A stochastic transcriptional switch model for single cell imaging data

Understanding the molecular mechanisms of transcriptional bursting

In recent years, it has been experimentally established that transcription, a fundamental biological process that involves the synthesis of messenger RNA molecules from DNA templates, does not proceed continuously as was expected. Rather, it exhibits a distinct dynamic behavior of alternating between productive phases when RNA molecules are actively synthesized and inactive phases when there is no RNA production at all. The bimodal transcriptional dynamics is now confirmed to be present in most living systems. This phenomenon is known as transcriptional bursting and it attracts significant amounts of attention from researchers in different fields. However, despite multiple experimental and theoretical investigations, the microscopic origin and biological functions of the transcriptional bursting remain unclear. Here we discuss the recent developments in uncovering the underlying molecular mechanisms of transcriptional bursting and our current understanding of them. Our analysis presents a physicochemical view of the processes that govern transcriptional bursting in living cells.

Transcription Factor Pit-1 Affects Transcriptional Timing in the Dual-Promoter Human Prolactin Gene

Gene transcription occurs in short bursts interspersed with silent periods, and these kinetics can be altered by promoter structure. The effect of alternate promoter architecture on transcription bursting is not known. We studied the human prolactin (hPRL) gene that contains 2 promoters, a pituitary-specific promoter that requires the transcription factor Pit-1 and displays dramatic transcriptional bursting activity and an alternate upstream promoter that is active in nonpituitary tissues. We studied large hPRL genomic fragments with luciferase reporters, and used bacterial artificial chromosome recombineering to manipulate critical promoter regions. Stochastic switch mathematical modelling of single-cell time-lapse luminescence image data revealed that the Pit-1-dependent promoter showed longer, higher-amplitude transcriptional bursts. Knockdown studies confirmed that the presence of Pit-1 stabilized and prolonged periods of active transcription. Pit-1 therefore plays an active role in establishing the timing of transcription cycles, in addition to its cell-specific functions.

Filtering and inference for stochastic oscillators with distributed delays

Motivation

The time evolution of molecular species involved in biochemical reaction networks often arises from complex stochastic processes involving many species and reaction events. Inference for such systems is profoundly challenged by the relative sparseness of experimental data, as measurements are often limited to a small subset of the participating species measured at discrete time points. The need for model reduction can be realistically achieved for oscillatory dynamics resulting from negative translational and transcriptional feedback loops by the introduction of probabilistic time-delays. Although this approach yields a simplified model, inference is challenging and subject to ongoing research. The linear noise approximation (LNA) has recently been proposed to address such systems in stochastic form and will be exploited here.

Results

We develop a novel filtering approach for the LNA in stochastic systems with distributed delays, which allows the parameter values and unobserved states of a stochastic negative feedback model to be inferred from univariate time-series data. The performance of the methods is tested for simulated data. Results are obtained for real data when the model is fitted to imaging data on Cry1, a key gene involved in the mammalian central circadian clock, observed via a luciferase reporter construct in a mouse suprachiasmatic nucleus.

Availability and implementation

Programmes are written in MATLAB and Statistics Toolbox Release 2016 b, The MathWorks, Inc., Natick, Massachusetts, USA. Sample code and Cry1 data are available on GitHub https://github.com/scalderazzo/FLNADD.

Supplementary information

Supplementary data are available at Bioinformatics online.

A Mechanochemical Model of Transcriptional Bursting

Populations of genetically identical cells generally show a large variability in cell phenotypes, which is typically associated with the stochastic nature of gene expression processes. It is widely believed that a significant source of such randomness is transcriptional bursting, which is when periods of active production of RNA molecules alternate with periods of RNA degradation. However, the molecular mechanisms of such strong fluctuations remain unclear. Recent studies suggest that DNA supercoiling, which happens during transcription, might be directly related to the bursting behavior. Stimulated by these observations, we developed a stochastic mechanochemical model of supercoiling-induced transcriptional bursting in which the RNA synthesis leads to the buildup of torsion in DNA. This slows down the RNA production until it is bound by the enzyme gyrase to DNA, which releases the stress and allows for the RNA synthesis to restart with the original rate. Using a thermodynamically consistent coupling between mechanical and chemical processes, the dynamic properties of transcription are explicitly evaluated. In addition, a first-passage method to evaluate the dynamics of transcription is developed. Theoretical analysis shows that transcriptional bursting is observed when both the supercoiling and the mechanical stress release due to gyrase are present in the system. It is also found that the overall RNA production rate is not constant and depends on the number of previously synthesized RNA molecules. A comparison with experimental data on bacteria allows us to evaluate the energetic cost of supercoiling during transcription. It is argued that the relatively weak mechanochemical coupling might allow transcription to be regulated most effectively.

Multimodal transcriptional control of pattern formation in embryonic development

Predicting how interactions between transcription factors and regulatory DNA sequence dictate rates of transcription and, ultimately, drive developmental outcomes remains an open challenge in physical biology. Using stripe 2 of the even-skipped gene in Drosophila embryos as a case study, we dissect the regulatory forces underpinning a key step along the developmental decision-making cascade: the generation of cytoplasmic mRNA patterns via the control of transcription in individual cells. Using live imaging and computational approaches, we found that the transcriptional burst frequency is modulated across the stripe to control the mRNA production rate. However, we discovered that bursting alone cannot quantitatively recapitulate the formation of the stripe and that control of the window of time over which each nucleus transcribes even-skipped plays a critical role in stripe formation. Theoretical modeling revealed that these regulatory strategies (bursting and the time window) respond in different ways to input transcription factor concentrations, suggesting that the stripe is shaped by the interplay of 2 distinct underlying molecular processes.

Lighting up the central dogma for predictive developmental biology

Although the last 30years have witnessed the mapping of the wiring diagrams of the gene regulatory networks that dictate cell fate and animal body plans, specific understanding building on such network diagrams that shows how DNA regulatory regions control gene expression lags far behind. These networks have yet to yield the predictive power necessary to, for example, calculate how the concentration dynamics of input transcription factors and DNA regulatory sequence prescribes output patterns of gene expression that, in turn, determine body plans themselves. Here, we argue that reaching a predictive understanding of developmental decision-making calls for an interplay between theory and experiment aimed at revealing how the regulation of the processes of the central dogma dictate network connections and how network topology guides cells toward their ultimate developmental fate. To make this possible, it is crucial to break free from the snapshot-based understanding of embryonic development facilitated by fixed-tissue approaches and embrace new technologies that capture the dynamics of developmental decision-making at the single cell level, in living embryos.

Bayesian inference on stochastic gene transcription from flow cytometry data

Motivation

Transcription in single cells is an inherently stochastic process as mRNA levels vary greatly between cells, even for genetically identical cells under the same experimental and environmental conditions. We present a stochastic two-state switch model for the population of mRNA molecules in single cells where genes stochastically alternate between a more active ON state and a less active OFF state. We prove that the stationary solution of such a model can be written as a mixture of a Poisson and a Poisson-beta probability distribution. This finding facilitates inference for single cell expression data, observed at a single time point, from flow cytometry experiments such as FACS or fluorescence in situ hybridization (FISH) as it allows one to sample directly from the equilibrium distribution of the mRNA population. We hence propose a Bayesian inferential methodology using a pseudo-marginal approach and a recent approximation to integrate over unobserved states associated with measurement error.

Results

We provide a general inferential framework which can be widely used to study transcription in single cells from the kind of data arising in flow cytometry experiments. The approach allows us to separate between the intrinsic stochasticity of the molecular dynamics and the measurement noise. The methodology is tested in simulation studies and results are obtained for experimental multiple single cell expression data from FISH flow cytometry experiments.

Availability and implementation

All analyses were implemented in R. Source code and the experimental data are available at https://github.com/SimoneTiberi/Bayesian-inference-on-stochastic-gene-transcription-from-flow-cytometry-data.

Supplementary information

Supplementary data are available at Bioinformatics online.

Disentangling juxtacrine from paracrine signalling in dynamic tissue

Prolactin is a major hormone product of the pituitary gland, the central endocrine regulator. Despite its physiological importance, the cell-level mechanisms of prolactin production are not well understood. Having significantly improved the resolution of real-time-single-cell-GFP-imaging, the authors recently revealed that prolactin gene transcription is highly dynamic and stochastic yet shows space-time coordination in an intact tissue slice. However, it still remains an open question as to what kind of cellular communication mediates the observed space-time organization. To determine the type of interaction between cells we developed a statistical model. The degree of similarity between two expression time series was studied in terms of two distance measures, Euclidean and geodesic, the latter being a network-theoretic distance defined to be the minimal number of edges between nodes, and this was used to discriminate between juxtacrine from paracrine signalling. The analysis presented here suggests that juxtacrine signalling dominates. To further determine whether the coupling is coordinating transcription or post-transcriptional activities we used stochastic switch modelling to infer the transcriptional profiles of cells and estimated their similarity measures to deduce that their spatial cellular coordination involves coupling of transcription via juxtacrine signalling. We developed a computational model that involves an inter-cell juxtacrine coupling, yielding simulation results that show space-time coordination in the transcription level that is in agreement with the above analysis. The developed model is expected to serve as the prototype for the further study of tissue-level organised gene expression for epigenetically regulated genes, such as prolactin.

Bayesian Estimation for Stochastic Gene Expression Using Multifidelity Models

The finite state projection (FSP) approach to solving the chemical master equation has enabled successful inference of discrete stochastic models to predict single-cell gene regulation dynamics. Unfortunately, the FSP approach is highly computationally intensive for all but the simplest models, an issue that is highly problematic when parameter inference and uncertainty quantification takes enormous numbers of parameter evaluations. To address this issue, we propose two new computational methods for the Bayesian inference of stochastic gene expression parameters given single-cell experiments. We formulate and verify an adaptive delayed acceptance Metropolis-Hastings (ADAMH) algorithm to utilize with reduced Krylov-basis projections of the FSP. We then introduce an extension of the ADAMH into a hybrid scheme that consists of an initial phase to construct a reduced model and a faster second phase to sample from the approximate posterior distribution determined by the constructed model. We test and compare both algorithms to an adaptive Metropolis algorithm with full FSP-based likelihood evaluations on three example models and simulated data to show that the new ADAMH variants achieve substantial speedup in comparison to the full FSP approach. By reducing the computational costs of parameter estimation, we expect the ADAMH approach to enable efficient data-driven estimation for more complex gene regulation models.

How can a binary switch within the pars tuberalis control seasonal timing of reproduction?

Life in seasonally changing environments is challenging. Biological systems have to not only respond directly to the environment, but also schedule life history events in anticipation of seasonal changes. The cellular and molecular basis of how these events are scheduled is unknown. Cellular decision-making processes in response to signals above certain thresholds regularly occur i.e. cellular fate determination, apoptosis and firing of action potentials. Binary switches, the result of cellular decision-making processes, are defined as a change in phenotype between two stable states. A recent study presents evidence of a binary switch operating in the pars tuberalis (PT) of the pituitary, seemingly timing seasonal reproduction in sheep. Though, how a binary switch would allow for anticipation of seasonal environmental changes, not just direct responsiveness, is unclear. The purpose of this review is to assess the evidence for a binary switching mechanism timing seasonal reproduction and to hypothesize how a binary switch would allow biological processes to be timed over weeks to years. I draw parallels with mechanisms used in development, cell fate determination and seasonal timing in plants. I propose that the adult PT is a plastic tissue, showing a seasonal cycle of cellular differentiation, and that the underlying processes are likely to be epigenetic. Therefore, considering the mechanisms behind adult cellular plasticity offers a framework to hypothesize how a long-term timer functions within the PT.

What shapes eukaryotic transcriptional bursting?

Isogenic cells in a common environment present a large degree of heterogeneity in gene expression. Part of this variability is attributed to transcriptional bursting: the stochastic activation and inactivation of promoters that leads to the discontinuous production of mRNA. The diversity in bursting patterns displayed by different genes suggests the existence of a connection between bursting and gene regulation. Experimental strategies such as single-molecule RNA FISH, MS2-GFP or short-lived protein reporters allow the quantification of transcriptional bursting and the comparison of bursting kinetics between conditions, allowing therefore the identification of molecular mechanisms modulating transcriptional bursting. In this review we recapitulate the impact on transcriptional bursting of different molecular aspects of transcription such as the chromatin environment, nucleosome occupancy, histone modifications, the number and affinity of regulatory elements, DNA looping and transcription factor availability. More specifically, we examine their role in tuning the burst size or the burst frequency. While some molecular mechanisms involved in transcription such as histone marks can affect every aspect of bursting, others predominantly influence the burst size (e.g. the number and affinity of cis-regulatory elements) or frequency (e.g. transcription factor availability).

Asymmetry between Activation and Deactivation during a Transcriptional Pulse

Transcription in eukaryotic cells occurs in gene-specific bursts or pulses of activity. Recent studies identified a spectrum of transcriptionally active “on-states,” interspersed with periods of inactivity, but these “off-states” and the process of transcriptional deactivation are poorly understood. To examine what occurs during deactivation, we investigate the dynamics of switching between variable rates. We measured live single-cell expression of luciferase reporters from human growth hormone or human prolactin promoters in a pituitary cell line. Subsequently, we applied a statistical variable-rate model of transcription, validated by single-molecule FISH, to estimate switching between transcriptional rates. Under the assumption that transcription can switch to any rate at any time, we found that transcriptional activation occurs predominantly as a single switch, whereas deactivation occurs with graded, stepwise decreases in transcription rate. Experimentally altering cAMP signalling with forskolin or chromatin remodelling with histone deacetylase inhibitor modifies the duration of defined transcriptional states. Our findings reveal transcriptional activation and deactivation as mechanistically independent, asymmetrical processes.

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Gene transcription switches between variable rates

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Single-cell microscopy and mathematical modeling quantifies switch dynamics

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We observe an asymmetry in the activation/deactivation of transcriptional bursts

ReTrOS: a MATLAB toolbox for reconstructing transcriptional activity from gene and protein expression data

Background

Given the development of high-throughput experimental techniques, an increasing number of whole genome transcription profiling time series data sets, with good temporal resolution, are becoming available to researchers. The ReTrOS toolbox (Reconstructing Transcription Open Software) provides MATLAB-based implementations of two related methods, namely ReTrOS–Smooth and ReTrOS–Switch, for reconstructing the temporal transcriptional activity profile of a gene from given mRNA expression time series or protein reporter time series. The methods are based on fitting a differential equation model incorporating the processes of transcription, translation and degradation.

Results

The toolbox provides a framework for model fitting along with statistical analyses of the model with a graphical interface and model visualisation. We highlight several applications of the toolbox, including the reconstruction of the temporal cascade of transcriptional activity inferred from mRNA expression data and protein reporter data in the core circadian clock in Arabidopsis thaliana, and how such reconstructed transcription profiles can be used to study the effects of different cell lines and conditions.

Conclusions

The ReTrOS toolbox allows users to analyse gene and/or protein expression time series where, with appropriate formulation of prior information about a minimum of kinetic parameters, in particular rates of degradation, users are able to infer timings of changes in transcriptional activity. Data from any organism and obtained from a range of technologies can be used as input due to the flexible and generic nature of the model and implementation. The output from this software provides a useful analysis of time series data and can be incorporated into further modelling approaches or in hypothesis generation.

Electronic supplementary material

The online version of this article (doi:10.1186/s12859-017-1695-8) contains supplementary material, which is available to authorized users.

Identifying stochastic oscillations in single-cell live imaging time series using Gaussian processes

Multiple biological processes are driven by oscillatory gene expression at different time scales. Pulsatile dynamics are thought to be widespread, and single-cell live imaging of gene expression has lead to a surge of dynamic, possibly oscillatory, data for different gene networks. However, the regulation of gene expression at the level of an individual cell involves reactions between finite numbers of molecules, and this can result in inherent randomness in expression dynamics, which blurs the boundaries between aperiodic fluctuations and noisy oscillators. This underlies a new challenge to the experimentalist because neither intuition nor pre-existing methods work well for identifying oscillatory activity in noisy biological time series. Thus, there is an acute need for an objective statistical method for classifying whether an experimentally derived noisy time series is periodic. Here, we present a new data analysis method that combines mechanistic stochastic modelling with the powerful methods of non-parametric regression with Gaussian processes. Our method can distinguish oscillatory gene expression from random fluctuations of non-oscillatory expression in single-cell time series, despite peak-to-peak variability in period and amplitude of single-cell oscillations. We show that our method outperforms the Lomb-Scargle periodogram in successfully classifying cells as oscillatory or non-oscillatory in data simulated from a simple genetic oscillator model and in experimental data. Analysis of bioluminescent live-cell imaging shows a significantly greater number of oscillatory cells when luciferase is driven by a Hes1 promoter (10/19), which has previously been reported to oscillate, than the constitutive MoMuLV 5’ LTR (MMLV) promoter (0/25). The method can be applied to data from any gene network to both quantify the proportion of oscillating cells within a population and to measure the period and quality of oscillations. It is publicly available as a MATLAB package.

Technological advances now allow us to observe gene expression in real-time at a single-cell level. In a wide variety of biological contexts this new data has revealed that gene expression is highly dynamic and possibly oscillatory. It is thought that periodic gene expression may be useful for keeping track of time and space, as well as transmitting information about signalling cues. Classifying a time series as periodic from single cell data is difficult because it is necessary to distinguish whether peaks and troughs are generated from an underlying oscillator or whether they are aperiodic fluctuations. To this end, we present a novel tool to classify live-cell data as oscillatory or non-oscillatory that accounts for inherent biological noise. We first demonstrate that the method outperforms a competing scheme in classifying computationally simulated single-cell data, and we subsequently analyse live-cell imaging time series. Our method is able to successfully detect oscillations in a known genetic oscillator, but it classifies data from a constitutively expressed gene as aperiodic. The method forms a basis for discovering new gene expression oscillators and quantifying how oscillatory activity alters in response to changes in cell fate and environmental or genetic perturbations.

Single-cell transcriptome sequencing: recent advances and remaining challenges

Single-cell RNA-sequencing methods are now robust and economically practical and are becoming a powerful tool for high-throughput, high-resolution transcriptomic analysis of cell states and dynamics. Single-cell approaches circumvent the averaging artifacts associated with traditional bulk population data, yielding new insights into the cellular diversity underlying superficially homogeneous populations. Thus far, single-cell RNA-sequencing has already shown great effectiveness in unraveling complex cell populations, reconstructing developmental trajectories, and modeling transcriptional dynamics. Ongoing technical improvements to single-cell RNA-sequencing throughput and sensitivity, the development of more sophisticated analytical frameworks for single-cell data, and an increasing array of complementary single-cell assays all promise to expand the usefulness and potential applications of single-cell transcriptomic profiling.

Spatially coordinated dynamic gene transcription in living pituitary tissue

Transcription at individual genes in single cells is often pulsatile and stochastic. A key question emerges regarding how this behaviour contributes to tissue phenotype, but it has been a challenge to quantitatively analyse this in living cells over time, as opposed to studying snap-shots of gene expression state. We have used imaging of reporter gene expression to track transcription in living pituitary tissue. We integrated live-cell imaging data with statistical modelling for quantitative real-time estimation of the timing of switching between transcriptional states across a whole tissue. Multiple levels of transcription rate were identified, indicating that gene expression is not a simple binary 'on-off' process. Immature tissue displayed shorter durations of high-expressing states than the adult. In adult pituitary tissue, direct cell contacts involving gap junctions allowed local spatial coordination of prolactin gene expression. Our findings identify how heterogeneous transcriptional dynamics of single cells may contribute to overall tissue behaviour.

Role of Estrogen Response Element in the Human Prolactin Gene: Transcriptional Response and Timing

The use of bacterial artificial chromosome (BAC) reporter constructs in molecular physiology enables the inclusion of large sections of flanking DNA, likely to contain regulatory elements and enhancers regions that contribute to the transcriptional output of a gene. Using BAC recombineering, we have manipulated a 160-kb human prolactin luciferase (hPRL-Luc) BAC construct and mutated the previously defined proximal estrogen response element (ERE) located -1189 bp relative to the transcription start site, to assess its involvement in the estrogen responsiveness of the entire hPRL locus. We found that GH3 cell lines stably expressing Luc under control of the ERE-mutated hPRL promoter (ERE-Mut) displayed a dramatically reduced transcriptional response to 17β-estradiol (E2) treatment compared with cells expressing Luc from the wild-type (WT) ERE hPRL-Luc promoter (ERE-WT). The -1189 ERE controls not only the response to E2 treatment but also the acute transcriptional response to TNFα, which was abolished in ERE-Mut cells. ERE-WT cells displayed a biphasic transcriptional response after TNFα treatment, the acute phase of which was blocked after treatment with the estrogen receptor antagonist 4-hydroxy-tamoxifen. Unexpectedly, we show the oscillatory characteristics of hPRL promoter activity in individual living cells were unaffected by disruption of this crucial response element, real-time bioluminescence imaging showed that transcription cycles were maintained, with similar cycle lengths, in ERE-WT and ERE-Mut cells. These data suggest the -1189 ERE is the dominant response element involved in the hPRL transcriptional response to both E2 and TNFα and, crucially, that cycles of hPRL promoter activity are independent of estrogen receptor binding.