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Cortical spreading depression (CSD) is a pathophysiological phenomenon, which underlies some neurological disorders, such as migraine and stroke, but its mechanisms are still not completely understood. One of the striking facts is that the spatiotemporal evolution of CSD wave is varying. Observations in experiments reveal that a CSD wave may propagate through the entire cortex, or just bypass some areas of the cortex. In this paper, we have applied a 2D reaction-diffusion equation with recovery term to study the spatiotemporal evolution of CSD. By modulating the recovery rate from CSD in the modeled cortex, CSD waves with different spatiotemporal evolutions, either bypassing some areas or propagating slowly in these areas, were present. Moreover, spiral CSD waves could also be induced in case of the transiently altered recovery rate, i.e. block release from the absolute refractory period. These results suggest that the refractory period contributes to the different propagation patterns of CSD, which may help to interpret the mechanisms of CSD propagation. [ABSTRACT FROM AUTHOR]

A variety of cardiac arrhythmias are initiated by a focal excitation that disrupts the regular beating of the heart. In some cases it is known that these excitations are due to calcium (Ca) release from the sarcoplasmic reticulum (SR) via propagating subcellular Ca waves. However, it is not understood what are the physiological factors that determine the timing of these excitations at both the subcellular and tissue level. In this paper we apply analytic and numerical approaches to determine the timing statistics of spontaneous Ca release (SCR) in a simplified model of a cardiac myocyte. In particular, we compute the mean first passage time (MFPT) to SCR, in the case where SCR is initiated by spontaneous Ca sparks, and demonstrate that this quantity exhibits either an algebraic or exponential dependence on system parameters. Based on this analysis we identify the necessary requirements so that SCR occurs on a time scale comparable to the cardiac cycle. Finally, we study how SCR is synchronized across many cells in cardiac tissue, and identify a quantitative measure that determines the relative timing of SCR in an ensemble of cells. Using this approach we identify the physiological conditions so that cell-to-cell variations in the timing of SCR is small compared to the typical duration of an SCR event. We argue further that under these conditions inward currents due to SCR can summate and generate arrhythmogenic triggered excitations in cardiac tissue. [ABSTRACT FROM AUTHOR]

Tumors are often heterogeneous in which tumor cells of different phenotypes have distinct properties. For scientific and clinical interests, it is of fundamental importance to understand their properties and the dynamic variations among different phenotypes, specifically under radio- and/or chemo-therapy. Currently there are two controversial models describing tumor heterogeneity, the cancer stem cell (CSC) model and the stochastic model. To clarify the controversy, we measured probabilities of different division types and transitions of cells via in situ immunofluorescence. Based on the experiment data, we constructed a model that combines the CSC with the stochastic concepts, showing the existence of both distinctive CSC subpopulations and the stochastic transitions from NSCCs to CSCs. The results showed that the dynamic variations between CSCs and non-stem cancer cells (NSCCs) can be simulated with the model. Further studies also showed that the model can be used to describe the dynamics of the two subpopulations after radiation treatment. More importantly, analysis demonstrated that the experimental detectable equilibrium CSC proportion can be achieved only when the stochastic transitions from NSCCs to CSCs occur, indicating that tumor heterogeneity may exist in a model coordinating with both the CSC and the stochastic concepts. The mathematic model based on experimental parameters may contribute to a better understanding of the tumor heterogeneity, and provide references on the dynamics of CSC subpopulation during radiotherapy. [ABSTRACT FROM AUTHOR]

We construct a stress p53-Mdm2-p300-HDAC1 regulatory network that is activated and stabilised by two regulatory proteins, p300 and HDAC1. Different activation levels of observed due to these regulators during stress condition have been investigated using a deterministic as well as a stochastic approach to understand how the cell responds during stress conditions. We found that these regulators help in adjusting p53 to different conditions as identified by various oscillatory states, namely fixed point oscillations, damped oscillations and sustain oscillations. On assessing the impact of p300 on p53-Mdm2 network we identified three states: first stabilised or normal condition where the impact of p300 is negligible, second an interim region where p53 is activated due to interaction between p53 and p300, and finally the third regime where excess of p300 leads to cell stress condition. Similarly evaluation of HDAC1 on our model led to identification of the above three distinct states. Also we observe that noise in stochastic cellular system helps to reach each oscillatory state quicker than those in deterministic case. The constructed model validated different experimental findings qualitatively. [ABSTRACT FROM AUTHOR]