Fundamental limits on the suppression of molecular fluctuations

Abstract

Negative feedback is common in biological processes and can increase a system’s stability to internal and external perturbations. But at the molecular level, control loops always involve signalling steps with finite rates for random births and deaths of individual molecules. Here we show, by developing mathematical tools that merge control and information theory with physical chemistry, that seemingly mild constraints on these rates place severe limits on the ability to suppress molecular fluctuations. Specifically, the minimum standard deviation in abundances decreases with the quartic root of the number of signalling events, making it extremely expensive to increase accuracy. Our results are formulated in terms of experimental observables, and existing data show that cells use brute force when noise suppression is essential; for example, regulatory genes are transcribed tens of thousands of times per cell cycle. The theory challenges conventional beliefs about biochemical accuracy and presents an approach to the rigorous analysis of poorly characterized biological systems.

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Figure 1: Schematic of optimal control networks and information loss.
Figure 2: Hard limits on standard deviations.
Figure 3: Plasmid replication control.

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Acknowledgements

This research was supported by the BBSRC under grant BB/C008073/1, by the National Science Foundation grants DMS-074876-0 and CAREER 0720056, and by grants GM081563-02 and GM068763-06 from the National Institutes of Health.

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Contributions

I.L., G.V. and J.P. contributed equally, and all conceived the study, derived the equations and wrote the paper.

Corresponding authors

Correspondence to Glenn Vinnicombe or Johan Paulsson.

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The authors declare no competing financial interests.

Supplementary information

Supplementary Information

This file contains Supplementary Information comprising: 1 Introduction; 2 Preliminaries; 3 The informationcapacity of molecular channels; 4 The bounds; 5 Serial and parallel cascades; 6 Tradeoffs; Supplementary Appendices A, B and C and additional references. (PDF 529 kb)

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Lestas, I., Vinnicombe, G. & Paulsson, J. Fundamental limits on the suppression of molecular fluctuations. Nature 467, 174–178 (2010). https://doi.org/10.1038/nature09333

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