Mathematical analysis and quantification of fluorescent proteins as transcriptional reporters

Maturation models of fluorescent proteins are necessary for unbiased estimates of promoter activity

Fluorescent proteins (FPs) are a powerful tool to quantitatively monitor gene expression. The dynamics of a promoter and its regulation can be inferred from fluorescence data. The interpretation of fluorescent data, however, is strongly dependent on the maturation of FPs since different proteins mature in distinct ways. We propose a novel approach for analyzing fluorescent reporter data by incorporating maturation dynamics in the reconstruction of promoter activities. Our approach consists of developing and calibrating mechanistic maturation models for distinct FPs. These models are then used alongside a Bayesian approach to estimate promoter activities from fluorescence data. We demonstrate by means of targeted experiments in Escherichia coli that our approach provides robust estimates and that accounting for maturation is, in many cases, essential for the interpretation of gene expression data.

A Mathematical Modeling and Statistical Analysis of Phycobiliprotein Fluorescence Decay under Exposure to Excitation Light

Photosynthetic phycobiliprotein complexes from Spirulina maxima were purified and fractioned by gel chromatography. A mathematical model was developed for the fractionated phycobiliprotein complexes to successfully represent the fluorescence decay rate under exposure to excitation light. Each fractionated complex had a different ratio of phycobiliproteins, such as allophycocyanin, phycocyanin, or phycoerythrin, but their fluorescence decay trends were determined to statistically have a high similarity. The mathematical model was derived based on mass balance in the sense that the fluorescence of phycobiliprotein complex was linearly dependent on its mass. The model considered both exponentially decreasing (early light-exposure period) and linearly decreasing (later period), and successfully fit the whole period of fluorescence decay trend.

Systematic In Vivo Characterization of Fluorescent Protein Maturation in Budding Yeast

Fluorescent protein (FP) maturation can limit the accuracy with which dynamic intracellular processes are captured and reduce the in vivo brightness of a given FP in fast-dividing cells. The knowledge of maturation timescales can therefore help users determine the appropriate FP for each application. However, in vivo maturation rates can greatly deviate from in vitro estimates that are mostly available. In this work, we present the first systematic study of in vivo maturation for 12 FPs in budding yeast. To overcome the technical limitations of translation inhibitors commonly used to study FP maturation, we implemented a new approach based on the optogenetic stimulations of FP expression in cells grown under constant nutrient conditions. Combining the rapid and orthogonal induction of FP transcription with a mathematical model of expression and maturation allowed us to accurately estimate maturation rates from microscopy data in a minimally invasive manner. Besides providing a useful resource for the budding yeast community, we present a new joint experimental and computational approach for characterizing FP maturation, which is applicable to a wide range of organisms.

Genetically Encoded Fluorescent Biosensor for Rapid Detection of Protein Expression

Fluorescent proteins are widely used as fusion tags to detect protein expression in vivo. To become fluorescent, these proteins must undergo chromophore maturation, a slow process with a half-time of 5 to >30 min that causes delays in real-time detection of protein expression. Here, we engineer a genetically encoded fluorescent biosensor to enable detection of protein expression within seconds in live bacteria. This sensor for transiently expressed proteins (STEP) is based on a fully matured but dim green fluorescent protein in which pre-existing fluorescence increases 11-fold in vivo following the specific and rapid binding of a protein tag (K_d 120 nM, k_on 1.7 × 10⁵ M^-1 s^-1). In live E. coli cells, our STEP biosensor enables detection of protein expression twice as fast as the use of standard fluorescent protein fusions. Our biosensor opens the door to the real-time study of short timescale processes in live cells with high spatiotemporal resolution.

Microfluidic platforms for the dynamic characterisation of synthetic circuitry

Generating novel functionality from well characterised synthetic parts and modules lies at the heart of synthetic biology. Ideally, circuitry is rationally designed in silico with quantitatively predictive models to predetermined design specifications. Synthetic circuits are intrinsically stochastic, often dynamically modulated and set in a dynamic fluctuating environment within a living cell. To build more complex circuits and to gain insight into context effects, intrinsic noise and transient performance, characterisation techniques that resolve both heterogeneity and dynamics are required. Here we review recent advances in both in vitro and in vivo microfluidic technologies that are suitable for the characterisation of synthetic circuitry, modules and parts.

Differential scaling between G1 protein production and cell size dynamics promotes commitment to the cell division cycle in budding yeast

In the unicellular eukaryote Saccharomyces cerevisiae, Cln3-cyclin-dependent kinase activity enables Start, the irreversible commitment to the cell division cycle. However, the concentration of Cln3 has been paradoxically considered to remain constant during G1, due to the presumed scaling of its production rate with cell size dynamics. Measuring metabolic and biosynthetic activity during cell cycle progression in single cells, we found that cells exhibit pulses in their protein production rate. Rather than scaling with cell size dynamics, these pulses follow the intrinsic metabolic dynamics, peaking around Start. Using a viral-based bicistronic construct and targeted proteomics to measure Cln3 at the single-cell and population levels, we show that the differential scaling between protein production and cell size leads to a temporal increase in Cln3 concentration, and passage through Start. This differential scaling causes Start in both daughter and mother cells across growth conditions. Thus, uncoupling between two fundamental physiological parameters drives cell cycle commitment.

WellInverter: a web application for the analysis of fluorescent reporter gene data

Background

Fluorescent reporter genes have become widely used for monitoring gene expression in living cells. When a microbial strain carrying a reporter gene is grown in a microplate reader, the fluorescence and the absorbance (optical density) of the culture can be automatically measured every few minutes in a highly parallelized way. The extraction of useful information from the resulting large amounts of data is not easy to achieve, because the fluorescence and absorbance measurements are only indirectly related to promoter activities and protein concentrations, requiring mathematical models of the expression of reporter genes for their interpretation. Although the principles of the analysis of reporter gene data are well-established today, there is a lack of general-purpose bioinformatics tools based on generic measurement models and sound inference procedures. This has motivated the development of WellInverter, a web application based on well-known methods for regularized linear inversion.

Results

We present a new version of WellInverter that considerably improves the performance and usability of the original application. In particular, we have put in place a parallel computing architecture with a load balancer to distribute analysis queries over several back-end servers, we have completely redesigned the graphical user interface to better support the different analysis steps, and we have developed a plug-in system for the parsing of data files produced by microplate readers from different manufacturers. We illustrate the functioning of WellInverter by analyzing data of the expression of a fluorescent reporter gene controlled by a phage promoter in growing Escherichia coli populations. We show that the expression pattern in different growth media, supporting different growth rates, corresponds to the pattern expected for a constitutive gene.

Conclusions

The new version of WellInverter is a robust, easy-to-use and scalable web application, which has been deployed on two publicly accessible web servers and which can also be installed locally. A demo version of the application with two sample datasets is available on-line.

Electronic supplementary material

The online version of this article (10.1186/s12859-019-2920-4) contains supplementary material, which is available to authorized users.

In vivo study of gene expression with an enhanced dual-color fluorescent transcriptional timer

Fluorescent transcriptional reporters are widely used as signaling reporters and biomarkers to monitor pathway activities and determine cell type identities. However, a large amount of dynamic information is lost due to the long half-life of the fluorescent proteins. To better detect dynamics, fluorescent transcriptional reporters can be destabilized to shorten their half-lives. However, applications of this approach in vivo are limited due to significant reduction of signal intensities. To overcome this limitation, we enhanced translation of a destabilized fluorescent protein and demonstrate the advantages of this approach by characterizing spatio-temporal changes of transcriptional activities in Drosophila. In addition, by combining a fast-folding destabilized fluorescent protein and a slow-folding long-lived fluorescent protein, we generated a dual-color transcriptional timer that provides spatio-temporal information about signaling pathway activities. Finally, we demonstrate the use of this transcriptional timer to identify new genes with dynamic expression patterns.

Mean-Independent Noise Control of Cell Fates via Intermediate States

Stochasticity affects accurate signal detection and robust generation of correct cell fates. Although many known regulatory mechanisms may reduce fluctuations in signals, most simultaneously influence their mean dynamics, leading to unfaithful cell fates. Through analysis and computation, we demonstrate that a reversible signaling mechanism acting through intermediate states can reduce noise while maintaining the mean. This mean-independent noise control (MINC) mechanism is investigated in the context of an intracellular binding protein that regulates retinoic acid (RA) signaling during zebrafish hindbrain development. By comparing our models with experimental data, we find that the MINC mechanism allows for sharp boundaries of gene expression without sacrificing boundary accuracy. In addition, this MINC mechanism can modulate noise to levels that we show are beneficial to spatial patterning through noise-induced cell fate switching. These results reveal a design principle that may be important for noise regulation in many systems that control cell fate determination.

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Mean-independent noise control allows noise attenuation without affecting the mean

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Intermediate states enable such control through proportional coupling

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This controls spatial gene expression noise without shifting boundary locations

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Specific noise levels are required for successful downstream boundary sharpening

Build to understand: synthetic approaches to biology

In this review we discuss how synthetic biology facilitates the task of investigating genetic circuits that are observed in naturally occurring biological systems. Specifically, we give examples where experimentation with synthetic gene circuits has been used to understand four fundamental mechanisms intrinsic to development and disease: multistability, stochastic gene expression, oscillations, and cell-cell communication. Within each area, we also discuss how mathematical modeling has been employed as an essential tool to guide the design of novel gene circuits and as a theoretical basis for exploring circuit topologies exhibiting robust behaviors in the presence of noise.

Robust reconstruction of gene expression profiles from reporter gene data using linear inversion

MOTIVATION

Time-series observations from reporter gene experiments are commonly used for inferring and analyzing dynamical models of regulatory networks. The robust estimation of promoter activities and protein concentrations from primary data is a difficult problem due to measurement noise and the indirect relation between the measurements and quantities of biological interest.

RESULTS

We propose a general approach based on regularized linear inversion to solve a range of estimation problems in the analysis of reporter gene data, notably the inference of growth rate, promoter activity, and protein concentration profiles. We evaluate the validity of the approach using in silico simulation studies, and observe that the methods are more robust and less biased than indirect approaches usually encountered in the experimental literature based on smoothing and subsequent processing of the primary data. We apply the methods to the analysis of fluorescent reporter gene data acquired in kinetic experiments with Escherichia coli. The methods are capable of reliably reconstructing time-course profiles of growth rate, promoter activity and protein concentration from weak and noisy signals at low population volumes. Moreover, they capture critical features of those profiles, notably rapid changes in gene expression during growth transitions.

AVAILABILITY AND IMPLEMENTATION

The methods described in this article are made available as a Python package (LGPL license) and also accessible through a web interface. For more information, see https://team.inria.fr/ibis/wellinverter.

Cell-to-cell variability in the propensity to transcribe explains correlated fluctuations in gene expression

Random fluctuations in gene expression lead to wide cell-to-cell differences in RNA and protein counts. Most efforts to understand stochastic gene expression focus on local (intrinisic) fluctuations, which have an exact theoretical representation. However, no framework exists to model global (extrinsic) mechanisms of stochasticity. We address this problem by dissecting the sources of stochasticity that influence the expression of a yeast heat shock gene, SSA1. Our observations suggest that extrinsic stochasticity does not influence every step of gene expression, but rather arises specifically from cell-to-cell differences in the propensity to transcribe RNA. This led us to propose a framework for stochastic gene expression where transcription rates vary globally in combination with local, gene-specific fluctuations in all steps of gene expression. The proposed model better explains total expression stochasticity than the prevailing ON-OFF model and offers transcription as the specific mechanism underlying correlated fluctuations in gene expression.

Inference of quantitative models of bacterial promoters from time-series reporter gene data

The inference of regulatory interactions and quantitative models of gene regulation from time-series transcriptomics data has been extensively studied and applied to a range of problems in drug discovery, cancer research, and biotechnology. The application of existing methods is commonly based on implicit assumptions on the biological processes under study. First, the measurements of mRNA abundance obtained in transcriptomics experiments are taken to be representative of protein concentrations. Second, the observed changes in gene expression are assumed to be solely due to transcription factors and other specific regulators, while changes in the activity of the gene expression machinery and other global physiological effects are neglected. While convenient in practice, these assumptions are often not valid and bias the reverse engineering process. Here we systematically investigate, using a combination of models and experiments, the importance of this bias and possible corrections. We measure in real time and in vivo the activity of genes involved in the FliA-FlgM module of the E. coli motility network. From these data, we estimate protein concentrations and global physiological effects by means of kinetic models of gene expression. Our results indicate that correcting for the bias of commonly-made assumptions improves the quality of the models inferred from the data. Moreover, we show by simulation that these improvements are expected to be even stronger for systems in which protein concentrations have longer half-lives and the activity of the gene expression machinery varies more strongly across conditions than in the FliA-FlgM module. The approach proposed in this study is broadly applicable when using time-series transcriptome data to learn about the structure and dynamics of regulatory networks. In the case of the FliA-FlgM module, our results demonstrate the importance of global physiological effects and the active regulation of FliA and FlgM half-lives for the dynamics of FliA-dependent promoters.

A wide variety of methods for the reverse engineering of regulatory networks and the identification of quantitative regulation functions are available. We investigate some common assumptions that are made in the application of these methods to time-series transcriptomics data, in the context of a central module in the motility network of E. coli. We show that these assumptions, which hypothesize that mRNA concentrations are good proxies for protein concentrations and that the gene expression machinery is equally active across different physiological conditions, are often not valid and may lead to biased inference results. We also show how models of gene expression can be used in combination with suitable experimental controls to correct for this bias and improve the inference process. The contribution of our work is thus not the addition of another method to the rich store of available reverse engineering algorithms, but lies in the critical examination of the information provided by the experimental data and new ways to exploit this information in the algorithms. The proposed approach is relevant for a wide range of applications using time-series transcriptomics data. For the motility system under study, it has underlined the importance of global physiological effects, the active degradation of the transcription factor FliA as well as the secretion of the anti-sigma factor FlgM for the network dynamics.

Measuring fast gene dynamics in single cells with time-lapse luminescence microscopy

Beetle luciferases and time-lapse luminescence microscopy were optimized to measure the dynamics of cell cycle genes in yeast with subminute time resolution. This method is faster and the cells are smaller than in previous work. It is shown that luciferase reporters are better than fluorescent proteins at tracking gene expression.

Time-lapse fluorescence microscopy is an important tool for measuring in vivo gene dynamics in single cells. However, fluorescent proteins are limited by slow chromophore maturation times and the cellular autofluorescence or phototoxicity that arises from light excitation. An alternative is luciferase, an enzyme that emits photons and is active upon folding. The photon flux per luciferase is significantly lower than that for fluorescent proteins. Thus time-lapse luminescence microscopy has been successfully used to track gene dynamics only in larger organisms and for slower processes, for which more total photons can be collected in one exposure. Here we tested green, yellow, and red beetle luciferases and optimized substrate conditions for in vivo luminescence. By combining time-lapse luminescence microscopy with a microfluidic device, we tracked the dynamics of cell cycle genes in single yeast with subminute exposure times over many generations. Our method was faster and in cells with much smaller volumes than previous work. Fluorescence of an optimized reporter (Venus) lagged luminescence by 15–20 min, which is consistent with its known rate of chromophore maturation in yeast. Our work demonstrates that luciferases are better than fluorescent proteins at faithfully tracking the underlying gene expression.

Temporal and spatial properties of a yeast multi-cellular amplification system based on signal molecule diffusion

We report on the spatial and temporal signaling properties of a yeast pheromone-based cell communication and amplifier system. It utilizes the Saccharomyces cerevisiae mating response pathway and relies on diffusion of the pheromone α-factor as key signaling molecule between two cell types. One cell type represents the α-factor secreting sensor part and the other the reporter part emitting fluorescence upon activation. Although multi-cellular signaling systems promise higher specificity and modularity, the complex interaction of the cells makes prediction of sensor performance difficult. To test the maximum distance and response time between sensor and reporter cells, the two cell types were spatially separated in defined compartments of agarose hydrogel (5 x 5 mm) and reconnected by diffusion of the yeast pheromone. Different ratios of sensor to reporter cells were tested to evaluate the minimum amount of sensor cells required for signal transduction. Even the smallest ratio, one α-factor-secreting cell to twenty reporter cells, generated a distinct fluorescence signal. When using a 1:1 ratio, the secreted pheromone induced fluorescence in a distance of up to four millimeters after six hours. We conclude from both our experimental results and a mathematical diffusion model that in our approach: (1) the maximum dimension of separated compartments should not exceed five millimeters in gradient direction; and (2) the time-limiting step is not diffusion of the signaling molecule but production of the reporter protein.

An improved short-lived fluorescent protein transcriptional reporter for Saccharomyces cerevisiae

Ideal reporter genes for temporal transcription programmes have short half-lives that restrict their detection to the window in which their transcripts are present and translated. In an effort to meet this criterion for reporters of transcription in individual living cells, we adapted the ubiquitin fusion strategy for programmable N-end rule degradation to generate an N-degron version of green fluorescent protein (GFP) with a half-life of ~7 min. The GFP variant we used here (designated GFP*) has excellent fluorescence brightness and maturation properties, which make the destabilized reporter well suited for tracking the induction and attenuation kinetics of gene expression in living cells. These attributes are illustrated by its ability to track galactose- and pheromone-induced transcription in S. cerevisiae. We further show that the fluorescence measurements using the short-lived N-degron GFP* reporter gene accurately predict the transient mRNA profile of the prototypical pheromone-induced FUS1 gene.

Quantitative measurement of single cell dynamics

Over the past 20 years luminescent and fluorescent imaging assays have been developed to report on the dynamics of transcription and protein translocation in single cells. The combination of these measurements with mathematical analysis is having an increasingly significant impact on cell biology. There is an urgent need to translate these assays to the study of cells and tissues in vivo, which requires new tools and technologies. Emergence of these new tools and techniques will further the understanding of the role of signalling and transcriptional dynamics in the generation of cellular heterogeneity and the control of cell fate.

Genetic design automation: engineering fantasy or scientific renewal?

The aim of synthetic biology is to make genetic systems more amenable to engineering, which has naturally led to the development of computer-aided design (CAD) tools. Experimentalists still primarily rely on project-specific ad hoc workflows instead of domain-specific tools, which suggests that CAD tools are lagging behind the front line of the field. Here, we discuss the scientific hurdles that have limited the productivity gains anticipated from existing tools. We argue that the real value of efforts to develop CAD tools is the formalization of genetic design rules that determine the complex relationships between genotype and phenotype.

Using a single fluorescent reporter gene to infer half-life of extrinsic noise and other parameters of gene expression

Fluorescent and luminescent proteins are often used as reporters of transcriptional activity. Given the prevalence of noise in biochemical systems, the time-series data arising from these is of significant interest in efforts to calibrate stochastic models of gene expression and obtain information about sources of nongenetic variability. We present a statistical inference framework that can be used to estimate kinetic parameters of gene expression, as well as the strength and half-life of extrinsic noise from single fluorescent-reporter-gene time-series data. The method takes into account stochastic variability in a fluorescent signal resulting from intrinsic noise of gene expression, kinetics of fluorescent protein maturation, and extrinsic noise, which is assumed to arise at transcriptional level. We use the linear noise approximation and derive an explicit formula for the likelihood of observed fluorescent data. The method is embedded in a Bayesian paradigm, so that certain parameters can be informed from other experiments allowing portability of results across different studies. Inference is performed using Markov chain Monte Carlo. Fluorescent reporters are primary tools to observe dynamics of gene expression and the correct interpretation of fluorescent data is crucial to investigating these fundamental processes of cellular life. As both magnitude and frequency of the noise may have a dramatic effect on the cell fitness, the quantification of stochastic fluctuation is essential to the understanding of how genes are regulated. Our method provides a framework that addresses this important question.

Experimental and computational validation of models of fluorescent and luminescent reporter genes in bacteria

BACKGROUND

Fluorescent and luminescent reporter genes have become popular tools for the real-time monitoring of gene expression in living cells. However, mathematical models are necessary for extracting biologically meaningful quantities from the primary data.

RESULTS

We present a rigorous method for deriving relative protein synthesis rates (mRNA concentrations) and protein concentrations by means of kinetic models of gene expression. We experimentally and computationally validate this approach in the case of the protein Fis, a global regulator of transcription in Escherichia coli. We show that the mRNA and protein concentration profiles predicted from the models agree quite well with direct measurements obtained by Northern and Western blots, respectively. Moreover, we present computational procedures for taking into account systematic biases like the folding time of the fluorescent reporter protein and differences in the half-lives of reporter and host gene products. The results show that large differences in protein half-lives, more than mRNA half-lives, may be critical for the interpretation of reporter gene data in the analysis of the dynamics of regulatory systems.

CONCLUSIONS

The paper contributes to the development of sound methods for the interpretation of reporter gene data, notably in the context of the reconstruction and validation of models of regulatory networks. The results have wide applicability for the analysis of gene expression in bacteria and may be extended to higher organisms.