Characterization of local calcium signals in tubular networks of endoplasmic reticulum

Mean field strategies induce unrealistic non-linearities in calcium puffs

Mean field models are often useful approximations to biological systems, but sometimes, they can yield misleading results. In this work, we compare mean field approaches with stochastic models of intracellular calcium release. In particular, we concentrate on calcium signals generated by the concerted opening of several clustered channels (calcium puffs). To this end we simulate calcium puffs numerically and then try to reproduce features of the resulting calcium distribution using mean field models were all the channels open and close simultaneously. We show that an unrealistic non-linear relationship between the current and the number of open channels is needed to reproduce the simulated puffs. Furthermore, a single channel current which is five times smaller than the one of the stochastic simulations is also needed. Our study sheds light on the importance of the stochastic kinetics of the calcium release channel activity to estimate the release fluxes.

Diffusion-convection effects on drug distribution at the cell membrane level in a patch-clamp setup

We present a model-based method for estimating the effective concentration of the active drug applied by a pressure pulse to an individual cell in a patch-clamp setup, which could be of practical use in the analysis of ligand-induced whole-cell currents recorded in patch-clamp experiments. Our modelling results outline several important factors which may be involved in the high variability of the electric response of the cells, and indicate that with a pressure pulse duration of 1s and diameter of the perfusion tip of 600 μm, elevated amounts of drug can accumulate locally between the pipette tip and the cell. Hence, the effective agonist concentration at the cell membrane level can be consistently higher than the initial concentration inside the perfusion tubes. We performed finite-difference and finite-element simulations to investigate the diffusion/convection effects on the agonist distribution on the cell membrane. Our model can explain the delay between the commencement of acetylcholine application and the onset of the whole-cell current that we recorded on human rhabdomyosarcoma TE671 cells, and reproduce quantitatively the decrease of signal latency with the concentration of agonist in the pipette. Results also show that not only the geometry of the bath chamber and pipette tip, but also the transport parameters of the diffusive and convective phenomena in the bath solution are determinant for the amplitude and kinetics of the recorded currents and have to be accounted for when analyzing patch-clamp data.

Quantifying calcium fluxes underlying calcium puffs in Xenopus laevis oocytes

We determine the calcium fluxes through inositol 1,4,5-trisphosphate receptor/channels underlying calcium puffs of Xenopus laevis oocytes using a simplified version of the algorithm of Ventura et al. An analysis of 130 puffs obtained with Fluo-4 indicates that Ca2+ release comes from a region of width approximately 450 nm, that the release duration is peaked around 18 s and that the underlying Ca2+ currents range between 0.12 and 0.95 pA. All these parameters are independent of IP(3) concentration. We explore what distributions of channels that open during a puff, N(p), and what relations between current and number of open channels, I(N(p)), are compatible with our findings and with the distribution of puff-to-trigger amplitude ratio reported in Rose et al. To this end, we use simple "mean field" models in which all channels open and close simultaneously. We find that the variability among clusters plays an important role in shaping the observed puff amplitude distribution and that a model for which I(N(p)) approximately N(p) for small N(p) and I(N(p)) approximately N(p)(1/alpha) (alpha > 1) for large N(p), provides the best agreement. Simulations of more detailed models in which channels open and close stochastically show that this nonlinear behavior can be attributed to the limited time resolution of the observations and to the averaging procedure that is implicit in the mean-field models. These conclusions are also compatible with observations of approximately 400 puffs obtained using the dye Oregon green.

A model-based method for estimating Ca2+ release fluxes from linescan images in Xenopus oocytes

We propose a model-based method of interpreting linescan images observed in Xenopus oocytes with the use of Oregon Green-1 as a fluorescent dye. We use a detailed modeling formalism based on numerical simulations that incorporate physical barriers for local diffusion, and, by assuming a Gaussian distribution of release durations, we derive the distributions of release Ca(2+) amounts and currents, fluorescence amplitudes, and puff widths. We analyze a wide set of available data collected from 857 and 281 events observed in the animal and the vegetal hemispheres of the oocyte, respectively. A relatively small fraction of events appear to involve coupling of two or three adjacent clusters of Ca(2+) releasing channels. In the animal hemisphere, the distribution of release currents with a mean of 1.4 pA presents a maximum at 1.0 pA and a rather long tail extending up to 5 pA. The overall distribution of liberated Ca(2+) amounts exhibits a dominant peak at 120 fC, a smaller peak at 375 fC, and an average of 166 fC. Ca(2+) amounts and release fluxes in the vegetal hemisphere appear to be 3.6 and 1.6 times smaller than in the animal hemisphere, respectively. Predicted diameters of elemental release sites are approximately 1.0 microm in the animal and approximately 0.5 microm in the vegetal hemisphere, but the side-to-side separation between adjacent sites appears to be identical (approximately 0.4 microm). By fitting the model to individual puffs we can estimate the quantity of liberated calcium, the release current, the orientation of the scan line, and the dimension of the corresponding release site.

Modulation of calcium signals by fluorescent dyes in the presence of tubular endoplasmic reticulum: a modelling approach

The complex network of Ca(2+) signals uses local events as building blocks for generating global calcium signals with different shapes. However, the nature of the large time- and space-scales of local calcium signals observed in Xenopus oocytes has remained unclear. By numeric simulations that include optical blurring of the image and the geometrical restrictions imposed by tubules of the endoplasmic reticulum or other cell structures, we investigate how the fluorescent dye affect the observed features of calcium events, such as rate of signal decay, spatial size, fluorescence amplitude, or the apparent diffusion like from a point source in a spherically symmetric space. We add more evidence that, irrespective of the dye properties, local calcium signals produced in the presence of tubular cellular structures are consistently wider than expected in a homogeneous environment. Moreover, the spatial dimension and the decay time of the event increase with the quantity of liberated Ca(2+). Our results also indicate that a fast binding Ca(2+) indicator that does not bind to cytosolic proteins yields fast signals when the event is observed in the front of the release site, and slow signals when the event is viewed from the opposite side of the tubule. We propose several ways to test our model by various experimental procedures.