Modification of cell volume and proliferative capacity of Pseudokirchneriella subcapitata cells exposed to metal stress

The impact of metals (Cd, Cr, Cu and Zn) on growth, cell volume and cell division of the freshwateralga Pseudokirchneriella subcapitata exposed over a period of 72 h was investigated. The algal cells wereexposed to three nominal concentrations of each metal: low (closed to 72 h-EC10values), intermediate(closed to 72 h-EC50values) and high (upper than 72 h-EC90values). The exposure to low metal concen-trations resulted in a decrease of cell volume. On the contrary, for the highest metal concentrations anincrease of cell volume was observed; this effect was particularly notorious for Cd and less pronouncedfor Zn. Two behaviours were found when algal cells were exposed to intermediate concentrations ofmetals: Cu(II) and Cr(VI) induced a reduction of cell volume, while Cd(II) and Zn(II) provoked an oppositeeffect. The simultaneous nucleus staining and cell image analysis, allowed distinguishing three phases inP. subcapitata cell cycle: growth of mother cell; cell division, which includes two divisions of the nucleus;and, release of four autospores. The exposure of P. subcapitata cells to the highest metal concentrationsresulted in the arrest of cell growth before the first nucleus division [for Cr(VI) and Cu(II)] or after thesecond nucleus division but before the cytokinesis (release of autospores) when exposed to Cd(II). Thedifferent impact of metals on algal cell volume and cell-cycle progression, suggests that different toxic-ity mechanisms underlie the action of different metals studied. The simultaneous nucleus staining andcell image analysis, used in the present work, can be a useful tool in the analysis of the toxicity of thepollutants, in P. subcapitata, and help in the elucidation of their different modes of action.

Mathematical model for HIV dynamics in HIV-specific helper cells

In this paper we study a delay mathematical model for the dynamics of HIV in HIV-specific CD4 + T helper cells. We modify the model presented by Roy and Wodarz in 2012, where the HIV dynamics is studied, considering a single CD4 + T cell population. Non-specific helper cells are included as alternative target cell population, to account for macrophages and dendritic cells. In this paper, we include two types of delay: (1) a latent period between the time target cells are contacted by the virus particles and the time the virions enter the cells and; (2) virus production period for new virions to be produced within and released from the infected cells. We compute the reproduction number of the model, R0, and the local stability of the disease free equilibrium and of the endemic equilibrium. We find that for values of R0<1, the model approaches asymptotically the disease free equilibrium. For values of R0>1, the model approximates asymptotically the endemic equilibrium. We observe numerically the phenomenon of backward bifurcation for values of R0⪅1. This statement will be proved in future work. We also vary the values of the latent period and the production period of infected cells and free virus. We conclude that increasing these values translates in a decrease of the reproduction number. Thus, a good strategy to control the HIV virus should focus on drugs to prolong the latent period and/or slow down the virus production. These results suggest that the model is mathematically and epidemiologically well-posed.

Activation of effector immune cells promotes tumor stochastic extinction: A homotopy analysis approach

In this article we provide homotopy solutions of a cancer nonlinear model describing the dynamics of tumor cells in interaction with healthy and effector immune cells. We apply a semi-analytic technique for solving strongly nonlinear systems – the Step Homotopy Analysis Method (SHAM). This algorithm, based on a modification of the standard homotopy analysis method (HAM), allows to obtain a one-parameter family of explicit series solutions. By using the homotopy solutions, we first investigate the dynamical effect of the activation of the effector immune cells in the deterministic dynamics, showing that an increased activation makes the system to enter into chaotic dynamics via a period-doubling bifurcation scenario. Then, by adding demographic stochasticity into the homotopy solutions, we show, as a difference from the deterministic dynamics, that an increased activation of the immune cells facilitates cancer clearance involving tumor cells extinction and healthy cells persistence. Our results highlight the importance of therapies activating the effector immune cells at early stages of cancer progression.

Explicit series solution for a glucose-induced electrical activity model of pancreatic beta-cells

In this work, we present the explicit series solution of a specific mathematical model from the literature, the Deng bursting model, that mimics the glucose-induced electrical activity of pancreatic beta-cells (Deng, 1993). To serve to this purpose, we use a technique developed to find analytic approximate solutions for strongly nonlinear problems. This analytical algorithm involves an auxiliary parameter which provides us with an efficient way to ensure the rapid and accurate convergence to the exact solution of the bursting model. By using the homotopy solution, we investigate the dynamical effect of a biologically meaningful bifurcation parameter rho, which increases with the glucose concentration. Our analytical results are found to be in excellent agreement with the numerical ones. This work provides an illustration of how our understanding of biophysically motivated models can be directly enhanced by the application of a newly analytic method.