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Abstract:
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.

Abstract:
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.

Abstract:
The innate immune system processes pathogen-induced signals into cell fate decisions. How information is turned to decision remains unknown. By combining stochastic mathematical modelling and experimentation, we demonstrate that feedback interactions between the IRF3, NF-κB and STAT pathways lead to switch-like responses to a viral analogue, poly(I:C), in contrast to pulse-like responses to bacterial LPS. Poly(I:C) activates both IRF3 and NF-κB, a requirement for induction of IFNβ expression. Autocrine IFNβ initiates a JAK/STAT-mediated positive-feedback stabilising nuclear IRF3 and NF-κB in first responder cells. Paracrine IFNβ, in turn, sensitises second responder cells through a JAK/STAT-mediated positive feedforward pathway that upregulates the positive-feedback components: RIG-I, PKR and OAS1A. In these sensitised cells, the 'live-or-die' decision phase following poly(I:C) exposure is shorter—they rapidly produce antiviral responses and commit to apoptosis. The interlinked positive feedback and feedforward signalling is key for coordinating cell fate decisions in cellular populations restricting pathogen spread.

Keywords:
cellular signalling networks, innate immunity, regulatory networks, stochastic modelling

Abstract:
We present an integrated dynamical cross-talk model of the epithelial innate immune reponse (IIR) incorporating RIG-I and TLR3 as the two major pattern recognition receptors (PRR) converging on the RelA and IRF3 transcriptional effectors. bioPN simulations reproduce biologically relevant gene-and protein abundance measurements in response to time course, gene silencing and dose-response perturbations both at the population and single cell level. Our computational predictions suggest that RelA and IRF3 are under auto- and cross-regulation. We predict, and confirm experimentally, that RIG-I mRNA expression is controlled by IRF7. We also predict the existence of a TLR3-dependent, IRF3-independent transcription factor (or factors) that control(s) expression of MAVS, IRF3 and members of the IKK family. Our model confirms the observed dsRNA dose-dependence of oscillatory patterns in single cells, with periods of 1–3 hr. Model fitting to time series, matched by knockdown data suggests that the NF-κB module operates in a different regime (with different coefficient values) than in the TNFα-stimulation experiments. In future studies, this model will serve as a foundation for identification of virus-encoded IIR antagonists and examination of stochastic effects of viral replication.

Our model generates simulated time series, which reproduce the noisy oscillatory patterns of activity (with 1–3 hour period) observed in individual cells. Our work supports the hypothesis that the IIR is a phenomenon that emerged by evolution despite highly variable responses at an individual cell level.

Abstract:
Bistable regulatory elements are important for nongenetic inheritance, increase of cell-to-cell heterogeneity allowing adaptation, and robust responses at the population level. Here, we study computationally the bistable genetic toggle switch—a small regulatory network consisting of a pair of mutual repressors—in growing and dividing bacteria. We show that as cells with an inhibited growth exhibit high stability of toggle states, cell growth and divisions lead to a dramatic increase of toggling rates. The toggling rates were found to increase with rate of cell growth, and can be up to six orders of magnitude larger for fast growing cells than for cells with the inhibited growth. The effect is caused mainly by the increase of protein and mRNA burst sizes associated with the faster growth. The observation that fast growth dramatically destabilizes toggle states implies that rapidly growing cells may vigorously explore the epigenetic landscape enabling nongenetic evolution, while cells with inhibited growth adhere to the local optima. This can be a clever population strategy that allows the slow growing (but stress resistant) cells to survive long periods of unfavorable conditions. Simultaneously, at favorable conditions, this stress resistant (but slowly growing—or not growing) subpopulation may be replenished due to a high switching rate from the fast growing population.

Keywords:
Gene expression, Bistability, Stochastic processes, Genetic toggle switch, Cell growth and division

Abstract:
The paper concerns the problem of fitting mathematical models of cell signaling pathways. Such models frequently take the form of sets of nonlinear ordinary differential equations. While the model is continuous in time, the performance index used in the fitting procedure involves measurements taken at discrete time moments. Adjoint sensitivity analysis is a tool which can be used for finding the gradient of a performance index in the space of parameters of the model. In the paper, a structural formulation of adjoint sensitivity analysis called the Generalized Backpropagation Through Time (GBPTT) is used. The method is especially suited for hybrid, continuous-discrete time systems. As an example, we use the mathematical model of the NF-kB regulatory module, which plays a major role in the innate immune response in animals.

Keywords:
Biology and genetics, modeling, ordinary differential equations, parameter learni

Abstract:
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.

Abstract:
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.

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

Abstract:
In the article, we discuss the state of art and perspectives in deterministic and stochastic models of NFκB regulatory module. The NFκB is a transcription factor controlling various immune responses including inflammation and apoptosis. It is tightly regulated by at least two negative feedback loops involving IκBα and A20. This mode of regulation results in nucleus-to-cytoplasm oscillations in NFκB localization, which induce subsequent waves of NFκB responsive genes. Single cell experiments carried by several groups provided comprehensive evidence that stochastic effects play an important role in NFκB regulation. From modeling point of view, living cells might be considered noisy or stochastic biochemical reactors. In eukaryotic cells, in which the number of protein or mRNA molecules is relatively large, stochastic effects primarily originate in regulation of gene activity. Transcriptional activity of a gene can be initiated by trans-activator molecules binding to the specific regulatory site(s) in the target gene. The stochastic event of gene activation is amplified by transcription and translation, since it results in a burst of mRNA molecules, and each copy of mRNA then serves as a template for numerous protein molecules. Another potential source of variability can be receptors activation. At low-dose stimulation, important in cell-to-cell signaling, the number of active receptors can be low enough to introduce substantial noise to downstream signaling. Stochastic modeling confirms the large variability in cell responses and shows that no cell behaves like an “average” cell. This high cell-to-cell variability can be one of the weapons of the immune defense. Such non-deterministic defense may be harder to overcome by relatively simple programs coded in viruses and other pathogens.

Keywords:
Mathematical modeling, Systems biology, Immune response, NFκB, Stochastic regulation, Stochastic robustness, Single cell

Abstract:
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.

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

Abstract:
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.

Abstract:
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.

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