Population PBPK modeling using parametric and nonparametric methods of the Simcyp Simulator, and Bayesian samplers.

Physiologically-based pharmacokinetic (PBPK) models usually include a large number of parameters whose values are obtained using in vitro to in vivo extrapolation. However, such extrapolations can be uncertain and may benefit from inclusion of evidence from clinical observations via parametric inference. When clinical interindividual variability is high, or the data sparse, it is essential to use a population pharmacokinetics inferential framework to estimate unknown or uncertain parameters. Several approaches are available for that purpose, but their relative advantages for PBPK modeling are unclear. We compare the results obtained using a minimal PBPK model of a canonical theophylline dataset with quasi-random parametric expectation maximization (QRPEM), nonparametric adaptive grid estimation (NPAG), Bayesian Metropolis-Hastings (MH), and Hamiltonian Markov Chain Monte Carlo sampling. QRPEM and NPAG gave consistent population and individual parameter estimates, mostly agreeing with Bayesian estimates. MH simulations ran faster than the others methods, which together had similar performance.

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.

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.

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.

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.

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.

Frequency modulated translocational oscillations of Nrf2, a transcription factor functioning like a wireless sensor.

The discovery that nuclear factor erythroid 2-related factor 2 (Nrf2) undergoes translocational oscillations from cytoplasm to nucleus in human cells with frequency modulation linked to activation of a stress-stimulated cytoprotective response raises the prospect that the Nrf2 works mechanistically analogous to a wireless sensor. Herein, we consider how this new model of Nrf2 oscillation resolves previous inexplicable experimental findings on Nrf2 regulation and why it is fit-for-purpose. Further investigation is required to assess how generally applicable the oscillatory mechanism is and if characteristics of this regulatory control can be found in vivo. It suggests there are multiple, potentially re-enforcing receptors for Nrf2 activation, indicating that potent Nrf2 activation for improved health and treatment of disease may be achieved through combination of Nrf2 system stimulants.

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.

Frequency Modulated Translocational Oscillations of Nrf2 Mediate the Antioxidant Response Element Cytoprotective Transcriptional Response.

AIMS: Stress responsive signaling coordinated by nuclear factor erythroid 2-related factor 2 (Nrf2) provides an adaptive response for protection of cells against toxic insults, oxidative stress and metabolic dysfunction. Nrf2 regulates a battery of protective genes by binding to regulatory antioxidant response elements (AREs). The aim of this study was to examine how Nrf2 signals cell stress status and regulates transcription to maintain homeostasis. RESULTS: In live cell microscopy we observed that Nrf2 undergoes autonomous translocational frequency-modulated oscillations between cytoplasm and nucleus. Oscillations occurred in quiescence and when cells were stimulated at physiological levels of activators, they decrease in period and amplitude and then evoke a cytoprotective transcriptional response. We propose a mechanism whereby oscillations are produced by negative feedback involving successive de-phosphorylation and phosphorylation steps. Nrf2 was inactivated in the nucleus and reactivated on return to the cytoplasm. Increased frequency of Nrf2 on return to the cytoplasm with increased reactivation or refresh-rate under stress conditions activated the transcriptional response mediating cytoprotective effects. The serine/threonine-protein phosphatase PGAM5, member of the Nrf2 interactome, was a key regulatory component. INNOVATION: We found that Nrf2 is activated in cells without change in total cellular Nrf2 protein concentration. Regulation of ARE-linked protective gene transcription occurs rather through translocational oscillations of Nrf2. We discovered cytoplasmic refresh rate of Nrf2 is important in maintaining and regulating the transcriptional response and links stress challenge to increased cytoplasmic surveillance. We found silencing and inhibition of PGAM5 provides potent activation of Nrf2. CONCLUSION: Frequency modulated translocational oscillations of Nrf2 mediate the ARE-linked cytoprotective transcriptional response.

Transcriptional control of glyoxalase 1 by Nrf2 provides a stress-responsive defence against dicarbonyl glycation.

Abnormal cellular accumulation of the dicarbonyl metabolite MG (methylglyoxal) occurs on exposure to high glucose concentrations, inflammation, cell aging and senescence. It is associated with increased MG-adduct content of protein and DNA linked to increased DNA strand breaks and mutagenesis, mitochondrial dysfunction and ROS (reactive oxygen species) formation and cell detachment from the extracellular matrix. MG-mediated damage is countered by glutathione-dependent metabolism by Glo1 (glyoxalase 1). It is not known, however, whether Glo1 has stress-responsive up-regulation to counter periods of high MG concentration or dicarbonyl stress. We identified a functional ARE (antioxidant-response element) in the 5'-untranslated region of exon 1 of the mammalian Glo1 gene. Transcription factor Nrf2 (nuclear factor-erythroid 2 p45 subunit-related factor 2) binds to this ARE, increasing basal and inducible expression of Glo1. Activators of Nrf2 induced increased Glo1 mRNA, protein and activity. Increased expression of Glo1 decreased cellular and extracellular concentrations of MG, MG-derived protein adducts, mutagenesis and cell detachment. Hepatic, brain, heart, kidney and lung Glo1 mRNA and protein were decreased in Nrf2-/- mice, and urinary excretion of MG protein and nucleotide adducts were increased approximately 2-fold. We conclude that dicarbonyl stress is countered by up-regulation of Glo1 in the Nrf2 stress-responsive system, protecting protein and DNA from increased damage and preserving cell function.

Distinct contributions of rod, cone, and melanopsin photoreceptors to encoding irradiance.

Photoreceptive, melanopsin-expressing retinal ganglion cells (mRGCs) encode ambient light (irradiance) for the circadian clock, the pupillomotor system, and other influential behavioral/physiological responses. mRGCs are activated both by their intrinsic phototransduction cascade and by the rods and cones. However, the individual contribution of each photoreceptor class to irradiance responses remains unclear. We address this deficit using mice expressing human red cone opsin, in which rod-, cone-, and melanopsin-dependent responses can be identified by their distinct spectral sensitivity. Our data reveal an unexpectedly important role for rods. These photoreceptors define circadian responses at very dim "scotopic" light levels but also at irradiances at which pattern vision relies heavily on cones. By contrast, cone input to irradiance responses dissipates following light adaptation to the extent that these receptors make a very limited contribution to circadian and pupillary light responses under these conditions. Our data provide new insight into retinal circuitry upstream of mRGCs and optimal stimuli for eliciting irradiance responses.

Oscillatory Notch-pathway activity in a delay model of neuronal differentiation.

Lateral inhibition resulting from a double-negative feedback loop underlies the assignment of different fates to cells in many developmental processes. Previous studies have shown that the presence of time delays in models of lateral inhibition can result in significant oscillatory transients before patterned steady states are reached. We study the impact of local feedback loops in a model of lateral inhibition based on the Notch signaling pathway, elucidating the roles of intracellular and intercellular delays in controlling the overall system behavior. The model exhibits both in-phase and out-of-phase oscillatory modes and oscillation death. Interactions between oscillatory modes can generate complex behaviors such as intermittent oscillations. Our results provide a framework for exploring the recent observation of transient Notch-pathway oscillations during fate assignment in vertebrate neurogenesis.

Oscillatory expression of Hes family transcription factors: insights from mathematical modelling.

Oscillatory expression of the Hes family of transcription factors plays a central role in the segmentation of the vertebrate body during embryonic development. Analogous oscillations in cultured cells suggest that Hes oscillations may be important in other developmental processes, and provide an excellent opportunity to explore the origin of these oscillations in a relatively simple setting. Mathematical and computational modelling have been used in combination with quantitative mRNA and protein expression data to analyse the origin and properties of Hes oscillations, and have highlighted the important roles played by time delays in negative feedback circuits. In this chapter, we review recent theoretical and experimental results, and discuss how analysis of existing models suggests potential avenues for further study of delayed feedback oscillators.

Dissecting the dynamics of the Hes1 genetic oscillator.

Serum stimulation of a number of different mouse cell lines results in sustained oscillations of Hes1, a member of this Hes/Her family of transcription factors. Quantitative time-course expression data obtained in this system provide an excellent opportunity to explore transcriptional oscillations in a relatively simple setting. Simple models of the Hes1 regulatory circuit are capable of generating oscillations that share many features with those observed in mouse fibroblasts, and highlight the central role played by delayed negative feedback. However, taking into account constraints on model parameters imposed by experimental data, these models can only generate oscillations with quite low peak-to-trough expression ratios. To explore the origin of this limitation, we develop a more detailed model of the Hes1 circuit, incorporating nucleo-cytoplasmic transport, Hes1 dimerisation, and differential stability of Hes1 monomers and dimers. We show that differential protein stability can increase the amplitude of Hes1 oscillations, but that the resulting expression profiles do not fully match experimental data. We extend the model by incorporating periodic forcing of the Hes1 circuit by cyclic phosphorylation of the protein Stat3. We show that time delays and differential stability act synergistically in this extended model to generate large amplitude oscillatory solutions that match the experimental data well.

A numerical study of red-green colour opponent properties in the primate retina.

It remains an important question whether neural function is mediated entirely by its tailored circuitry. A persistent debate in retinal colour vision is whether the centre and the surround of a ganglion cell receptive field receive dominant inputs either from L or M cones in an antagonistic manner (the selective wiring model) or mixed inputs (the mixed wiring model). Despite many anatomical, physiological and psychophysical experiments, a decisive conclusion has not been reached. An in-depth examination of what the pure mixed wiring mechanisms predicts is therefore important. These two models make different predictions both for the fovea and for the peripheral retina. Recently, a dynamic cellular model of the primate fovea was developed [Momiji et al. (2006) Vis. Res., 46, 365-381]. Unlike earlier models, it explicitly incorporates spatial non-uniformities, such as the random arrangement of L and M cones. Here, a related model is developed for the peripheral retina by incorporating anatomically reasonable degrees of convergence between cones, bipolar cells and ganglion cells. These two models, in which selective wiring mechanisms are absent, are applied to describe both foveal and peripheral colour vision. In numerical simulations, peripheral ganglion cells are less colour sensitive than foveal counterparts, but none-the-less display comparative sensitivities. Furthermore, peripheral colour sensitivity increases with temporal frequency, relative to foveal sensitivity. These results are congruent with recent physiological experiments.

Numerical study of short-term afterimages and associate properties in foveal vision.

A cellular model of the primate retina has been developed. Unlike existing models, it incorporates spatial non-uniformities, such as the random arrangement of L and M cones, and the radial dilation with eccentricity. Based on a population of ganglion cell activities, colour-image representation is modelled with the luminance and the R-G opponent channels. The developed model reproduces experimentally known properties in temporal and spatial vision. Furthermore, spatio-temporally coupled properties such as transition from positive to negative phases in an afterimage, are recapped. In colour vision, the model can explain the insensitivity in our colour perception to the L/M cone ratio.