The number and spatial distribution of IP3 receptors underlying calcium puffs in Xenopus oocytes

Abstract

Calcium puffs are local Ca(2+) release events that arise from a cluster of inositol 1,4,5-trisphosphate receptor channels (IP(3)Rs) and serve as a basic "building block" from which global Ca(2+) waves are generated. Important questions remain as to the number of IP(3)Rs that open during a puff, their spatial distribution within a cluster, and how much Ca(2+) current flows through each channel. The recent discovery of "trigger" events-small Ca(2+) signals that immediately precede puffs and are interpreted to arise through opening of single IP(3)R channels-now provides a useful yardstick by which to calibrate the Ca(2+) flux underlying puffs. Here, we describe a deterministic numerical model to simulate puffs and trigger events. Based on confocal linescan imaging in Xenopus oocytes, we simulated Ca(2+) release in two sequential stages; representing the trigger by the opening of a single IP(3)R in the center of a cluster for 12 ms, followed by the concerted opening of some number of IP(3)Rs for 19 ms, representing the rising phase of the puff. The diffusion of Ca(2+) and Ca(2+)-bound indicator dye were modeled in a three-dimensional cytosolic volume in the presence of immobile and mobile Ca(2+) buffers, and were used to predict the observed fluorescence signal after blurring by the microscope point-spread function. Optimal correspondence with experimental measurements of puff spatial width and puff/trigger amplitude ratio was obtained assuming that puffs arise from the synchronous opening of 25-35 IP(3)Rs, each carrying a Ca(2+) current of approximately 0.4 pA, with the channels distributed through a cluster 300-800 nm in diameter.

FIGURE 1

Design of the Ca²⁺ puff model. (A) Diffusion of Ca²⁺ within the cytosol is modeled within a cuboid space with dimensions . IP₃R channels are distributed on a square plane (solid) centered within the cubic cytosolic space, i.e., the plane of (x, y, z = 3000 nm). (B) Distribution of IP₃Rs (shaded circles) within a square cluster of length L. The ER pool is assumed to be a two-dimensional flat plane occupying no volume. (C) The point-spread function of the confocal microscopes is modeled as a weighted Gaussian distribution in all dimensions, with widths (FWHM) of 300 nm in the lateral (x,y) dimensions and 800 nm in the axial (z) dimension.

FIGURE 2

Deterministic simulation of a typical triggered puff. (A) The event is assumed to arise through the opening of a single IP₃R channel for 12 ms (from time 0 to time T₁) that gives rise to the trigger, followed by the simultaneous opening of a total of 25 channels for 19 ms (times T₁ to T₂), corresponding to the rising phase of the puff. The plot shows number of open channels (N_open) as a function of time. Simulations in Figs. 3 and 4 also assume the same number and kinetics of channel openings. (B) Resulting changes in free [Ca²⁺] in the grid element centered within the channel cluster and containing the trigger channel. (C) Corresponding changes in [FluoCa] at the same central grid element. (D) Simulated confocal fluorescence signal (Con) as would be recorded by a confocal spot centered on the trigger channel. The trace was derived from the distribution of [FluoCa] throughout the model space as a weighted average of the microscope point-spread function. (E) Graphical representation of the evolution of the trigger event. The panel shows a simulated linescan (x–t) confocal image, with increasing fluorescence signal (Con) depicted by increasingly “warm” colors and increasing height. (F) Corresponding simulated linescan image showing both the trigger and puff at reduced magnification.

FIGURE 3

Spatial distributions during the trigger event (○) at time T₁ and during the puff (▪) at time T₂ for [FreeCa] (A), [FluoCa] (B), and confocal signal Con (C). The spatial distributions are plotted along the x axis (see Fig. 1 A), centered on the triggering channel (x = 3000 nm). The inset in A shows the [FreeCa] distribution of the trigger replotted on semilogarithmic axes.

FIGURE 4

Spatial width and signal mass of the triggered puff event. (A) Changes in spatial widths (FWHM) of [FreeCa] (dashed line), [FluoCa] (dot-dashed line), and Con (solid line) as functions of time resulting from openings of IP₃R channels as shown in C. (B) Corresponding changes in signal mass of the fluorescence signal from the model, computed as a symmetrical integral of [FluoCa] in three dimensions from a one-dimensional section along the x axis centered on the trigger channel.

FIGURE 5

Effects of changing open IP₃R number N on puff width at time T₂ (A), and on the amplitude ratio R between puff and trigger (B). Different clusters with lengths L = 200 nm (○), 520 nm (★), and 1000 nm (□) were simulated. For comparison, the dashed lines in A and B show the mean FWHM (W₀ = 1500 nm) and amplitude ratio (R₀ = 6) of experimental observations of puffs.

FIGURE 6

Effects of changing cluster dimensions (length L) on puff FWHM at time T₂ (A) and the amplitude ratio R between puff and trigger (B). Clusters containing 49 (○), 25 (★), and 9 (□) open channels were simulated. For comparison, the dashed lines in A and B show, respectively, the mean FWHM (W₀ = 1500 nm) and the amplitude ratio (R₀ = 6) of averaged experimental puffs.

FIGURE 7

Influence of IP₃R channel Ca²⁺ current on puff FWHM at time T₂ (A), confocal image amplitude (B), and the amplitude ratio R between puff and trigger (C). Three different clusters are considered: open channel number N = 25 and cluster length L = 520 nm (★); N = 9, and L= 520 nm (○); and N = 9 and L = 200 nm (□). Additionally, solid triangles show the corresponding relationships for the trigger event at time T₁. For comparison, the dashed lines in A and C mark, respectively, the FWHM (W₀ = 1500 nm) and the amplitude ratio (R₀ = 6) of the mean experimental puff.

FIGURE 8

Matching degree function showing the correspondence between puffs simulated with various parameter values and the mean characteristics (puff/trigger amplitude ratio R₀ = 6 and FWHM W₀ = 1500 nm) of experimentally recorded puffs with triggers. In each panel, puffs were simulated across a wide parameter space of cluster length L and open channel number N. For any given pair of parameter values, the correspondence between the resultant simulated puff and the experimentally observed puff was calculated by a matching function (see text for details). A perfect correspondence (matching degree = 2) is depicted in red, with matching degrees <1.94 in black, and intermediate values on a pseudocolor scale as indicated by the color bar. (Left to right) Results assuming single-channel IP₃R currents of 0.2, 0.4, and 0.5 pA, respectively.