Synthesizing attractors of Hindmarsh-Rose neuronal systems

In this paper a periodic parameter switching scheme is applied to the Hindmarsh-Rose neuronal system to synthesize certain attractors. Results show numerically, via computer graphic simulations, that the obtained synthesized attractor belongs to the class of all admissible attractors for the Hindmarsh-Rose neuronal system and matches the averaged attractor obtained with the control parameter replaced with the averaged switched parameter values. This feature allows us to imagine that living beings are able to maintain vital behavior while the control parameter switches so that their dynamical behavior is suitable for the given environment.Comment: published in Nonlinear Dynamic

Proton transport across charged membrane and pH oscillations

Based on Eyring's multibarrier activation process, a mathematical model and equation is developed to account for proton diffusion through an immobilized protein and enzyme membrane perfused with an electrolyte, substrate, and a buffer. With this model we find that, in the presence of a buffer, our solution approaches the continuum case very rapidly. We apply our model to membranes composed of papain and bovine serum albumin and find that our theory closely stimulates the experimental observations on the effect of salt and buffer on proton diffusion. Our theory shows that the pH oscillations observed in the diffusion controlled papain-benzoyl-L-arginine ethyl ester (BAEE) reaction may be the result of CO2 dissolved in the bath at high pH. In our theory, under certain conditions and in agreement with experimental observation, the buffer penetration depth oscillates near the boundary of a papain membrane in a solution containing BAEE and borate. We also find that at low ionic strength small ions as well as a buffer are seen to oscillate if a membrane is highly charged

On the effect of the intracellular calcium-sensitive K+ channel in the bursting pancreatic beta-cell

Based on the observation that the calcium-activated K+ channel in the pancreatic islet cells can also be activated by the membrane potential, we have formulated a mathematical model for the electrical activity in the pancreatic beta-cell. Our model contains two types of ionic channels, which are active above the subthreshold glucose concentration in the limit-cycle region: a Ca2+-activated, voltage-gated K+ channel and voltage-gated Ca2+ channel. Numerical simulation of the model generates bursts of electrical activity in response to a variation of kCa, the rate constant for sequestration of intracellular calcium ions. The period and duration of the bursts in response to kCa are in good agreement with experiment. The model predicts that a combined spike and burst pattern can be created using only single species of inward and outward currents, the inactivation kinetics (i.e., h) in the inward current is not a necessary condition for the generation of the pattern, and a given pattern or intensity of electrical activity may produce different levels of intracellular Ca2+ depending on the set of certain electrical parameters

Effects of extracellular calcium on electrical bursting and intracellular and luminal calcium oscillations in insulin secreting pancreatic beta-cells

The extracellular calcium concentration has interesting effects on bursting of pancreatic beta-cells. The mechanism underlying the extracellular Ca2+ effect is not well understood. By incorporating a low-threshold transient inward current to the store-operated bursting model of Chay, this paper elucidates the role of the extracellular Ca2+ concentration in influencing electrical activity, intracellular Ca2+ concentration, and the luminal Ca2+ concentration in the intracellular Ca2+ store. The possibility that this inward current is a carbachol-sensitive and TTX-insensitive Na+ current discovered by others is discussed. In addition, this paper explains how these three variables respond when various pharmacological agents are applied to the store-operated model