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Algebraic Biochemistry: A Framework for Analog Online Computation in Cells

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Computational Methods in Systems Biology (CMSB 2022)

Part of the book series: Lecture Notes in Computer Science ((LNBI,volume 13447))

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Abstract

The Turing completeness of continuous chemical reaction networks (CRNs) states that any computable real function can be computed by a continuous CRN on a finite set of molecular species, possibly restricted to elementary reactions, i.e. with at most two reactants and mass action law kinetics. In this paper, we introduce a notion of online analog computation for the CRNs that stabilize the concentration of their output species to the result of some function of the concentration values of their input species, whatever changes are operated on the inputs during the computation. We prove that the set of real functions stabilized by a CRN with mass action law kinetics is precisely the set of real algebraic functions.

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Notes

  1. 1.

    All the computational results presented in this paper are available in an executable Biocham notebook at https://lifeware.inria.fr/wiki/Main/Software#CMSB22.

  2. 2.

    The terminology of “algebraic functions” used in the title of [1] refers in fact to its restriction to algebraic expressions.

  3. 3.

    An Ubuntu 20.04, with an Intel Core i6, 2.4 GHz x 4 cores and 15.5 GB of memory.

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Acknowledgments

We are grateful to Amaury Pouly and Sylvain Soliman for interesting discussions on this work, and to ANR-20-CE48-0002 and Inria AEx GRAM grants for partial support.

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Authors and Affiliations

  1. Inria Saclay, Palaiseau, France

    Mathieu Hemery & François Fages

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  1. Mathieu Hemery
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  2. François Fages
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Correspondence to François Fages .

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Editors and Affiliations

  1. University of Turku, Turku, Finland

    Ion Petre

  2. University of Bucharest, Bucharest, Romania

    Andrei Păun

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Hemery, M., Fages, F. (2022). Algebraic Biochemistry: A Framework for Analog Online Computation in Cells. In: Petre, I., Păun, A. (eds) Computational Methods in Systems Biology. CMSB 2022. Lecture Notes in Computer Science(), vol 13447. Springer, Cham. https://doi.org/10.1007/978-3-031-15034-0_1

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  • DOI: https://doi.org/10.1007/978-3-031-15034-0_1

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