Browsing by Author "Paszek, Pawel"

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    Modeling stochasticity in gene regulation
    (2006) Paszek, Pawel; Kimmel, Marek; Lipniacki, Tomasz
    Intrinsic stochasticity plays an essential role in gene regulation because of the small number of involved molecules of DNA, mRNA and protein of a given species. To better understand this phenomenon, small gene regulatory systems are mathematically modeled as systems of coupled chemical reactions, but the existing exact description utilizing a Chapman-Kolmogorov equation or simulation algorithms is limited and inefficient. The present work introduces a much more efficient yet accurate modeling approach, which allows analyzing stochasticity in the system in terms of the underlying distribution function. The novel modeling approach is motivated by the analysis of a single gene regulatory module with three sources of stochasticity: intermittent gene activity, mRNA transcription/decay and protein translation/decay noise. Although the corresponding Chapman Kolmogorov equation cannot be solved when a large number of molecules are considered, it is used to analytically derive the first two moments of the underlying distribution function. The mRNA and protein variance is found decomposable into additive terms resulting from the respective sources of stochasticity, which allow quantifying their significance in the process. The variance decomposition is asserted by constructing two approximations that establish a novel modeling approach: First, the continuous approximation, which considers only the stochasticity due to the intermittent gene activity. Second, the mixed approximation, which in addition attributes stochasticity to the mRNA transcription/decay process. Introduced approximations yield systems of first order partial differential equations for the underlying distribution function, which can be efficiently solved using developed numerical methods. Single cell simulations and numerical two-dimensional mRNA-protein stationary distribution functions are presented to confirm accuracy of introduced models. Further simplifications in the model allow considering regulation of the two- (possibly three-) gene systems for which two-dimensional protein-protein distributions are calculated. Finally, the assumption that gene activity is due to the binding and dissociation of a single regulatory molecule is relaxed. Based on the gene expression data, the models developed are applied to hypothesize the existence of a sequential activation mechanism of NF-kappaB dependent genes important in cell survival and inflammation. Future applications include analysis of small genetic networks, which are being currently engineered based on the prokaryotic and eukaryotic components.
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    Quantitative analysis reveals crosstalk mechanisms of heat shock-induced attenuation of NF-κB signaling at the single cell level
    (Public Library of Science, 2018) Kardyńska, Maøgorzata; Paszek, Anna; Śmieja, Jarosøaw; Spiller, David; Widøak, Wiesøawa; White, Michael R.H.; Paszek, Pawel; Kimmel, Marek
    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.