Persistent localized states for a chaotically mixed bistable reaction

We describe the evolution of a bistable chemical reaction in a closed two-dimensional chaotic laminar flow, from a localized initial disturbance. When the fluid mixing is sufficiently slow, the disturbance may spread and eventually occupy the entire fluid domain. By contrast, rapid mixing tends to dilute the initial state and so extinguish the disturbance. Such a dichotomy is well known. However, we report here a hitherto apparently unremarked intermediate case, a persistent highly localized disturbance. Such a localized state arises when the Damkoehler number is great enough to sustain a "hot spot," but not so great as to lead to global spread. We show that such a disturbance is located in the neighborhood of an unstable periodic orbit of the flow, and we describe some limited aspects of its behavior using a reduced, lamellar model. Copyright American Physical Society (APS) 2006.

Release currents of IP₃ receptor channel clusters and concentration profiles

We simulate currents and concentration profiles generated by Ca2+ release from the endoplasmic reticulum (ER) to the cytosol through IP3 receptor channel clusters. Clusters are described as conducting pores in the lumenal membrane with a diameter from 6 nm to 36 nm. The endoplasmic reticulum is modeled as a disc with a radius of 1–12 mm and an inner height of 28 nm. We adapt the dependence of the currents on the trans Ca2+ concentration (intralumenal) measured in lipid bilayer experiments to the cellular geometry. Simulated currents are compared with signal mass measurements in Xenopus oocytes. We find that release currents depend linearly on the concentration of free Ca2+ in the lumen. The release current is approximately proportional to the square root of the number of open channels in a cluster. Cytosolic concentrations at the location of the cluster range from 25 μM to 170 μM. Concentration increase due to puffs in a distance of a few micrometers from the puff site is found to be in the nanomolar range. Release currents decay biexponentially with timescales of < 1 s and a few seconds. Concentration profiles decay with timescales of 0.125–0.250 s upon termination of release.