Using movies to analyse gene circuit dynamics in single cells

Many bacterial systems rely on dynamic genetic circuits to control crucial biological processes. A major goal of systems biology is to understand these behaviours in terms of individual genes and their interactions. However, traditional techniques based on population averages 'wash out' crucial dynamics that are either unsynchronized between cells or are driven by fluctuations, or 'noise', in cellular components. Recently, the combination of time-lapse microscopy, quantitative image analysis and fluorescent protein reporters has enabled direct observation of multiple cellular components over time in individual cells. In conjunction with mathematical modelling, these techniques are now providing powerful insights into genetic circuit behaviour in diverse microbial systems

Rate of environmental change determines stress response specificity

Cells use general stress response pathways to activate diverse target genes in response to a variety of stresses. However, general stress responses coexist with more specific pathways that are activated by individual stresses, provoking the fundamental question of whether and how cells control the generality or specificity of their response to a particular stress. Here we address this issue using quantitative time-lapse microscopy of the Bacillus subtilis environmental stress response, mediated by σ^B. We analyzed σ^B activation in response to stresses such as salt and ethanol imposed at varying rates of increase. Dynamically, σ^B responded to these stresses with a single adaptive activity pulse, whose amplitude depended on the rate at which the stress increased. This rate-responsive behavior can be understood from mathematical modeling of a key negative feedback loop in the underlying regulatory circuit. Using RNAseq we analyzed the effects of both rapid and gradual increases of ethanol and salt stress across the genome. Because of the rate responsiveness of σ^B activation, salt and ethanol regulons overlap under rapid, but not gradual, increases in stress. Thus, the cell responds specifically to individual stresses that appear gradually, while using σ^B to broaden the cellular response under more rapidly deteriorating conditions. Such dynamic control of specificity could be a critical function of other general stress response pathways

A systems biology approach to the Arabidopsis circadian clock

Circadian clocks involve feedback loops that generate rhythmic expression of key genes. Molecular genetic studies in the higher plant Arabidopsis theliene have revealed a complex clock network. We begin by modelling the first part of the Arabidopsis clock network to be identified, a transcriptional feedback loop comprising TIMING OF CAB EXPRESSION 1 (TOCl), LATE ELONGATED HYPOCOTYL (LHY) and CIRCADIAN CLOCK ASSOCIATED 1 (CCA1). As for many biological systems, there are no experimental values for the parameters in our model, and the data available for parameter fitting is noisy and varied. To tackle this we construct a cost function, which quantifies the agreement between our model and various key experimental features. We then undertake a global search of parameter space, to test whether the proposed circuit can fit the experimental data. Our optimized solution for the Arabidopsis clock model is unable to account for significant experimental data. Thanks to our search of parameter space, we are able to interpret this as a failure of the network architecture. We develop an extended clock model that is based upon a wider range of data and accurately predicts additional experimental results. The model comprises two interlocking feedback loops comparable to those identified experimentally in other circadian systems. We propose that each loop receives input signals from light, and that each loop includes a hypothetical component that had not been explicitly identified. Analysis of the model predicts the properties of these components, including an acute light induction at dawn that is rapidly repressed by LHY and CCAL We find this unexpected regulation in RNA levels of the evening-expressed gene GIGANTEA (GI), supporting our proposed network and making GI a strong candidate for this component. We go on to develop reduced models of the Arabidopsis clock to aid conceptual understanding, and add a further proposed feedback loop to develop a 3-loop model of the circadian clock. This 3-loop model is able to reproduce further key experimental data.EThOS - Electronic Theses Online ServiceGBUnited Kingdo

Modelling of natural convection flows with large temperature differences : a benchmark problem for low Mach number solvers. Part 1, Reference solutions

There are very few reference solutions in the literature on non-Boussinesq natural convection flows. We propose here a test case problem which extends the well-known De Vahl Davis differentially heated square cavity problem to the case of large temperature differences for which the Boussinesq approximation is no longer valid. The paper is split in two parts: in this first part, we propose as yet unpublished reference solutions for cases characterized by a non-dimensional temperature difference of 0.6, (constant property and variable property cases) and (variable property case). These reference solutions were produced after a first international workshop organized by CEA and LIMSI in January 2000, in which the above authors volunteered to produce accurate numerical solutions from which the present reference solutions could be established

Stochastic Pulse Regulation in Bacterial Stress Response

Gene regulatory circuits can use dynamic, and even stochastic, strategies to respond to environmental conditions. We examined activation of the general stress response mediated by the alternative sigma factor, σ^B, in individual Bacillus subtilis cells. We observed that energy stress activates σ^B in discrete stochastic pulses, with increasing levels of stress leading to higher pulse frequencies. By perturbing and rewiring the endogenous system, we found that this behavior results from three key features of the σ^B circuit: an ultrasensitive phosphorylation switch; stochasticity (“noise”), which activates that switch; and a mixed (positive and negative) transcriptional feedback, which can both amplify a pulse and switch it off. Together, these results show how prokaryotes encode signals using stochastic pulse frequency modulation through a compact regulatory architecture

Measuring single-cell gene expression dynamics in bacteria using fluorescence time-lapse microscopy

Quantitative single-cell time-lapse microscopy is a powerful method for analyzing gene circuit dynamics and heterogeneous cell behavior. We describe the application of this method to imaging bacteria by using an automated microscopy system. This protocol has been used to analyze sporulation and competence differentiation in Bacillus subtilis, and to quantify gene regulation and its fluctuations in individual Escherichia coli cells. The protocol involves seeding and growing bacteria on small agarose pads and imaging the resulting microcolonies. Images are then reviewed and analyzed using our laboratory's custom MATLAB analysis code, which segments and tracks cells in a frame-to-frame method. This process yields quantitative expression data on cell lineages, which can illustrate dynamic expression profiles and facilitate mathematical models of gene circuits. With fast-growing bacteria, such as E. coli or B. subtilis, image acquisition can be completed in 1 d, with an additional 1–2 d for progressing through the analysis procedure

Stochastic pulsing of gene expression enables the generation of spatial patterns in Bacillus subtilis biofilms

Abstract: Stochastic pulsing of gene expression can generate phenotypic diversity in a genetically identical population of cells, but it is unclear whether it has a role in the development of multicellular systems. Here, we show how stochastic pulsing of gene expression enables spatial patterns to form in a model multicellular system, Bacillus subtilis bacterial biofilms. We use quantitative microscopy and time-lapse imaging to observe pulses in the activity of the general stress response sigma factor σB in individual cells during biofilm development. Both σB and sporulation activity increase in a gradient, peaking at the top of the biofilm, even though σB represses sporulation. As predicted by a simple mathematical model, increasing σB expression shifts the peak of sporulation to the middle of the biofilm. Our results demonstrate how stochastic pulsing of gene expression can play a key role in pattern formation during biofilm development

Stochastic pulsing of gene expression enables the generation of spatial patterns in Bacillus subtilis biofilms

Abstract: Stochastic pulsing of gene expression can generate phenotypic diversity in a genetically identical population of cells, but it is unclear whether it has a role in the development of multicellular systems. Here, we show how stochastic pulsing of gene expression enables spatial patterns to form in a model multicellular system, Bacillus subtilis bacterial biofilms. We use quantitative microscopy and time-lapse imaging to observe pulses in the activity of the general stress response sigma factor σB in individual cells during biofilm development. Both σB and sporulation activity increase in a gradient, peaking at the top of the biofilm, even though σB represses sporulation. As predicted by a simple mathematical model, increasing σB expression shifts the peak of sporulation to the middle of the biofilm. Our results demonstrate how stochastic pulsing of gene expression can play a key role in pattern formation during biofilm development

Tunable phenotypic variability through an autoregulatory alternative sigma factor circuit.

Genetically identical individuals in bacterial populations can display significant phenotypic variability. This variability can be functional, for example by allowing a fraction of stress prepared cells to survive an otherwise lethal stress. The optimal fraction of stress prepared cells depends on environmental conditions. However, how bacterial populations modulate their level of phenotypic variability remains unclear. Here we show that the alternative sigma factor σV circuit in Bacillus subtilis generates functional phenotypic variability that can be tuned by stress level, environmental history and genetic perturbations. Using single-cell time-lapse microscopy and microfluidics, we find the fraction of cells that immediately activate σV under lysozyme stress depends on stress level and on a transcriptional memory of previous stress. Iteration between model and experiment reveals that this tunability can be explained by the autoregulatory feedback structure of the sigV operon. As predicted by the model, genetic perturbations to the operon also modulate the response variability. The conserved sigma-anti-sigma autoregulation motif is thus a simple mechanism for bacterial populations to modulate their heterogeneity based on their environment