Suppressing effect of $\mathrm{C}{\mathrm{a}}^{2+}$ blips on puff amplitudes by inhibiting channels to prevent recovery

As local signals, calcium puffs arise from the concerted opening of a few nearby inositol 1,4,5-trisphospate receptor channels to release $\mathrm{C}{\mathrm{a}}^{2+}$ ions from the endoplasmic reticulum. Although $\mathrm{C}{\mathrm{a}}^{2+}$ puffs have been well studied, little is known about the modulation of cytosolic basal $\mathrm{C}{\mathrm{a}}^{2+}$ concentration (${\left[\mathrm{C}{\mathrm{a}}^{2+}\right]}_{\mathrm{Basal}}$) on puff dynamics. In this paper we consider a puff model to study how the statistical properties of puffs are modulated by ${\left[\mathrm{C}{\mathrm{a}}^{2+}\right]}_{\mathrm{Basal}}$. The puff frequency and lifetime trivially increase with the increasing ${\left[\mathrm{C}{\mathrm{a}}^{2+}\right]}_{\mathrm{Basal}}$, but an unexpected result is that the puff amplitude and the maximum open-channel number of the puff show decreasing relationship with the increasing ${\left[\mathrm{C}{\mathrm{a}}^{2+}\right]}_{\mathrm{Basal}}$. The underlying dynamics is related not only to the increasing puff frequency which gives a shorter recovery time, but also to the increasing frequency of blips with only one channel open. We indicate that $\mathrm{C}{\mathrm{a}}^{2+}$ blips cause the channels to be inhibited and prevent their recovery during interpuff intervals, resulting in the suppressing effect on puff amplitudes. With increasing ${\left[\mathrm{C}{\mathrm{a}}^{2+}\right]}_{\mathrm{Basal}}$, more blips occur to cause more channels to be inhibited, leaving fewer channels available for puff events. This study shows that the blips may play relevant functions in global $\mathrm{C}{\mathrm{a}}^{2+}$ waves through modulating puff dynamics.

Figure 1

(a) The schematic diagram of the DYK model for a subunit of the $\mathrm{I}{\mathrm{P}}_3\mathrm{R}$ channel. Ca and I represent $\left[\mathrm{C}{\mathrm{a}}^{2+}\right]$ and $\left[\mathrm{I}{\mathrm{P}}_3\right]$, respectively. $a_i$ and $b_i$ denote the on and off rates given in Table 1. (b) The open probability curve for the DYK model in different cytosolic $\left[\mathrm{C}{\mathrm{a}}^{2+}\right]$ and $\left[\mathrm{I}{\mathrm{P}}_3\right]$. Symbols are experimental data from Refs. [26, 27].

Figure 2

An example of the simulation result of the model with (a) the evolution of $N_{\mathrm{Open}}$ and (b) ${\left[\mathrm{C}{\mathrm{a}}^{2+}\right]}_{\mathrm{Close}}$ at $N=4$. The inner figures are the amplifying puff for $N_{\mathrm{Open}}$ and ${\left[\mathrm{C}{\mathrm{a}}^{2+}\right]}_{\mathrm{Close}}$. (c) The comparison between experiment and model results for puff frequency against cluster size $N$. The red stars are experimental data [13]. The solid lines with symbols are obtained with the model at different ${\left[\mathrm{C}{\mathrm{a}}^{2+}\right]}_{\mathrm{Basal}}$ and $\left[\mathrm{I}{\mathrm{P}}_3\right]$.

Figure 3

(a) The puff frequency, (b) puff lifetime, (c) puff amplitude, and (d) the maximal open-channel number against cluster size $N$ at ${\left[\mathrm{C}{\mathrm{a}}^{2+}\right]}_{\mathrm{Basal}}=0.02\mu M$ (circles), $0.04\mu M$ (squares), $0.10\mu M$ (rhombus), and $0.14\mu M$ (triangles).

Figure 4

(a) Puff frequency, (b) puff lifetime, (c) puff amplitude, and (d) the maximum open-channel number against ${\left[\mathrm{C}{\mathrm{a}}^{2+}\right]}_{\mathrm{Basal}}$ at $N=4$ (circles), 6 (squares), 8 (rhombus), and 10 (triangles).

Figure 5

(a) The probabilities at the eight states and (b) the probabilities of subunits in active state (stars), inhibited states (rhombus), and closed states (circles) against ${\left[\mathrm{C}{\mathrm{a}}^{2+}\right]}_{\mathrm{Basal}}$ at $N=8$.

Figure 6

The evolution of probabilities $P_{\mathrm{Active}}, P_{\mathrm{Inhibited}}$, and $P_{\mathrm{Closed}}$ for 50 ms right after the termination of puffs and right before the beginning of puffs at ${\left[\mathrm{C}{\mathrm{a}}^{2+}\right]}_{\mathrm{Basal}}=0.04\mu M$ (a), and at ${\left[\mathrm{C}{\mathrm{a}}^{2+}\right]}_{\mathrm{Basal}}=0.14\mu M$ (b) with $N=8$. The circles denote the active state, triangles the inhibited states, and rhombus the closed states.

Figure 7

The detailed traces with ${\left[\mathrm{C}{\mathrm{a}}^{2+}\right]}_{\mathrm{Basal}}=0.04\mu M$ (left) and $0.14\mu M$ (right) at $N=8$ in the cluster. The traces are for the number of the open channels (a,f), the domain ${\left[\mathrm{C}{\mathrm{a}}^{2+}\right]}_{\mathrm{Close}}$ (b,g), and the probabilities of $P_{\mathrm{Active}}$ (c,h), $P_{\mathrm{Closed}}$ (d,i), and $P_{\mathrm{Inhibited}}$ (e,j).

Figure 8

The blip frequency against ${\left[\mathrm{C}{\mathrm{a}}^{2+}\right]}_{\mathrm{Basal}}$ in $N=4$ (circles), 6 (squares), 8 (rhombus), 10 (triangles).