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First published online 3 August 2004
doi: 10.1242/jcs.01278

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Simulation of calcium waves in ascidian eggs: insights into the origin of the pacemaker sites and the possible nature of the sperm factor

¹ Unité de Chronobiologie Théorique, Université Libre de Bruxelles, Faculté des Sciences CP231, Boulevard du Triomphe, Brussels 1050, Belgium
² Department of Physiology, University College London, Gower Street, London, WC1E 6BT, UK

View larger version (16K): [in a new window]   Fig. 1. Model developed to account for Ca2+ oscillations and waves in ascidian eggs. The red pathway shows experiments of gPtdIns(4,5)P2 (gPIP2) or Ins(1,4,5)P3 (IP3) flash photolysis, while the blue pathway shows the events supposed to occur at fertilization. The model is adapted from previous reports (Dupont and Swillens, 1996; Dupont and Erneux, 1997).

View larger version (19K): [in a new window]   Fig. 2. Grey-scale representation of the density of the endoplasmic reticulum (parameter ) used in the simulations of Ca2+ oscillations and waves in ascidian eggs. The ER is assumed to be more concentrated in the cortex of the egg, with a maximal value in the animal cortex. Parameter measures the local ratio between the ER and the cytosolic volumes. Scale: black, =0.12; white, =0.07. This ER density is given by equations (6) and (7) with the following parameter values to characterize the gradient of ER-density from the periphery to the center and the shape of the pacemaker (see text): basal density of ER B=0.07, C=0.10, w=0.04, rC=75 µm, h=0.04 and d=15 µm. a, animal pole; v, vegetal pole.

View larger version (42K): [in a new window]   Fig. 3. Simulations of the effect of localized Ins(1,4,5)P3 injections. Results have been obtained by integration of equations (1) to (5) with the ER density represented in Fig. 2 and the following parameter values: Dcyto=40 µm2 second-1, DER=4 µm2 second-1, DIP=280 µm2 second-1, Kact=0.54 µM, Kinh (=(k-/k+)1/ni) 0.28 µM, k-=4 10-3 second-1, k1=1.285 second-1, b=2.5 10-4 second-1, K=1 µM, vMP=1.2 µM second-1, KP=0.35 µM, VPLC=0.015 µM second-1, V5P=0.67 µM second-1, K5P=8 µM, V3K=3.35 10-2 µM second-1, K3K=0.5 µM, KA3K=0.3 µM, na=2, ni=3. Most of these values come from previous modelling studies, where they were either taken from the literature or fitted to get agreement with the observations (Dupont and Erneux, 1997; Dupont et al., 2000). In the three simulations, during the flash time IIP=7 µM second-1 in the mesh points (46 to 54) along the X axis, and (89 to 97) along the Y axis (this region is indicated as a black square in the first panel). The resulting Ins(1,4,5)P3 increase taken as an average on the whole egg ranges between 0.05 and 2.5 µM depending on the flash duration. Initial conditions are Ccyto=0.1 µM, Clum=875 µM and the corresponding steady-state values of the other variables. To perform the simulations, mesh points are labelled 1 to 100 from left to right, and from top to bottom. To account for the circular shape of the egg (in two dimensions), the appropriate mesh points are excluded from the system. In this and all subsequent figures, the level of cytosolic Ca2+ is represented by the amount of Ca2+ bound to an indicator whose K1/2 for Ca2+ is 0.7 µM. When representing the Ca2+ waves, the scale is different for each image, with red and blue representing the highest and the lowest instantaneous levels of cytosolic Ca2+, respectively.

View larger version (29K): [in a new window]   Fig. 4. Simulation of the effect of a global increase in [gPtdIns(4,5)P2]. Results have been obtained by integration of equations (1) to (5) with the ER density represented in Fig. 2 and the same parameter values as in Fig. 3, except for the fact that gPtdIns(4,5)P2 has been used instead of Ins(1,4,5)P3. Thus the rates of degradation (V5P and V3K) have been divided by ten. To simulate the activation of the Ins(1,4,5)P3R by both gPtdIns(4,5)P2 and the basal Ins(1,4,5)P3 level, we must replace the second part of equation (3) by: with KgPtdIns(4,5)P2=8 µM. These latter changes reflect the facts that gPtdIns(4,5)P2 is slowly metabolized and that Ins(1,4,5)P3 and gPtdIns(4,5)P2 bind to the same site of the receptor, and that gIns(4,5)P2 has less affinity for the receptor. A basal level of Ins(1,4,5)P3 equal to 18 nM (corresponding to the stationary state in Ins(1,4,5)P3 with the basal LC activity) is always present. During the flash time (2 seconds), IgPtdIns(4,5)P2=0.045 µM second-1 in the whole system. The successive panels show the spatial distribution of Ca2+ at the times indicated by the points on the curve on the left.

View larger version (15K): [in a new window]   Fig. 5. Relationship between the mean velocity and global amplitude of the artificially induced Ca2+ waves and the intensity of the stimulus. Points have been obtained as in Fig. 4 with the same parameter values, except for the rate of gPtdIns(4,5)P2 influx. For influx rates lower than 0.03 µM second-1, the Ca2+ waves do not propagate throughout the whole egg (abortive waves). Conversely, for influx rates higher than 0.05 µM second-1, the Ca2+ increases occur nearly homogeneously over the whole egg.

View larger version (51K): [in a new window]   Fig. 6. (A) Theoretical prediction of the effect of a gPtdIns(4,5)P2 increase in the vegetal hemisphere of the ascidian egg. A high amplitude increase in gPtdIns(4,5)P2 initiated in the vegetal hemisphere of the egg (indicated by a black square) evokes two successive Ca2+ waves, the first one emanating from the locus of stimulation and the second one emanating from the region of higher ER density in the animal pole region (PM3). Simulations have been performed as in Fig. 4 with a gPtdIns(4,5)P2 increase IgPtdIns(4,5)P2=12 µM second-1 for 4 seconds, at the mesh points (45 to 55) along the X axis and (80 to 90) along the Y axis, as indicated by the black box in the first panel. The successive panels show the spatial distribution of Ca2+ at the times indicated by the points on the curve on the left. (B) Effect of local photo-release of gPtdIns(4,5)P2 in an unfertilized ascidian egg. First row: confocal image of [Ca2+]c (the concentration of cytosolic Ca2+) taken 2 seconds (2'') after local UV uncaging, the area of UV uncaging is indicated by a black square. Second row: a Ca2+ wave is initiated at 1 minute 45 seconds (t=1'45'') in the animal pole and traverses the whole egg.

View larger version (33K): [in a new window]   Fig. 7. Simulation of the effect of a massive, global increase of gIns(4,5)P2 in the ascidian egg. The temporal pattern of the Ca2+ spike much resembles that observed at fertilization. Simulation has been performed as in Fig. 4 with IgPtdIns(4,5)P2=25 µM second-1 in the whole system during the flash time (0.3 seconds). The black, red and blue traces represent the average level of cytosolic Ca2+, gPtdIns(4,5)P2 and luminal Ca2+, respectively.

View larger version (16K): [in a new window]   Fig. 8. Simulation of the series I Ca2+ oscillations induced by fertilization. Shown are the evolutions of the average concentrations in Ca2+ (black), Ins(1,4,5)P3 (blue) and SF (red). Results have been obtained by numerical simulations of equations (1), (4), (5') and (8) with the same parameter values as in Fig. 3. Moreover KASF=0.15 µM, kSF=5.56 10-3 second-1 and DSF=150 µm2 second-1. Initial conditions are the same as in Fig. 3, except that [SF]=50 µM in the mesh points (16 to 20) along the X and Y axes.

View larger version (24K): [in a new window]   Fig. 9. Effect of varying the dose of SF injected into the egg. Simulations are the same as in Fig. 8, except for the initial localized rise in [SF], which equals 35 µM for panel (A) and 60 µM for panel (B).