Krzysztof Puszynski

Single TNFα trimers mediating NF-κB activation: stochastic robustness of NF-κB signaling

BackgroundThe 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.ResultsWe 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.ConclusionThese 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.

CELL CYCLE AS AN OBJECT OF CONTROL

This chapter is devoted to models of cancer growth and anticancer therapies that put special emphasis on the dependence of therapy efficiency on cell cycle. First, biological background is introduced and detailed description of a cell cycle is given, based on the review of biological literature. It is supplemented with information about chosen chemotherapeutic drugs and their efficacy with respect to the cell cycle. Next, pharmacokinetic and pharmacodynamics aspects of chemotherapeutics are briefly described. They along with cell cycle specificity of drugs may lead to various phenomena of resonances and aftereffects that need to be taken into account in therapy and synchronization of treatment protocols. These issues are mentioned in a separate section of this chapter. Finally, models that incorporate evolution of drug resistance are presented. For all models, the problem of finding a suitable treatment protocol is formulated as a problem of control optimization and some results of application of optimization theory to solve these problems are presented.

The Pharmacodynamics of the p53-Mdm2 Targeting Drug Nutlin: The Role of Gene-Switching Noise

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.

Regulation of p53 by siRNA in radiation treated cells

Ionizing radiation activates a large variety of intracellular mechanisms responsible for maintaining appropriate cell functionality or activation of apoptosis which eliminates damaged cells from the population. The mechanism of such induced cellular death is widely used in radiotherapy in order to eliminate cancer cells, although in some cases it is highly limited by increased cellular radio-resistance due to aberrations in molecular regulation mechanisms of malignant cells. Despite the positive correlation between the radiation dose and the number of apoptotic cancer cells, radiation has to be limited because of extensive side effects. Therefore, additional control signals whose role will be to maximize the cancer cells death-ratio while minimizing the radiation dose and by that the potential side effects are worth considering. In this work we present the results of simulation studies showing possibilities of single gene regulation by small interfering RNA (siRNA) that can increase radio-sensitivity of malignant cells showing aberrations in the p53 signaling pathway, responsible for DNA damage-dependant apoptosis. By blocking the production of the p53 inhibitor Mdm2, radiation treated cancer cells are pushed into the apoptotic state on a level normally achievable only with high radiation doses. The presented approach, based on a simulation study originating from experimentally validated regulatory events, concerns one of the basic problems of radiotherapy dosage limitations, which, as will be shown, can be partially avoided by using the appropriate siRNA based control mechanism.

Erratum to: A novel mathematical model of ATM/p53/NF-κB pathways points to the importance of the DDR switch-off mechanisms.

BackgroundAtaxia 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.ResultsTo 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.ConclusionsIn 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.

Integrated System Supporting Research on Environment Related Cancers

There are many impediments to progress in cancer research. Insufficient or low quality data and computational tools that are dispersed among various sites are one of them. In this paper we present an integrated system that combines all stages of cancer studies, from gathering of clinical data, through elaborate patient questionnaires and bioinformatics tools, to data warehousing and preparation of analysis reports.

Application of bifurcation theory and siRNA-based control signal to restore the proper response of cancer cells to DNA damage.

Many diseases with a genetic background such as some types of cancer are caused by damage in the p53 signaling pathway. The damage changes the system dynamics providing cancer cells with resistance to therapy such as radiation therapy. The change can be observed as the difference in bifurcation diagrams and equilibria type and location between normal and damaged cells, and summarized as the changes of the mathematical model parameters and following changes of the eigenvalues of Jacobian matrix. Therefore a change in other model parameters, such as mRNA degradation rates, may restore the proper eigenvalues and by that proper system dynamics. From the biological point of view, the change of mRNA degradation rate can be achieved by application of the small interfering RNA (siRNA). Here, we propose a general mathematical framework based on the bifurcation theory and siRNA-based control signal in order to study how to restore the proper response of cells with damaged p53 signaling pathway to therapy by using ionizing radiation (IR) therapy as an example. We show the difference between the cells with normal p53 signaling pathway and cells with abnormalities in the negative (as observed in SJSA-1 cell line) or positive (as observed in MCF-7 or PNT1a cell lines) feedback loop. Then we show how the dynamics of these cells can be restored to normal cell dynamics by using selected siRNA.

Prediction of the Behavior of Mammalian Cells after Exposure to Ionizing Radiation Based on the New Mathematical Model of ATM-Mdm2-p53 Regulatory Pathway

Eukaryotic cells are exposed continuously to the genotoxic stresses caused by various sources, such as ionizing radiation (IR) that generates DNA double-strand breaks (DSBs). In order to maintain genomic integrity, the DNA damage response is activated. DSBs are detected by ATM protein kinase that stabilizes and activates p53 tumor suppressor, which target genes are involved in cell cycle arrest, DNA repair and apoptosis. We propose a preliminary mathematical model that explains p53 regulation based on ATM-dependent detector system. We linked the existing p53-Mdm2 pathway model with checkpoint kinase 2 that inhibits p53 degradation, and MRN complex that activates ATM upon DSBs induction. Moreover, recent works shown that the critical component of ATM-dependent signaling pathway is played by phosphatase Wip1 that regulates dephosphorylation events. Additionally, in the presented model we included Wip1 transcriptionally dependent on p53. The preliminary results of simulation analysis show that ATM pathway is an effective system for DSBs detection with strong amplification signal for Wip1 and p53 and quick response. Furthermore, we observed strong dependence of the cellular response to the DNA damage on Wip1, what leads to the conclusion that it plays a role as a gatekeeper in the ATM-Mdm2-p53 regulatory loop.

Reachability of the Therapeutic Target in the Systems with Parameters Switch

Human organism is a complex system whose functioning is still under investigation. The biological models of intercellular interactions are created for better understanding of the complex system behaviour and prediction of the system response to the given stimuli. Medical system such as drug application to organism can be described as a piece-wise non-linear model. In our work we consider the influence of the parameter deviations of the systems with fixed terminal state. There are investigated two types of deviations: small changes of system parameters and changes in particular parameter switching time. We considered three different types of the systems, without self-regulation, with negative feedback loop and with positive feedback loop. We considered differences between these types and influence of the small changes in parameters values to the reachability of therapeutic goal after the drug application.

The role of stochastic gene switching in determining the pharmacodynamics of certain drugs: basic mechanisms

In this paper we analyze the impact of the stochastic fluctuation of genes between their ON and OFF states on the pharmacodynamics of a potentially large class of drugs. We focus on basic mechanisms underlying the onset of in vitro experimental dose-response curves, by investigating two elementary molecular circuits. Both circuits consist in the transcription of a gene and in the successive translation into the corresponding protein. Whereas in the first the activation/deactivation rates of the single gene copy are constant, in the second the protein, now a transcription factor, amplifies the deactivation rate, so introducing a negative feedback. The drug is assumed to enhance the elimination of the protein, and in both cases the success of therapy is assured by keeping the level of the given protein under a threshold for a fixed time. Our numerical simulations suggests that the gene switching plays a primary role in determining the sigmoidal shape of dose-response curves. Moreover, the simulations show interesting phenomena related to the magnitude of the average gene switching time and to the drug concentration. In particular, for slow gene switching a significant fraction of cells can respond also in the absence of drug or with drug concentrations insufficient for the response in a deterministic setting. For higher drug concentrations, the non-responding fraction exhibits a maximum at intermediate values of the gene switching rates. For fast gene switching, instead, the stochastic prediction follows the prediction of the deterministic approximation, with all the cells responding or non-responding according to the drug dose.