A method for determining the dependence of calcium oscillations on inositol trisphosphate oscillations

Abstract

In some cell types, oscillations in the concentration of free intracellular calcium ([Ca2+]) are accompanied by oscillations in the concentration of inositol 1,4,5-trisphosphate ([IP3]). However, in most cell types it is still an open question as to whether oscillations in [IP3] are necessary for Ca2+ oscillations in vivo, or whether they merely follow passively. Using a wide range of models, we show that the response to an artificially applied pulse of IP3 can be used to distinguish between these two cases. Hence, we show that muscarinic receptor-mediated, long-period Ca2+ oscillations in pancreatic acinar cells depend on [IP3] oscillations, whereas short-period Ca2+ oscillations in airway smooth muscle do not.

Fig. 1.

Model responses to pulses of IP₃. (A and B) Responses of class 1 models to a pulse of IP₃. (A) Response of the Atri model (4); p_st = 10, M = 20, t_pulse = 70, t_width = 3. The solid line is [Ca²⁺] and is plotted against the left axis; the dotted line is [IP₃] and is plotted against the right axis. (B) Response of the Li–Rinzel model (6); p_st = 0.8, M = 0.05, t_pulse = 250, t_width = 10. (C and D) Responses of class 2 models to a pulse of IP₃. These responses were calculated from the same models as A and B but modified so that Ca²⁺ oscillations depend on oscillations in [IP₃] (details in Appendix). In each panel a pulse of IP₃ was added at the arrow. (C) Response of the modified Atri model (4); ν₄ = 6, M = 3, t_pulse = 100, t_width = 3. (D) Response of the modified Li–Rinzel model (6); ν₄ = 0.7, M = 5, t_pulse = 600, t_width = 2.

Fig. 2.

Responses of ASM and PAC to pulses of IP₃. (A) In ASM, photorelease of IP₃ causes a transient increase in oscillation frequency. (B) In PAC, photorelease of IP₃ causes a delay in the next peak of the Ca²⁺ oscillation.

Fig. 3.

Comparison of model and experimental results. (A and B) The dose-dependence of the changes in the oscillation frequency induced by flash photolysis of caged IP₃ in ASM. The initial baseline rate of Ca²⁺ oscillations was induced by MCh (100 nM). The incremental increase in IP₃ concentration was achieved by increasing the UV flash intensity with a series of neutral density filters with optical density (OD) values of 1.0. 0.8, and 0.6 where transmission % equals 10^OD× 100. The UV exposure time was constant (100 ms) and the diameter of the area illuminated was 50 μm in all experiments. Data were obtained from different airways of two mice. The same dye and caged IP₃ loading process was used for each slice. Each data point is the average of responses from four different cells. (A) Solid symbols: the ratio of the average frequency of Ca²⁺ oscillations during the first 20 s after the UV exposure to the preexposed frequency (30 s) induced by MCh was plotted with respect to the flash intensity (UV transmission percentage). Smooth curve: frequency increase in the class 1 Li–Rinzel model (p_st = 0.6), plotted against the pulse strength (the upper axis). Calculations were performed by using the bifurcation tracking program auto, as incorporated into xppaut (29), using M as the principal bifurcation parameter. The relationship between M and transmission percentage is arbitrary but the same in A and B. (B) Time taken (T₅₀) for the oscillation frequency to return to 50% of the average frequency increase achieved during the first 20 s after UV exposure. The open symbols are from the class 1 Li–Rinzel model (p_st = 0.6) and are plotted against the upper axis. The model results are estimated at three different values of M. (C) Percent change in interspike interval in PAC for three approximate timings of the IP₃ pulse. Immediate, IP₃ pulse occurs right after a Ca²⁺ spike; intermediate, IP₃ pulse occurs between two Ca²⁺ spikes, but not close to either one; simultaneous, IP₃ pulse occurs at the same time as a Ca²⁺ spike would have occurred, judging by the previous oscillations. The model results are from the class 2 Atri model.

Fig. 4.

Response of PAC (Upper) and the class 2 Atri model (Lower) to a pulse of IP₃ that occurs right on a Ca²⁺ spike. In both the experiment and the model the IP₃ pulse causes a Ca²⁺ spike of slightly greater amplitude, with little change in subsequent spike frequency (see Fig. 3C).

Fig. 5.

Model and experimental responses to IP₃ pulses of increasing magnitude. (A) In class 1 models, an increase in the strength of the IP₃ pulse causes oscillations of greater frequency and smaller amplitude, superimposed on a raised baseline. If the pulse is large enough, the oscillations can disappear entirely, leaving only the raised baseline (traces calculated from the Li–Rinzel model). (B) In class 2 models, an increase in the strength of the IP₃ flash leads to a greater phase delay (traces calculated from the Atri model). (C) In ASM, an increase in the strength of the IP₃ pulse leads to fast oscillations superimposed on a raised baseline, as in class 1 models. C Upper was with a smaller light flash, and thus a smaller IP₃ release than in C Lower. The responses of all four cells (from two different animals) were qualitatively similar.