Article

Fundamental limits on the suppression of molecular fluctuations. Nature

Department of Engineering, University of Cambridge, Cambridge CB2 1PZ, UK.
Nature (Impact Factor: 41.46). 09/2010; 467(7312):174-8. DOI: 10.1038/nature09333
Source: PubMed

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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    • "We should note that, despite its generality, the modeling framework assumed in [19] does not apply in our case, since our system contains a controlled degradation reaction, whereas [19] considers only control of production. More specifically, [19] examines the case where a given species regulates its own production through an arbitrary stochastic signaling network. In this setting, it is shown that, no matter the form or complexity of the intermediate signaling, the loss of information induced by stochasticity places severe fundamental limits on the levels of noise suppression that such feedback loops can achieve. "
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    ABSTRACT: Nature presents multiple intriguing examples of processes which proceed at high precision and regularity. This remarkable stability is frequently counter to modelers' experience with the inherent stochasticity of chemical reactions in the regime of low copy numbers. Moreover, the effects of noise and nonlinearities can lead to "counter-intuitive" behavior, as demonstrated for a basic enzymatic reaction scheme that can display stochastic focusing (SF). Under the assumption of rapid signal fluctuations, SF has been shown to convert a graded response into a threshold mechanism, thus attenuating the detrimental effects of signal noise. However, when the rapid fluctuation assumption is violated, this gain in sensitivity is generally obtained at the cost of very large product variance, and this unpredictable behavior may be one possible explanation of why, more than a decade after its introduction, SF has still not been observed in real biochemical systems. In this work we explore the noise properties of a simple enzymatic reaction mechanism with a small and fluctuating number of active enzymes that behaves as a high-gain, noisy amplifier due to SF caused by slow enzyme fluctuations. We then show that the inclusion of a plausible negative feedback mechanism turns the system from a noisy signal detector to a strong homeostatic mechanism by exchanging high gain with strong attenuation in output noise and robustness to parameter variations. Moreover, we observe that the discrepancy between deterministic and stochastic descriptions of stochastically focused systems in the evolution of the means almost completely disappears, despite very low molecule counts and the additional nonlinearity due to feedback. The reaction mechanism considered here can provide a possible resolution to the apparent conflict between intrinsic noise and high precision in critical intracellular processes.
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    • "One can then envision two fundamental sources of variability in gene expression: variability in the number of molecular constituents , both metabolites and components of the gene expression machinery, and variability in the biochemical reactions involved in the gene expression cycle[6]. Indeed, both sources are not independent[7], even though they are often treated as separate contributions[8,9]. Biochemical reactions can be considered as probabilistic events creating spontaneous fluctuations in mRNA and protein abundances, while cellto-cell differences in molecular components are assumed to change the rates at which these reactions take place[10]. "
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    ABSTRACT: Gene expression activity is heterogeneous in a population of isogenic cells. Identifying the molecular basis of this variability will improve our understanding of phenomena like tumor resistance to drugs, virus infection, or cell fate choice. The complexity of the molecular steps and machines involved in transcription and translation could introduce sources of randomness at many levels, but a common constraint to most of these processes is its energy dependence. In eukaryotic cells, most of this energy is provided by mitochondria. A clonal population of cells may show a large variability in the number and functionality of mitochondria. Here, we discuss how differences in the mitochondrial content of each cell contribute to heterogeneity in gene products. Changes in the amount of mitochondria can also entail drastic alterations of a cell's gene expression program, which ultimately leads to phenotypic diversity. Also watch the Video Abstract.
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    • "Much theoretical work has been devoted to discovering features of biological networks that permit living systems to function correctly under noisy conditions. Examples of such features include kinetic proof-reading [1] [2], network motifs that confer robustness [3] [4], and feedback [5]. The context of embryonic development offers an especially promising setting for investigating principles of network design because for a complex multicellular organism, the reliability of its developmental program directly determines the probability of reaching reproductive age. "
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    ABSTRACT: In pattern-forming developmental systems, cells commonly interpret graded input signals, known as morphogens. Morphogens often pattern tissues through cascades of sequential gene expression steps. Such a multi-tiered structure appears to constitute suboptimal use of the positional information provided by the input morphogen because noise is added at each tier. However, the conventional theory neglects the role of the format in which information is encoded. We argue that the relevant performance measure is not solely the amount of information carried by the morphogen, but the amount of information that can be accessed by the downstream network. We demonstrate that quantifying the information that is accessible to the system naturally explains the prevalence of multi-tiered network architectures as a consequence of the noise inherent to the control of gene expression. We support our argument with empirical observations from patterning along the major body axis of the fruit fly embryo.
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