Gene network shaping of inherent noise spectra

Recent work demonstrates that stochastic fluctuations in molecular populations have consequences for gene regulation. Previous experiments focused on noise sources or noise propagation through gene networks by measuring noise magnitudes. However, in theoretical analysis, we showed that noise frequency content is determined by the underlying gene circuits, leading to a mapping between gene circuit structure and the noise frequency range. An intriguing prediction from our previous studies was that negative autoregulation shifts noise to higher frequencies where it is more easily filtered out by gene networks--a property that may contribute to the prevalence of autoregulation motifs (for example, found in the regulation of approximately 40% of Escherichia coli genes). Here we measure noise frequency content in growing cultures of E. coli, and verify the link between gene circuit structure and noise spectra by demonstrating the negative autoregulation-mediated spectral shift. We further demonstrate that noise spectral measurements provide mechanistic insights into gene regulation, as perturbations of gene circuit parameters are discernible in the measured noise frequency ranges. These results suggest that noise spectral measurements could facilitate the discovery of novel regulatory relationships.     

Interdependence of behavioural variability and response to small stimuli in bacteria

The chemotaxis signalling network in Escherichia coli that controls the locomotion of bacteria is a classic model system for signal transduction. This pathway modulates the behaviour of flagellar motors to propel bacteria towards sources of chemical attractants. Although this system relaxes to a steady state in response to environmental changes, the signalling events within the chemotaxis network are noisy and cause large temporal variations of the motor behaviour even in the absence of stimulus. That the same signalling network governs both behavioural variability and cellular response raises the question of whether these two traits are independent. Here, we experimentally establish a fluctuation-response relationship in the chemotaxis system of living bacteria. Using this relationship, we demonstrate the possibility of inferring the cellular response from the behavioural variability measured before stimulus. In monitoring the pre- and post-stimulus switching behaviour of individual bacterial motors, we found that variability scales linearly with the response time for different functioning states of the cell. This study highlights that the fundamental relationship between fluctuation and response is not constrained to physical systems at thermodynamic equilibrium but is extensible to living cells. Such a relationship not only implies that behavioural variability and cellular response can be coupled traits, but it also provides a general framework within which we can examine how the selection of a network design shapes this interdependence.     

A bottom-up approach to gene regulation

The ability to construct synthetic gene networks enables experimental investigations of deliberately simplified systems that can be compared to qualitative and quantitative models. If simple, well-characterized modules can be coupled together into more complex networks with behaviour that can be predicted from that of the individual components, we may begin to build an understanding of cellular regulatory processes from the 'bottom up'. Here we have engineered a promoter to allow simultaneous repression and activation of gene expression in Escherichia coli. We studied its behaviour in synthetic gene networks under increasingly complex conditions: unregulated, repressed, activated, and simultaneously repressed and activated. We develop a stochastic model that quantitatively captures the means and distributions of the expression from the engineered promoter of this modular system, and show that the model can be extended and used to accurately predict the in vivo behaviour of the network when it is expanded to include positive feedback. The model also reveals the counterintuitive prediction that noise in protein expression levels can increase upon arrest of cell growth and division, which we confirm experimentally. This work shows that the properties of regulatory subsystems can be used to predict the behaviour of larger, more complex regulatory networks, and that this bottom-up approach can provide insights into gene regulation.     

生化反应系统的建模与分析

很多细胞行为受细胞内基因表达和蛋白质相互作用等生物化学反应的调控.这些细胞内的生化反应表现出明显的随机性,它成为描述细胞行为的可计算建模中不可忽略的因素.该文是关于计算系统生物学中随机模拟的基本理论和新进展的自洽综述.本综述从生化反应系统的基本假设出发,介绍关于生化反应内部噪声、外部随机扰动和包含时间滞后的反应过程的各种数学描述,包括化学主方程、化学福克尔-普朗克方程、化学速率方程、化学郎之万方程等; 还介绍了相关的数值模拟方法,包括随机模拟算法和τ跳跃算法.     

A sensory source for motor variation

Suppose that the variability in our movements is caused not by noise in the motor system itself, nor by fluctuations in our intentions or plans, but rather by errors in our sensory estimates of the external parameters that define the appropriate action. For tasks in which precision is at a premium, performance would be optimal if no noise were added in movement planning and execution: motor output would be as accurate as possible given the quality of sensory inputs. Here we use visually guided smooth-pursuit eye movements in primates as a testing ground for this notion of optimality. In response to repeated presentations of identical target motions, nearly 92% of the variance in eye trajectory can be accounted for as a consequence of errors in sensory estimates of the speed, direction and timing of target motion, plus a small background noise that is observed both during eye movements and during fixations. The magnitudes of the inferred sensory errors agree with the observed thresholds for sensory discrimination by perceptual systems, suggesting that the very different neural processes of perception and action are limited by the same sources of noise.     

Resilient circadian oscillator revealed in individual cyanobacteria

Circadian oscillators, which provide internal daily periodicity, are found in a variety of living organisms, including mammals, insects, plants, fungi and cyanobacteria. Remarkably, these biochemical oscillators are resilient to external and internal modifications, such as temperature and cell division cycles. They have to be 'fluctuation (noise) resistant' because relative fluctuations in the number of messenger RNA and protein molecules forming the intracellular oscillators are likely to be large. In multicellular organisms, the strong temporal stability of circadian clocks, despite molecular fluctuations, can easily be explained by intercellular interactions. Here we study circadian rhythms and their stability in unicellular cyanobacteria Synechoccocus elongatus. Low-light-level microscopy has allowed us to measure gene expression under circadian control in single bacteria, showing that the circadian clock is indeed a property of individual cells. Our measurements show that the oscillators have a strong temporal stability with a correlation time of several months. In contrast to many circadian clocks in multicellular organisms, this stability seems to be ensured by the intracellular biochemical network, because the interactions between oscillators seem to be negligible.     

Light acts directly on organs and cells in culture to set the vertebrate circadian clock

The expression of clock genes in vertebrates is widespread and not restricted to classical clock structures. The expression of the Clock gene in zebrafish shows a strong circadian oscillation in many tissues in vivo and in culture, showing that endogenous oscillators exist in peripheral organs. A defining feature of circadian clocks is that they can be set or entrained to local time, usually by the environmental light-dark cycle. An important question is whether peripheral oscillators are entrained to local time by signals from central pacemakers such as the eyes or are themselves directly light-responsive. Here we show that the peripheral organ clocks of zebrafish are set by light-dark cycles in culture. We also show that a zebrafish-derived cell line contains a circadian oscillator, which is also directly light entrained.     

化学反应交联的随机热力学效应

根据受噪声作用的有限化学反应系统的随机热力学理论，以存在膜平衡交联的简单反应模型为例，建立了交联体系的有效主方程及有效随机熵平衡方程。进而阐了这类体系中有效熵产生的统计内涵，初步揭示出内涨落和来自化学反应交联的外噪声的随机热化学效应。     

Spectroscopy of spontaneous spin noise as a probe of spin dynamics and magnetic resonance

Not all noise in experimental measurements is unwelcome. Certain fundamental noise sources contain valuable information about the system itself-a notable example being the inherent voltage fluctuations (Johnson noise) that exist across any resistor, which allow the temperature to be determined. In magnetic systems, fundamental noise can exist in the form of random spin fluctuations. For example, statistical fluctuations of N paramagnetic spins should generate measurable noise of order N spins, even in zero magnetic field. Here we exploit this effect to perform perturbation-free magnetic resonance. We use off-resonant Faraday rotation to passively detect the magnetization noise in an equilibrium ensemble of paramagnetic alkali atoms; the random fluctuations generate spontaneous spin coherences that precess and decay with the same characteristic energy and timescales as the macroscopic magnetization of an intentionally polarized or driven ensemble. Correlation spectra of the measured spin noise reveal g-factors, nuclear spin, isotope abundance ratios, hyperfine splittings, nuclear moments and spin coherence lifetimes-without having to excite, optically pump or otherwise drive the system away from thermal equilibrium. These noise signatures scale inversely with interaction volume, suggesting a possible route towards non-perturbative, sourceless magnetic resonance of small systems.     

用复规范形法研究窄带随机动力系统

为了深入研究窄带噪声作用下随机动力系统的特性,将复规范形法用于窄带随机动力系统研究了Duffing、Rayleigh和Vanderpol方程在谐和与窄带随机参数激励联合作用下的主共振响应和稳定性．由复规范形法得到了此系统响应振幅和相住所满足的方程,再由摄动法分析了系统的主共振响应和稳定性,并用随机增维精细积分法验证了方程理论分析结果的正确性,用数值法计算了平凡解的Lyaputov指数曲面．结果表明,随着窄带随机扰动强度的增加,系统稳态解的相图从极限环变为扩散的极限环．研究证实了复规范形法用于窄带随机动力系统是有效的．     

Establishment of developmental precision and proportions in the early Drosophila embryo

During embryonic development, orderly patterns of gene expression eventually assign each cell in the embryo its particular fate. For the anteroposterior axis of the Drosophila embryo, the first step in this process depends on a spatial gradient of the maternal morphogen Bicoid (Bcd). Positional information of this gradient is transmitted to downstream gap genes, each occupying a well defined spatial domain. We determined the precision of the initial process by comparing expression domains in different embryos. Here we show that the Bcd gradient displays a high embryo-to-embryo variability, but that this noise in the positional information is strongly decreased ('filtered') at the level of hunchback (hb) gene expression. In contrast to the Bcd gradient, the hb expression pattern already includes the information about the scale of the embryo. We show that genes known to interact directly with Hb are not responsible for its spatial precision, but that the maternal gene staufen may be crucial.     

Summing up the noise in gene networks

Random fluctuations in genetic networks are inevitable as chemical reactions are probabilistic and many genes, RNAs and proteins are present in low numbers per cell. Such 'noise' affects all life processes and has recently been measured using green fluorescent protein (GFP). Two studies show that negative feedback suppresses noise, and three others identify the sources of noise in gene expression. Here I critically analyse these studies and present a simple equation that unifies and extends both the mathematical and biological perspectives.