Quantification of propidium iodide delivery with millisecond electric pulses: A model study

A model study of propidium iodide delivery with millisecond electric pulses is presented; this work is a companion of the experimental efforts by Sadik et al. [1]. Both membrane permeabilization and delivery are examined with respect to six extra-cellular conductivities. The transmembrane potential of the permeabilized regions exhibits a consistent value, which corresponds to a bifurcation point in the pore-radius-potential relation. Both the pore area density and membrane conductance increase with an increasing extra-cellular conductivity. On the other hand, the inverse correlation between propidium iodide delivery and extra-cellular conductivity as observed in the experiments is quantitatively captured by the model. This agreement confirms that this behavior is primarily mediated by electrophoretic transport during the pulse. The results suggest that electrophoresis is important even for the delivery of small molecules such as propidium iodide. The direct comparison between model prediction and experimental data presented in this work helps validate the former as a robust predictive tool for the study of electroporation

Thermodynamics of the Schwarzschild-AdS black hole with a minimal length

Using the mass-smeared scheme of black holes, we study the thermodynamics of black holes. Two interesting models are considered. One is the self-regular Schwarzschild-AdS black hole whose mass density is given by the analogue to probability densities of quantum hydrogen atoms. The other model is the same black hole but whose mass density is chosen to be a rational fractional function of radial coordinates. Both mass densities are in fact analytic expressions of the ${\delta}$-function. We analyze the phase structures of the two models by investigating the heat capacity at constant pressure and the Gibbs free energy in an isothermal-isobaric ensemble. Both models fail to decay into the pure thermal radiation even with the positive Gibbs free energy due to the existence of a minimal length. Furthermore, we extend our analysis to a general mass-smeared form that is also associated with the ${\delta}$-function, and indicate the similar thermodynamic properties for various possible mass-smeared forms based on the ${\delta}$-function.Comment: v1: 25 pages, 14 figures; v2: 26 pages, 15 figures; v3: minor revisions, final version to appear in Adv. High Energy Phy