Institute of Fundamental Technological Research

Mutagenesis is responsive to many environmental factors. Evolution therefore depends on the environment not only for selection but also in determining the variation available in a population. One such environmental dependency is the inverse relationship between mutation rates and population density in many microbial species. Here, we determine the mechanism responsible for this mutation rate plasticity. Using dynamical computational modelling and in culture mutation rate estimation, we show that the negative relationship between mutation rate and population density arises from the collective ability of microbial populations to control concentrations of hydrogen peroxide. We demonstrate a loss of this density-associated mutation rate plasticity (DAMP) when Escherichia coli populations are deficient in the degradation of hydrogen peroxide. We further show that the reduction in mutation rate in denser populations is restored in peroxide degradation-deficient cells by the presence of wild-type cells in a mixed population. Together, these model-guided experiments provide a mechanistic explanation for DAMP, applicable across all domains of life, and frames mutation rate as a dynamic trait shaped by microbial community composition.

Dissemination of food-borne L. monocytogenes in the host relies on internalin-mediated invasion, but the underlying invasion strategies remain elusive. Here we use live-cell microscopy to follow single cell interactions between individual human cells and L. monocytogenes and elucidate mechanisms associated with internalin B (InlB)-mediated invasion. We demonstrate that whilst a replicative invasion of nonphagocytic cells is a rare event even at high multiplicities of invasion, L. monocytogenes overcomes this by utilising a strategy relaying on PrfA-mediated ActA-based aggregation. We show that L. monocytogenes forms aggregates in extracellular host cell environment, which promote approximately 5-fold more host cell adhesions than the non-aggregating actA-ΔC mutant (which lacks the C-terminus coding region), with the adhering bacteria inducing 3-fold more intracellular invasions. Aggregation is associated with robust MET tyrosine kinase receptor clustering in the host cells, a hallmark of InlB-mediated invasion, something not observed with the actA-ΔC mutant. Finally, we show via RNA-seq analyses that aggregation involves a global adaptive response to host cell environment (including iron depletion), resulting in metabolic changes in L. monocytogenes and upregulation of the PrfA virulence regulon. Overall, our analyses provide new mechanistic insights into internalin-mediated host-pathogen interactions of L. monocytogenes.

Listeria monocytogenes, host-pathogen interactions, aggregation, PrfA regulon, livecell microscopy

Pathogens have developed intricate strategies to overcome the host’s innate immune responses. In this paper we use live-cell microscopy with a single bacterium resolution to follow in real time interactions between the food-borne pathogen L. monocytogenes and host macrophages, a key event controlling the infection in vivo. We demonstrate that infection results in heterogeneous outcomes, with only a subset of bacteria able to establish a replicative invasion of macrophages. The fate of individual bacteria in the same host cell was independent from the host cell and non-cooperative, being independent from co-infecting bacteria. A higher multiplicity of infection resulted in a reduced probability of replication of the overall bacterial population. By use of internalisation assays and conditional probabilities to mathematically describe the two-stage invasion process, we demonstrate that the higher MOI compromises the ability of macrophages to phagocytose bacteria. We found that the rate of phagocytosis is mediated via the secreted Listeriolysin toxin (LLO), while the probability of replication of intracellular bacteria remained constant. Using strains expressing fluorescent reporters to follow transcription of either the LLO-encoding hly or actA genes, we show that replicative bacteria exhibited higher PrfA regulon expression in comparison to those bacteria that did not replicate, however elevated PrfA expression per se was not sufficient to increase the probability of replication. Overall, this demonstrates a new role for the population-level, but not single cell, PrfA-mediated activity to regulate outcomes of host pathogen interactions.

Listeria monocytogenes, macrophage, single cell heterogeneity, phagocytosis, PrfA regulon, listeriolysin

Transcription of almost all mammalian genes occurs in stochastic bursts, however the fundamental control mechanisms that allow appropriate single-cell responses remain unresolved. Here we utilise single cell genomics data and stochastic models of transcription to perform global analysis of the toll-like receptor (TLR)-induced gene expression variability. Based on analysis of more than 2000 TLR-response genes across multiple experimental conditions we demonstrate that the single-cell, gene-by-gene expression variability can be empirically described by a linear function of the population mean. We show that response heterogeneity of individual genes can be characterised by the slope of the mean-variance line, which captures how cells respond to stimulus and provides insight into evolutionary differences between species. We further demonstrate that linear relationships theoretically determine the underlying transcriptional bursting kinetics, revealing different regulatory modes of TLR response heterogeneity. Stochastic modelling of temporal scRNA-seq count distributions demonstrates that increased response variability is associated with larger and more frequent transcriptional bursts, which emerge via increased complexity of transcriptional regulatory networks between genes and different species. Overall, we provide a methodology relying on inference of empirical mean-variance relationships from single cell data and new insights into control of innate immune response variability.

Cells respond to inflammatory stimuli such as cytokines by activation of the nuclear factor-κB (NF-κB) signalling pathway, resulting in oscillatory translocation of the transcription factor p65 between nucleus and cytoplasm in some cell types. We investigate the relationship between p65 and inhibitor-κB⍺ (IκBα) protein levels and dynamic properties of the system, and how this interaction impacts on the expression of key inflammatory genes. Using bacterial artificial chromosomes, we developed new cell models of IκB⍺-eGFP protein overexpression in a pseudo-native genomic context. We find that cells with high levels of the negative regulator IκBα remain responsive to inflammatory stimuli and maintain dynamics for both p65 and IκBα. In contrast, canonical target gene expression is dramatically reduced by overexpression of IκBα, but can be partially rescued by overexpression of p65. Treatment with leptomycin B to promote nuclear accumulation of IκB⍺ also suppresses canonical target gene expression, suggesting a mechanism in which nuclear IκB⍺ accumulation prevents productive p65 interaction with promoter binding sites. This causes reduced target promoter binding and gene transcription, which we validate by chromatin immunoprecipitation and in primary cells. Overall, we show how inflammatory gene transcription is modulated by the expression levels of both IκB⍺ and p65. This results in an anti-inflammatory effect on transcription, demonstrating a broad mechanism to modulate the strength of inflammatory response.

NF-κB, inflammation, IκB⍺, overexpression, gene expression, localisation

Bilateral vestibular schwannoma is the hallmark of NF2-related schwannomatosis, a rare tumour predisposition syndrome associated with a lifetime of surgical interventions, radiotherapy and off-label use of the anti-angiogenic drug bevacizumab. Unilateral vestibular schwannoma develops sporadically in non-NF2-related schwannomatosis patients for which there are no drug treatment options available. Tumour-infiltrating immune cells such as macrophages and T-cells correlate with increased vestibular schwannoma growth, which is suggested to be similar in sporadic and NF2-related schwannomatosis tumours. However, differences between NF2-related schwannomatosis and the more common sporadic disease include NF2-related schwannomatosis patients presenting an increased number of tumours, multiple tumour types and younger age at diagnosis. A comparison of the tumour microenvironment in sporadic and NF2-related schwannomatosis tumours is therefore required to underpin the development of immunotherapeutic targets, identify the possibility of extrapolating ex vivo data from sporadic vestibular schwannoma to NF2-related schwannomatosis and help inform clinical trial design with the feasibility of co-recruiting sporadic and NF2-related schwannomatosis patients. This study drew together bulk transcriptomic data from three published Affymetrix microarray datasets to compare the gene expression profiles of sporadic and NF2-related schwannomatosis vestibular schwannoma and subsequently deconvolved to predict the abundances of distinct tumour immune microenvironment populations. Data were validated using quantitative PCR and Hyperion imaging mass cytometry. Comparative bioinformatic analyses revealed close similarities in NF2-related schwannomatosis and sporadic vestibular schwannoma tumours across the three datasets. Significant inflammatory markers and signalling pathways were closely matched in NF2-related schwannomatosis and sporadic vestibular schwannoma, relating to the proliferation of macrophages, angiogenesis and inflammation. Bulk transcriptomic and imaging mass cytometry data identified macrophages as the most abundant immune population in vestibular schwannoma, comprising one-third of the cell mass in both NF2-related schwannomatosis and sporadic tumours. Importantly, there were no robust significant differences in signalling pathways, gene expression, cell type abundance or imaging mass cytometry staining between NF2-related schwannomatosis and sporadic vestibular schwannoma. These data indicate strong similarities in the tumour immune microenvironment of NF2-related schwannomatosis and sporadic vestibular schwannoma.

tumour microenvironment, vestibular schwannoma, tumour-associated macrophages, NF2, NF2-related schwannomatosis

Immune cells fine tune their responses to infection and inflammatory cues. Here, using live-cell confocal microscopy and mathematical modelling, we investigate interferon-induced JAK-STAT signalling in innate immune macrophages. We demonstrate that transient exposure to IFN-γ stimulation induces a long-term desensitisation of STAT1 signalling and gene expression responses, revealing a dose- and time-dependent regulatory feedback that controls JAK-STAT responses upon re-exposure to stimulus. We show that IFN-α/β1 elicit different level of desensitisation from IFN-γ, where cells refractory to IFN-α/β1 are sensitive to IFN-γ, but not vice versa. We experimentally demonstrate that the underlying feedback mechanism involves regulation of STAT1 phosphorylation but is independent of new mRNA synthesis and cognate receptor expression. A new feedback model of the protein tyrosine phosphatase activity recapitulates experimental data and demonstrates JAK-STAT network’s ability to decode relative changes of dose, timing, and type of temporal interferon stimulation. These findings reveal that STAT desensitisation renders cells with signalling memory of type I and II interferon stimulation, which in the future may improve administration of interferon therapy.

JAK-STAT network, STAT1 kinetics, interferons, pathway desensitisation, mathematical modelling, signal memory, live-cell microscopy

Mathematical modeling of signaling pathways and regulatory networks has been supporting experimental research for some time now. Sensitivity analysis, aimed at finding model parameters whose changes yield significantly altered cellular responses, is an important part of modeling work. However, sensitivity methods are often directly transplanted from analysis of technical systems, and thus, they may not serve the purposes of analysis of biological systems. This paper presents a novel sensitivity analysis method that is particularly suited to the task of searching for potential molecular drug targets in signaling pathways. Using two sample models of pathways, p53/Mdm2 regulatory module and IFN-

bioinformatics, chemotherapy, sensitivity analysis, molecular drug targets, systems biology

Single-cell gene expression is inherently variable, but how this variability is controlled in response to stimulation remains unclear. Here, we use single-cell RNA-seq and single-molecule mRNA counting (smFISH) to study inducible gene expression in the immune toll-like receptor system. We show that mRNA counts of tumor necrosis factor α conform to a standard stochastic switch model, while transcription of interleukin-1β involves an additional regulatory step resulting in increased heterogeneity. Despite different modes of regulation, systematic analysis of single-cell data for a range of genes demonstrates that the variability in transcript count is linearly constrained by the mean response over a range of conditions. Mathematical modeling of smFISH counts and experimental perturbation of chromatin state demonstrates that linear constraints emerge through modulation of transcriptional bursting along with gene-specific relationships. Overall, our analyses demonstrate that the variability of the inducible single-cell mRNA response is constrained by transcriptional bursting.

cellular heterogeneity, transcriptional bursting, stochastic gene expression, toll-like receptor, single-cell transcriptomics, stochastic modeling, TNF-α, IL-1β

Background

Ability to adapt to temperature changes trough the Heat Shock Response (HSR) pathways is one of the most fundamental and clinically relevant cellular response systems. Heat Shock (HS) affects the signalling and gene expression responses of the Nuclear Factor κB (NF-κB) transcription factor, a critical regulator of proliferation and inflammation, however, our quantitative understanding of how cells sense and adapt to temperature changes is limited.
Methods

We used live-cell time-lapse microscopy and mathematical modelling to understand the signalling of the NF-κB system in the human MCF7 breast adenocarcinoma cells in response to pro-inflammatory Interleukin 1β (IL1β) and Tumour Necrosis Factor α (TNFα) cytokines, following exposure to a 37–43 °C range of physiological and clinical temperatures.
Results

We show that exposure to 43 °C 1 h HS inhibits the immediate NF-κB signalling response to TNFα and IL1β stimulation although uptake of cytokines is not impaired. Within 4 h after HS treatment IL1β-induced NF-κB responses return to normal levels, but the recovery of the TNFα-induced responses is still affected. Using siRNA knock-down of Heat Shock Factor 1 (HSF1) we show that this stimulus-specificity is conferred via the Inhibitory κB kinase (IKK) signalosome where HSF1-dependent feedback regulates TNFα, but not IL1β-mediated IKK recovery post HS. Furthermore, we demonstrate that through the temperature-dependent denaturation and recovery of IKK, TNFα and IL1β-mediated signalling exhibit different temperature sensitivity and adaptation to repeated HS when exposed to a 37–43 °C temperature range. Specifically, IL1β-mediated NF-κB responses are more robust to temperature changes in comparison to those induced by TNFα treatment.

The heterogeneous nature of inflammatory bowel disease (IBD) presents challenges, particularly when choosing therapy. Activation of the NF-κB transcription factor is a highly regulated, dynamic event in IBD pathogenesis. Using a lentivirus approach, NF-κB-regulated luciferase was expressed in patient macrophages, isolated from frozen peripheral blood mononuclear cell samples. Following activation, samples could be segregated into three clusters based on the NF-κB-regulated luciferase response. The ulcerative colitis (UC) samples appeared only in the hypo-responsive Cluster 1, and in Cluster 2. Conversely, Crohn's disease (CD) patients appeared in all Clusters with their percentage being higher in the hyper-responsive Cluster 3. A positive correlation was seen between NF-κB-induced luciferase activity and the concentrations of cytokines released into medium from stimulated macrophages, but not with serum or biopsy cytokine levels. Confocal imaging of lentivirally-expressed p65 activation revealed that a higher proportion of macrophages from CD patients responded to endotoxin lipid A compared to controls. In contrast, cells from UC patients exhibited a shorter duration of NF-κB p65 subunit nuclear localization compared to healthy controls, and CD donors. Analysis of macrophage cytokine responses and patient metadata revealed a strong correlation between CD patients who smoked and hyper-activation of p65. These in vitro dynamic assays of NF-κB activation in blood-derived macrophages have the potential to segregate IBD patients into groups with different phenotypes and may therefore help determine response to therapy.

inflammatory bowel disease, NF-kB, macrophages, cytokines, Crohn’s disease, ulcerative colitis

Elevated temperature induces the heat shock (HS) response, which modulates cell proliferation, apoptosis, the immune and inflammatory responses. However, specific mechanisms linking the HS response pathways to major cellular signaling systems are not fully understood. Here we used integrated computational and experimental approaches to quantitatively analyze the crosstalk mechanisms between the HS-response and a master regulator of inflammation, cell proliferation, and apoptosis the Nuclear Factor κB (NF-κB) system. We found that populations of human osteosarcoma cells, exposed to a clinically relevant 43°C HS had an attenuated NF-κB p65 response to Tumor Necrosis Factor α (TNFα) treatment. The degree of inhibition of the NF-κB response depended on the HS exposure time. Mathematical modeling of single cells indicated that individual crosstalk mechanisms differentially encode HS-mediated NF-κB responses while being consistent with the observed population-level responses. In particular “all-or-nothing” encoding mechanisms were involved in the HS-dependent regulation of the IKK activity and IκBα phosphorylation, while others involving transport were “analogue”. In order to discriminate between these mechanisms, we used live-cell imaging of nuclear translocations of the NF-κB p65 subunit. The single cell responses exhibited “all-or-nothing” encoding. While most cells did not respond to TNFα stimulation after a 60 min HS, 27% showed responses similar to those not receiving HS. We further demonstrated experimentally and theoretically that the predicted inhibition of IKK activity was consistent with the observed HS-dependent depletion of the IKKα and IKKβ subunits in whole cell lysates. However, a combination of “all-or-nothing” crosstalk mechanisms was required to completely recapitulate the single cell data. We postulate therefore that the heterogeneity of the single cell responses might be explained by the cell-intrinsic variability of HS-modulated IKK signaling. In summary, we show that high temperature modulates NF-κB responses in single cells in a complex and unintuitive manner, which needs to be considered in hyperthermia-based treatment strategies.

Toll-like receptor (TLR) signaling regulates macrophage activation and effector cytokine propagation in the constrained environment of a tissue. In macrophage populations, TLR4 stimulates the dose-dependent transcription of nuclear factor κB (NF-κB) target genes. However, using single-RNA counting, we found that individual cells exhibited a wide range (three orders of magnitude) of expression of the gene encoding the proinflammatory cytokine tumor necrosis factor–α (TNF-α). The TLR4-induced TNFA transcriptional response correlated with the extent of NF-κB signaling in the cells and their size. We compared the rates of TNF-α production and uptake in macrophages and mouse embryonic fibroblasts and generated a mathematical model to explore the heterogeneity in the response of macrophages to TLR4 stimulation and the propagation of the TNF-α signal in the tissue. The model predicts that the local propagation of the TLR4-dependent TNF-α response and cellular NF-κB signaling are limited to small distances of a few cell diameters between neighboring tissue-resident macrophages. In our predictive model, TNF-α propagation was constrained by competitive uptake of TNF-α from the environment, rather than by heterogeneous production of the cytokine. We propose that the highly constrained architecture of tissues enables effective localized propagation of inflammatory cues while avoiding out-of-context responses at longer distances.

TCR signaling pathways cooperate to activate the inducible transcription factors NF-κB, NFAT, and AP-1. In this study, using the calcium ionophore ionomycin and/or PMA on Jurkat T cells, we show that the gene expression program associated with activation of TCR signaling is closely related to specific chromatin landscapes. We find that calcium and kinase signaling cooperate to induce chromatin remodeling at ∼2100 chromatin regions, which demonstrate enriched binding motifs for inducible factors and correlate with target gene expression. We found that these regions typically function as inducible enhancers. Many of these elements contain composite NFAT/AP-1 sites, which typically support cooperative binding, thus further reinforcing the need for cooperation between calcium and kinase signaling in the activation of genes in T cells. In contrast, treatment with PMA or ionomycin alone induces chromatin remodeling at far fewer regions (∼600 and ∼350, respectively), which mostly represent a subset of those induced by costimulation. This suggests that the integration of TCR signaling largely occurs at the level of chromatin, which we propose plays a crucial role in regulating T cell activation.

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.

Non-steroidal anti-inflammatory drugs (NSAIDs) inhibit cyclooxygenase-1 (COX-1) and COX-2 enzymes. The NLRP3 inflammasome is a multi-protein complex responsible for the processing of the proinflammatory cytokine interleukin-1β and is implicated in many inflammatory diseases. Here we show that several clinically approved and widely used NSAIDs of the fenamate class are effective and selective inhibitors of the NLRP3 inflammasome via inhibition of the volume-regulated anion channel in macrophages, independently of COX enzymes. Flufenamic acid and mefenamic acid are efficacious in NLRP3-dependent rodent models of inflammation in air pouch and peritoneum. We also show therapeutic effects of fenamates using a model of amyloid beta induced memory loss and a transgenic mouse model of Alzheimer’s disease. These data suggest that fenamate NSAIDs could be repurposed as NLRP3 inflammasome inhibitors and Alzheimer’s disease therapeutics.

Interleukin-1β (IL-1β) is a critical regulator of the inflammatory response. IL-1β is not secreted through the conventional ER–Golgi route of protein secretion, and to date its mechanism of release has been unknown. Crucially, its secretion depends upon the processing of a precursor form following the activation of the multimolecular inflammasome complex. Using a novel and reversible pharmacological inhibitor of the IL-1β release process, in combination with biochemical, biophysical, and real-time single-cell confocal microscopy with macrophage cells expressing Venus-labelled IL-1β, we have discovered that the secretion of IL-1β after inflammasome activation requires membrane permeabilisation, and occurs in parallel with the death of the secreting cell. Thus, in macrophages the release of IL-1β in response to inflammasome activation appears to be a secretory process independent of nonspecific leakage of proteins during cell death. The mechanism of membrane permeabilisation leading to IL-1β release is distinct from the unconventional secretory mechanism employed by its structural homologues fibroblast growth factor 2 (FGF2) or IL-1α, a process that involves the formation of membrane pores but does not result in cell death. These discoveries reveal key processes at the initiation of an inflammatory response and deliver new insights into the mechanisms of protein release.

Dynamic cellular systems reprogram gene expression to ensure appropriate cellular fate responses to specific extracellular cues. Here we demonstrate that the dynamics of Nuclear Factor kappa B (NF-κB) signalling and the cell cycle are prioritised differently depending on the timing of an inflammatory signal. Using iterative experimental and computational analyses, we show physical and functional interactions between NF-κB and the E2 Factor 1 (E2F-1) and E2 Factor 4 (E2F-4) cell cycle regulators. These interactions modulate the NF-κB response. In S-phase, the NF-κB response was delayed or repressed, while cell cycle progression was unimpeded. By contrast, activation of NF-κB at the G1/S boundary resulted in a longer cell cycle and more synchronous initial NF-κB responses between cells. These data identify new mechanisms by which the cellular response to stress is differentially controlled at different stages of the cell cycle.

Recent studies suggest that cells make stochastic choices with respect to differentiation or division. However, the molecular mechanism underlying such stochasticity is unknown. We previously proposed that the timing of vertebrate neuronal differentiation is regulated by molecular oscillations of a transcriptional repressor, HES1, tuned by a post-transcriptional repressor, miR-9. Here, we computationally model the effects of intrinsic noise on the Hes1/miR-9 oscillator as a consequence of low molecular numbers of interacting species, determined experimentally. We report that increased stochasticity spreads the timing of differentiation in a population, such that initially equivalent cells differentiate over a period of time. Surprisingly, inherent stochasticity also increases the robustness of the progenitor state and lessens the impact of unequal, random distribution of molecules at cell division on the temporal spread of differentiation at the population level. This advantageous use of biological noise contrasts with the view that noise needs to be counteracted.

The relationship between components of biochemical network and the resulting dynamics of the overall system is a key focus of computational biology. However, as these networks and resulting mathematical models are inherently complex and non-linear, the understanding of this relationship becomes challenging. Among many approaches, model reduction methods provide an avenue to extract components responsible for the key dynamical features of the system. Unfortunately, these approaches often require intuition to apply. In this manuscript we propose a practical algorithm for the reduction of biochemical reaction systems using fast-slow asymptotics. This method allows the ranking of system variables according to how quickly they approach their momentary steady state, thus selecting the fastest for a steady state approximation. We applied this method to derive models of the Nuclear Factor kappa B network, a key regulator of the immune response that exhibits oscillatory dynamics. Analyses with respect to two specific solutions, which corresponded to different experimental conditions identified different components of the system that were responsible for the respective dynamics. This is an important demonstration of how reduction methods that provide approximations around a specific steady state, could be utilised in order to gain a better understanding of network topology in a broader context.

A single cell is inherently noisy. This noise is observed as a variability or heterogeneity between individual cells' responses in an isogenic population, and emerges from fundamental physical process governing state of the cell over time. In practice, states of two seemingly identical cells may be different in the same environment; and in fact the behavior of the population average my not correspond to any of the individual cells. Recent decades brought a technological breakthrough in many areas in our ability to measure and interpret cellular heterogeneity, including live-cell imaging (Spiller et al., 2010) and genome-wide epigenetic and expression analyses (in particular next generation sequencing) (Chattopadhyay et al., 2014). The emerging picture is that the cellular noise is not a nuisance, but a ubiquitous functional trait that could perhaps be therapeutically exploited. Here we discuss relevant technological advances as well as postulate the need for more quantitative and integrated temporal single cell biology approaches to study cellular heterogeneity.

single-cell analysis, single-cell genomics, cellular heterogeneity, biological noise, measuring noise

White's lab established that strong, continuous stimulation with tumour necrosis factor- () can induce sustained oscillations in the subcellular localisation of the transcription factor nuclear factor (NF-). But the intensity of the signal varies substantially, from picomolar in the blood plasma of healthy organisms to nanomolar in diseased states. We report on a systematic survey using computational bifurcation theory to explore the relationship between the intensity of stimulation and the existence of sustained NF- oscillations. Using a deterministic model developed by Ashall et al. in 2009, we find that the system's responses to are characterised by a supercritical Hopf bifurcation point: above a critical intensity of the system exhibits sustained oscillations in NF-kB localisation. For below this critical value, damped oscillations are observed. This picture depends, however, on the values of the model's other parameters. When the values of certain reaction rates are altered the response of the signalling pathway to stimulation changes: in addition to the sustained oscillations induced by high-dose stimulation, a second oscillatory regime appears at much lower doses. Finally, we define scores to quantify the sensitivity of the dynamics of the system to variation in its parameters and use these scores to establish that the qualitative dynamics are most sensitive to the details of NF- mediated gene transcription.

NF-kB signalling pathway, Parameter sensitivity, Bifurcation analysis, Oscillations

Background

Sustained stimulation with tumour necrosis factor alpha (TNF-alpha) induces substantial oscillations—observed at both the single cell and population levels—in the nuclear factor kappa B (NF-kappa B) system. Although the mechanism has not yet been elucidated fully, a core system has been identified consisting of a negative feedback loop involving NF-kappa B (RelA:p50 hetero-dimer) and its inhibitor I-kappa B-alpha. Many authors have suggested that this core oscillator should couple to other oscillatory pathways.
Results

First we analyse single-cell data from experiments in which the NF-kappa B system is forced by short trains of strong pulses of TNF-alpha. Power spectra of the ratio of nuclear-to-cytoplasmic concentration of NF-kappa B suggest that the cells' responses are entrained by the pulsing frequency. Using a recent model of the NF-kappa B system due to Caroline Horton, we carried out extensive numerical simulations to analyze the response frequencies induced by trains of pulses of TNF-alpha stimulation having a wide range of frequencies and amplitudes. These studies suggest that for sufficiently weak stimulation, various nonlinear resonances should be observable. To explore further the possibility of probing alternative feedback mechanisms, we also coupled the model to sinusoidal signals with a wide range of strengths and frequencies. Our results show that, at least in simulation, frequencies other than those of the forcing and the main NF-kappa B oscillator can be excited via sub- and superharmonic resonance, producing quasiperiodic and even chaotic dynamics.
Conclusions

Our numerical results suggest that the entrainment phenomena observed in pulse-stimulated experiments is a consequence of the high intensity of the stimulation. Computational studies based on current models suggest that resonant interactions between periodic pulsatile forcing and the system's natural frequencies may become evident for sufficiently weak stimulation. Further simulations suggest that the nonlinearities of the NF-kappa B feedback oscillator mean that even sinusoidally modulated forcing can induce a rich variety of nonlinear interactions.

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-κB signaling system, the precise timing of a dual-delayed negative feedback motif [involving stochastic transcription of inhibitor κB (IκB)-α and -ε] is optimized to induce heterogeneous timing of NF-κB oscillations between individual cells. We suggest that this dual-delayed negative feedback motif enables NF-κB 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.

Gene expression in living cells is highly dynamic, but temporal patterns of gene expression in intact tissues are largely unknown. The mammalian pituitary gland comprises several intermingled cell types, organised as interdigitated networks that interact functionally to generate co-ordinated hormone secretion. Live-cell imaging was used to quantify patterns of reporter gene expression in dispersed lactotrophic cells or intact pituitary tissue from bacterial artificial chromosome (BAC) transgenic rats in which a large prolactin genomic fragment directed expression of luciferase or destabilised enhanced green fluorescent protein (d2EGFP). Prolactin promoter activity in transgenic pituitaries varied with time across different regions of the gland. Although amplitude of transcriptional responses differed, all regions of the gland displayed similar overall patterns of reporter gene expression over a 50-hour period, implying overall co-ordination of cellular behaviour. By contrast, enzymatically dispersed pituitary cell cultures showed unsynchronised fluctuations of promoter activity amongst different cells, suggesting that transcriptional patterns were constrained by tissue architecture. Short-term, high resolution, single cell analyses in prolactin-d2EGFP transgenic pituitary slice preparations showed varying transcriptional patterns with little correlation between adjacent cells. Together, these data suggest that pituitary tissue comprises a series of cell ensembles, which individually display a variety of patterns of short-term stochastic behaviour, but together yield long-range and long-term coordinated behaviour.

Live-cell, Microscopy, Pituitary, Prolactin, Transcription

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.

NF-

The emergence of biological function from the dynamic control of cellular signalling molecules is a fundamental process in biology. Key questions include: How do cells decipher noisy environmental cues, encode these signals to control fate decisions and propagate information through tissues? Recent advances in systems biology, and molecular and cellular biology, exemplified by analyses of signalling via the transcription factor Nuclear Factor kappaB (NF-κB), reveal a critical role of oscillatory control in the regulation of these biological functions. The emerging view is that the oscillatory dynamics of signalling molecules and the epigenetically regulated specificity for target genes contribute to robust regulation of biological function at different levels of cellular organisation through frequency-dependent information encoding.

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The nuclear factor κB (NF-κB) transcription factor regulates cellular stress responses and the immune response to infection. NF-κB activation results in oscillations in nuclear NF-κB abundance. To define the function of these oscillations, we treated cells with repeated short pulses of tumor necrosis factor–α at various intervals to mimic pulsatile inflammatory signals. At all pulse intervals that were analyzed, we observed synchronous cycles of NF-κB nuclear translocation. Lower frequency stimulations gave repeated full-amplitude translocations, whereas higher frequency pulses gave reduced translocation, indicating a failure to reset. Deterministic and stochastic mathematical models predicted how negative feedback loops regulate both the resetting of the system and cellular heterogeneity. Altering the stimulation intervals gave different patterns of NF-κB–dependent gene expression, which supports the idea that oscillation frequency has a functional role.

Background
The NF-κ B regulatory network controls innate immune response by transducing variety of pathogen-derived and cytokine stimuli into well defined single-cell gene regulatory events.

Results
We analyze the network by means of the model combining a deterministic description for molecular species with large cellular concentrations with two classes of stochastic switches: cell-surface receptor activation by TNFα ligand, and Iκ Bα and A20 genes activation by NF-κ B molecules. Both stochastic switches are associated with amplification pathways capable of translating single molecular events into tens of thousands of synthesized or degraded proteins. Here, we show that at a low TNFα dose only a fraction of cells are activated, but in these activated cells the amplification mechanisms assure that the amplitude of NF-κ B nuclear translocation remains above a threshold. Similarly, the lower nuclear NF-κ B concentration only reduces the probability of gene activation, but does not reduce gene expression of those responding.

Conclusion
These two effects provide a particular stochastic robustness in cell regulation, allowing cells to respond differently to the same stimuli, but causing their individual responses to be unequivocal. Both effects are likely to be crucial in the early immune response: Diversity in cell responses causes that the tissue defense is harder to overcome by relatively simple programs coded in viruses and other pathogens. The more focused single-cell responses help cells to choose their individual fates such as apoptosis or proliferation. The model supports the hypothesis that binding of single TNFα ligands is sufficient to induce massive NF-κ B translocation and activation of NF-κ B dependent genes.

Intrinsic stochasticity plays an essential role in gene regulation because of a small number of involved molecules of DNA, mRNA and protein of a given species. To better understand this phenomenon, small gene regulatory systems are mathematically modeled as systems of coupled chemical reactions, but the existing exact description utilizing a Chapman–Kolmogorov equation or simulation algorithms is limited and inefficient. The present work considers a much more efficient yet accurate modeling approach, which allows analyzing stochasticity in the system in the terms of the underlying distribution function. We depart from the analysis of a single gene regulatory module to find that the mRNA and protein variance is decomposable into additive terms resulting from respective sources of stochasticity. This variance decomposition is asserted by constructing two approximations to the exact stochastic description: First, the continuous approximation, which considers only the stochasticity due to the intermittent gene activity. Second, the mixed approximation, which in addition attributes stochasticity to the mRNA transcription/decay process. Considered approximations yield systems of first order partial differential equations for the underlying distribution function, which can be efficiently solved using developed numerical methods. Single cell simulations and numerical two-dimensional mRNA–protein stationary distribution functions are presented to confirm accuracy of approximating models.

Stochastic gene regulation, Transcriptional noise, Distribution function, Chapman–Kolmogorov equation, Fokker–Planck equation

The higher organisms, eukaryotes, are diploid and most of their genes have two homological copies (alleles). However, the number of alleles in a cell is not constant. In the S phase of the cell cycle all the genome is duplicated and then in the G2 phase and mitosis, which together last for several hours, most of the genes have four copies instead of two. Cancer development is, in many cases, associated with a change in allele number. Several genetic diseases are caused by haploinsufficiency: Lack of one of the alleles or its improper functioning. In the paper we consider the stochastic expression of a gene having a variable number of copies. We applied our previously developed method in which the reaction channels are split into slow (connected with change of gene state) and fast (connected with mRNA/protein synthesis/decay), the later being approximated by deterministic reaction rate equations. As a result we represent gene expression as a piecewise deterministic time-continuous Markov process, which is further related with a system of partial differential hyperbolic equations for probability density functions (pdfs) of protein distribution. The stationary pdfs are calculated analytically for haploidal gene or numerically for diploidal and tetraploidal ones. We distinguished nine classes of simultaneous activation of haploid, diploid and tetraploid genes. This allows for analysis of potential consequences of gene duplication or allele loss. We show that when gene activity is autoregulated by a positive feedback, the change in number of gene alleles may have dramatic consequences for its regulation and may not be compensated by the change of efficiency of mRNA synthesis per allele.

stochastic gene expression, feedback regulation, diploid genes, haploinsufficiency, piecewise deterministic time-continuous Markov process

Living cells may be considered noisy or stochastic biochemical reactors. In eukaryotic cells, in which the number of protein or mRNA molecules is relatively large, the stochastic effects originate primarily in regulation of gene activity. Transcriptional activity of a gene can be initiated by transactivator molecules binding to the specific regulatory site(s) in the target gene. The stochasticity of activator binding and dissociation is amplified by transcription and translation, since target gene activation results in a burst of mRNAs molecules, and each copy of mRNA then serves as a template for numerous protein molecules. In this article, we reformulate our model of the NF-κB regulatory module to analyze a single cell regulation. Ordinary differential equations, used for description of fast reaction channels of processes involving a large number of molecules, are combined with a stochastic switch to account for the activity of the genes involved. The stochasticity in gene transcription causes simulated cells to exhibit large variability. Moreover, none of them behaves like an average cell. Although the average mRNA and protein levels remain constant before tumor necrosis factor (TNF) stimulation, and stabilize after a prolonged TNF stimulation, in any single cell these levels oscillate stochastically in the absence of TNF and keep oscillating under the prolonged TNF stimulation. However, in a short period of ∼90 min, most cells are synchronized by the TNF signal, and exhibit similar kinetics. We hypothesize that this synchronization is crucial for proper activation of early genes controlling inflammation. Our theoretical predictions of single cell kinetics are supported by recent experimental studies of oscillations in NF-κB signaling made on single cells.

Due to the small number of copies of molecular species involved, such as DNA, mRNA and regulatory proteins, gene expression is a stochastic phenomenon. In eukaryotic cells, the stochastic effects primarily originate in regulation of gene activity. Transcription can be initiated by a single transcription factor binding to a specific regulatory site in the target gene. Stochasticity of transcription factor binding and dissociation is then amplified by transcription and translation, since target gene activation results in a burst of mRNA molecules, and each mRNA copy serves as a template for translating numerous protein molecules. In the present paper, we explore a mathematical approach to stochastic modeling. In this approach, the ordinary differential equations with a stochastic component for mRNA and protein levels in a single cells yield a system of first-order partial differential equations (PDEs) for two-dimensional probability density functions (pdf). We consider the following examples: Regulation of a single auto-repressing gene, and regulation of a system of two mutual repressors and of an activator–repressor system. The resulting PDEs are approximated by a system of many ordinary equations, which are then numerically solved.

Gene regulation, Transcription, Stochasticity, Probability density function, Transport-type equations

The stochastic nature of gene regulation still remains not fully understood. In eukaryotes, the stochastic effects are primarily attributable to the binary nature of genes, which are considered either switched “on” or “off” due to the action of the transcription factors binding to the promoter. In the time period when the gene is activated, bursts of mRNA transcript are produced. In the present paper, we investigate regulation of gene expression at the single cell level. We propose a mechanism of gene regulation, which is able to explain the observed distinct transcription profiles assuming the number of co-regulatory activities, without attempting to identify the specific proteins involved. The model is motivated by our experiments on NF-κBκB-dependent genes in HeLa cells. Our experimental data shows that NF-κBκB-dependent genes can be stratified into three characteristic groups according to their expression profiles: early, intermediate and late having maximum of expression at about 1, 3 and 6 h, respectively, from the beging of TNF stimulation. We provide a tractable analytical approach, not only in the terms of expected expression profiles and their moments, which corresponds to the measurements on the cell population, but also in the terms of single cell behavior. Comparison between these two modes of description reveals that single cells behave qualitatively different from the cell population. This analysis provides insights useful for understanding of microarray experiments.

Stochastic gene regulation, Expression profiles, Single cell simulations, NF-κκB