Bärbel Finkenstädt - Academia.edu (original) (raw)

Papers by Bärbel Finkenstädt

Bayesian inference of biochemical kinetic parameters using the linear noise approximation

We propose to model time-varying periodic and oscillatory processes by means of a hidden Markov m... more We propose to model time-varying periodic and oscillatory processes by means of a hidden Markov model where the states are defined through the spectral properties of a periodic regime. The number of states is unknown along with the relevant periodicities, the role and number of which may vary across states. We address this inference problem by a Bayesian nonparametric hidden Markov model assuming a sticky hierarchical Dirichlet process for the switching dynamics between different states while the periodicities characterizing each state are explored by means of a trans-dimensional Markov chain Monte Carlo sampling step. We develop the full Bayesian inference algorithm and illustrate the use of our proposed methodology for different simulation studies as well as an application related to respiratory research which focuses on the detection of apnea instances in human breathing traces.

The Annals of Applied Statistics, 2021

We propose to model time-varying periodic and oscillatory processes by means of a hidden Markov m... more We propose to model time-varying periodic and oscillatory processes by means of a hidden Markov model where the states are defined through the spectral properties of a periodic regime. The number of states is unknown along with the relevant periodicities, the role and number of which may vary across states. We address this inference problem by a Bayesian nonparametric hidden Markov model assuming a sticky hierarchical Dirichlet process for the switching dynamics between different states while the periodicities characterizing each state are explored by means of a trans-dimensional Markov chain Monte Carlo sampling step. We develop the full Bayesian inference algorithm and illustrate the use of our proposed methodology for different simulation studies as well as an application related to respiratory research which focuses on the detection of apnea instances in human breathing traces.

Cancers, 2020

The dichotomy index (I < O), a quantitative estimate of the circadian regulation of daytime ac... more The dichotomy index (I < O), a quantitative estimate of the circadian regulation of daytime activity and sleep, predicted overall cancer survival and emergency hospitalization, supporting its integration in a mHealth platform. Modifiable causes of I < O deterioration below 97.5%—(I < O)low—were sought in 25 gastrointestinal cancer patients and 33 age- and sex-stratified controls. Rest-activity and temperature were tele-monitored with a wireless chest sensor, while daily activities, meals, and sleep were self-reported for one week. Salivary cortisol rhythm and dim light melatonin onset (DLMO) were determined. Circadian parameters were estimated using Hidden Markov modelling, and spectral analysis. Actionable predictors of (I < O)low were identified through correlation and regression analyses. Median compliance with protocol exceeded 95%. Circadian disruption—(I < O)low—was identified in 13 (52%) patients and four (12%) controls (p = 0.002). Cancer patients with (I <...

JCI Insight, 2019

Background: Circadian timing of treatments can largely improve tolerability and efficacy in patie... more Background: Circadian timing of treatments can largely improve tolerability and efficacy in patients. Thus, drug metabolism and cell cycle are controlled by molecular clocks in each cell, and coordinated by the core body temperature 24-hour rhythm, which is generated by the hypothalamic pacemaker. Individual circadian phase is currently estimated with questionnaire-based chronotype, center-of-rest time, dim light melatonin onset (DLMO), or timing of CBT maximum (acrophase) or minimum (bathyphase). Methods: We aimed at circadian phase determination and read-out during daily routine in volunteers stratified by sex and age. We measured (i) chronotype; (ii) q1min CBT using two electronic pills swallowed 24-hours apart; (iii) DLMO through hourly salivary samples from 18:00 to bedtime; (iv) q1min accelerations and surface temperature at anterior chest level for seven days, using a tele-transmitting sensor. Circadian phases were computed using cosinor and Hidden-Markov modelling. Multivariate regression identified the combination of biomarkers that best predicted core temperature circadian bathyphase. Results: Amongst the 33 participants, individual circadian phases were spread over 5h10min (DLMO), 7h (CBT bathyphase) and 9h10 min (surface temperature acrophase). CBT bathyphase was accurately predicted, i.e. with an error <1h for 78.8% of the subjects, using a new digital health algorithm (INTime), combining time-invariant sex and chronotype score, with computed center-of-rest time and surface temperature bathyphase (adjusted R-squared = 0.637). Conclusion: INTime provided a continuous and reliable circadian phase estimate in real time. This model helps integrate circadian clocks into precision medicine and will enable treatment timing personalisation following further validation.

Journal of Computational and Graphical Statistics, 2019

Bayesian inference for coupled hidden Markov models frequently relies on data augmentation techni... more Bayesian inference for coupled hidden Markov models frequently relies on data augmentation techniques for imputation of the hidden state processes. Considerable progress has been made on developing such techniques, mainly using Markov chain Monte Carlo (MCMC) methods. However, as the dimensionality and complexity of the hidden processes increase some of these methods become inefficient, either because they produce MCMC chains with high autocorrelation or because they become computationally intractable. Motivated by this fact we developed a novel MCMC algorithm, which is a modification of the forward filtering backward sampling algorithm, that achieves a good balance between computation and mixing properties, and thus can be used to analyze models with large numbers of hidden chains. Even though our approach is developed under the assumption of a Markovian model, we show how this assumption can be relaxed leading to minor modifications in the algorithm. Our approach is particularly well suited to epidemic models, where the hidden Markov chains represent the infection status of an individual through time. The performance of our method is assessed on simulated data on epidemic models for the spread of Escherichia coli O157:H7 in cattle. Supplementary materials for this article are available online.

PLOS Computational Biology, 2019

Please refer to published version for the most recent bibliographic citation information. If a pu... more Please refer to published version for the most recent bibliographic citation information. If a published version is known of, the repository item page linked to above, will contain details on accessing it.

Journal of the American Statistical Association, 2019

We propose a novel Bayesian methodology for analyzing nonstationary time series that exhibit osci... more We propose a novel Bayesian methodology for analyzing nonstationary time series that exhibit oscillatory behavior. We approximate the time series using a piecewise oscillatory model with unknown periodicities, where our goal is to estimate the change-points while simultaneously identifying the potentially changing periodicities in the data. Our proposed methodology is based on a trans-dimensional Markov chain Monte Carlo algorithm that simultaneously updates the change-points and the periodicities relevant to any segment between them. We show that the proposed methodology successfully identifies time changing oscillatory behavior in two applications which are relevant to e-Health and sleep research, namely the occurrence of ultradian oscillations in human skin temperature during the time of night rest, and the detection of instances of sleep apnea in plethysmographic respiratory traces. Supplementary materials for this article are available online.

Bioinformatics, 2018

Motivation: The time evolution of molecular species involved in biochemical reaction networks oft... more 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.

BackgroundTranscription in mammalian cells is a complex stochastic process involving shuttling of... more BackgroundTranscription in mammalian cells is a complex stochastic process involving shuttling of polymerase between genes and phase-separated liquid condensates. It occurs in bursts, which results in vastly different numbers of an mRNA species in isogenic cell populations. Several factors contributing to transcriptional bursting have been identified, usually classified as intrinsic, in other words local to single genes, or extrinsic, relating to the macroscopic state of the cell. However, some possible contributors have not been explored yet. Here, we focus on processes at the 3’ and 5’ ends of a gene that enable reinitiation of transcription upon termination.ResultsUsing Bayesian methodology, we measure the transcriptional bursting in inducible transgenes, showing that perturbation of polymerase shuttling typically reduces burst size, increases burst frequency, and thus limits transcriptional noise. Analysis based on paired-end tag sequencing (PolII ChIA-PET) suggests that this ef...

Bioinformatics, 2018

Motivation: Transcription in single cells is an inherently stochastic process as mRNA levels vary... more 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-stochas tic-gene-transcription-from-flow-cytometry-data.

Journal of medical Internet research, Jan 11, 2018

Experimental and epidemiologic studies have shown that circadian clocks' disruption can play ... more Experimental and epidemiologic studies have shown that circadian clocks' disruption can play an important role in the development of cancer and metabolic diseases. The cellular clocks outside the brain are effectively coordinated by the body temperature rhythm. We hypothesized that concurrent measurements of body temperature and rest-activity rhythms would assess circadian clocks coordination in individual patients, thus enabling the integration of biological rhythms into precision medicine. The objective was to evaluate the circadian clocks' coordination in healthy subjects and patients through simultaneous measurements of rest-activity and body temperature rhythms. Noninvasive real-time measurements of rest-activity and chest temperature rhythms were recorded during the subject's daily life, using a dedicated new mobile electronic health platform (PiCADo). It involved a chest sensor that jointly measured accelerations, 3D orientation, and skin surface temperature every...

Cell systems, Jan 27, 2017

Transcription in eukaryotic cells occurs in gene-specific bursts or pulses of activity. Recent st... more 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 a...

BMC bioinformatics, Jan 26, 2017

Given the development of high-throughput experimental techniques, an increasing number of whole g... more 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. 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 ...

The Plant cell, Jan 3, 2016

Water availability is the biggest single limitation on plant productivity worldwide. In Arabidops... more Water availability is the biggest single limitation on plant productivity worldwide. In Arabidopsis, changes in metabolism and gene expression drive increased drought tolerance and initiate diverse drought avoidance and escape responses. To address regulatory processes that link these responses together, we set out to identify novel genes that govern early responses to drought. To do this, a high-resolution time series transcriptomics dataset was produced, coupled with detailed physiological and metabolic analyses of plants subjected to a slow transition from well-watered to drought conditions. 1815 drought-responsive differentially expressed genes were identified. The major early changes in gene expression coincided with a drop in carbon assimilation, and only in the late stages with an increase in foliar abscisic acid content. In order to identify gene regulatory networks (GRNs) mediating the transition between the early and late stages of drought, we used Bayesian network modelli...

Genome biology, Jan 3, 2014

Sensing and responding to ambient temperature is important for controlling growth and development... more Sensing and responding to ambient temperature is important for controlling growth and development of many organisms, in part by regulating mRNA levels. mRNA abundance can change with temperature, but it is unclear whether this results from changes in transcription or decay rates, and whether passive or active temperature regulation is involved. Using a base analog labelling method, we directly measured the temperature coefficient, Q10, of mRNA synthesis and degradation rates of the Arabidopsis transcriptome. We show that for most genes, transcript levels are buffered against passive increases in transcription rates by balancing passive increases in the rate of decay. Strikingly, for temperature-responsive transcripts, increasing temperature raises transcript abundance primarily by promoting faster transcription relative to decay and not vice versa, suggesting a global transcriptional process exists that controls mRNA abundance by temperature. This is partly accounted for by gene bod...

PLoS Biology, 2011

In individual mammalian cells the expression of some genes such as prolactin is highly variable o... more In individual mammalian cells the expression of some genes such as prolactin is highly variable over time and has been suggested to occur in stochastic pulses. To investigate the origins of this behavior and to understand its functional relevance, we quantitatively analyzed this variability using new mathematical tools that allowed us to reconstruct dynamic transcription rates of different reporter genes controlled by identical promoters in the same living cell. Quantitative microscopic analysis of two reporter genes, firefly luciferase and destabilized EGFP, was used to analyze the dynamics of prolactin promoter-directed gene expression in living individual clonal and primary pituitary cells over periods of up to 25 h. We quantified the time-dependence and cyclicity of the transcription pulses and estimated the length and variation of active and inactive transcription phases. We showed an average cycle period of approximately 11 h and demonstrated that while the measured time distribution of active phases agreed with commonly accepted models of transcription, the inactive phases were differently distributed and showed strong memory, with a refractory period of transcriptional inactivation close to 3 h. Cycles in transcription occurred at two distinct prolactin-promoter controlled reporter genes in the same individual clonal or primary cells. However, the timing of the cycles was independent and out-of-phase. For the first time, we have analyzed transcription dynamics from two equivalent loci in real-time in single cells. In unstimulated conditions, cells showed independent transcription dynamics at each locus. A key result from these analyses was the evidence for a minimum refractory period in the inactive-phase of transcription. The response to acute signals and the result of manipulation of histone acetylation was consistent with the hypothesis that this refractory period corresponded to a phase of chromatin remodeling which significantly increased the cyclicity. Stochastically timed bursts of transcription in an apparently random subset of cells in a tissue may thus produce an overall coordinated but heterogeneous phenotype capable of acute responses to stimuli.

Molecular Systems Biology, 2014

Circadian clocks exhibit 'temperature compensation', meaning that they show only small changes in... more Circadian clocks exhibit 'temperature compensation', meaning that they show only small changes in period over a broad temperature range. Several clock genes have been implicated in the temperature-dependent control of period in Arabidopsis. We show that blue light is essential for this, suggesting that the effects of light and temperature interact or converge upon common targets in the circadian clock. Our data demonstrate that two cryptochrome photoreceptors differentially control circadian period and sustain rhythmicity across the physiological temperature range. In order to test the hypothesis that the targets of light regulation are sufficient to mediate temperature compensation, we constructed a temperature-compensated clock model by adding passive temperature effects into only the light-sensitive processes in the model. Remarkably, this model was not only capable of full temperature compensation and consistent with mRNA profiles across a temperature range, but also predicted the temperature-dependent change in the level of LATE ELONGATED HYPOCOTYL, a key clock protein. Our analysis provides a systems-level understanding of period control in the plant circadian oscillator.

Ecological Monographs, 2002

Before the development of mass-vaccination campaigns, measles exhibited persistent fluctuations (... more Before the development of mass-vaccination campaigns, measles exhibited persistent fluctuations (endemic dynamics) in large British cities, and recurrent outbreaks (episodic dynamics) in smaller communities. The critical community size separating the two regimes was ϳ300 000-500 000. We develop a model, the TSIR (Time-series Susceptible-Infected-Recovered) model, that can capture both endemic cycles and episodic outbreaks in measles. The model includes the stochasticity inherent in the disease transmission (giving rise to a negative binomial conditional distribution) and random immigration. It is thus a doubly stochastic model for disease dynamics. It further includes seasonality in the transmission rates. All parameters of the model are estimated on the basis of time series data on reported cases and reconstructed susceptible numbers from a set of cities in England and Wales in the prevaccination era (1944-1966). The 60 cities analyzed span a size range from London (3.3 ϫ 10 6 inhabitants) to Teignmouth (10 500 inhabitants). The dynamics of all cities fit the model well. Transmission rates scale with community size, as expected from dynamics adhering closely to frequency dependent transmission (''true mass action''). These rates are further found to reveal strong seasonal variation, corresponding to high transmission during school terms and lower transmission during the school holidays. The basic reproductive ratio, R 0 , is found to be invariant across the observed range of host community size, and the mean proportion of susceptible individuals also appears to be constant. Through the epidemic cycle, the susceptible population is kept within a 3% interval. The disease is, thus, efficient in ''regulating'' the susceptible population-even in small cities that undergo recurrent epidemics with frequent extinction of the disease agent. Recolonization is highly sensitive to the random immigration process. The initial phase of the epidemic is also stochastic (due to demographic stochasticity and random immigration). However, the epidemic is nearly ''deterministic'' through most of the growth and decline phase.

Bayesian inference of biochemical kinetic parameters using the linear noise approximation

We propose to model time-varying periodic and oscillatory processes by means of a hidden Markov m... more We propose to model time-varying periodic and oscillatory processes by means of a hidden Markov model where the states are defined through the spectral properties of a periodic regime. The number of states is unknown along with the relevant periodicities, the role and number of which may vary across states. We address this inference problem by a Bayesian nonparametric hidden Markov model assuming a sticky hierarchical Dirichlet process for the switching dynamics between different states while the periodicities characterizing each state are explored by means of a trans-dimensional Markov chain Monte Carlo sampling step. We develop the full Bayesian inference algorithm and illustrate the use of our proposed methodology for different simulation studies as well as an application related to respiratory research which focuses on the detection of apnea instances in human breathing traces.

The Annals of Applied Statistics, 2021

We propose to model time-varying periodic and oscillatory processes by means of a hidden Markov m... more We propose to model time-varying periodic and oscillatory processes by means of a hidden Markov model where the states are defined through the spectral properties of a periodic regime. The number of states is unknown along with the relevant periodicities, the role and number of which may vary across states. We address this inference problem by a Bayesian nonparametric hidden Markov model assuming a sticky hierarchical Dirichlet process for the switching dynamics between different states while the periodicities characterizing each state are explored by means of a trans-dimensional Markov chain Monte Carlo sampling step. We develop the full Bayesian inference algorithm and illustrate the use of our proposed methodology for different simulation studies as well as an application related to respiratory research which focuses on the detection of apnea instances in human breathing traces.

Cancers, 2020

The dichotomy index (I < O), a quantitative estimate of the circadian regulation of daytime ac... more The dichotomy index (I < O), a quantitative estimate of the circadian regulation of daytime activity and sleep, predicted overall cancer survival and emergency hospitalization, supporting its integration in a mHealth platform. Modifiable causes of I < O deterioration below 97.5%—(I < O)low—were sought in 25 gastrointestinal cancer patients and 33 age- and sex-stratified controls. Rest-activity and temperature were tele-monitored with a wireless chest sensor, while daily activities, meals, and sleep were self-reported for one week. Salivary cortisol rhythm and dim light melatonin onset (DLMO) were determined. Circadian parameters were estimated using Hidden Markov modelling, and spectral analysis. Actionable predictors of (I < O)low were identified through correlation and regression analyses. Median compliance with protocol exceeded 95%. Circadian disruption—(I < O)low—was identified in 13 (52%) patients and four (12%) controls (p = 0.002). Cancer patients with (I <...

JCI Insight, 2019

Background: Circadian timing of treatments can largely improve tolerability and efficacy in patie... more Background: Circadian timing of treatments can largely improve tolerability and efficacy in patients. Thus, drug metabolism and cell cycle are controlled by molecular clocks in each cell, and coordinated by the core body temperature 24-hour rhythm, which is generated by the hypothalamic pacemaker. Individual circadian phase is currently estimated with questionnaire-based chronotype, center-of-rest time, dim light melatonin onset (DLMO), or timing of CBT maximum (acrophase) or minimum (bathyphase). Methods: We aimed at circadian phase determination and read-out during daily routine in volunteers stratified by sex and age. We measured (i) chronotype; (ii) q1min CBT using two electronic pills swallowed 24-hours apart; (iii) DLMO through hourly salivary samples from 18:00 to bedtime; (iv) q1min accelerations and surface temperature at anterior chest level for seven days, using a tele-transmitting sensor. Circadian phases were computed using cosinor and Hidden-Markov modelling. Multivariate regression identified the combination of biomarkers that best predicted core temperature circadian bathyphase. Results: Amongst the 33 participants, individual circadian phases were spread over 5h10min (DLMO), 7h (CBT bathyphase) and 9h10 min (surface temperature acrophase). CBT bathyphase was accurately predicted, i.e. with an error <1h for 78.8% of the subjects, using a new digital health algorithm (INTime), combining time-invariant sex and chronotype score, with computed center-of-rest time and surface temperature bathyphase (adjusted R-squared = 0.637). Conclusion: INTime provided a continuous and reliable circadian phase estimate in real time. This model helps integrate circadian clocks into precision medicine and will enable treatment timing personalisation following further validation.

Journal of Computational and Graphical Statistics, 2019

Bayesian inference for coupled hidden Markov models frequently relies on data augmentation techni... more Bayesian inference for coupled hidden Markov models frequently relies on data augmentation techniques for imputation of the hidden state processes. Considerable progress has been made on developing such techniques, mainly using Markov chain Monte Carlo (MCMC) methods. However, as the dimensionality and complexity of the hidden processes increase some of these methods become inefficient, either because they produce MCMC chains with high autocorrelation or because they become computationally intractable. Motivated by this fact we developed a novel MCMC algorithm, which is a modification of the forward filtering backward sampling algorithm, that achieves a good balance between computation and mixing properties, and thus can be used to analyze models with large numbers of hidden chains. Even though our approach is developed under the assumption of a Markovian model, we show how this assumption can be relaxed leading to minor modifications in the algorithm. Our approach is particularly well suited to epidemic models, where the hidden Markov chains represent the infection status of an individual through time. The performance of our method is assessed on simulated data on epidemic models for the spread of Escherichia coli O157:H7 in cattle. Supplementary materials for this article are available online.

PLOS Computational Biology, 2019

Please refer to published version for the most recent bibliographic citation information. If a pu... more Please refer to published version for the most recent bibliographic citation information. If a published version is known of, the repository item page linked to above, will contain details on accessing it.

Journal of the American Statistical Association, 2019

We propose a novel Bayesian methodology for analyzing nonstationary time series that exhibit osci... more We propose a novel Bayesian methodology for analyzing nonstationary time series that exhibit oscillatory behavior. We approximate the time series using a piecewise oscillatory model with unknown periodicities, where our goal is to estimate the change-points while simultaneously identifying the potentially changing periodicities in the data. Our proposed methodology is based on a trans-dimensional Markov chain Monte Carlo algorithm that simultaneously updates the change-points and the periodicities relevant to any segment between them. We show that the proposed methodology successfully identifies time changing oscillatory behavior in two applications which are relevant to e-Health and sleep research, namely the occurrence of ultradian oscillations in human skin temperature during the time of night rest, and the detection of instances of sleep apnea in plethysmographic respiratory traces. Supplementary materials for this article are available online.

Bioinformatics, 2018

Motivation: The time evolution of molecular species involved in biochemical reaction networks oft... more 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.

BackgroundTranscription in mammalian cells is a complex stochastic process involving shuttling of... more BackgroundTranscription in mammalian cells is a complex stochastic process involving shuttling of polymerase between genes and phase-separated liquid condensates. It occurs in bursts, which results in vastly different numbers of an mRNA species in isogenic cell populations. Several factors contributing to transcriptional bursting have been identified, usually classified as intrinsic, in other words local to single genes, or extrinsic, relating to the macroscopic state of the cell. However, some possible contributors have not been explored yet. Here, we focus on processes at the 3’ and 5’ ends of a gene that enable reinitiation of transcription upon termination.ResultsUsing Bayesian methodology, we measure the transcriptional bursting in inducible transgenes, showing that perturbation of polymerase shuttling typically reduces burst size, increases burst frequency, and thus limits transcriptional noise. Analysis based on paired-end tag sequencing (PolII ChIA-PET) suggests that this ef...

Bioinformatics, 2018

Motivation: Transcription in single cells is an inherently stochastic process as mRNA levels vary... more 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-stochas tic-gene-transcription-from-flow-cytometry-data.

Journal of medical Internet research, Jan 11, 2018

Experimental and epidemiologic studies have shown that circadian clocks' disruption can play ... more Experimental and epidemiologic studies have shown that circadian clocks' disruption can play an important role in the development of cancer and metabolic diseases. The cellular clocks outside the brain are effectively coordinated by the body temperature rhythm. We hypothesized that concurrent measurements of body temperature and rest-activity rhythms would assess circadian clocks coordination in individual patients, thus enabling the integration of biological rhythms into precision medicine. The objective was to evaluate the circadian clocks' coordination in healthy subjects and patients through simultaneous measurements of rest-activity and body temperature rhythms. Noninvasive real-time measurements of rest-activity and chest temperature rhythms were recorded during the subject's daily life, using a dedicated new mobile electronic health platform (PiCADo). It involved a chest sensor that jointly measured accelerations, 3D orientation, and skin surface temperature every...

Cell systems, Jan 27, 2017

Transcription in eukaryotic cells occurs in gene-specific bursts or pulses of activity. Recent st... more 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 a...

BMC bioinformatics, Jan 26, 2017

Given the development of high-throughput experimental techniques, an increasing number of whole g... more 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. 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 ...

The Plant cell, Jan 3, 2016

Water availability is the biggest single limitation on plant productivity worldwide. In Arabidops... more Water availability is the biggest single limitation on plant productivity worldwide. In Arabidopsis, changes in metabolism and gene expression drive increased drought tolerance and initiate diverse drought avoidance and escape responses. To address regulatory processes that link these responses together, we set out to identify novel genes that govern early responses to drought. To do this, a high-resolution time series transcriptomics dataset was produced, coupled with detailed physiological and metabolic analyses of plants subjected to a slow transition from well-watered to drought conditions. 1815 drought-responsive differentially expressed genes were identified. The major early changes in gene expression coincided with a drop in carbon assimilation, and only in the late stages with an increase in foliar abscisic acid content. In order to identify gene regulatory networks (GRNs) mediating the transition between the early and late stages of drought, we used Bayesian network modelli...

Genome biology, Jan 3, 2014

Sensing and responding to ambient temperature is important for controlling growth and development... more Sensing and responding to ambient temperature is important for controlling growth and development of many organisms, in part by regulating mRNA levels. mRNA abundance can change with temperature, but it is unclear whether this results from changes in transcription or decay rates, and whether passive or active temperature regulation is involved. Using a base analog labelling method, we directly measured the temperature coefficient, Q10, of mRNA synthesis and degradation rates of the Arabidopsis transcriptome. We show that for most genes, transcript levels are buffered against passive increases in transcription rates by balancing passive increases in the rate of decay. Strikingly, for temperature-responsive transcripts, increasing temperature raises transcript abundance primarily by promoting faster transcription relative to decay and not vice versa, suggesting a global transcriptional process exists that controls mRNA abundance by temperature. This is partly accounted for by gene bod...

PLoS Biology, 2011

In individual mammalian cells the expression of some genes such as prolactin is highly variable o... more In individual mammalian cells the expression of some genes such as prolactin is highly variable over time and has been suggested to occur in stochastic pulses. To investigate the origins of this behavior and to understand its functional relevance, we quantitatively analyzed this variability using new mathematical tools that allowed us to reconstruct dynamic transcription rates of different reporter genes controlled by identical promoters in the same living cell. Quantitative microscopic analysis of two reporter genes, firefly luciferase and destabilized EGFP, was used to analyze the dynamics of prolactin promoter-directed gene expression in living individual clonal and primary pituitary cells over periods of up to 25 h. We quantified the time-dependence and cyclicity of the transcription pulses and estimated the length and variation of active and inactive transcription phases. We showed an average cycle period of approximately 11 h and demonstrated that while the measured time distribution of active phases agreed with commonly accepted models of transcription, the inactive phases were differently distributed and showed strong memory, with a refractory period of transcriptional inactivation close to 3 h. Cycles in transcription occurred at two distinct prolactin-promoter controlled reporter genes in the same individual clonal or primary cells. However, the timing of the cycles was independent and out-of-phase. For the first time, we have analyzed transcription dynamics from two equivalent loci in real-time in single cells. In unstimulated conditions, cells showed independent transcription dynamics at each locus. A key result from these analyses was the evidence for a minimum refractory period in the inactive-phase of transcription. The response to acute signals and the result of manipulation of histone acetylation was consistent with the hypothesis that this refractory period corresponded to a phase of chromatin remodeling which significantly increased the cyclicity. Stochastically timed bursts of transcription in an apparently random subset of cells in a tissue may thus produce an overall coordinated but heterogeneous phenotype capable of acute responses to stimuli.

Molecular Systems Biology, 2014

Circadian clocks exhibit 'temperature compensation', meaning that they show only small changes in... more Circadian clocks exhibit 'temperature compensation', meaning that they show only small changes in period over a broad temperature range. Several clock genes have been implicated in the temperature-dependent control of period in Arabidopsis. We show that blue light is essential for this, suggesting that the effects of light and temperature interact or converge upon common targets in the circadian clock. Our data demonstrate that two cryptochrome photoreceptors differentially control circadian period and sustain rhythmicity across the physiological temperature range. In order to test the hypothesis that the targets of light regulation are sufficient to mediate temperature compensation, we constructed a temperature-compensated clock model by adding passive temperature effects into only the light-sensitive processes in the model. Remarkably, this model was not only capable of full temperature compensation and consistent with mRNA profiles across a temperature range, but also predicted the temperature-dependent change in the level of LATE ELONGATED HYPOCOTYL, a key clock protein. Our analysis provides a systems-level understanding of period control in the plant circadian oscillator.

Ecological Monographs, 2002

Before the development of mass-vaccination campaigns, measles exhibited persistent fluctuations (... more Before the development of mass-vaccination campaigns, measles exhibited persistent fluctuations (endemic dynamics) in large British cities, and recurrent outbreaks (episodic dynamics) in smaller communities. The critical community size separating the two regimes was ϳ300 000-500 000. We develop a model, the TSIR (Time-series Susceptible-Infected-Recovered) model, that can capture both endemic cycles and episodic outbreaks in measles. The model includes the stochasticity inherent in the disease transmission (giving rise to a negative binomial conditional distribution) and random immigration. It is thus a doubly stochastic model for disease dynamics. It further includes seasonality in the transmission rates. All parameters of the model are estimated on the basis of time series data on reported cases and reconstructed susceptible numbers from a set of cities in England and Wales in the prevaccination era (1944-1966). The 60 cities analyzed span a size range from London (3.3 ϫ 10 6 inhabitants) to Teignmouth (10 500 inhabitants). The dynamics of all cities fit the model well. Transmission rates scale with community size, as expected from dynamics adhering closely to frequency dependent transmission (''true mass action''). These rates are further found to reveal strong seasonal variation, corresponding to high transmission during school terms and lower transmission during the school holidays. The basic reproductive ratio, R 0 , is found to be invariant across the observed range of host community size, and the mean proportion of susceptible individuals also appears to be constant. Through the epidemic cycle, the susceptible population is kept within a 3% interval. The disease is, thus, efficient in ''regulating'' the susceptible population-even in small cities that undergo recurrent epidemics with frequent extinction of the disease agent. Recolonization is highly sensitive to the random immigration process. The initial phase of the epidemic is also stochastic (due to demographic stochasticity and random immigration). However, the epidemic is nearly ''deterministic'' through most of the growth and decline phase.