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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Ozbudak, E. M., Thattai, M., Kurtser, I., Grossman, A. D. & van Oudenaarden, A. Regulation of noise in the expression of a single gene. Nature Genet. 31, 69–73 (2002)
Elowitz, M. B., Levine, A. J., Siggia, E. D. & Swain, P. S. Stochastic gene expression in a single cell. Science 297, 1183–1186 (2002)
Newman, J. R. et al. Single-cell proteomic analysis of S. cerevisiae reveals the architecture of biological noise. Nature 441, 840–846 (2006)
Golding, I., Paulsson, J., Zawilski, S. M. & Cox, E. C. Real-time kinetics of gene activity in individual bacteria. Cell 123, 1025–1036 (2005)
Paulsson, J. & Ehrenberg, M. Noise in a minimal regulatory network: plasmid copy number control. Q. Rev. Biophys. 34, 1–59 (2001)
Paulsson, J. Summing up the noise in gene networks. Nature 427, 415–418 (2004)
Dublanche, Y., Michalodimitrakis, K., Kuemmerer, N., Foglierini, M. & Serrano, L. Noise in transcription negative feedback loops: simulation and experimental analysis. Mol. Syst. Biol. 2, 41 (2006)
Barkai, N. & Shilo, B. Z. Variability and robustness in biomolecular systems. Mol. Cell 28, 755–760 (2007)
Maxwell, J. On governors. Proc. R. Soc. Lond. 16, 270–283 (1867)
Cover, T. M. & Thomas, J. A. Elements of Information Theory 2nd edn (Wiley, 1991)
Pedraza, J. M. & Paulsson, J. Effects of molecular memory and bursting on fluctuations in gene expression. Science 319, 339–343 (2008)
Cai, L., Friedman, N. & Xie, X. S. Stochastic protein expression in individual cells at the single molecule level. Nature 440, 358–362 (2006)
Tkacik, G., Callan, C. G., Jr & Bialek, W. Information flow and optimization in transcriptional regulation. Proc. Natl Acad. Sci. USA 105, 12265–12270 (2008)
Savageau, M. A. Parameter sensitivity as a criterion for evaluating and comparing the performance of biochemical systems. Nature 229, 542–544 (1971)
Keizer, J. Statistical Thermodynamics of Nonequilibrium Processes (Springer, 1987)
Singh, A. & Hespanha, J. P. Optimal feedback strength for noise suppression in autoregulatory gene networks. Biophys. J. 96, 4013–4023 (2009)
Korobkova, E. A., Emonet, T., Park, H. & Cluzel, P. Hidden stochastic nature of a single bacterial motor. Phys. Rev. Lett. 96, 058105 (2006)
Doan, T., Mendez, A., Detwiler, P. B., Chen, J. & Rieke, F. Multiple phosphorylation sites confer reproducibility of the rod’s single-photon responses. Science 313, 530–533 (2006)
Martins, N. C., Dahleh, M. A. & Doyle, J. C. Fundamental limitations of disturbance attenuation in the presence of side information. IEEE Trans. Automat. Contr. 52, 56–66 (2007)
Martins, N. C. & Dahleh, M. A. Feedback control in the presence of noisy channels: “bode-like” fundamental limitations of performance. IEEE Trans. Automat. Contr. 53, 1604–1615 (2008)
El-Samad, H., Kurata, H., Doyle, J. C., Gross, C. A. & Khammash, M. Surviving heat shock: control strategies for robustness and performance. Proc. Natl Acad. Sci. USA 102, 2736–2741 (2005)
Yi, T. M., Huang, Y., Simon, M. I. & Doyle, J. Robust perfect adaptation in bacterial chemotaxis through integral feedback control. Proc. Natl Acad. Sci. USA 97, 4649–4653 (2000)
Bialek, W. & Setayeshgar, S. Cooperativity, sensitivity, and noise in biochemical signaling. Phys. Rev. Lett. 100, 258101 (2008)
Gregor, T., Tank, D. W., Wieschaus, E. F. & Bialek, W. Probing the limits to positional information. Cell 130, 153–164 (2007)
Walczak, A. M., Mugler, A. & Wiggins, C. H. A stochastic spectral analysis of transcriptional regulatory cascades. Proc. Natl Acad. Sci. USA 106, 6529–6534 (2009)
Bialek, W. & Setayeshgar, S. Physical limits to biochemical signaling. Proc. Natl Acad. Sci. USA 102, 10040–10045 (2005)
Tomizawa, J. Control of ColE1 plasmid replication: binding of RNA I to RNA II and inhibition of primer formation. Cell 47, 89–97 (1986)
Das, N. et al. Multiple homeostatic mechanisms in the control of P1 plasmid replication. Proc. Natl Acad. Sci. USA 102, 2856–2861 (2005)
Shannon, C. E. A mathematical theory of communication. Bell Syst. Tech. J. 27, 379–423, 623–656 (1948)
Gorbunov, A. K. & Pinsker, M. S. Nonanticipatory and prognostic epsilon entropies and message generation rates. Probl. Inf. Transm. 9, 184–191 (1973)
Kabanov, Y. The capacity of a channel of the Poisson type. Theory Probab. Appl. 23, 143–147 (1978)
Davis, M. H. A. Capacity and cut-off rate for Poisson type channels. IEEE Trans. Inf. Theory 26, 710–715 (1980)
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.
The authors declare no competing financial interests.
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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