In our simulations presented in the original article of this chapter, we did not take into account reflections of Ca2+ ions and buffer molecules from presynaptic vesicles. This is partially justified by the previous simulation results (Shahrezaei & Delaney, 2004) which showed that [Ca2+] is
is immediately (a few nm) above the Ca2+ channel mouth. Thus, the reflections of Ca2+ ions could, at most, boost the contributions of those channels which are located just below the vesicles. Measuresm andRcdo not allow to constrain the AZ topographies to such a certainty that the mentioned effect could be determined. Some researchers proposed that the synaptic ribbons could act as diffusion barriers as well (Roberts, 1994; Graydon et al., 2011). No evidence exists to support this idea so far. However, simulations showed that [Ca2+] at the sensor of exocytosis could be elevated severalfold at hair cells from bullfrog sacculus (Roberts, 1994) or amphibian papilla (Graydon et al., 2011), if the ribbons were indeed reflective to Ca2+. It has to be noted, though, that synaptic ribbons of the aforementioned hair cells are much larger (wider) than the majority of ribbons observed in IHCs from mature mice (compare Fig. 1 from (Lenzi et al., 1999) and Fig. 2 of the original article of this chapter). Thus, our expectation was that ribbons at afferent IHC synapses should not influence [Ca2+] at presynaptic AZs substantially even if they are reflective to Ca2+ ions and/or Ca2+ buffer molecules. In particular, we expect that the reflections from the ribbon do not affect the exponent m values. Here, we provide additional results to evaluate the validity of this assumption.
To examine the effect of RRP vesicles and synaptic ribbon as diffusion barriers, we performed additional numerical simulations. Presynaptic AZ topography scenarios M1, M2, and M3 were considered as representatives of (relatively) loose and tight coupling between the Ca2+ channels and sensors of exocytosis. The spatiotemporal dynamics of Ca2+ was simulated by using CalC (version 7.7.4), a finite-difference solver of reaction-diffusion equations (Matveev et al., 2002).
Our simulations featured a uniform 3D rectangular grid with 5 nm spatial resolution. Con-centrations of Ca2+ at intermediate points in space were estimated by using the cubic spline interpolation. The simulation volume was defined by a rectangular box with the dimensions of 480 nm×820 nm×200 nm. The AZ was positioned in the middle of the lower face of the box (dimensions 480 nm×820 nm), so that the corresponding edges of both rectangles were in par-allel. The lower face of the box was assumed to be reflective to Ca2+ ions and buffer molecules.
Dirichlet boundary conditions were set on the remaining faces of the simulation volume, with concentrations of Ca2+ and buffer molecules fixed to their background levels ([Ca2+]0 = 50 nm, [BAPTA]T = 0.5 mM). RRP vesicles, when treating them as diffusion barriers, were approxi-mated by 30 nm×30 nm×30 nm cubes, placed in parallel with the plasma membrane, 5 nm above it. The ribbon was approximated by a rectangular box which was positioned with one of its faces in parallel with presynaptic density, 40 nm above the plasma membrane, as shown in Fig. 2.4A, B. The height of the ribbon was unlimited, i.e., was as high as allowed by the simulation volume. We considered two options for the ribbon width, 40 nm and 80 nm, which correspond to half and full width of the presynaptic density respectively (Fig. 2.4A, B). While the first of them is supposed to account for “wedge” and “droplet” like ribbons (see Fig. 2 in the original publication of the present chapter), the second one represents the the “oval” ribbons.
It has to be noted that, regarding its effect on AZ [Ca2+], the width of the ribbon is important only up to 100 nm or so above the plasma membrane.
Figure 2.4: Effect of potential diffusion barriers on presynaptic [Ca2+]. (A) The geometry and placement of the synaptic ribbon with respect to the presynaptic density in the simulations. Width of the ribbon was set to 40 nm in this case. (B) The same as (A), but with the ribbon width set to 80 nm. (C) Simulation results for AZ topography scenarios M1-3 corresponding to the ribbon geometry shown in (A). Entries of the columns “−vesicles−ribbon” correspond to the estimates ofnchand the time-averaged steady state [Ca2+] by ignoring reflections of Ca2+ ions and buffer molecules from the ribbon and RRP vesicles. Whereas entries of the columns “+vesicles +ribbon” contain estimates of the same variables obtained with the aforementioned reflections taken into account. (D) the same as (C), but assuming the ribbon geometry shown in (B).
As in the original article of the present chapter, we considered responses to depolarizations to -17 mV, which evoke maximal Ca2+ influx. In order to calculate the averaged steady state [Ca2+], we fixed all Ca2+ channels in their open states and set the current flowing through each of these channels to a product of a nominal single channel current (0.3 pA) multiplied by the open probability of the channel (0.32). The steady state [Ca2+] at the sensors of exocytosis was then calculated 2 ms after the stimulus onset, when initial equilibration of [Ca2+] was reached.
20 random realizations of each of the three AZ topography scenarios M1-3 were considered and the results presented here represent average values over those 20 realizations. All the remaining parameters of the model were set to the same values as in the original article of this chapter.
To decrease the computation time to a convenient level (order of a few hours), each realization was run on separate CPU cores in parallel (60 cores in total).
The simulation results are summarized in Fig. 2.4 C, D. When the ribbon width was set to 40 nm, The elevations of [Ca2+] at the sensor of exocytosis were 22%, 19%, and 8% for scenarios M1, M2, and M3 respectively. These estimates increased to, respectively, 48%, 39%, and 16% when the ribbon width of 80 nm was assumed. In both cases, changes of the effective number of contributing channels, nch, were negligible, suggesting that the diffusion barriers proportionally scale up the contribution of all channels to [Ca2+] at the sensors of exocytosis to a certain degree. Taking into account the strong correlation betweennch and exponentm based on the change of the number of open channels (see previous section), these results suggest no considerable effect of the ribbon on them estimates for AZ topography scenarios considered in our work.