Gating mechanisms of the type-1 inositol trisphosphate receptor

Inositol trisphosphate receptor and ion channel models based on single-channel data

The inositol trisphosphate receptor (IPR) plays an important role in controlling the dynamics of intracellular Ca(2+). Single-channel patch-clamp recordings are a typical way to study these receptors as well as other ion channels. Methods for analyzing and using this type of data have been developed to fit Markov models of the receptor. The usual method of parameter fitting is based on maximum-likelihood techniques. However, Bayesian inference and Markov chain Monte Carlo techniques are becoming more popular. We describe the application of the Bayesian methods to real experimental single-channel data in three ion channels: the ryanodine receptor, the K(+) channel, and the IPR. One of the main aims of all three studies was that of model selection with different approaches taken. We also discuss the modeling implications for single-channel data that display different levels of channel activity within one recording.

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.

Calcium oscillations

Changes in cellular Ca2+ concentration control a wide range of physiological processes, from the subsecond release of synaptic neurotransmitters, to the regulation of gene expression over months or years. Ca2+ can also trigger cell death through both apoptosis and necrosis, and so the regulation of cellular Ca2+ concentration must be tightly controlled through the concerted action of pumps, channels and buffers that transport Ca2+ into and out of the cell cytoplasm. A hallmark of cellular Ca2+ signalling is its spatiotemporal complexity: stimulation of cells by a hormone or neurotransmitter leads to oscillations in cytoplasmic Ca2+ concentration that can vary markedly in time course, amplitude, frequency, and spatial range. In this chapter we review some of the biological roles of Ca2+, the experimental characterisation of complex dynamic changes in Ca2+ concentration, and attempts to explain this complexity using computational models. We consider the 'toolkit' of cellular proteins which influence Ca2+ concentrarion, describe mechanistic models of key elements of the toolkit, and fit these into the framework of whole cell models of Ca2+ oscillations and waves. Finally, we will touch on recent efforts to use stochastic modelling to elucidate elementary Ca2+ signal events, and how these may evolve into global signals.

Characterization of local calcium signals in tubular networks of endoplasmic reticulum

To explain the large time and space scales of elementary calcium events in Xenopus oocytes it is assumed that the Ca2+ source is located on tubules of the endoplasmic reticulum, which provide local barriers for diffusion. The event duration, width and signal mass dependence on the total quantity of released Ca2+ is determined at different orientations of the scan line and different ionic currents. Excellent agreement with published data is obtained with on- and off-rate constants of the fluorescent indicator of 15 microM(-1) s(-1) and 2.55 s(-1), respectively. It is found that one signal mass unit, calculated with the classical method that assumes spherical symmetry of the cytosolic space surrounding the release site, corresponds to 0.189 fC of released Ca2+ in the presence of a tubular network. It is estimated that release Ca2+ currents and amounts are randomly distributed, with averages of 0.165 pA and 3.66 fC per event and average release duration of 22.2 ms. The total quantity of liberated Ca2+ and the release current amplitude in the presence of endoplasmic reticulum tubules is predicted to be about one order of magnitude lower than estimated within the isotropic diffusion formalism. This could have implications in muscle cell Ca2+ imaging as well.

Reaction diffusion modeling of calcium dynamics with realistic ER geometry

We describe a finite-element model of mast cell calcium dynamics that incorporates the endoplasmic reticulum's complex geometry. The model is built upon a three-dimensional reconstruction of the endoplasmic reticulum (ER) from an electron tomographic tilt series. Tetrahedral meshes provide volumetric representations of the ER lumen, ER membrane, cytoplasm, and plasma membrane. The reaction-diffusion model simultaneously tracks changes in cytoplasmic and ER intraluminal calcium concentrations and includes luminal and cytoplasmic protein buffers. Transport fluxes via PMCA, SERCA, ER leakage, and Type II IP3 receptors are also represented. Unique features of the model include stochastic behavior of IP3 receptor calcium channels and comparisons of channel open times when diffusely distributed or aggregated in clusters on the ER surface. Simulations show that IP3R channels in close proximity modulate activity of their neighbors through local Ca2+ feedback effects. Cytoplasmic calcium levels rise higher, and ER luminal calcium concentrations drop lower, after IP3-mediated release from receptors in the diffuse configuration. Simulation results also suggest that the buffering capacity of the ER, and not restricted diffusion, is the predominant factor influencing average luminal calcium concentrations.