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Thermodynamics of Computational Copying in Biochemical Systems

Thomas E. Ouldridge, Christopher C. Govern, and Pieter Rein ten Wolde
Phys. Rev. X 7, 021004 – Published 7 April 2017
An article within the collection: Special Collection on Stochastic Thermodynamics
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Abstract

Living cells use readout molecules to record the state of receptor proteins, similar to measurements or copies in typical computational devices. But is this analogy rigorous? Can cells be optimally efficient, and if not, why? We show that, as in computation, a canonical biochemical readout network generates correlations; extracting no work from these correlations sets a lower bound on dissipation. For general input, the biochemical network cannot reach this bound, even with arbitrarily slow reactions or weak thermodynamic driving. It faces an accuracy-dissipation trade-off that is qualitatively distinct from and worse than implied by the bound, and more complex steady-state copy processes cannot perform better. Nonetheless, the cost remains close to the thermodynamic bound unless accuracy is extremely high. Additionally, we show that biomolecular reactions could be used in thermodynamically optimal devices under exogenous manipulation of chemical fuels, suggesting an experimental system for testing computational thermodynamics.

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  • Received 30 September 2016

DOI:https://doi.org/10.1103/PhysRevX.7.021004

Published by the American Physical Society under the terms of the Creative Commons Attribution 3.0 License. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.

Published by the American Physical Society

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This article appears in the following collection:

Special Collection on Stochastic Thermodynamics

A Physical Review X special collection on stochastic thermodynamics.

Authors & Affiliations

Thomas E. Ouldridge1,*, Christopher C. Govern2, and Pieter Rein ten Wolde2

  • 1Department of Bioengineering, Imperial College London, London, SW7 2AZ, United Kingdom
  • 2FOM Institute AMOLF, Science Park 104, 1098 XE Amsterdam, The Netherlands

  • *t.ouldridge@imperial.ac.uk

Popular Summary

Cells use molecules to make long-lived copies of other molecules, similar to how computers copy bits of information. Performing multiple computational copies using a single bit requires a small but nonzero amount of energy per copy. Everyday computers actually use far more than this theoretical limit, but it has been suggested that cells might get closer to the lower bound. In this work, we precisely link typical cellular processes to their computational counterparts. We show that although cellular processes can be quite efficient, they necessarily use more fuel than the lower bound; this inefficiency grows as copying gets more accurate. In principle, however, biomolecules can perform maximally efficient copies if the concentrations of chemical fuels are manipulated externally.

Specifically, we consider a steady-state network of cell-surface receptors and readout molecules. The chemical rate equations can be interpreted as copying with a certain rate and accuracy. We compare the energy dissipation per copy to that of a maximally efficient device performing the same copies with the same accuracy. The biochemical network is less efficient, and its thermodynamic cost diverges logarithmically as accuracy approaches 100%.

Our findings provide a rigorous connection between biochemical systems and fundamental theories of computation. The design of efficient copying techniques will be essential to synthetic biology and biological engineering. We also propose a new experimental paradigm for testing nonequilibrium thermodynamics using biomolecules in variable concentrations of chemical fuels.

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Vol. 7, Iss. 2 — April - June 2017

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