Roles of spatial parameters on the oscillation of nuclear NF-κB: computer simulations of a 3D spherical cell

Negative feedback systems for modelling NF-κB transcription factor oscillatory activity

Low-dimensional negative feedback systems (NFSs) were developed within a signal flow model to describe the oscillatory activities of NF-κB caused by interactions with its inhibitor IκBα. The NFSs were established as 3rd- and 4th-order linear systems containing unperturbed and perturbed negative feedback (NF) loops with constant or time-varying NF strengths and a feed-forward loop. NF-related analytical solutions to the NFSs representing the time courses of NF-κB and IκBα were determined and their exact mathematical relationship was found. The NFS's parameters were determined to fit the experimental time courses of NF-κB in TNF-α-stimulated embryonic fibroblasts, rela-/- embryonic fibroblasts reconstituted with RelA, C9L cells, GFP-p65 knock-in embryonic fibroblasts and embryogenic fibroblasts lacking Iκβ and IκBε, LPS-stimulated IC-21 macrophages treated or not with DCPA, and anti-IgM-stimulated DT40 B-lymphocytes. The unperturbed and perturbed NFSs describing the above biosystems generated isochronous and non-isochronous solutions, depending on a constant or time-varying NF strength, respectively. The oscillation period of the NF-coupled solutions, the phase difference between them and the time delays in the appearance of cytoplasmic IκBα after stimulation of NF-κB were determined. A significant divergence between the IκBα solutions to the NFSs and the IκBα experimental courses led to a rejection of the NF coupling between NF-κB and IκBα in the above biosystems. It was shown that neither the linearity nor the low dimensionality of the NFSs altered the NF relationship and the divergence between the IκBα solutions to the NFS and IκBα experimental time courses. Although the NF relationship between IκBα and NF-κB was not confirmed in all the experimental data analyzed, delayed negative feedback was found in some cases.

Cellular and Mathematical Analyses of LUBAC Involvement in T Cell Receptor-Mediated NF-κB Activation Pathway

The LUBAC ubiquitin ligase complex, composed of the HOIP, HOIL-1L, and SHARPIN subunits, stimulates the canonical nuclear factor-κB (NF-κB) activation pathways through its Met1-linked linear ubiquitination activity. Here we performed cellular and mathematical modeling analyses of the LUBAC involvement in the T cell receptor (TCR)-mediated NF-κB activation pathway, using the Jurkat human T cell line. LUBAC is indispensable for TCR-induced NF-κB and T cell activation, and transiently associates with and linearly ubiquitinates the CARMA1-BCL10-MALT1 (CBM) complex, through the catalytic HOIP subunit. In contrast, the linear ubiquitination of NEMO, a substrate of the TNF-α-induced canonical NF-κB activation pathway, was limited during the TCR pathway. Among deubiquitinases, OTULIN, but not CYLD, plays a major role in downregulating LUBAC-mediated TCR signaling. Mathematical modeling indicated that linear ubiquitination of the CBM complex accelerates the activation of IκB kinase (IKK), as compared with the activity induced by linear ubiquitination of NEMO alone. Moreover, simulations of the sequential linear ubiquitination of the CBM complex suggested that the allosteric regulation of linear (de)ubiquitination of CBM subunits is controlled by the ubiquitin-linkage lengths. These results indicated that, unlike the TNF-α-induced NF-κB activation pathway, the TCR-mediated NF-κB activation in T lymphocytes has a characteristic mechanism to induce LUBAC-mediated NF-κB activation.

Combinatorial dynamics of protein synthesis time delay and negative feedback loop in NF-κB signalling pathway

The transcription factor NF-κB links immune response and inflammatory reaction and its different oscillation patterns determine different cell fates. In this study, a mathematical model with IκBα protein synthesis time delay is developed based on the experimental evidences. The results show that time delay has the ability to drive oscillation of NF-κB via Hopf bifurcation. Meanwhile, the amplitude and period are sensitive to the time delay. Moreover, the time delay threshold is a function of four parameters characterising the negative feedback loop. Likewise, the parameters also have effects on the amplitude and period of NF-κB oscillation induced by time delay. Therefore, the oscillation patterns of NF-κB are collaborative results of time delay coupled with the negative feedback loop. These results not only enhance the understanding of NF-κB biological oscillation but also provide clues for the development of anti-inflammatory or anti-cancer drugs.

NFκB and Kidney Injury

The global burden of chronic kidney disease will increase during the next century. As NFκB, first described more than 30 years ago, plays a major role in immune and non-immune-mediated diseases and in inflammatory and metabolic disorders, this review article summarizes current knowledge on the role of NFκB in in vivo kidney injury and describes the new and so far not completely understood crosstalk between canonical and non-canonical NFκB pathways in T-lymphocyte activation in renal disease.

Modulation of Macrophage Inflammatory Nuclear Factor κB (NF-κB) Signaling by Intracellular Cryptococcus neoformans

Cryptococcus neoformans (Cn) is a common facultative intracellular pathogen that can cause life-threatening fungal meningitis in immunocompromised individuals. Shortly after infection, Cn is detectable as both extra- and intracellular yeast particles, with Cn being capable of establishing long-lasting latent infections within host macrophages. Although recent studies have shown that shed capsular polysaccharides and intact extracellular Cn can compromise macrophage function through modulation of NF-κB signaling, it is currently unclear whether intracellular Cn also affects NF-κB signaling. Utilizing live cell imaging and computational modeling, we find that extra- and intracellular Cn support distinct modes of NF-κB signaling in cultured murine macrophages. Specifically, in RAW 264.7 murine macrophages treated with extracellular glucuronoxylomannan (GXM), the major Cn capsular polysaccharide, LPS-induced nuclear translocation of p65 is inhibited, whereas in cells with intracellular Cn, LPS-induced nuclear translocation of p65 is both amplified and sustained. Mathematical simulations and quantification of nascent protein expression indicate that this is a possible consequence of Cn-induced "translational interference," impeding IκBα resynthesis. We also show that long term Cn infection induces stable nuclear localization of p65 and IκBα proteins in the absence of additional pro-inflammatory stimuli. In this case, nuclear localization of p65 is not accompanied by TNFα or inducible NOS (iNOS) expression. These results demonstrate that capsular polysaccharides and intact intracellular yeast manipulate NF-κB via multiple distinct mechanisms and provide new insights into how Cn might modulate cellular signaling at different stages of an infection.

Regulation of signal transduction by spatial parameters: a case in NF-κB oscillation

NF-κB is a transcription factor regulating expression of more than 500 genes, and its dysfunction leads to the autoimmune and inflammatory diseases. In malignant cancer cells, NF-κB is constitutively activated. Thus the elucidation of mechanisms for NF-κB regulation is important for the establishment of therapeutic treatment caused by incorrect NF-κB responses. Cytoplasmic NF-κB translocates to the nucleus by the application of extracellular stimuli such as cytokines. Nuclear NF-κB is known to oscillate with the cycle of 1.5-4.5 h, and it is thought that the oscillation pattern regulates the expression profiles of genes. In this review, first we briefly describe regulation mechanisms of NF-κB. Next, published computational simulations on the oscillation of NF-κB are summarised. There are at least 60 reports on the computational simulation and analysis of NF-κB oscillation. Third, the importance of a 'space' for the regulation of oscillation pattern of NF-κB is discussed, showing altered oscillation pattern by the change in spatial parameters such as diffusion coefficient, nuclear to cytoplasmic volume ratio (N/C ratio), and transport through nuclear membrane. Finally, simulations in a true intracellular space (TiCS), which is an intracellular 3D space reconstructed in a computer with organelles such as nucleus and mitochondria are discussed.

Regulation of NF-κB Oscillation by Nuclear Transport: Mechanisms Determining the Persistency and Frequency of Oscillation

The activated transcription factor NF-κB shuttles between the cytoplasm and the nucleus resulting in the oscillation of nuclear NF-κB (NF-κB_n). The oscillation pattern of NF-κB_n is implicated in the regulation of gene expression profiles. Using computational models, we previously reported that spatial parameters, such as the diffusion coefficient, nuclear to cytoplasmic volume ratio, transport through the nuclear envelope, and the loci of translation of IκB protein, modified the oscillation pattern of NF-κB_n. In a subsequent report, we elucidated the importance of the “reset” of NF-κB_n (returning of NF-κB to the original level) and of a “reservoir” of IκB in the cytoplasm. When the diffusion coefficient of IκB was large, IκB stored at a distant location from the nucleus diffused back to the nucleus and “reset” NF-κB_n. Herein, we report mechanisms that regulate the persistency and frequency of NF-κB_n oscillation by nuclear transport. Among the four parameters of nuclear transport tested in our spatio-temporal computational model, the export of IκB mRNA from the nucleus regulated the persistency of oscillation. The import of IκB to the nucleus regulated the frequency of oscillation. The remaining two parameters, import and export of NF-κB to and from the nucleus, had virtually no effect on the persistency or frequency. Our analyses revealed that lesser export of IκB mRNA allowed NF-κB_n to transcript greater amounts of IκB mRNA, which was retained in the nucleus, and was subsequently exported to the cytoplasm, where large amounts of IκB were synthesized to “reset” NF-κB_n and drove the persistent oscillation. On the other hand, import of greater amounts of IκB led to an increase in the influx and the efflux of NF-κB to and from the nucleus, resulting in an increase in the oscillation frequency. Our study revealed the importance of nuclear transport in regulating the oscillation pattern of NF-κB_n.

Regulation of nuclear NF-κB oscillation by a diffusion coefficient and its biological implications

The transcription factor NF-κB shuttles between the cytoplasm and the nucleus, and nuclear NF-κB is known to oscillate with a cycle of 1.5-2.5 h following the application of external stimuli. Oscillation pattern of NF-κB is implicated in regulation of the gene expression profile. In a previous report, we found that the oscillation pattern of nuclear NF-κB in a computational 3D spherical cell was regulated by spatial parameters such as nuclear to cytoplasmic volume ratio, nuclear transport, locus of protein synthesis, and diffusion coefficient. Here we report analyses and a biological implication for the regulation of oscillation pattern by diffusion coefficient. Our analyses show that the “reset” of nuclear NF-κB, defined as the return of nuclear NF-κB to the initial level or lower, was crucial for the oscillation; this was confirmed by the flux analysis. In addition, we found that the distant cytoplasmic location from the nucleus acted as a “reservoir” for storing newly synthesized IκBα. When the diffusion coefficient of proteins was large (≥10⁻¹¹ m²/s), a larger amount of IκBα was stored in the “reservoir” with a large flux by diffusion. Subsequently, stored IκBα diffused back to the nucleus, where nuclear NF-κB was “reset” to the initial state. This initiated the next oscillation cycle. When the diffusion coefficient was small (≤10⁻¹³ m²/s), oscillation of nuclear NF-κB was not observed because a smaller amount of IκBα was stored in the “reservoir” and there was incomplete “reset” of nuclear NF-κB. If the diffusion coefficient for IκBα was increased to 10⁻¹¹ m²/s keeping other proteins at 10⁻¹³ m²/s, the oscillation was rescued confirming the “reset” and “reservoir” hypothesis. Finally, we showed altered effective value of diffusion coefficient by diffusion obstacles. Thus, organelle crowding seen in stressed cells possibly changes the oscillation pattern by controlling the effective diffusion coefficient.

A minimal spatio-temporal model of the NF-κB signalling pathway exhibits a range of behaviours

In animal cells, the transcription factor NF-κB regulates many stressful, inflammatory, and innate immune responses. Experiments have revealed that, in response to cell stimulation, NF-κB can exhibit oscillatory dynamics where the nature of these dynamics can influence the pattern of NF-κB-dependent gene expression. Oscillations in NF-κB are believed to depend on a negative feedback loop linking NF-κB and one of its downstream products, namely IκBα. This negative feedback loop is enhanced by cell stimulation. However, it also exists in the absence of cell stimulation. Here we propose a minimal spatio-temporal model of the NF-κB signalling pathway, composed of partial differential equations. Through numerical simulations, we find various combinations of behaviours before and during cell stimulation: equilibrium dynamics (rapid convergence to a solution that is everywhere constant) before cell stimulation, followed by oscillatory dynamics during cell stimulation; oscillatory dynamics before and during cell stimulation; oscillatory dynamics before cell stimulation, followed by equilibrium dynamics during cell stimulation; and equilibrium dynamics before and during cell stimulation. In each case, when cell stimulation ceases, the model quickly returns to its pre-stimulation behaviour. All of these different combinations of behaviours occur for similar sets of parameter values. Therefore, our results may help to explain why, in experiments on the NF-κB pathway involving populations of cells, only a certain fraction of the cells exhibit oscillatory dynamics.

Spatial chaos and complexity in the intracellular space of cancer and normal cells

Background

One of the most challenging problems in biological image analysis is the quantification of the dynamical mechanism and complexity of the intracellular space. This paper investigates potential spatial chaos and complex behavior of the intracellular space of typical cancer and normal cell images whose structural details are revealed by the combination of scanning electron microscopy and focused ion beam systems. Such numerical quantifications have important implications for computer modeling and simulation of diseases.

Methods

Cancer cell lines derived from a human head and neck squamous cell carcinoma (SCC-61) and normal mouse embryonic fibroblast (MEF) cells produced by focused ion beam scanning electron microscopes were used in this study. Spatial distributions of the organelles of cancer and normal cells can be analyzed at both short range and long range of the bounded dynamical system of the image space, depending on the orientations of the spatial cell. A procedure was designed for calculating the largest Lyapunov exponent, which is an indicator of the potential chaotic behavior in intracellular images. Furthermore, the sample entropy and regularity dimension were applied to measure the complexity of the intracellular images.

Results

Positive values of the largest Lyapunov exponents (LLEs) of the intracellular space of the SCC-61 were obtained in different spatial orientations for both long-range and short-range models, suggesting the chaotic behavior of the cell. The MEF has smaller positive values of LLEs in the long range than those of the SCC-61, and zero vales of the LLEs in the short range analysis, suggesting a non-chaotic behavior. The intracellular space of the SCC-61 is found to be more complex than that of the MEF. The degree of complexity measured in the spatial distribution of the intracellular space in the diagonal direction was found to be approximately twice larger than the complexity measured in the horizontal and vertical directions.

Conclusion

Initial findings are promising for characterizing different types of cells and therefore useful for studying cancer cells in the spatial domain using state-of-the-art imaging technology. The measures of the chaotic behavior and complexity of the spatial cell will help computational biologists gain insights into identifying associations between the oscillation patterns and spatial parameters of cells, and appropriate model for simulating cancer cell signaling networks for cancer treatment and new drug discovery.