B Cell Activation Triggered by the Formation of the Small Receptor Cluster: A Computational Study

We proposed a spatially extended model of early events of B cell receptors (BCR) activation, which is based on mutual kinase-receptor interactions that are characteristic for the immune receptors and the Src family kinases. These interactions lead to the positive feedback which, together with two nonlinearities resulting from the double phosphorylation of receptors and Michaelis-Menten dephosphorylation kinetics, are responsible for the system bistability. We demonstrated that B cell can be activated by a formation of a tiny cluster of receptors or displacement of the nucleus. The receptors and Src kinases are activated, first locally, in the locus of the receptor cluster or the region where the cytoplasm is the thinnest. Then the traveling wave of activation propagates until activity spreads over the whole cell membrane. In the models in which we assume that the kinases are free to diffuse in the cytoplasm, we found that the fraction of aggregated receptors, capable to initiate B cell activation decreases with the decreasing thickness of cytoplasm and decreasing kinase diffusion. When kinases are restricted to the cell membrane - which is the case for most of the Src family kinases - even a cluster consisting of a tiny fraction of total receptors becomes activatory. Interestingly, the system remains insensitive to the modest changes of total receptor level. The model provides a plausible mechanism of B cells activation due to the formation of small receptors clusters collocalized by binding of polyvalent antigens or arising during the immune synapse formation

Feedbacks, Bifurcations, and Cell Fate Decision-Making in the p53 System.

The p53 transcription factor is a regulator of key cellular processes including DNA repair, cell cycle arrest, and apoptosis. In this theoretical study, we investigate how the complex circuitry of the p53 network allows for stochastic yet unambiguous cell fate decision-making. The proposed Markov chain model consists of the regulatory core and two subordinated bistable modules responsible for cell cycle arrest and apoptosis. The regulatory core is controlled by two negative feedback loops (regulated by Mdm2 and Wip1) responsible for oscillations, and two antagonistic positive feedback loops (regulated by phosphatases Wip1 and PTEN) responsible for bistability. By means of bifurcation analysis of the deterministic approximation we capture the recurrent solutions (i.e., steady states and limit cycles) that delineate temporal responses of the stochastic system. Direct switching from the limit-cycle oscillations to the "apoptotic" steady state is enabled by the existence of a subcritical Neimark-Sacker bifurcation in which the limit cycle loses its stability by merging with an unstable invariant torus. Our analysis provides an explanation why cancer cell lines known to have vastly diverse expression levels of Wip1 and PTEN exhibit a broad spectrum of responses to DNA damage: from a fast transition to a high level of p53 killer (a p53 phosphoform which promotes commitment to apoptosis) in cells characterized by high PTEN and low Wip1 levels to long-lasting p53 level oscillations in cells having PTEN promoter methylated (as in, e.g., MCF-7 cell line)

Simplified scheme of the model.

<p>Arrow-headed dashed lines indicate positive transcriptional regulation, arrow-headed solid lines—protein transformation, circle-headed solid lines—positive influence or activation, hammer-headed solid lines—inhibitory regulation. Pro-survival and cell cycle-promoting proteins are represented with blue boxes, pro-apoptotic proteins with yellow boxes, proteins involved in cell cycle arrest with green boxes. Details of the cell cycle arrest module and the apoptotic module are shown in Figs <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004787#pcbi.1004787.g002" target="_blank">2</a> and <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004787#pcbi.1004787.g003" target="_blank">3</a> respectively.</p

Critical irradiation doses as a function of Wip1 (<i>s</i>₁) and PTEN (<i>s</i>₂) mRNA synthesis rates.

<p>(A) Active PI3K level is decreased 2-fold from the nominal value. (B) The nominal value of active PI3K. (C) Active PI3K level is twice the nominal value. Color lines show the critical irradiation doses in the (<i>s</i>₁, <i>s</i>₂)-parameter space. Dashed line corresponds to the persistent (irreparable) DNA damage equal 100 DSBs. For each dose, the line separates the apoptotic region (above the line) and the survival region (below the line) in the (<i>s</i>₁, <i>s</i>₂)-parameter space. The black dot in (B) corresponds to nominal values of Wip1 and PTEN mRNA synthesis rates.</p

Analysis of the cell fate decision-making process.

<p>(A) PTEN levels in subpopulations of surviving (blue) and apoptotic (red) cells after 4-Gy irradiation. 10 000 cells are simulated in total. (B) Kolmogorov—Smirnov statistics between distributions of six variables which characterize surviving and apoptotic cells.</p

Deterministic simulation trajectories of the system with the suppressed DNA repair and either nominal or perturbed mRNA synthesis rates in response to 2-Gy irradiation.

<p>(A) Nominal Wip1 and PTEN mRNA synthesis rates (<i>s</i>₁ = 0.1, <i>s</i>₂ = 0.03). (B) Decreased PTEN mRNA synthesis rate (<i>s</i>₂ = 0.005). (C) Decreased PTEN mRNA synthesis rate (<i>s</i>₂ = 0.005) and zero Wip1 synthesis rate (<i>s</i>₁ = 0). The simulation started at Time = 0 h from the steady state corresponding to the resting (unstimulated) cell. At Time = 10 h the irradiation phase started and lasted for 10 min. The faded line visualizes the trajectory after the initiation of apoptosis, and thus must be interpreted with caution.</p

Fraction of apoptotic cells as a function of irradiation dose for two types of stochastic simulations.

<p>For each of analyzed doses the fraction and corresponding error was calculated based on 5000 stochastic single-cell simulations. The state of the cell was checked at 72. hour after irradiation which, as shown in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004787#pcbi.1004787.g011" target="_blank">Fig 11</a>, is sufficient for unanimous cell fate decision.</p