Fractal analysis of extra-embryonic vascularization in Japanese quail embryos exposed to extremely low frequency magnetic fields.

Magnetic fields (MF) can alter the dynamic behavior of vascular tissue and may have a stimulatory or inhibitory effect on blood vessel growth. Fractal geometry has been used in several studies as a tool to describe the development of blood vascular networks. Due to its self-similarity, irregularity, fractional dimension, and dependence on the scale of vessel dimensions, vascular networks can be taken as fractal objects. In this work, we calculated the fractal dimension by the methods of box counting (D(bc)) and information dimension (D(inf)) to evaluate the development of blood vessels of the yolk sac membrane (YSM) from quail embryos exposed to MF with a magnetic flux density of 1 mT and a frequency of 60 Hz. The obtained results showed that when the MF was applied to embryos aged between 48 and 72 h, in sessions of 2 h (6 h/day) and 3 h (9 h/day) with exposure intervals between 6 and 5 h, respectively, blood vascular formation was inhibited. Exposure sessions shorter than 2 h or longer than 3 h had no observable change on the vascular process. In contrast, the magnetic field had no observable change on the YSM vascular network for embryos aged between 72 and 96 h, irrespective of the exposure time. In conclusion, these results show a "window effect" regarding exposure time.

Chaotic model and memory in single calcium-activated potassium channel kinetics.

Ion channels are pores formed by proteins and responsible for carrying ion fluxes through cellular membranes. The ion channels can assume conformational states thereby controlling ion flow. Physically, the conformational transitions from one state to another are associated with energy barriers between them and are dependent on stimulus, such as, electrical field, ligands, second messengers, etc. Several models have been proposed to describe the kinetics of ion channels. The classical Markovian model assumes that a future transition is independent of the time that the ion channel stayed in a previous state. Others models as the fractal and the chaotic assume that the rate of transitions between the states depend on the time that the ionic channel stayed in a previous state. For the calcium activated potassium channels of Leydig cells the R/S Hurst analysis has indicated that the channels are long-term correlated with a Hurst coefficient H around 0.7, showing a persistent memory in this kinetic. Here, we applied the RS analysis to the opening and closing dwell time series obtained from simulated data from a chaotic model proposed by L. Liebovitch and T. Tóth [J. Theor. Biol. 148, 243 (1991)] and we show that this chaotic model or any model that treats the set of channel openings and closings as independent events is inadequate to describe the long-term correlation (memory) already described for the experimental data.