Deterministic and stochastic models of NFkappaB pathway

Systems approaches to investigate the role of NF-κB signaling in aging

The nuclear factor-κB (NF-κB) signaling pathway is one of the most well-studied pathways related to inflammation, and its involvement in aging has attracted considerable attention. As aging is a complex phenomenon and is the result of a multi-step process, the involvement of the NF-κB pathway in aging remains unclear. To elucidate the role of NF-κB in the regulation of aging, different systems biology approaches have been employed. A multi-omics data-driven approach can be used to interpret and clarify unknown mechanisms but cannot generate mechanistic regulatory structures alone. In contrast, combining this approach with a mathematical modeling approach can identify the mechanistics of the phenomena of interest. The development of single-cell technologies has also helped clarify the heterogeneity of the NF-κB response and underlying mechanisms. Here, we review advances in the understanding of the regulation of aging by NF-κB by focusing on omics approaches, single-cell analysis, and mathematical modeling of the NF-κB network.

A Quantitative Modular Modeling Approach Reveals the Effects of Different A20 Feedback Implementations for the NF-kB Signaling Dynamics

Signaling pathways involve complex molecular interactions and are controled by non-linear regulatory mechanisms. If details of regulatory mechanisms are not fully elucidated, they can be implemented by different, equally reasonable mathematical representations in computational models. The study presented here focusses on NF-κB signaling, which is regulated by negative feedbacks via IκBα and A20. A20 inhibits NF-κB activation indirectly through interference with proteins that transduce the signal from the TNF receptor complex to activate the IκB kinase (IKK) complex. A number of pathway models has been developed implementing the A20 effect in different ways. We here focus on the question how different A20 feedback implementations impact the dynamics of NF-κB. To this end, we develop a modular modeling approach that allows combining previously published A20 modules with a common pathway core module. The resulting models are fitted to a published comprehensive experimental data set and therefore show quantitatively comparable NF-κB dynamics. Based on defined measures for the initial and long-term behavior we analyze the effects of a wide range of changes in the A20 feedback strength, the IκBα feedback strength and the TNFα stimulation strength on NF-κB dynamics. This shows similarities between the models but also model-specific differences. In particular, the A20 feedback strength and the TNFα stimulation strength affect initial and long-term NF-κB concentrations differently in the analyzed models. We validated our model predictions experimentally by varying TNFα concentrations applied to HeLa cells. These time course data indicate that only one of the A20 feedback models appropriately describes the impact of A20 on the NF-κB dynamics in this cell type.

Identification of a time-varying intracellular signalling model through data clustering and parameter selection: application to NF-[inline-formula removed]B signalling pathway induced by LPS in the presence of BFA

Developing a model for a signalling pathway requires several iterations of experimentation and model refinement to obtain an accurate model. However, the implementation of such an approach to model a signalling pathway induced by a poorly-known stimulus can become labour intensive because only limited information on the pathway is available beforehand to formulate an initial model. Therefore, a large number of iterations are required since the initial model is likely to be erroneous. In this work, a numerical scheme is proposed to construct a time-varying model for a signalling pathway induced by a poorly-known stimulus when its nominal model is available in the literature. Here, the nominal model refers to one that describes the signalling dynamics under a well-characterised stimulus. First, global sensitivity analysis is implemented on the nominal model to identify the most important parameters, which are assumed to be piecewise constants. Second, measurement data are clustered to determine temporal subdomains where the parameters take different values. Finally, a least-squares problem is solved to estimate the parameter values in each temporal subdomain. The effectiveness of this approach is illustrated by developing a time-varying model for NF-[inline-formula removed]B signalling dynamics induced by lipopolysaccharide in the presence of brefeldin A.

Controlling Nuclear NF-κB Dynamics by β-TrCP-Insights from a Computational Model

The canonical nuclear factor kappa-light-chain-enhancer of activated B cells (NF-κB) signaling pathway regulates central processes in mammalian cells and plays a fundamental role in the regulation of inflammation and immunity. Aberrant regulation of the activation of the transcription factor NF-κB is associated with severe diseases such as inflammatory bowel disease and arthritis. In the canonical pathway, the inhibitor IκB suppresses NF-κB’s transcriptional activity. NF-κB becomes active upon the degradation of IκB, a process that is, in turn, regulated by the β-transducin repeat-containing protein (β-TrCP). β-TrCP has therefore been proposed as a promising pharmacological target in the development of novel therapeutic approaches to control NF-κB’s activity in diseases. This study explores the extent to which β-TrCP affects the dynamics of nuclear NF-κB using a computational model of canonical NF-κB signaling. The analysis predicts that β-TrCP influences the steady-state concentration of nuclear NF-κB, as well as changes characteristic dynamic properties of nuclear NF-κB, such as fold-change and the duration of its response to pathway stimulation. The results suggest that the modulation of β-TrCP has a high potential to regulate the transcriptional activity of NF-κB.

Targeting Oncogenic Nuclear Factor Kappa B Signaling with Redox-Active Agents for Cancer Treatment

SIGNIFICANCE

Nuclear factor kappa B (NF-κB) signaling is essential under physiologically relevant conditions. However, aberrant activation of this pathway plays a pertinent role in tumorigenesis and contributes to resistance. Recent Advances: The importance of the NF-κB pathway means that its targeting must be specific to avoid side effects. For many currently used therapeutics and those under development, the ability to generate reactive oxygen species (ROS) is a promising strategy.

CRITICAL ISSUES

As cancer cells exhibit greater ROS levels than their normal counterparts, they are more sensitive to additional ROS, which may be a potential therapeutic niche. It is known that ROS are involved in (i) the activation of NF-κB signaling, when in sublethal amounts; and (ii) high levels induce cytotoxicity resulting in apoptosis. Indeed, ROS-induced cytotoxicity is valuable for its capabilities in killing cancer cells, but establishing the potency of ROS for effective inhibition of NF-κB signaling is necessary. Indeed, some cancer treatments, currently used, activate NF-κB and may stimulate oncogenesis and confer resistance.

FUTURE DIRECTIONS

Thus, combinatorial approaches using ROS-generating agents alongside conventional therapeutics may prove an effective tactic to reduce NF-κB activity to kill cancer cells. One strategy is the use of thiosemicarbazones, which form redox-active metal complexes that generate high ROS levels to deliver potent antitumor activity. These agents also upregulate the metastasis suppressor, N-myc downstream regulated gene 1 (NDRG1), which functions as an NF-κB signaling inhibitor. It is proposed that targeting NF-κB signaling may proffer a new therapeutic niche to improve the efficacy of anticancer regimens.

Computational Modelling of Cancer Development and Growth: Modelling at Multiple Scales and Multiscale Modelling

In this paper, we present two mathematical models related to different aspects and scales of cancer growth. The first model is a stochastic spatiotemporal model of both a synthetic gene regulatory network (the example of a three-gene repressilator is given) and an actual gene regulatory network, the NF-[Formula: see text]B pathway. The second model is a force-based individual-based model of the development of a solid avascular tumour with specific application to tumour cords, i.e. a mass of cancer cells growing around a central blood vessel. In each case, we compare our computational simulation results with experimental data. In the final discussion section, we outline how to take the work forward through the development of a multiscale model focussed at the cell level. This would incorporate key intracellular signalling pathways associated with cancer within each cell (e.g. p53-Mdm2, NF-[Formula: see text]B) and through the use of high-performance computing be capable of simulating up to [Formula: see text] cells, i.e. the tissue scale. In this way, mathematical models at multiple scales would be combined to formulate a multiscale computational model.

Importins promote high-frequency NF-κB oscillations increasing information channel capacity

Background

Importins and exportins influence gene expression by enabling nucleocytoplasmic shuttling of transcription factors. A key transcription factor of innate immunity, NF-κB, is sequestered in the cytoplasm by its inhibitor, IκBα, which masks nuclear localization sequence of NF-κB. In response to TNFα or LPS, IκBα is degraded, which allows importins to bind NF-κB and shepherd it across nuclear pores. NF-κB nuclear activity is terminated when newly synthesized IκBα enters the nucleus, binds NF-κB and exportin which directs the complex to the cytoplasm. Although importins/exportins are known to regulate spatiotemporal kinetics of NF-κB and other transcription factors governing innate immunity, the mechanistic details of these interactions have not been elucidated and mathematically modelled.

Results

Based on our quantitative experimental data, we pursue NF-κB system modelling by explicitly including NF-κB–importin and IκBα–exportin binding to show that the competition between importins and IκBα enables NF-κB nuclear translocation despite high levels of IκBα. These interactions reduce the effective relaxation time and allow the NF-κB regulatory pathway to respond to recurrent TNFα pulses of 45-min period, which is about twice shorter than the characteristic period of NF-κB oscillations. By stochastic simulations of model dynamics we demonstrate that randomly appearing, short TNFα pulses can be converted to essentially digital pulses of NF-κB activity, provided that intervals between input pulses are not shorter than 1 h.

Conclusions

By including interactions involving importin-α and exportin we bring the modelling of spatiotemporal kinetics of transcription factors to a more mechanistic level. Basing on the analysis of the pursued model we estimated the information transmission rate of the NF-κB pathway as 1 bit per hour.

Reviewers

This article was reviewed by Marek Kimmel, James Faeder and William Hlavacek.

Electronic supplementary material

The online version of this article (doi:10.1186/s13062-016-0164-z) contains supplementary material.

Spontaneous NF-κB activation by autocrine TNFα signaling: a computational analysis

NF-κB is a key transcription factor that regulates innate immune response. Its activity is tightly controlled by numerous feedback loops, including two negative loops mediated by NF-κB inducible inhibitors, IκBα and A20, which assure oscillatory responses, and by positive feedback loops arising due to the paracrine and autocrine regulation via TNFα, IL-1 and other cytokines. We study the NF-κB system of interlinked negative and positive feedback loops, combining bifurcation analysis of the deterministic approximation with stochastic numerical modeling. Positive feedback assures the existence of limit cycle oscillations in unstimulated wild-type cells and introduces bistability in A20-deficient cells. We demonstrated that cells of significant autocrine potential, i.e., cells characterized by high secretion of TNFα and its receptor TNFR1, may exhibit sustained cytoplasmic-nuclear NF-κB oscillations which start spontaneously due to stochastic fluctuations. In A20-deficient cells even a small TNFα expression rate qualitatively influences system kinetics, leading to long-lasting NF-κB activation in response to a short-pulsed TNFα stimulation. As a consequence, cells with impaired A20 expression or increased TNFα secretion rate are expected to have elevated NF-κB activity even in the absence of stimulation. This may lead to chronic inflammation and promote cancer due to the persistent activation of antiapoptotic genes induced by NF-κB. There is growing evidence that A20 mutations correlate with several types of lymphomas and elevated TNFα secretion is characteristic of many cancers. Interestingly, A20 loss or dysfunction also leaves the organism vulnerable to septic shock and massive apoptosis triggered by the uncontrolled TNFα secretion, which at high levels overcomes the antiapoptotic action of NF-κB. It is thus tempting to speculate that some cancers of deregulated NF-κB signaling may be prone to the pathogen-induced apoptosis.

Noisy transcription factor NF-κB oscillations stabilize and sensitize cytokine signaling in space

NF-κB is a major transcription factor mediating inflammatory response. In response to a pro-inflammatory stimulus, it exhibits a characteristic response-a pulse followed by noisy oscillations in concentrations of considerably smaller amplitude. NF-κB is an important mediator of cellular communication, as it is both activated by and upregulates production of cytokines, signals used by white blood cells to find the source of inflammation. While the oscillatory dynamics of NF-κB has been extensively investigated both experimentally and theoretically, the role of the noise and the lower secondary amplitude has not been addressed. We use a cellular automaton model to address these issues in the context of spatially distributed communicating cells. We find that noisy secondary oscillations stabilize concentric wave patterns, thus improving signal quality. Furthermore, both lower secondary amplitude as well as noise in the oscillation period might be working against chronic inflammation, the state of self-sustained and stimulus-independent excitations. Our findings suggest that the characteristic irregular secondary oscillations of lower amplitude are not accidental. On the contrary, they might have evolved to increase robustness of the inflammatory response and the system's ability to return to a pre-stimulated state.

Single-cell and population NF-κB dynamic responses depend on lipopolysaccharide preparation

Background

Lipopolysaccharide (LPS), found in the outer membrane of gram-negative bacteria, elicits a strong response from the transcription factor family Nuclear factor (NF)-κB via Toll-like receptor (TLR) 4. The cellular response to lipopolysaccharide varies depending on the source and preparation of the ligand, however. Our goal was to compare single-cell NF-κB dynamics across multiple sources and concentrations of LPS.

Methodology/Principal Findings

Using live-cell fluorescence microscopy, we determined the NF-κB activation dynamics of hundreds of single cells expressing a p65-dsRed fusion protein. We used computational image analysis to measure the nuclear localization of the fusion protein in the cells over time. The concentration range spanned up to nine orders of magnitude for three E. coli LPS preparations. We find that the LPS preparations induce markedly different responses, even accounting for potency differences. We also find that the ability of soluble TNF receptor to affect NF-κB dynamics varies strikingly across the three preparations.

Conclusions/Significance

Our work strongly suggests that the cellular response to LPS is highly sensitive to the source and preparation of the ligand. We therefore caution that conclusions drawn from experiments using one preparation may not be applicable to LPS in general.

Lessons from mathematically modeling the NF-κB pathway

Mathematical modeling has proved to be a critically important approach in the study of many complex networks and dynamic systems in physics, engineering, chemistry, and biology. The nuclear factor κB (NF-κB) system consists of more than 50 proteins and protein complexes and is both a highly networked and dynamic system. To date, mathematical modeling has only addressed a small fraction of the molecular species and their regulation, but when employed in conjunction with experimental analysis has already led to important insights. Here, we provide a personal account of studying how the NF-κB signaling system functions using mathematical descriptions of the molecular mechanisms. We focus on the insights gained about some of the key regulatory components: the control of the steady state, the signaling dynamics, and signaling crosstalk. We also discuss the biological relevance of these regulatory systems properties.

High-throughput, single-cell NF-κB dynamics

Single cells in a population often respond differently to perturbations in the environment. Live-cell microscopy has enabled scientists to observe these differences at the single-cell level. Some advantages of live-cell imaging over population-based methods include better time resolution, higher sensitivity, automation, and richer datasets. One specific area where live-cell microscopy has made a significant impact is the field of NF-κB signaling dynamics, and recent efforts have focused on making live-cell imaging of these dynamics more high-throughput. We highlight the major aspects of increasing throughput and describe a current system that can monitor, image and analyze the NF-κB activation of thousands of single cells in parallel.

Systems engineering medicine: engineering the inflammation response to infectious and traumatic challenges

The complexity of the systemic inflammatory response and the lack of a treatment breakthrough in the treatment of pathogenic infection demand that advanced tools be brought to bear in the treatment of severe sepsis and trauma. Systems medicine, the translational science counterpart to basic science's systems biology, is the interface at which these tools may be constructed. Rapid initial strides in improving sepsis treatment are possible through the use of phenomenological modelling and optimization tools for process understanding and device design. Higher impact, and more generalizable, treatment designs are based on mechanistic understanding developed through the use of physiologically based models, characterization of population variability, and the use of control-theoretic systems engineering concepts. In this review we introduce acute inflammation and sepsis as an example of just one area that is currently underserved by the systems medicine community, and, therefore, an area in which contributions of all types can be made.

An iterative identification procedure for dynamic modeling of biochemical networks

Background

Mathematical models provide abstract representations of the information gained from experimental observations on the structure and function of a particular biological system. Conferring a predictive character on a given mathematical formulation often relies on determining a number of non-measurable parameters that largely condition the model's response. These parameters can be identified by fitting the model to experimental data. However, this fit can only be accomplished when identifiability can be guaranteed.

Results

We propose a novel iterative identification procedure for detecting and dealing with the lack of identifiability. The procedure involves the following steps: 1) performing a structural identifiability analysis to detect identifiable parameters; 2) globally ranking the parameters to assist in the selection of the most relevant parameters; 3) calibrating the model using global optimization methods; 4) conducting a practical identifiability analysis consisting of two (a priori and a posteriori) phases aimed at evaluating the quality of given experimental designs and of the parameter estimates, respectively and 5) optimal experimental design so as to compute the scheme of experiments that maximizes the quality and quantity of information for fitting the model.

Conclusions

The presented procedure was used to iteratively identify a mathematical model that describes the NF-κB regulatory module involving several unknown parameters. We demonstrated the lack of identifiability of the model under typical experimental conditions and computed optimal dynamic experiments that largely improved identifiability properties.

A noisy paracrine signal determines the cellular NF-kappaB response to lipopolysaccharide

Nearly identical cells can exhibit substantially different responses to the same stimulus. We monitored the nuclear localization dynamics of nuclear factor kappaB (NF-kappaB) in single cells stimulated with tumor necrosis factor-alpha (TNF-alpha) and lipopolysaccharide (LPS). Cells stimulated with TNF-alpha have quantitative differences in NF-kappaB nuclear localization, whereas LPS-stimulated cells can be clustered into transient or persistent responders, representing two qualitatively different groups based on the NF-kappaB response. These distinct behaviors can be linked to a secondary paracrine signal secreted at low concentrations, such that not all cells undergo a second round of NF-kappaB activation. From our single-cell data, we built a computational model that captures cell variability, as well as population behaviors. Our findings show that mammalian cells can create "noisy" environments to produce diversified responses to stimuli.

Postrecruitment regulation of RNA polymerase II directs rapid signaling responses at the promoters of estrogen target genes

Under classical models for signal-dependent transcription in eukaryotes, DNA-binding activator proteins regulate the recruitment of RNA polymerase II (Pol II) to a set of target promoters. However, recent studies, as well as our results herein, show that Pol II is widely distributed (i.e., "preloaded") at the promoters of many genes prior to specific signaling events. How Pol II recruitment and Pol II preloading fit within a unified model of gene regulation is unclear. In addition, the mechanisms through which cellular signals activate preloaded Pol II across mammalian genomes remain largely unknown. We show here that the predominant genomic outcome of estrogen signaling is the postrecruitment regulation of Pol II activity at target gene promoters, likely through specific changes in Pol II phosphorylation rather than through recruitment of Pol II to the promoters. Furthermore, we show that negative elongation factor binds to estrogen target promoters in conjunction with preloaded Pol II and represses gene expression until the appropriate signal is received. Finally, our studies reveal that the estrogen-dependent activation of preloaded Pol II facilitates rapid gene regulatory responses which play important physiological roles in regulating estrogen signaling itself. Our results reveal a broad use of postrecruitment Pol II regulation by the estrogen signaling pathway, a mode of regulation that is likely to apply to a wide variety of signal-regulated pathways.

Single TNFalpha trimers mediating NF-kappaB activation: stochastic robustness of NF-kappaB signaling

Background

The NF-κB 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 IκBα and A20 genes activation by NF-κB 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-κB nuclear translocation remains above a threshold. Similarly, the lower nuclear NF-κB 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-κB translocation and activation of NF-κB dependent genes.