Computational investigation of IP3 diffusion

Abstract

Inositol 1,4,5-trisphosphate (IP₃) plays a key role in calcium signaling. After stimulation, it diffuses from the plasma membrane where it is produced to the endoplasmic reticulum where its receptors are localized. Based on in vitro measurements, IP₃ was long thought to be a global messenger characterized by a diffusion coefficient of ~ 280 μm²s^-1. However, in vivo observations revealed that this value does not match with the timing of localized Ca²⁺ increases induced by the confined release of a non-metabolizable IP₃ analog. A theoretical analysis of these data concluded that in intact cells diffusion of IP₃ is strongly hindered, leading to a 30-fold reduction of the diffusion coefficient. Here, we performed a new computational analysis of the same observations using a stochastic model of Ca²⁺ puffs. Our simulations concluded that the value of the effective IP₃ diffusion coefficient is close to 100 μm²s^-1. Such moderate reduction with respect to in vitro estimations quantitatively agrees with a buffering effect by non-fully bound inactive IP₃ receptors. The model also reveals that IP₃ spreading is not much affected by the endoplasmic reticulum, which represents an obstacle to the free displacement of molecules, but can be significantly increased in cells displaying elongated, 1-dimensional like geometries.

Figure 1

Theoretical values of the effective IP₃ diffusion coefficient depending on the concentration of IP₃ and of the monomers of IP₃ receptors (S_T). The dashed line shows this diffusion coefficient as a function of [IP₃] for S_T = 542 nM, which is the value estimated for SH-S5Y5 neuroblastoma cells. Values have been calculated using Eq. 1. See text for details.

Figure 2

Stochastic simulations of Ca²⁺ puffs and spikes. (A and B) show the evolution of Ca²⁺ concentration in a 1 fL volume (1.5 × 1.5 μm² in the 2D simulations, see Voorsluijs et al.) centered around the cluster at two [IP₃]. For the 2 panels, one cluster, located at the centre of a 5 × 5 μm² 2D system is considered. For panels (C and D), a larger 5 × 10 μm² system containing 10 clusters is simulated. All values of parameters are the same as in A and B and listed in Table S2. Time series show the evolution of Ca²⁺ concentration averaged on the whole system. Panels (E and F) show the spatio-temporal evolutions of Ca²⁺ puffs and spikes, respectively. In the two cases, the system is 50 × 10 μm² large and 10% of the total surface is occupied by clusters (200 clusters). For panel E, [IP₃] is constant and equal to 0.075 μM everywhere in the cell. For panel F, IP₃ was released in one spot (with dimensions 0.5 × 0.5 μm²) located in the bottom center of the simulated cell. For panels E and F, times corresponding to each subpanels are: 0.1, 0.6, 2.5, 3.4 and 5.2 s after the increase in [IP₃] from 10 nM. In panels A-E, [IP₃] is increased at time 0, and Eqs. (3) and (5) are not considered. In panel F, the release of IP₃ is simulated using Eq. (3), with $\theta$ = 1000µMs⁻¹, D_I = 100 μm²s⁻¹ and t_ph = 500 ms.

Figure 3

Statistics of the latencies of first puffs simulated with the model. Panels (A and B) show histograms of first puff latencies resulting from simulations of one cluster site in a square 5 × 5μm² 2D geometry. A puff is defined as an increase in the cytosolic Ca²⁺ concentration in a 1 fL volume (1.5 × 1.5 μm² in the 2D simulations, see Voorsluijs et al.) centered around the cluster that exceeds 0.1 μM. First puff latencies show an exponential distribution with characteristic decrease times matching experimental observations. Time t = 0 corresponds to the moment of [IP₃] increase from 50 nM to indicated values. The black stars in panel (C) show the mean first puff latencies (ML) as a function of [IP₃]. The blue dashed line shows the minimal first puff latencies (MFP), i.e. the time at which the first puff occurred. Minimal first puffs are practically independent of [IP₃] and are always close to 300 ms. For each [IP₃], 50 independent simulations were run. In panels A, B and C, [IP₃] is increased at time 0, and Eqs. (3) and (5) are not considered. In panel D, photorelease of caged IP₃ is also simulated, using Eq. (5). Best fit with the observations of Dickinson et al. was found when considering θ = 600 μMs⁻¹. This value was found by looking for the value of θ that allows to obtain the steady states [IP₃] leading to the ML’s corresponding to the flash durations (t_ph) used in Dickinson et al.’s experiments, i.e. 8.9 ± 0.5 s, 6.4 ± 1.2 s and 1.9 ± 0.2 s for the 0.1, 0.2 and 0.5 s flash durations, respectively. Error bars indicate ± SEM.

Figure 4

Mean latencies (ML) and minimal first puff latencies (MFP) as simulated with an effective IP₃ diffusion coefficient equal to 100 μm²s⁻¹ (first and second rows) or 10 μm²s⁻¹ (third row) and a rate of IP₃ increase at the photorelease spot of 600 μMs⁻¹ (first and third rows) or 250 μMs⁻¹ (second row). In all panels, squares represent mean latencies and stars, minimal first puff latencies. Plain symbols are theoretical predictions while empty symbols are the experimental observations of Dickinson et al., estimated from their figures. Lines are drawn between simulation results. Simulations are performed in a 2D ellipse-shaped geometry with the spot of IP₃ release occurring in a 0.25 μm radius circle at one extremity of the simulated cell. For each theoretical point, 50 independent simulations were run, considering one cluster at a time. Error bars indicate ± SEM. For minimal first puffs, the 50 simulations were divided in 10 groups of 5 simulations among which the minimal first puff was considered, except for the case θ = 250 μMs⁻¹ and the 500 ms flash for which 100 simulations were run for the shortest distance.

Figure 5

Comparison between puff latencies theoretically predicted with the rate of IP₃ release θ = 250 μm²s⁻¹ and observed by Dickinson et al.. Panels (A and B) show minimal first puff latencies and mean latencies simulated with different values of the effective diffusion coefficient for IP₃, D_I. All points correspond to a 200 ms flash. Plain symbols are theoretical predictions while empty symbols are the experimental observations of Dickinson et al.. Lines are drawn between simulation results. Simulations are performed in a 2D ellipse-shaped system with the spot of IP₃ release being a 0.25 μm radius disk at one extremity of the simulated cell. For each theoretical point, 50 independent simulations were run. Error bars indicate ± SEM. For minimal first puffs, the 50 simulations were divided in 10 groups of 5 simulations among which the minimal first puff was considered.

Figure 6

Computational simulations of IP₃ diffusion and Ca²⁺ puff occurrence in response to the localized photorelease of a non-metabolizable IP₃ analogue in an ellipsoidal 3D geometry, assuming an effective diffusion coefficient of IP₃ (D_I) of 100 μm²s⁻¹. The upper panel shows IP₃ distribution 2 s after the flash. Lower panels show time series of local Ca²⁺ concentrations at cluster sites (in a 1 fL volume) located at increasing distances from the flash. Simulation procedures are the same as for Fig. 4. The rate of localized IP₃ photorelease, θ, is taken equal to 2500 μMs⁻¹, which allows to obtain the same spatiotemporal profile of IP₃ increase as the 250 μMs⁻¹ value for the 2D case, because of changes in volume.

Figure 7

Computational simulations of IP₃ diffusion and Ca²⁺ puff occurrence in response to the localized photorelease of a non-metabolizable IP₃ analogue in a 2D geometry resembling an astrocyte, assuming an effective diffusion coefficient of IP₃ (D_I) of 100 μm²s⁻¹. (A) Shape of the astrocyte redrawn in COMSOL Multiphysics from images of Gonçalves-Pimentel et al.. Locations of the clusters considered in the simulations are indicated and labelled in black in the astrocytic process and in blue and green in the cell body. IP₃ photorelease was assumed to occur between locations 1 and 5. Simulation procedures are the same as for Fig. 4 (main text), with θ = 250 μms⁻¹ and flash duration = 500 ms. Panels (B and C) show the minimal first puffs and the mean first puff latencies at the different locations, respectively. At equal distance from the IP₃ release point, puffs occur sooner in the process than in the body. Panel (D) shows the distribution of IP₃ 2 s after the flash: higher local IP₃ concentrations are reached in the process in which there is no dilution effect. The spatio-temporal evolution of [IP₃] can be seen in the Supplement Video S5.

Figure 8

Theoretical investigation of the influence of the ER membranes on the diffusion of IP₃ and Ca²⁺ puff occurrence. Panels (A and B) show the 2D geometry considered in the computational simulations of IP₃ diffusion and Ca²⁺ puff occurrence in response to the localized photorelease of a non-metabolizable IP₃ analogue. The shape of the cell was redrawn from Dickinson et al. (2016) and that of the ER was largely inspired from De Angelis et al.. Panels (C and D) show the simulated (plain symbols) and experimental (empty symbols) mean latencies (blue) and minimal first puff latencies (black). Flash duration is 500 ms. Simulation procedures are the same as for Fig. 4. The rates of localized IP₃ photorelease, θ, is taken equal to 400.6 μMs⁻¹ and 284.65 μMs⁻¹, respectively which corresponds to the 250 μMs⁻¹ used in the other simulations with the volumetric adjustments.

Figure 9

Theoretical investigation of the influence of the ER membranes on the diffusion of IP₃ in a 2D ellipse-shaped cell (50 × 10 μm²). Panel (A) shows the central part of the simulated cell together with the locations of the clusters considered. Panels (B and C) show the IP₃ temporal profiles at the different cluster locations considering a spot of photorelease of IP₃ located at the left (B) or at the right (C) extremity of the cell. Line colors correspond to the points in panel A. In panel (D), the profiles of the IP₃ concentrations averaged over the six cluster sites are shown for the two situations corresponding to B and C. Simulation procedures are the same as for Fig. 4. The rate of localized IP₃ photorelease, θ, is taken equal to 179.42 μMs⁻¹, which corresponds to the 250 μMs⁻¹ used in the other simulations with the volumetric adjustments.