky

  3. Mathematics Institute, University of Warwick, Coventry, CV47AL, UK

    Ian Stewart

  4. Department of Biology, Duke University, Durham, NC, 27708, USA

    H. Frederik Nijhout

Authors
  1. Michael Reed
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  2. Janet Best
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  3. Martin Golubitsky
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  4. Ian Stewart
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  5. H. Frederik Nijhout
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Contributions

All authors contributed to the ideas in the manuscript. Golubitsky and Stewart did the calculations about GS homeostasis points and GS chairs. MR and JB did the other analytical calculations. MR, JB, and HFN wrote the manuscript. All authors read, edited, and approved the manuscript.

Corresponding author

Correspondence to Michael Reed.

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Reed, M., Best, J., Golubitsky, M. et al. Analysis of Homeostatic Mechanisms in Biochemical Networks. Bull Math Biol 79, 2534–2557 (2017). https://doi.org/10.1007/s11538-017-0340-z

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  • DOI: https://doi.org/10.1007/s11538-017-0340-z

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