Multi-scale data-driven modeling and observation of calcium puffs

Abstract

The spatiotemporal dynamics of elementary Ca(2+) release events, such as "blips" and "puffs" shapes the hierarchal Ca(2+) signaling in many cell types. Despite being the building blocks of Ca(2+) patterning, the mechanism responsible for the observed properties of puffs, especially their termination is incompletely understood. In this paper, we employ a data-driven approach to gain insights into the complex dynamics of blips and puffs. We use a model of inositol 1,4,5-trisphosphate (IP(3)) receptor (IP(3)R) derived directly from single channel patch clamp data taken at 10 μM concentration of IP(3) to simulate calcium puffs. We first reproduce recent observations regarding puffs and blips and then investigate the mechanism of puff termination. Our model suggests that during a puff, IP(3)R s proceed around a loop through kinetic states from "rest" to "open" to "inhibited" and back to "rest". A puff terminates because of self-inhibition. Based on our simulations, we rule out the endoplasmic reticulum (ER) Ca(2+) depletion as a possible cause for puff termination. The data-driven approach also enables us to estimate the current through a single IP(3)R and the peak Ca(2+) concentration near the channel pore.

Fig. 1

Equilibrium open probability of the single IP₃R channel as a function of C at IP₃ concentration of 10 μM. The solid line and circles represent the model fit and the mean P_O from patch clamp experiments on Xenopus Laevis occytes [21] respectively. Error bars represent standard errors of the mean.

Fig. 2

Schematic of the four state model for single IP₃R channel. K_ij represents the transition rate from state i to j where i, j =R, A, O, I.

Fig. 3

Random blips as openings of single channels and puffs as cooperative openings of multiple channels. Change in modeled fluorescence as a result of channel openings and closings in unit of average fluorescence change due to single channel events (i.e. fluorescence changes during thousands of blips were averaged and used as unit for the fluorescence change during puffs) (A) and the corresponding number of channel openings during puffs (B). The insets in (A) and (B) show an expanded view of the same puff.

Fig. 4

Distribution of simulated fluorescence changes due to channel openings during the puff in units of unitary Ca²⁺ events (averaged fluorescence change during blips).

Fig. 5

Statistics of Ca²⁺ puffs and blips: (A) Distribution of puff peak amplitude obtained from open channels (solid line with open squares), modeled fluorescence (solid line with filled squares), and experimental data (gray bars). The dotted line with triangles is the distribution obtained from modeled fluorescence when mean time for O to I and I to O transitions is decreased from 290 ms to 230 ms and 2.4 s to 1.92 s respectively. (B) Puff life time distribution. (C) Distribution of puff termination time obtained from open channels (black line), modeled fluorescence (dark gray line), and experimental data (gray bars). The dotted line represents the distribution obtained from the modeled fluorescence when mean times of 230 ms and 1.92 s are used for O to I and I to O transitions respectively. (D) Life time distribution for blips from simulations (solid line with squares) and experiment (gray bars). (E) Mean termination time of puffs as a function of amplitude estimated from open channels (solid line with open squares) and modeled fluorescence (solid line with filled squares). The light gray bullets are the experimental data and dashed line is harmonic series with n = 10 and τ = 50 ms. The dotted line with triangles is the model result when mean times of 230 ms and 1.92 s are used for O to I and I to O transitions respectively. (F) The number of openings/ms (upper panel) and closings/ms (lower panel) per puff as a function of time into puff given by the model. In (F) the gray bullets represent the experimentally observed openings/ms (upper panel) and closings/ms (lower panel). Experimental data reproduced from [5] with permission.

Fig. 6

Puffs are terminated by IP₃R inhibition not local ER depletion. (A) Distribution of time to termination of puffs for f = 2.5, 5, and 10 (solid, dotted, and dashed line respectively). The inset is an expanded view from 600 ms to 1000 ms. (B) Termination time distribution for $C_{\mathit{ER}}^{\mathit{rest}}=700\mu \mathrm{M}$, 900 μM, and 1300 μM (solid, dotted, and dashed line respectively). (C) Local ER Ca²⁺ concentration for simulations in (B). Different line patterns correspond to the same $C_{\mathit{ER}}^{\mathit{rest}}$ values as in (B). The inset is an expanded view from 0 to 100 μM.