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. 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. 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.

Nuclear factors p53 and NF-κB control many physiological processes including cell cycle arrest, DNA repair, apoptosis, death, innate and adaptive immune responses, and inflammation. There are numerous pathways linking these systems and there is a bulk of evidence for cooperation as well as for antagonisms between p53 and NF-κB. In this theoretical study, the authors use earlier models of p53 and NF-κB systems and construct a crosstalk model of p53–NF-κB network in order to explore the consequences of the two-way coupling, in which NF-κB upregulates the transcription of p53, whereas in turn p53 attenuates transcription of NF-κB inhibitors IκBα and A20. We consider a number of protocols in which cells are stimulated by tumour necrosis factor-α (TNFα) (that activates NF-κB pathway) and/or gamma irradiation (that activates p53 pathway). The authors demonstrate that NF-κB may have both anti- and pro-apoptotic roles. TNFα stimulation, preceding DNA damaging irradiation, makes cells more resistant to irradiation-induced apoptosis, whereas the same TNFα stimulation, when preceded by irradiation, increases the apoptotic cell fraction. The finding suggests that diverse roles of NF-κB in apoptosis and cancer could be related to the dynamical context of activation of p53 and NF-κB pathways. [Includes supplementary material]

In this work we investigate, by means of a computational stochastic model, how tumor cells with wild-type p53 gene respond to the drug Nutlin, an agent that interferes with the Mdm2-mediated p53 regulation. In particular, we show how the stochastic gene-switching controlled by p53 can explain experimental dose-response curves, i.e., the observed inter-cell variability of the cell viability under Nutlin action. The proposed model describes in some detail the regulation network of p53, including the negative feedback loop mediated by Mdm2 and the positive loop mediated by PTEN, as well as the reversible inhibition of Mdm2 caused by Nutlin binding. The fate of the individual cell is assumed to be decided by the rising of nuclear-phosphorylated p53 over a certain threshold. We also performed in silico experiments to evaluate the dose-response curve after a single drug dose delivered in mice, or after its fractionated administration. Our results suggest that dose-splitting may be ineffective at low doses and effective at high doses. This complex behavior can be due to the interplay among the existence of a threshold on the p53 level for its cell activity, the nonlinearity of the relationship between the bolus dose and the peak of active p53, and the relatively fast elimination of the drug. P53 is an antitumor gene regulating vital cellular functions such as repair of DNA damage, cellular suicide, and cell proliferation: in many tumors p53 is lowly expressed and/or mutated. Drugs targeting the biomolecular network of p53 are becoming important. The network includes the key proteins Mdm2 and PTEN, whose production is regulated by p53, and which, in turn, enact positive and negative feedbacks on p53. Drug Nutlin, inhibiting the p53 inhibitor Mdm2, might be important for tumors where p53 is underproduced but unmutated. We investigate the cellular mechanism of action of Nutlin. The basic concept of our mathematical model is that the experimentally observed cell-to-cell variability of Nutlin efficacy is caused by the randomness of gene activation/deactivation of Mdmd2 and PTEN. Indeed, the abundance/scarceness of p53 regulates the probability that the relative genes are active or inactive. The model reproduced the experimental cell-specific response to different doses of Nutlin (dose-response curves) in some types of tumor cells. Much clinical research focus on 'metronomic' drug delivery regimens, where instead of giving large doses with long intervals, smaller doses are frequently delivered. In our simulations, dose-splitting of Nutlin produced a response generally worse than the response to a single dose.

Ataxia telangiectasia mutated (ATM) is a detector of double-strand breaks (DSBs) and a crucial component of the DNA damage response (DDR) along with p53 and NF- κB transcription factors and Wip1 phosphatase. Despite the recent advances in studying the DDR, the mechanisms of cell fate determination after DNA damage induction is still poorly understood. To investigate the importance of various DDR elements with particular emphasis on Wip1, we developed a novel mathematical model of ATM/p53/NF- κB pathways. Our results from in silico and in vitro experiments performed on U2-OS cells with Wip1 silenced to 25 % (Wip1-RNAi) revealed a strong dependence of cellular response to DNA damages on this phosphatase. Notably, Wip1-RNAi cells exhibited lower resistance to ionizing radiation (IR) resulting in smaller clonogenicity and higher apoptotic fraction. In this article, we demonstrated that Wip1 plays a role as a gatekeeper of apoptosis and influences the pro-survival behaviour of cells – the level of Wip1 increases to block the apoptotic decision when DNA repair is successful. Moreover, we were able to verify the dynamics of proteins and transcripts, apoptotic fractions and cells viability obtained from stochastic simulations using in vitro approaches. Taken together, we demonstrated that the model can be successfully used in prediction of cellular behaviour after exposure to IR. Thus, our studies may provide further insights into key elements involved in the underlying mechanisms of the DDR.

A number of regulatory networks have the potential to generate sustained oscillations of irregular amplitude, but well conserved period. Single-cell experiments revealed that in p53 and nuclear factor (NF)-κB systems the oscillation period is homogenous in cell populations, insensitive to the strength of the stimulation, and is not influenced by the overexpression of p53 or NF-κB transcription factors. We propose a novel computational method of validation of molecular pathways models, based on the analysis of sensitivity of the oscillation period to the particular gene(s) copy number and the level of stimulation. Using this method, the authors demonstrate that existing p53 models, in which oscillations are borne at a saddle-node-on-invariant-circle or subcritical Hopf bifurcations (characteristic for systems with interlinked positive and negative feedbacks), are highly sensitive to gene copy number. Hence, these models cannot explain existing experiments. Analysing NF-κB system, the authors show the importance of saturation in transcription of the NF-κB inhibitor IκBα. Models without saturation predict that the oscillation period is a rapidly growing function of total NF-κB level, which is in disagreement with experiments. The study supports the hypothesis that oscillations of robust period are based on supercritical Hopf bifurcation, characteristic for dynamical systems involving negative feedback and time delay. We hypothesise that in the p53 system, the role of positive feedback is not sustaining oscillations, but terminating them in severely damaged cells in which the apoptotic programme should be initiated.