Search

Background: It is proven that children have significantly milder COVID-19 disease compared to adults. Various immunological characteristics influence this age-related difference in protection against COVID-19. Pediatric COVID-19 in Jordan is extremely under reported. Objectives: The primary goal of this work is to identify the anti_S and anti_N antibody responses in a random group of children in Jordan and compare it to that of naturally infected-unvaccinated adults. Methods: 151 unvaccinated children, 4 days to 18 years old, were screened for anti_S and anti_N antibodies. History of COVID-19 infection or exposure to infection and symptom severity were reported by parents on a special questionnaire. Results: 78.9 % and 65.3 % of participants were seropositive for anti_S IgG and anti_N Abs, respectively. There was a remarkable association between age and anti_S IgG and anti_N IgG antibody titers, as children aged 12 years or older had increased anti_S IgG titers (mean = 19.3 BAU/mL) compared to younger groups (means of 10.15, 9.24, 7.91 BAU/mL for age groups 6–12, 1–6, less than 1 year, respectively). Gender did not show a statistically important role in anti_S and anti_N IgG seropositivity rates or titers. Children displayed significantly elevated anti_S titers (mean = 13.23 BAU/mL) compared to naturally infected adults (mean = 9.72 BAU/mL), in contrast, adults’ anti_N titers (mean = 39.64 U/mL) were significantly higher compared to those of children (mean = 10.77 U/mL). Conclusions: The current work provides evidence of distinctly robust and persistent humoral immunity displayed by high anti_S and anti_N IgG in children, even >12 months post-infection. Age was the only factor that had a significant statistical impact on anti_S and anti_N Ab levels among the pediatric group in this study. Children exhibited significantly higher anti_S titers than naturally infected adults. In contrast, adults’ anti_N titers were significantly higher. Such information can assist direct pediatric SARS-CoV-2 immunization programs, with implications for creating age-targeted strategies for diagnostic and population protection measures.

Background: Synchronous bilateral breast cancer (SBBC) provides a special condition where two independent breast tumors are exposed to cancer pharmacotherapy within a uniform pharmacokinetic milieu. Both senescence and apoptosis are established responses to therapy; however, they have potentially variable contributions to the overall outcome of treatment, which are yet to be determined. Methods: In this report, we describe the clinicopathological picture of two SBBC cases that received standard anticancer treatment and assess their expression profile of several molecular hallmarks of senescence and apoptosis. Results: Our analysis identified that synchronous tumors have variable expression profiles of both senescence- and apoptosis-associated biomarkers, despite comparable pathological responses to neoadjuvant chemotherapy and current survival rates. Conclusions: Our results highlight the variable expression of senescence- and apoptosis-associated markers in breast tumors (despite the shared somatic genetic background) and invites a large-scale assessment of both senescence and apoptosis in breast cancer tissue in vivo and their contribution to the pathological response and overall survival.

The long-term immunoglobulin responses of COVID-19 vaccinations is important to determine the efficacy of these vaccinations. This study aimed to investigate and compare the long-term immunoglobulin response of COVID-19 vaccination recipients, using anti-S IgG, anti-N IgG, and IgM titer levels. This study included 267 participants, comprising individuals who tested positive for COVID-19 through PCR testing (n = 125), and those who received the Pfizer (n = 133), Sinopharm (n = 112), AstraZeneca (n = 20), or Sputnik (n = 2) vaccines. Female participants comprised the largest share of this study (n = 147, 55.1%). This study found that most participants had positive IgG antibodies, with 96.3% having anti-S IgG and 75.7% having anti-N IgG. Most participants (90.3%) tested negative for anti-N IgM antibodies. Sinopharm-vaccinated individuals exhibited a notably lower rate of positive anti-S IgG (93.8%) and a significantly higher rate of positive anti-N IgG antibodies (91%). Anti-N IgG levels were significantly correlated with the number of prior COVID-19 infections (p = 0.015). Specifically, individuals with a history of four COVID-19 infections had higher anti-N IgG titers (14.1 ± 1.4) than those with only one experience of COVID-19 infection (9.4 ± 7.2). Individuals who were infected with COVID-19 after receiving the vaccine demonstrated higher levels of anti-N IgG, exhibiting a 25% increase in mean titer levels compared to those who were infected prior to vaccination. There was a statistically significant association between anti-N IgG positivity with age (p = 0.034), and smoking status (p = 0.006) of participants. Participants younger than 20 and older than 60 showed the highest positivity rate of anti-N (>90%). Smokers had a low positivity rate of anti-N (68.8%) compared to nonsmokers (83.6%). In conclusion, this study demonstrated that most COVID-19 vaccination recipients had positive IgG antibodies, with differences in the long-term immunoglobulin response depending on the type of vaccine administered and occurrence of COVID-19 infection.

There is controversial evidence that Planck’s constant shows unexpected variations with altitude above the earth due to Kentosh and Mohageg, and yearly systematic changes with the orbit of the earth about the sun due to Hutchin. Many others have postulated that the fundamental constants of nature are not constant, either in locally flat reference frames, or on larger scales. This work is a mathematical study examining the impact of a position dependent Planck’s constant in the Schrödinger equation. With no modifications to the equation, the Hamiltonian becomes a non-Hermitian radial frequency operator. The frequency operator does not conserve normalization, time evolution is no longer unitary, and frequency eigenvalues can be complex. The wavefunction must continually be normalized at each time in order that operators commuting with the frequency operator produce constants of the motion. To eliminate these problems, the frequency operator is replaced with a symmetrizing anti-commutator so that it is once again Hermitian. It is found that particles statistically avoid regions of higher Planck’s constant in the absence of an external potential. Frequency is conserved, and the total frequency equals “kinetic frequency” plus “potential frequency”. No straightforward connection to classical mechanics is found, that is, the Ehrenfest’s theorems are more complicated, and the usual quantities related by them can be complex or imaginary. Energy is conserved only locally with small gradients in Planck’s constant. Two Lagrangian densities are investigated to determine whether they result in a classical field equation of motion resembling the frequency-conserving Schrödinger equation. The first Largrangian is the “energy squared” form, the second is a “frequency squared” form. Neither reproduces the target equation, and it is concluded that the frequency-conserving Schrödinger equation may defy deduction from field theory.

Using the classical vacuum solutions of Newtonian gravity that do not explicitly involve matter, dark matter, or the gravitational constant, subject to an averaging process, a form of gravity relevant to the flattening of galaxy rotation curves results. The latter resembles the solution found if the vacuum is simply assigned a gravitational field density, and a volume of the vacuum is then excluded, with no averaging process. A rationale then follows for why these terms would become important on the galactic scale. Then, a modification of General Relativity, motivated by the Newtonian solutions, that are equivalent to a charge void, is partially defined and discussed in terms of a least action principle.

Abstract Background During the lifetime of a fermenter culture, the soil bacterium S. coelicolor undergoes a major metabolic switch from exponential growth to antibiotic production. We have studied gene expression patterns during this switch, using a specifically designed Affymetrix genechip and a high-resolution time-series of fermenter-grown samples. Results Surprisingly, we find that the metabolic switch actually consists of multiple finely orchestrated switching events. Strongly coherent clusters of genes show drastic changes in gene expression already many hours before the classically defined transition phase where the switch from primary to secondary metabolism was expected. The main switch in gene expression takes only 2 hours, and changes in antibiotic biosynthesis genes are delayed relative to the metabolic rearrangements. Furthermore, global variation in morphogenesis genes indicates an involvement of cell differentiation pathways in the decision phase leading up to the commitment to antibiotic biosynthesis. Conclusions Our study provides the first detailed insights into the complex sequence of early regulatory events during and preceding the major metabolic switch in S. coelicolor, which will form the starting point for future attempts at engineering antibiotic production in a biotechnological setting.

Abstract Background Fluorescent and luminescent gene reporters allow us to dynamically quantify changes in molecular species concentration over time on the single cell level. The mathematical modeling of their interaction through multivariate dynamical models requires the deveopment of effective statistical methods to calibrate such models against available data. Given the prevalence of stochasticity and noise in biochemical systems inference for stochastic models is of special interest. In this paper we present a simple and computationally efficient algorithm for the estimation of biochemical kinetic parameters from gene reporter data. Results We use the linear noise approximation to model biochemical reactions through a stochastic dynamic model which essentially approximates a diffusion model by an ordinary differential equation model with an appropriately defined noise process. An explicit formula for the likelihood function can be derived allowing for computationally efficient parameter estimation. The proposed algorithm is embedded in a Bayesian framework and inference is performed using Markov chain Monte Carlo. Conclusion The major advantage of the method is that in contrast to the more established diffusion approximation based methods the computationally costly methods of data augmentation are not necessary. Our approach also allows for unobserved variables and measurement error. The application of the method to both simulated and experimental data shows that the proposed methodology provides a useful alternative to diffusion approximation based methods.

Recent studies have established that the circadian clock influences onset, progression and therapeutic outcomes in a number of diseases including cancer and heart diseases. Therefore, there is a need for tools to measure the functional state of the molecular circadian clock and its downstream targets in patients. Moreover, the clock is a multi-dimensional stochastic oscillator and there are few tools for analysing it as a noisy multigene dynamical system. In this paper we consider the methodology behind TimeTeller, a machine learning tool that analyses the clock as a noisy multigene dynamical system and aims to estimate circadian clock function from a single transcriptome by modelling the multi-dimensional state of the clock. We demonstrate its potential for clock systems assessment by applying it to mouse, baboon and human microarray and RNA-seq data and show how to visualise and quantify the global structure of the clock, quantitatively stratify individual transcriptomic samples by clock dysfunction and globally compare clocks across individuals, conditions and tissues thus highlighting its potential relevance for advancing circadian medicine., Competing Interests: The authors have declared that no competing interests exist., (Copyright: © 2024 Vlachou et al. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.)

The generation of cellular diversity during development involves differentiating cells transitioning between discrete cell states. In the 1940s, the developmental biologist Conrad Waddington introduced a landscape metaphor to describe this process. The developmental path of a cell was pictured as a ball rolling through a terrain of branching valleys with cell fate decisions represented by the branch points at which the ball decides between one of two available valleys. Here we discuss progress in constructing quantitative dynamical models inspired by this view of cellular differentiation. We describe a framework based on catastrophe theory and dynamical systems methods that provides the foundations for quantitative geometric models of cellular differentiation. These models can be fit to experimental data and used to make quantitative predictions about cellular differentiation. The theory indicates that cell fate decisions can be described by a small number of decision structures, such that there are only two distinct ways in which cells make a binary choice between one of two fates. We discuss the biological relevance of these mechanisms and suggest the approach is broadly applicable for the quantitative analysis of differentiation dynamics and for determining principles of developmental decisions., (© 2022 The Authors.)

Fate decisions in developing tissues involve cells transitioning between discrete cell states, each defined by distinct gene expression profiles. The Waddington landscape, in which the development of a cell is viewed as a ball rolling through a valley filled terrain, is an appealing way to describe differentiation. To construct and validate accurate landscapes, quantitative methods based on experimental data are necessary. We combined principled statistical methods with a framework based on catastrophe theory and approximate Bayesian computation to formulate a quantitative dynamical landscape that accurately predicts cell fate outcomes of pluripotent stem cells exposed to different combinations of signaling factors. Analysis of the landscape revealed two distinct ways in which cells make a binary choice between one of two fates. We suggest that these represent archetypal designs for developmental decisions. The approach is broadly applicable for the quantitative analysis of differentiation and for determining the logic of developmental decisions., Competing Interests: Declaration of interests The authors declare no competing interests., (Copyright © 2021 The Author(s). Published by Elsevier Inc. All rights reserved.)

Embryonic development leads to the reproducible and ordered appearance of complexity from egg to adult. The successive differentiation of different cell types that elaborate this complexity results from the activity of gene networks and was likened by Waddington to a flow through a landscape in which valleys represent alternative fates. Geometric methods allow the formal representation of such landscapes and codify the types of behaviors that result from systems of differential equations. Results from Smale and coworkers imply that systems encompassing gene network models can be represented as potential gradients with a Riemann metric, justifying the Waddington metaphor. Here, we extend this representation to include parameter dependence and enumerate all three-way cellular decisions realizable by tuning at most two parameters, which can be generalized to include spatial coordinates in a tissue. All diagrams of cell states vs. model parameters are thereby enumerated. We unify a number of standard models for spatial pattern formation by expressing them in potential form (i.e., as topographic elevation). Turing systems appear nonpotential, yet in suitable variables the dynamics are low dimensional and potential. A time-independent embedding recovers the original variables. Lateral inhibition is described by a saddle point with many unstable directions. A model for the patterning of the Drosophila eye appears as relaxation in a bistable potential. Geometric reasoning provides intuitive dynamic models for development that are well adapted to fit time-lapse data., Competing Interests: The authors declare no competing interest.

Increasing interest has emerged in new mathematical approaches that simplify the study of complex differentiation processes by formalizing Waddington's landscape metaphor. However, a rational method to build these landscape models remains an open problem. Here we study vulval development in C. elegans by developing a framework based on Catastrophe Theory (CT) and approximate Bayesian computation (ABC) to build data-fitted landscape models. We first identify the candidate qualitative landscapes, and then use CT to build the simplest model consistent with the data, which we quantitatively fit using ABC. The resulting model suggests that the underlying mechanism is a quantifiable two-step decision controlled by EGF and Notch-Delta signals, where a non-vulval/vulval decision is followed by a bistable transition to the two vulval states. This new model fits a broad set of data and makes several novel predictions., Competing Interests: The authors have declared that no competing interests exist.

We consider how a signalling system can act as an information hub by multiplexing information arising from multiple signals. We formally define multiplexing, mathematically characterise which systems can multiplex and how well they can do it. While the results of this paper are theoretical, to motivate the idea of multiplexing, we provide experimental evidence that tentatively suggests that the NF-κB transcription factor can multiplex information about changes in multiple signals. We believe that our theoretical results may resolve the apparent paradox of how a system like NF-κB that regulates cell fate and inflammatory signalling in response to diverse stimuli can appear to have the low information carrying capacity suggested by recent studies on scalar signals. In carrying out our study, we introduce new methods for the analysis of large, nonlinear stochastic dynamic models, and develop computational algorithms that facilitate the calculation of fundamental constructs of information theory such as Kullback-Leibler divergences and sensitivity matrices, and link these methods to a new theory about multiplexing information. We show that many current models such as those of the NF-κB system cannot multiplex effectively and provide models that overcome this limitation using post-transcriptional modifications., Competing Interests: No authors have competing interests.

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., Competing Interests: The authors have declared that no competing interests exist.

Biochemical reaction networks describe the chemical interactions occurring between molecular populations inside the living cell. These networks can be very noisy and complex and they often involve many variables and even more parameters. Parameter sensitivity analysis that studies the effects of parameter changes to the behaviour of biochemical networks can be a powerful tool in unravelling their key parameters and interactions. It can also be very useful in designing experiments that study these networks and in addressing parameter identifiability issues. This article develops a general methodology for analysing the sensitivity of probability distributions of stochastic processes describing the time-evolution of biochemical reaction networks to changes in their parameter values. We derive the coefficients that efficiently summarise the sensitivity of the probability distribution of the network to each parameter and discuss their properties. The methodology is scalable to large and complex stochastic reaction networks involving many parameters and can be applied to oscillatory networks. We use the two-dimensional Brusselator system as an illustrative example and apply our approach to the analysis of the Drosophila circadian clock. We investigate the impact of using stochastic over deterministic models and provide an analysis that can support key decisions for experimental design, such as the choice of variables and time-points to be observed.

NF-κB signaling plays a pivotal role in control of the inflammatory response. We investigated how the dynamics and function of NF-κB were affected by temperature within the mammalian physiological range (34 °C to 40 °C). An increase in temperature led to an increase in NF-κB nuclear/cytoplasmic oscillation frequency following Tumor Necrosis Factor alpha (TNFα) stimulation. Mathematical modeling suggested that this temperature sensitivity might be due to an A20-dependent mechanism, and A20 silencing removed the sensitivity to increased temperature. The timing of the early response of a key set of NF-κB target genes showed strong temperature dependence. The cytokine-induced expression of many (but not all) later genes was insensitive to temperature change (suggesting that they might be functionally temperature-compensated). Moreover, a set of temperature- and TNFα-regulated genes were implicated in NF-κB cross-talk with key cell-fate-controlling pathways. In conclusion, NF-κB dynamics and target gene expression are modulated by temperature and can accurately transmit multidimensional information to control inflammation., Competing Interests: The authors declare no conflict of interest., (Copyright © 2018 the Author(s). Published by PNAS.)

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., (Copyright © 2017 The Authors. Published by Elsevier Inc. All rights reserved.)

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., (© The Author(s) 2017. Published by Oxford University Press.)

In order to analyse large complex stochastic dynamical models such as those studied in systems biology there is currently a great need for both analytical tools and also algorithms for accurate and fast simulation and estimation. We present a new stochastic approximation of biological oscillators that addresses these needs. Our method, called phase-corrected LNA (pcLNA) overcomes the main limitations of the standard Linear Noise Approximation (LNA) to remain uniformly accurate for long times, still maintaining the speed and analytically tractability of the LNA. As part of this, we develop analytical expressions for key probability distributions and associated quantities, such as the Fisher Information Matrix and Kullback-Leibler divergence and we introduce a new approach to system-global sensitivity analysis. We also present algorithms for statistical inference and for long-term simulation of oscillating systems that are shown to be as accurate but much faster than leaping algorithms and algorithms for integration of diffusion equations. Stochastic versions of published models of the circadian clock and NF-κB system are used to illustrate our results.

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.

Chronotherapeutics aim at treating illnesses according to the endogenous biologic rhythms, which moderate xenobiotic metabolism and cellular drug response. The molecular clocks present in individual cells involve approximately fifteen clock genes interconnected in regulatory feedback loops. They are coordinated by the suprachiasmatic nuclei, a hypothalamic pacemaker, which also adjusts the circadian rhythms to environmental cycles. As a result, many mechanisms of diseases and drug effects are controlled by the circadian timing system. Thus, the tolerability of nearly 500 medications varies by up to fivefold according to circadian scheduling, both in experimental models and/or patients. Moreover, treatment itself disrupted, maintained, or improved the circadian timing system as a function of drug timing. Improved patient outcomes on circadian-based treatments (chronotherapy) have been demonstrated in randomized clinical trials, especially for cancer and inflammatory diseases. However, recent technological advances have highlighted large interpatient differences in circadian functions resulting in significant variability in chronotherapy response. Such findings advocate for the advancement of personalized chronotherapeutics through interdisciplinary systems approaches. Thus, the combination of mathematical, statistical, technological, experimental, and clinical expertise is now shaping the development of dedicated devices and diagnostic and delivery algorithms enabling treatment individualization. In particular, multiscale systems chronopharmacology approaches currently combine mathematical modeling based on cellular and whole-body physiology to preclinical and clinical investigations toward the design of patient-tailored chronotherapies. We review recent systems research works aiming to the individualization of disease treatment, with emphasis on both cancer management and circadian timing system-resetting strategies for improving chronic disease control and patient outcomes., (Copyright © 2017 by The Author(s).)

Cells respond dynamically to pulsatile cytokine stimulation. Here we report that single, or well-spaced pulses of TNFα (>100 min apart) give a high probability of NF-κB activation. However, fewer cells respond to shorter pulse intervals (<100 min) suggesting a heterogeneous refractory state. This refractory state is established in the signal transduction network downstream of TNFR and upstream of IKK, and depends on the level of the NF-κB system negative feedback protein A20. If a second pulse within the refractory phase is IL-1β instead of TNFα, all of the cells respond. This suggests a mechanism by which two cytokines can synergistically activate an inflammatory response. Gene expression analyses show strong correlation between the cellular dynamic response and NF-κB-dependent target gene activation. These data suggest that refractory states in the NF-κB system constitute an inherent design motif of the inflammatory response and we suggest that this may avoid harmful homogenous cellular activation.

Uterine smooth muscle cells remain quiescent throughout most of gestation, only generating spontaneous action potentials immediately prior to, and during, labor. This study presents a method that combines transcriptomics with biophysical recordings to characterise the conductance repertoire of these cells, the 'conductance repertoire' being the total complement of ion channels and transporters expressed by an electrically active cell. Transcriptomic analysis provides a set of potential electrogenic entities, of which the conductance repertoire is a subset. Each entity within the conductance repertoire was modeled independently and its gating parameter values were fixed using the available biophysical data. The only remaining free parameters were the surface densities for each entity. We characterise the space of combinations of surface densities (density vectors) consistent with experimentally observed membrane potential and calcium waveforms. This yields insights on the functional redundancy of the system as well as its behavioral versatility. Our approach couples high-throughput transcriptomic data with physiological behaviors in health and disease, and provides a formal method to link genotype to phenotype in excitable systems. We accurately predict current densities and chart functional redundancy. For example, we find that to evoke the observed voltage waveform, the BK channel is functionally redundant whereas hERG is essential. Furthermore, our analysis suggests that activation of calcium-activated chloride conductances by intracellular calcium release is the key factor underlying spontaneous depolarisations.

Background: Over the last decade sensitivity analysis techniques have been shown to be very useful to analyse complex and high dimensional Systems Biology models. However, many of the currently available toolboxes have either used parameter sampling, been focused on a restricted set of model observables of interest, studied optimisation of a objective function, or have not dealt with multiple simultaneous model parameter changes where the changes can be permanent or temporary., Results: Here we introduce our new, freely downloadable toolbox, PeTTSy (Perturbation Theory Toolbox for Systems). PeTTSy is a package for MATLAB which implements a wide array of techniques for the perturbation theory and sensitivity analysis of large and complex ordinary differential equation (ODE) based models. PeTTSy is a comprehensive modelling framework that introduces a number of new approaches and that fully addresses analysis of oscillatory systems. It examines sensitivity analysis of the models to perturbations of parameters, where the perturbation timing, strength, length and overall shape can be controlled by the user. This can be done in a system-global setting, namely, the user can determine how many parameters to perturb, by how much and for how long. PeTTSy also offers the user the ability to explore the effect of the parameter perturbations on many different types of outputs: period, phase (timing of peak) and model solutions. PeTTSy can be employed on a wide range of mathematical models including free-running and forced oscillators and signalling systems. To enable experimental optimisation using the Fisher Information Matrix it efficiently allows one to combine multiple variants of a model (i.e. a model with multiple experimental conditions) in order to determine the value of new experiments. It is especially useful in the analysis of large and complex models involving many variables and parameters., Conclusions: PeTTSy is a comprehensive tool for analysing large and complex models of regulatory and signalling systems. It allows for simulation and analysis of models under a variety of environmental conditions and for experimental optimisation of complex combined experiments. With its unique set of tools it makes a valuable addition to the current library of sensitivity analysis toolboxes. We believe that this software will be of great use to the wider biological, systems biology and modelling communities.

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., Competing Interests: The authors declare that no competing interests exist.

In Arabidopsis thaliana, 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, we set out to identify genes that govern early responses to drought. To do this, a high-resolution time series transcriptomics data set was produced, coupled with detailed physiological and metabolic analyses of plants subjected to a slow transition from well-watered to drought conditions. A total of 1815 drought-responsive differentially expressed genes were identified. The 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. To identify gene regulatory networks (GRNs) mediating the transition between the early and late stages of drought, we used Bayesian network modeling of differentially expressed transcription factor (TF) genes. This approach identified AGAMOUS-LIKE22 (AGL22), as key hub gene in a TF GRN. It has previously been shown that AGL22 is involved in the transition from vegetative state to flowering but here we show that AGL22 expression influences steady state photosynthetic rates and lifetime water use. This suggests that AGL22 uniquely regulates a transcriptional network during drought stress, linking changes in primary metabolism and the initiation of stress responses., (© 2016 American Society of Plant Biologists. All rights reserved.)

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., (© The Author 2015. Published by Oxford University Press.)

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.

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., (© 2015 Authors; published by Portland Press Limited.)

Uncontrolled cell proliferation is one of the key features leading to cancer. Seminal works in chronobiology have revealed that disruption of the circadian timing system in mice, either by surgical, genetic, or environmental manipulation, increased tumor development. In humans, shift work is a risk factor for cancer. Based on these observations, the link between the circadian clock and cell cycle has become intuitive. But despite identification of molecular connections between the two processes, the influence of the clock on the dynamics of the cell cycle has never been formally observed. Recently, two studies combining single live cell imaging with computational methods have shed light on robust coupling between clock and cell cycle oscillators. We recapitulate here these novel findings and integrate them with earlier results in both healthy and cancerous cells. Moreover, we propose that the cell cycle may be synchronized or slowed down through coupling with the circadian clock, which results in reduced tumor growth. More than ever, systems biology has become instrumental to understand the dynamic interaction between the circadian clock and cell cycle, which is critical in cellular coordination and for diseases such as cancer.

We provide analytical tools to facilitate a rigorous assessment of the quality and value of the fit of a complex model to data. We use this to provide approaches to model fitting, parameter estimation, the design of optimization functions and experimental optimization. This is in the context where multiple constraints are used to select or optimize a large model defined by differential equations. We illustrate the approach using models of circadian clocks and the NF-κB signalling system.

Abnormal uterine activity in pregnancy causes a range of important clinical disorders, including preterm birth, dysfunctional labour and post-partum haemorrhage. Uterine contractile patterns are controlled by the generation of complex electrical signals at the myometrial smooth muscle plasma membrane. To identify novel targets to treat conditions associated with uterine dysfunction, we undertook a genome-wide screen of potassium channels that are enriched in myometrial smooth muscle. Computational modelling identified Kir7.1 as potentially important in regulating uterine excitability during pregnancy. We demonstrate Kir7.1 current hyper-polarizes uterine myocytes and promotes quiescence during gestation. Labour is associated with a decline, but not loss, of Kir7.1 expression. Knockdown of Kir7.1 by lentiviral expression of miRNA was sufficient to increase uterine contractile force and duration significantly. Conversely, overexpression of Kir7.1 inhibited uterine contractility. Finally, we demonstrate that the Kir7.1 inhibitor VU590 as well as novel derivative compounds induces profound, long-lasting contractions in mouse and human myometrium; the activity of these inhibitors exceeds that of other uterotonic drugs. We conclude Kir7.1 regulates the transition from quiescence to contractions in the pregnant uterus and may be a target for therapies to control uterine contractility., (© 2014 The Authors. Published under the terms of the CC BY 4.0 license.)

Daily synchronous rhythms of cell division at the tissue or organism level are observed in many species and suggest that the circadian clock and cell cycle oscillators are coupled. For mammals, despite known mechanistic interactions, the effect of such coupling on clock and cell cycle progression, and hence its biological relevance, is not understood. In particular, we do not know how the temporal organization of cell division at the single-cell level produces this daily rhythm at the tissue level. Here we use multispectral imaging of single live cells, computational methods, and mathematical modeling to address this question in proliferating mouse fibroblasts. We show that in unsynchronized cells the cell cycle and circadian clock robustly phase lock each other in a 1:1 fashion so that in an expanding cell population the two oscillators oscillate in a synchronized way with a common frequency. Dexamethasone-induced synchronization reveals additional clock states. As well as the low-period phase-locked state there are distinct coexisting states with a significantly higher period clock. Cells transition to these states after dexamethasone synchronization. The temporal coordination of cell division by phase locking to the clock at a single-cell level has significant implications because disordered circadian function is increasingly being linked to the pathogenesis of many diseases, including cancer.

Background: 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., Results: 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 body H2A.Z which is associated with low transcription rate Q10, but is also influenced by other marks and transcription factor activities., Conclusions: Our data show that less frequent chromatin states can produce temperature responses simply by virtue of their rarity and the difference between their thermal properties and those of the most common states, and underline the advantages of directly measuring transcription rate changes in dynamic systems, rather than inferring rates from changes in mRNA abundance.

Estimation of the period length of time-course data from cyclical biological processes, such as those driven by the circadian pacemaker, is crucial for inferring the properties of the biological clock found in many living organisms. We propose a methodology for period estimation based on spectrum resampling (SR) techniques. Simulation studies show that SR is superior and more robust to non-sinusoidal and noisy cycles than a currently used routine based on Fourier approximations. In addition, a simple fit to the oscillations using linear least squares is available, together with a non-parametric test for detecting changes in period length which allows for period estimates with different variances, as frequently encountered in practice. The proposed methods are motivated by and applied to various data examples from chronobiology.

Motivation: cis-regulatory DNA sequence elements, such as enhancers and silencers, function to control the spatial and temporal expression of their target genes. Although the overall levels of gene expression in large cell populations seem to be precisely controlled, transcription of individual genes in single cells is extremely variable in real time. It is, therefore, important to understand how these cis-regulatory elements function to dynamically control transcription at single-cell resolution. Recently, statistical methods have been proposed to back calculate the rates involved in mRNA transcription using parameter estimation of a mathematical model of transcription and translation. However, a major complication in these approaches is that some of the parameters, particularly those corresponding to the gene copy number and transcription rate, cannot be distinguished; therefore, these methods cannot be used when the copy number is unknown., Results: Here, we develop a hierarchical Bayesian model to estimate biokinetic parameters from live cell enhancer-promoter reporter measurements performed on a population of single cells. This allows us to investigate transcriptional dynamics when the copy number is variable across the population. We validate our method using synthetic data and then apply it to quantify the function of two known developmental enhancers in real time and in single cells., Availability: Supporting information is submitted with the article.

Motivation: The analysis and mechanistic modelling of time series gene expression data provided by techniques such as microarrays, NanoString, reverse transcription-polymerase chain reaction and advanced sequencing are invaluable for developing an understanding of the variation in key biological processes. We address this by proposing the estimation of a flexible dynamic model, which decouples temporal synthesis and degradation of mRNA and, hence, allows for transcriptional activity to switch between different states., Results: The model is flexible enough to capture a variety of observed transcriptional dynamics, including oscillatory behaviour, in a way that is compatible with the demands imposed by the quality, time-resolution and quantity of the data. We show that the timing and number of switch events in transcriptional activity can be estimated alongside individual gene mRNA stability with the help of a Bayesian reversible jump Markov chain Monte Carlo algorithm. To demonstrate the methodology, we focus on modelling the wild-type behaviour of a selection of 200 circadian genes of the model plant Arabidopsis thaliana. The results support the idea that using a mechanistic model to identify transcriptional switch points is likely to strongly contribute to efforts in elucidating and understanding key biological processes, such as transcription and degradation.

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.

We present a novel and simple method to numerically calculate Fisher information matrices for stochastic chemical kinetics models. The linear noise approximation is used to derive model equations and a likelihood function that leads to an efficient computational algorithm. Our approach reduces the problem of calculating the Fisher information matrix to solving a set of ordinary differential equations. This is the first method to compute Fisher information for stochastic chemical kinetics models without the need for Monte Carlo simulations. This methodology is then used to study sensitivity, robustness, and parameter identifiability in stochastic chemical kinetics models. We show that significant differences exist between stochastic and deterministic models as well as between stochastic models with time-series and time-point measurements. We demonstrate that these discrepancies arise from the variability in molecule numbers, correlations between species, and temporal correlations and show how this approach can be used in the analysis and design of experiments probing stochastic processes at the cellular level. The algorithm has been implemented as a Matlab package and is available from the authors upon request.

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., Competing Interests: The authors have declared that no competing interests exist.

We present a new approach to understanding how regulatory networks such as circadian clocks might evolve robustness to environmental fluctuations. The approach is in terms of new balance equations that we derive. We use it to describe how an entrained clock can buffer the effects of daily fluctuations in light and temperature levels. We also use it to study a different approach to temperature compensation where instead of considering a free-running clock, we study temperature buffering of the phases in a light-entrained clock, which we believe is a more physiological setting.

A cryogenic Yb amplifier using two laser materials, Gd3Sc2Al3O12 and Y3Al5O12 (YAG), has been used to obtain 70 W average power at 5 kHz pulse repetition frequency; the output was compressed to 1.6 ps, compared with an input compressible to 1.4 ps. The gain broadening obtained by combining two media enables shorter pulses than using Yb:YAG alone but retains the power-scaling advantages of cryogenic Yb:YAG.

The circadian clock controls 24-h rhythms in many biological processes, allowing appropriate timing of biological rhythms relative to dawn and dusk. Known clock circuits include multiple, interlocked feedback loops. Theory suggested that multiple loops contribute the flexibility for molecular rhythms to track multiple phases of the external cycle. Clear dawn- and dusk-tracking rhythms illustrate the flexibility of timing in Ipomoea nil. Molecular clock components in Arabidopsis thaliana showed complex, photoperiod-dependent regulation, which was analysed by comparison with three contrasting models. A simple, quantitative measure, Dusk Sensitivity, was introduced to compare the behaviour of clock models with varying loop complexity. Evening-expressed clock genes showed photoperiod-dependent dusk sensitivity, as predicted by the three-loop model, whereas the one- and two-loop models tracked dawn and dusk, respectively. Output genes for starch degradation achieved dusk-tracking expression through light regulation, rather than a dusk-tracking rhythm. Model analysis predicted which biochemical processes could be manipulated to extend dusk tracking. Our results reveal how an operating principle of biological regulators applies specifically to the plant circadian clock.

Nuclear factor kappa B (NF-kappaB) signalling is activated by cellular stress and inflammation and regulates cytokine expression. We applied single-cell imaging to investigate dynamic responses to different doses of tumour necrosis factor alpha (TNFalpha). Lower doses activated fewer cells and those responding showed an increasingly variable delay in the initial NF-kappaB nuclear translocation and associated IkappaBalpha degradation. Robust 100 minute nuclear:cytoplasmic NF-kappaB oscillations were observed over a wide range of TNFalpha concentrations. The result is supported by computational analyses, which identified a limit cycle in the system with a stable 100 minute period over a range of stimuli, and indicated no co-operativity in the pathway activation. These results suggest that a stochastic threshold controls functional all-or-nothing responses in individual cells. Deterministic and stochastic models simulated the experimentally observed activation threshold and gave rise to new predictions about the structure of the system and open the way for better mechanistic understanding of physiological TNFalpha activation of inflammatory responses in cells and tissues.

Background: Robustness is a central property of living systems, enabling function to be maintained against environmental perturbations. A key challenge is to identify the structures in biological circuits that confer system-level properties such as robustness. Circadian clocks allow organisms to adapt to the predictable changes of the 24-hour day/night cycle by generating endogenous rhythms that can be entrained to the external cycle. In all organisms, the clock circuits typically comprise multiple interlocked feedback loops controlling the rhythmic expression of key genes. Previously, we showed that such architectures increase the flexibility of the clock's rhythmic behaviour. We now test the relationship between flexibility and robustness, using a mathematical model of the circuit controlling conidiation in the fungus Neurospora crassa., Results: The circuit modelled in this work consists of a central negative feedback loop, in which the frequency (frq) gene inhibits its transcriptional activator white collar-1 (wc-1), interlocked with a positive feedback loop in which FRQ protein upregulates WC-1 production. Importantly, our model reproduces the observed entrainment of this circuit under light/dark cycles with varying photoperiod and cycle duration. Our simulations show that whilst the level of frq mRNA is driven directly by the light input, the falling phase of FRQ protein, a molecular correlate of conidiation, maintains a constant phase that is uncoupled from the times of dawn and dusk. The model predicts the behaviour of mutants that uncouple WC-1 production from FRQ's positive feedback, and shows that the positive loop enhances the buffering of conidiation phase against seasonal photoperiod changes. This property is quantified using Kitano's measure for the overall robustness of a regulated system output. Further analysis demonstrates that this functional robustness is a consequence of the greater evolutionary flexibility conferred on the circuit by the interlocking loop structure., Conclusions: Our model shows that the behaviour of the fungal clock in light-dark cycles can be accounted for by a transcription-translation feedback model of the central FRQ-WC oscillator. More generally, we provide an example of a biological circuit in which greater flexibility yields improved robustness, while also introducing novel sensitivity analysis techniques applicable to a broader range of cellular oscillators.

Heterogeneity between individual cells is a common feature of dynamic cellular processes, including signaling, transcription, and cell fate; yet the overall tissue level physiological phenotype needs to be carefully controlled to avoid fluctuations. Here we show that in the NF-kappaB signaling system, the precise timing of a dual-delayed negative feedback motif [involving stochastic transcription of inhibitor kappaB (IkappaB)-alpha and -epsilon] is optimized to induce heterogeneous timing of NF-kappaB oscillations between individual cells. We suggest that this dual-delayed negative feedback motif enables NF-kappaB signaling to generate robust single cell oscillations by reducing sensitivity to key parameter perturbations. Simultaneously, enhanced cell heterogeneity may represent a mechanism that controls the overall coordination and stability of cell population responses by decreasing temporal fluctuations of paracrine signaling. It has often been thought that dynamic biological systems may have evolved to maximize robustness through cell-to-cell coordination and homogeneity. Our analyses suggest in contrast, that this cellular variation might be advantageous and subject to evolutionary selection. Alternative types of therapy could perhaps be designed to modulate this cellular heterogeneity.

Populations of cells are almost always heterogeneous in function and fate. To understand the plasticity of cells, it is vital to measure quantitatively and dynamically the molecular processes that underlie cell-fate decisions in single cells. Early events in cell signalling often occur within seconds of the stimulus, whereas intracellular signalling processes and transcriptional changes can take minutes or hours. By contrast, cell-fate decisions, such as whether a cell divides, differentiates or dies, can take many hours or days. Multiparameter experimental and computational methods that integrate quantitative measurement and mathematical simulation of these noisy and complex processes are required to understand the highly dynamic mechanisms that control cell plasticity and fate.