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Figure 1. Scheme of the numerical simulation steps. (A,B) An active IP3R (blue dot) becomes open with a probability per unit time that depends on [Ca2+]. (C) An open IP3R (green dot) induces the opening of all active IP3Rs in its cluster. (D) A cluster with No open IP3Rs induces the opening of all active IP3Rs inside clusters that are within a distance, rinf, from it (dotted circle). rinf is an increasing function of No and (cytosolic) [Ca2+] (yellow color bar). This “cascade” is instantaneous. (E) [Ca2+] increases and the open IP3Rs become inhibited (red dots). (F) When Ca2+ is removed the inhibited IP3Rs can become active.
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Figure 2. Example of a Ca2+ signal evoked in an immature oocyte. Frames of 250 × 250 pixels acquired at the indicated times. Warmer colors correspond to increasing fluorescence values in arbitrary units (a.u.). The UV illumination (used to uncage the IP3) was on between t = 11.2 s and t = 28 s and between t = 173.6 s and t = 190.4 s. At t ~ 11.8 s various localized Ca2+ elevations (spotlights) are apparent (A). They eventually lead to a wave (B) that propagates throughout the observed region. The maximum fluorescence level is reached at t ~ 16.8s (C). A frame obtained slightly after shows a lower fluorescence level (D). After the (first) UV flash is turned off (t = 28 s) the fluorescence decays rapidly until it reaches the basal level by t = 44.8 s (E). Various localized signals (puffs) arise in between the two UV flashes as illustrated in (F). The white boxes indicate two regions analyzed in Figure 4.
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Figure 3. Example of a Ca2+ signal evoked in an egg. Similar to Figure 2, but for an experiment performed in an egg. In this case the UV illumination was on between t = 11.2 s and t = 28 s and between t = 112 s and t = 128.8 s. At t ~ 12.9 s the Ca2+ release becomes apparent (A). The Ca2+ distribution is more spatially uniform than in the oocyte. The wave propagates (B,C) and the fluorescence keeps on increasing while the UV light is on (D). Approximately 16 s after the UV flash is turned off (t = 44.8 s), the fluorescence has not reached the basal level yet (E). Ca2+ puffs are not observed in between the two UV flashes (F). The white boxes indicate two regions analyzed in Figure 4.
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Figure 4. Comparison of the fluorescence time course obtained in the examples of Figures 2, 3. (A,B) Time course of the fluorescence, F⎯⎯⎯⎯k, averaged over the two 50 × 50 pixel subregions depicted in Figure 2F (A) and Figure 3F (B). In both cases, the solid line corresponds to k = 1 and the dashed one to k = 2. (C,D) Mean fluorescence, Fm given by Equation (1) (black curve), and region around determined by the standard deviation, Fm ± σF with σF given by Equation (3) (shaded area) as functions of time for the immature oocyte (C) and for the egg (D). Fits to the traces after the UV flash was turned off are shown in red [bi-exponential fit given by Equation 4 in (C) and linear fit given by Equation 6 in (D)]. The purple lines indicate the times during which the UV pulses were on. In the insets the ratio, σF(t)/σF⎯⎯⎯⎯b, with σF⎯⎯⎯⎯b, the deviation before the first UV flash was delivered, is plotted. The maximum ratio is indicated with a dotted red line and the solid red line indicates the time it takes for the ratio to fall by half.
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Figure 5. Comparison of the fluorescence time course obtained in experiments performed for different UV pulses. Fluorescence averaged over subregions with similar basal fluorescence levels (F⎯⎯⎯⎯k, Equation 1) as a function of time for experiments performed in an immature oocyte (A–C) and in an egg (D–F) in which two UV pulses of 11.2 s (A,D), 28 s (B,E), and 56 s (C,F) were applied to photo-release the caged IP3. The time elapsed between the end of the first flash and the beginning of the second was always s. The number of curves and, equivalently, of subregions, is n = 15 in the oocyte (A–C) and n = 16 in the egg (D–F).
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Figure 6. Distribution of the number of IP3Rs, No, that participate of a global Ca2+ release event derived from stochastic simulations of the model described in section 2.4 but with a mean separation between clusters of 4μm and δCa=200s−1 (A) and δCa=20s−1 (B), i.e., conditions S1 and S2 of Table 3, respectively.
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Figure 7. Similar to Figure 6 but with a mean separation between clusters of 0.4μm and δCa=200s−1 (A) and δCa=20s−1 (B), i.e., conditions S3 and S4 of Table 3, respectively.
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Figure 8. [Ca2+] distribution of events in three instants (A–C) of stochastic simulations with a mean separation between clusters of 4μm and δCa=200s−1 (condition S1). Example (A) corresponds to No = 68, (B) to 203 and (C) to 255.
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Figure 9. [Ca2+] distribution of events in three instants (A–C) of stochastic simulations with a mean separation between clusters of 0.4 μm and δCa=200s−1 (condition S3). Example (A) corresponds to No = 9, (B) to 49 and (C) to 215.
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Figure 10. [Ca2+] distribution of events in three instants (A–C) of stochastic simulations with a mean separation between clusters of 0.4μm and δCa=20s−1 (condition S4). Example (A) corresponds to No = 33, (B) to 44 and (C) to 48.
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Figure 11. Fraction of IP3Rs that participate of a global Ca2+ release event, No/NT, derived from stochastic simulations of the model described in section 2.4 with a mean separation between clusters of 0.4μm and δCa=200s−1 (A) and δCa=20s−1 (B), it is conditions S3 and S4 of Table 3, respectively.
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