A temporal switch model for estimating transcriptional activity in gene expression

A Parrondo paradox in susceptible-infectious-susceptible dynamics over periodic temporal networks

Many social and biological networks periodically change over time with daily, weekly, and other cycles. Thus motivated, we formulate and analyze susceptible-infectious-susceptible (SIS) epidemic models over temporal networks with periodic schedules. More specifically, we assume that the temporal network consists of a cycle of alternately used static networks, each with a given duration. We observe a phenomenon in which two static networks are individually above the epidemic threshold but the alternating network composed of them renders the dynamics below the epidemic threshold, which we refer to as a Parrondo paradox for epidemics. We find that network structure plays an important role in shaping this phenomenon, and we study its dependence on the connectivity between and number of subpopulations in the network. We associate such paradoxical behavior with anti-phase oscillatory dynamics of the number of infectious individuals in different subpopulations.

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.

Inferring kinetic parameters of oscillatory gene regulation from single cell time-series data

Gene expression dynamics, such as stochastic oscillations and aperiodic fluctuations, have been associated with cell fate changes in multiple contexts, including development and cancer. Single cell live imaging of protein expression with endogenous reporters is widely used to observe such gene expression dynamics. However, the experimental investigation of regulatory mechanisms underlying the observed dynamics is challenging, since these mechanisms include complex interactions of multiple processes, including transcription, translation and protein degradation. Here, we present a Bayesian method to infer kinetic parameters of oscillatory gene expression regulation using an auto-negative feedback motif with delay. Specifically, we use a delay-adapted nonlinear Kalman filter within a Metropolis-adjusted Langevin algorithm to identify posterior probability distributions. Our method can be applied to time-series data on gene expression from single cells and is able to infer multiple parameters simultaneously. We apply it to published data on murine neural progenitor cells and show that it outperforms alternative methods. We further analyse how parameter uncertainty depends on the duration and time resolution of an imaging experiment, to make experimental design recommendations. This work demonstrates the utility of parameter inference on time course data from single cells and enables new studies on cell fate changes and population heterogeneity.

Identifying a stochastic clock network with light entrainment for single cells of Neurospora crassa

Stochastic networks for the clock were identified by ensemble methods using genetic algorithms that captured the amplitude and period variation in single cell oscillators of Neurospora crassa. The genetic algorithms were at least an order of magnitude faster than ensemble methods using parallel tempering and appeared to provide a globally optimum solution from a random start in the initial guess of model parameters (i.e., rate constants and initial counts of molecules in a cell). The resulting goodness of fit [Formula: see text] was roughly halved versus solutions produced by ensemble methods using parallel tempering, and the resulting [Formula: see text] per data point was only [Formula: see text] = 2,708.05/953 = 2.84. The fitted model ensemble was robust to variation in proxies for "cell size". The fitted neutral models without cellular communication between single cells isolated by microfluidics provided evidence for only one Stochastic Resonance at one common level of stochastic intracellular noise across days from 6 to 36 h of light/dark (L/D) or in a D/D experiment. When the light-driven phase synchronization was strong as measured by the Kuramoto (K), there was degradation in the single cell oscillations away from the stochastic resonance. The rate constants for the stochastic clock network are consistent with those determined on a macroscopic scale of 10⁷ cells.

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.

Switched Latent Force Models for Reverse-Engineering Transcriptional Regulation in Gene Expression Data

To survive environmental conditions, cells transcribe their response activities into encoded mRNA sequences in order to produce certain amounts of protein concentrations. The external conditions are mapped into the cell through the activation of special proteins called transcription factors (TFs). Due to the difficult task to measure experimentally TF behaviors, and the challenges to capture their quick-time dynamics, different types of models based on differential equations have been proposed. However, those approaches usually incur in costly procedures, and they present problems to describe sudden changes in TF regulators. In this paper, we present a switched dynamical latent force model for reverse-engineering transcriptional regulation in gene expression data which allows the exact inference over latent TF activities driving some observed gene expressions through a linear differential equation. To deal with discontinuities in the dynamics, we introduce an approach that switches between different TF activities and different dynamical systems. This creates a versatile representation of transcription networks that can capture discrete changes and non-linearities. We evaluate our model on both simulated data and real data (e.g., microaerobic shift in E. coli, yeast respiration), concluding that our framework allows for the fitting of the expression data while being able to infer continuous-time TF profiles.

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

Inferring transcriptional logic from multiple dynamic experiments

MOTIVATION

The availability of more data of dynamic gene expression under multiple experimental conditions provides new information that makes the key goal of identifying not only the transcriptional regulators of a gene but also the underlying logical structure attainable.

RESULTS

We propose a novel method for inferring transcriptional regulation using a simple, yet biologically interpretable, model to find the logic by which a set of candidate genes and their associated transcription factors (TFs) regulate the transcriptional process of a gene of interest. Our dynamic model links the mRNA transcription rate of the target gene to the activation states of the TFs assuming that these interactions are consistent across multiple experiments and over time. A trans-dimensional Markov Chain Monte Carlo (MCMC) algorithm is used to efficiently sample the regulatory logic under different combinations of parents and rank the estimated models by their posterior probabilities. We demonstrate and compare our methodology with other methods using simulation examples and apply it to a study of transcriptional regulation of selected target genes of Arabidopsis Thaliana from microarray time series data obtained under multiple biotic stresses. We show that our method is able to detect complex regulatory interactions that are consistent under multiple experimental conditions.

AVAILABILITY AND IMPLEMENTATION

Programs are written in MATLAB and Statistics Toolbox Release 2016b, The MathWorks, Inc., Natick, Massachusetts, United States and are available on GitHub https://github.com/giorgosminas/TRS and at http://www2.warwick.ac.uk/fac/sci/systemsbiology/research/software.

CONTACT

giorgos.minas@warwick.ac.uk or b.f.finkenstadt@warwick.ac.uk.

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics online.

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.

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.

A stochastic transcriptional switch model for single cell imaging data

Gene expression is made up of inherently stochastic processes within single cells and can be modeled through stochastic reaction networks (SRNs). In particular, SRNs capture the features of intrinsic variability arising from intracellular biochemical processes. We extend current models for gene expression to allow the transcriptional process within an SRN to follow a random step or switch function which may be estimated using reversible jump Markov chain Monte Carlo (MCMC). This stochastic switch model provides a generic framework to capture many different dynamic features observed in single cell gene expression. Inference for such SRNs is challenging due to the intractability of the transition densities. We derive a model-specific birth–death approximation and study its use for inference in comparison with the linear noise approximation where both approximations are considered within the unifying framework of state-space models. The methodology is applied to synthetic as well as experimental single cell imaging data measuring expression of the human prolactin gene in pituitary cells.