A bidomain threshold model of propagating calcium waves

We present a bidomain fire-diffuse-fire model that facilitates mathematical analysis of propagating waves of elevated intracellular calcium (Ca) in living cells. Modelling Ca release as a threshold process allows the explicit construction of travelling wave solutions to probe the dependence of Ca wave speed on physiologically important parameters such as the threshold for Ca release from the endoplasmic reticulum (ER) to the cytosol, the rate of Ca resequestration from the cytosol to the ER, and the total [Ca] (cytosolic plus ER). Interestingly, linear stability analysis of the bidomain fire-diffuse-fire model predicts the onset of dynamic wave instabilities leading to the emergence of Ca waves that propagate in a back-and-forth manner. Numerical simulations are used to confirm the presence of these so-called "tango waves" and the dependence of Ca wave speed on the total [Ca]. The original publication is available at www.springerlink.com (Journal of Mathematical Biology)

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.

Recombinant expression of Aryl Hydrocarbon Receptor for quantitative ligand-binding analysis

Recombinant expression of the Aryl Hydrocarbon Receptor (AhR) yields small amounts of ligand- binding competent AhR. Therefore, Spodoptera frugiperda (Sf9) cells and baculovirus have been evaluated for high level and functional expression of AhR. Rat and human AhR were expressed as soluble protein in significant amounts. Expression of ligand-binding competent AhR was sensitive to the protein concentration of Sf9 extract, and co-expression of the chaperone p23 failed to affect the yield of functional ligand-binding AhR. The expression system yielded high levels of functional protein, with the ligand-binding capacity (Bmax) typically 20- fold higher than that obtained with rat liver cytosol. Quantitative estimates of the ligand-binding affinity of human and rat AhR were obtained; the Kd for recombinant rat AhR was indistinguishable from that of native rat AhR, thereby validating the expression system as a faithful model for native AhR. The human AhR bound TCDD with significantly lower affinity than the rat AhR. These findings demonstrate high-level expression of ligand-binding competent AhR, and sufficient AhR for quantitative analysis of ligand-binding.

Towards a predictive model of Ca²⁺ puffs

We investigate key characteristics of Ca²⁺ puffs in deterministic and stochastic frameworks that all incorporate the cellular morphology of IP[subscript]3 receptor channel clusters. In a first step, we numerically study Ca²⁺ liberation in a three dimensional representation of a cluster environment with reaction-diffusion dynamics in both the cytosol and the lumen. These simulations reveal that Ca²⁺ concentrations at a releasing cluster range from 80 µM to 170 µM and equilibrate almost instantaneously on the time scale of the release duration. These highly elevated Ca²⁺ concentrations eliminate Ca²⁺ oscillations in a deterministic model of an IP[subscript]3R channel cluster at physiological parameter values as revealed by a linear stability analysis. The reason lies in the saturation of all feedback processes in the IP[subscript]3R gating dynamics, so that only fluctuations can restore experimentally observed Ca²⁺ oscillations. In this spirit, we derive master equations that allow us to analytically quantify the onset of Ca²⁺ puffs and hence the stochastic time scale of intracellular Ca²⁺ dynamics. Moving up the spatial scale, we suggest to formulate cellular dynamics in terms of waiting time distribution functions. This approach prevents the state space explosion that is typical for the description of cellular dynamics based on channel states and still contains information on molecular fluctuations. We illustrate this method by studying global Ca²⁺ oscillations.