Figure 1.
A schematic diagram of the model.
(A) As to the single astrocyte, Ca2+ influx through voltage-gated calcium channels (VGCCs) triggers the fluctuation of Ca2+ in the intracellular space (ICS), enhancing the production of inositol 1,4,5-triphosphate (IP3), which is catalyzed by phospholipase C (PLC). Ca2+ and IP3 bind to IP3 receptors (IP3R), activating the process of calcium-induced calcium release (CICR). The endoplasmic reticulum (ER) is filled with Ca2+ by the sarcoplasmic/endoplasmic reticulum calcium ATPase (SERCA). A Ca2+ pump discharges Ca2+ from the ICS into the extracellular space (ECS). K+ in the ECS is partly uptaken into the ICS during cortical spreading depression (CSD). JVGCC, JCICR and JSERCA represent the Ca2+ flow through VGCCs, CICR and SERCA, respectively. Jpump represents the Ca2+ flow through the Ca2+ pump. Jleak represents the leak Ca2+ flow. Jupt represents the K+ flow untaken into ICS, and Jdis represents the K+ flow discharged into ECS. (B) Single astrocytes are coupled to the adjacent ones by the transfer of IP3 from cytosol to cytosol through gap junctions to form a one-dimensional astrocyte network.
Figure 2.
Characteristics of spontaneous Ca2+ oscillations (CASs) in the computerized astrocytic model.
(A) Ca2+ oscillations in the ICS occur without any stimulus. (B) Ca2+ oscillations in the ER occur earlier and last longer than those in the ICS. (C) The concentration of Ca2+ in the ECS decreases slightly before Ca2+ oscillations in the ICS and then increases after the oscillations. (D) IP3 oscillates in the ICS.
Figure 3.
The influence of different Ca2+ flows on CASs.
By inhibiting CICR (dashed triangle), the frequency (A) and amplitude (B) of CASs decrease, but the duration (C) increases. CASs do not occur when CICR is inhibited more than 95%. By inhibiting SERCA (dashed circle), the frequency (A) of CASs increases, but both the amplitude (B) and the duration (C) decrease. CASs do not occur when SERCA is inhibited more than 70%. Inhibiting VGCCs (solid star) has little effect on the amplitude (B) and duration (C) but great on frequency (A) before CASs disappear. CASs do not occur when VGCCs are inhibited more than 45%.
Figure 4.
The influence of different Ca2+ flows on CSD-triggered Ca2+ waves (CSDCWs).
A typical CSDCW is characterized as the significant elevation of Ca2+ in the ICS at successive astrocytes in the network (A), associated with the increase of Ca2+ in the ER (B), the increase of IP3 in the ICS (D) and the decrease of Ca2+ in the ECS (C). CICR inhibition shortens the duration of increased Ca2+ in the ICS (E), slows the recovery of Ca2+ in the ER (F), decreases Ca2+ in the ECS more than in the control condition (G) and increases the duration of increased IP3 in the ICS (H). SERCA inhibition increases the amplitude of Ca2+ in the ICS (I) and decreases that in the ER (J). Ca2+ in the ECS is increased compared to the control (K). Because high Ca2+ in the ICS would inhibit the process of CICR, the increase of IP3 in the ICS is shortened (L). After VGCCs inhibition, Ca2+ is largely weakened in the ICS (M), in the ER (N) and in the ECS (O). The changes of IP3 are also shortened because of the low Ca2+ in the ICS (P).
Figure 5.
Interactions between CASs and CSDCWs.
(A) A series of CASs occur without any stimulus. (B) The appearance of CSDCWs depresses CASs, and CASs reappear a few minutes after the pass of CSDCWs (the affected CASs are marked with asterisks in A and B). CSDCWs can appear immediately after CASs (marked with an arrow in B). By regulating the appearance time of CSDCWs through changing the time points of locally elevating Ko (marked with red bars in B), the peak-to-peak interval between the CSDCW and the following CAS is similar, and it is not related to the peak-to-peak interval between the CSDCW and the previous CAS. t1, the peak-to-peak interval between the CSDCW and the previous CAS. t2, the peak-to-peak interval between the CSDCW and the following CAS. (C) Depletion of Ca2+ stores in the ER abolishes CASs, but CSDCWs still spread. The bar illustrates the time of locally elevating Ko.
Figure 6.
Transition from CASs to CSDCWs.
(A) By locally increasing Ko to 5 or 9 mM, Ca2+ in ICS is increased, which facilitates the occurrence of CASs. When Ko is increased to 12 mM, a CSDCW is induced. (B) Increasing Ko in the present of CASs elevates Ca2+ in ICS and then the elevated Ca2+ will postpone the occurrence of the following CASs. Following oscillations are shown in the illustration. The bar illustrates the time of locally elevating Ko, the concentrations of which are shown in the legend. Arrows indicate the appearance time of CASs under the control condition.