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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    • "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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    • "Random dissociation of a transcriptional repressor can cause drastic changes in protein expression [9] (Fig. 1C). Negative feedback aims to keep protein levels constant [10], but the precision of regulation is limited due to delays and information loss by stochastic transcription and translation events [11]. Positive feedback is prone to bistable behavior in which random fluctuations above an induction threshold lead to a switch in protein expression [12] (Fig. 1D). "
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    ABSTRACT: DNA repair safeguards the genome against a diversity of DNA damaging agents. Although the mechanisms of many repair proteins have been examined separately in vitro, far less is known about the coordinated function of the whole repair machinery in vivo. Furthermore, single-cell studies indicate that DNA damage responses generate substantial variation in repair activities across cells. This review focuses on fluorescence imaging methods that offer a quantitative description of DNA repair in single cells by measuring protein concentrations, diffusion characteristics, localizations, interactions, and enzymatic rates. Emerging single-molecule and super-resolution microscopy methods now permit direct visualization of individual proteins and DNA repair events in vivo. We expect much can be learned about the organization of DNA repair by linking cell heterogeneity to mechanistic observations at the molecular level.
    DNA repair 08/2014; 20(100). DOI:10.1016/j.dnarep.2014.02.015 · 3.11 Impact Factor
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    • "2 ≤ k ≤ n + 1, k ∈ Z + . x 1 u = const −−−−−−→ x 1 + 1 x n f n−1 = f n−1 (x 1 t 0 , x n t 0 ) − −−−−−−−−−−−−− → x n + 1 x 2 f 1 = f 1 (x 1 t 0 , x 2 t 0 ) − −−−−−−−−− → x 2 + 1 x n+1 f n = f n (x 1 t 0 , x n+1 t 0 ) − −−−−−−−−−−− → x n+1 + 1 As in [12] "
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    ABSTRACT: Low molecule numbers and intrinsically noisy, cou-pled stochastic chemical reactions are common in cell biology. For such environments, [12] showed that the accuracy with which molecular populations can be estimated and controlled can be bounded from below by regarding molecular coupling as an information transfer across a finite capacity Poisson channel. In conjunction with a diffusion approximation for the target species, this leads to a clear distortion bound for arbitrary signal-target molecular coupling. For static signal-target coupling, sharp, biologically relevant bounds result, which appear to still hold for the original discrete system. However, when arbitrary non-linear, dynamic coupling is allowed, [13] showed that event-triggered codecs can be constructed that are capable of outperforming the general diffusion bound, both for estimation and control. This paper extends the estimation results from [13] to various molecular signalling topologies and integer encoders. It is found that the bound can be outperformed across all serial and parallel networks by a M|M|1 queue type codec, which is likely optimal for a single stage, over a small parameter regime. Outside this regime queueing delay leads to increas-ingly worse estimation. The application of integer coding variants in an attempt to improve stability and increase the regime of good performance is largely fruitless, thus indicating that even the simplest non-trivial estimation problem cannot be solved with intuitively sensible codecs.
    52nd Conference on Decision and Control, Florence, Italy; 12/2013
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