Ca 2+ regulated homotypic fusion

Next we studied Ca²⁺ regulated homotypic fusion, assuming homotypic fusion rates were depended on local [Ca²⁺] (He et al., 2009). Because [Ca²⁺] is known to decay with the distance from the AZ (Roberts, 1993; 1994; Naraghi and Neher, 1997; Frank et al., 2009), we let the homotypic fusion rate αHom decrease with the distance z from the AZ to the site of vesicle interaction, effectively constraining homotypic fusion to AZ proximity (Fig. 4.5a,b, Supplementary note): the AZ of the homotypic fusion rate, caused by the [Ca²⁺] decay. z0, the height where the homotypic fusion rate equals HMax, was set to 40 nm (a uniquantal vesicle diameter) and to 20 nm (a uniquantal vesicle radius) in 1D and in 2D, respectively. z0 corresponded to the lowest possible interaction point between two vesicles. θ(z) is the Heaviside step function. Experimentally, HMax and λZ could be manipulated by changing the [Ca²⁺] profile at the AZ. Note that HMax and the rate of vesicle fusion to the plasma membrane αExo might have different dependences on Ca²⁺ concentration. To screen a large parameter space, we varied HMax from 10 times smaller to 1000 times larger than the

79

exocytosis rate αExo and the characteristic homotypic fusion range λZ between ≈ 3 and ≈ 300 nm. Fig. 4.5e-f shows the key characteristics of the exocytosis quantal size distributions for the 1D and 2D simulations.

In the 1D model, the exocytic mean quantal content M increased with homotypic fusion rate HMax/ αExo and with length constant λZ. The CV of the distribution, however, exhibited a more complex dependence, but for M > 2, the CV decreased with increasing HMax / αExo and decreasing λZ. In this region, the skewness showed a similar behavior.

Where the ratio of uniquantal to most frequent events equaled 1, the mode of the distribution was at 1 quantum, i.e. most events were uniquantal. We found that this ratio decreased with increasing HMax, demonstrating a decrease in the fraction of uniquantal events. The consistency region (white stripes, where the model is consistent with experimental observations) extends from HMax / αExo > 7. It covers mean quantal contents M from around 1.5 to 7, spanning M estimates for all synapses considered (examples in Fig. 4.5c).

The behavior of the Ca²⁺ dependent homotypic fusion model radically changed when vesicles could diffuse freely on the entire 2D ribbon surface (Fig. 4.5d,f). In fact, the Ca²⁺ dependence of homotypic fusion rate did not any longer prevent homotypic fusion from being a self-amplifying process but instead, the model either generated vesicles of unrealistically large size or vesicle quantal content distributions with a mode at 1. First, although the mean quantal content M depended on HMax / αExo and λZ in a similar way as in 1D, it exhibited higher values for the same parameter values. Second, the region of runaway homotypic fusion (white space) was more prominent in the 2D case. Third, the CV of the quantal content distribution was larger and mainly above 0.4.

Finally the large skewness and ratio of uniquantal to most frequent events of 1 indicate that the mode of the distribution was almost always at 1 quantal. As a result, the consistency region disappeared completely.

Figure 4.5: Ca²⁺ dependent homotypic fusion model for MQR

(a) To model the Ca²⁺ dependence of homotypic fusion, homotypic fusion rates decreased with the distance of the vesicle interaction point z from the active zone. H_Max is the maximum homotypic fusion rate, λ_Z is the decay length of where homotypic fusion happens from the active zone.

(b) Examples of homotypic fusion rate decreasing with the distance from the membrane, for different values of λ_Z and H_Max = 100 s^-1.

(c) exocytic quantal content histogram for different values of H_Max / α_exo and λ_Z in the 1D model (Fig. 4.4a). These histograms quantitatively reproduced those observed experimentally.

(d) Same as (c) in the 2D model (Fig. 4.4b). These histograms did not reproduce those observed experimentally, either due to the high skewness of the distribution or due the emergence of extremely large vesicles.

(e),(f) Critical characteristics of the exocytic quantal content distributions in 1D and 2D models as a function of H_Max / α_Exo and λ_Z. Note that both parameters are in logarithmic scale. The consistency region (white stripes) corresponds to where the model reproduces experimental observation (Table 4.1), the criteria being in terms of CV (green dashed lines) and skewness (blue dashed lines) of the quantal content distribution. The runaway fusion area (plain white) indicate simulations that were discarded due to the formation of vesicle with quantal content Q

> 40 (diameter: 252 nm).

(e) 1D model. A consistency region is present for H_Max / α_exo > 7. Decreasing the extend of the Ca²⁺ signal, modeled by λ_Z, produces a switch from multiquantal release to uniquantal release. The areas excluded from the consistency region at the right of the parameter space arise from strongly negatively skewed (γ₁ ≈ -1) quantal content histogram.

(f) 2D model. No consistency region is present as the mode of the exocytic quantal content distribution is almost everywhere 1. A very large area of runaway fusion exists.

The vesicle packing densities φ_1D and φ_2D were 0.7 and 0.4, respectively.

81

This qualitative difference between the 1D and 2D homotypic fusion models resulted from two main mechanisms. Firstly, larger vesicles in 2D had more partners and therefore an increased probability to grow further by homotypic fusion, which was not the case in 1D. Secondly, distinct from the 1D geometry, as a vesicle grew near the active zone, its homotypic fusion rate to a lateral neighbor vesicle does not decrease as much as to its vertical neighbor. Therefore, in 2D once homotypic fusion has commenced, the resulting compound tended to continue fusing and growing, inevitably creating positively skewed quantal content histograms. For both 1D and 2D scenarios, we found that the exact shape of the consistency region depended on the vesicle packing density φ.

Increasing φ shifted the consistency region slightly towards smaller homotypic fusion rates (Supplementary Fig. 4.5-4.6).

Although only the 1D homotypic fusion model could reproduce experimental observations, both 1D and 2D models predicted an important qualitative feature of MQR in frog HC and RBC: the shift from MQR to uniquantal release when decreasing the stimulation strength or adding stronger buffer in the presynaptic solution (Singer et al., 2004; Li et al., 2009). In the model this condition was realized by reducing HMax / αExo

and λZ, because of the spatially less extended Ca²⁺ signal.

Our results thus indicate that unconstrained homotypic fusion cannot reproduce the experimentally observed featured of MQR in ribbon synapses. If the molecular architecture of the ribbon constrains vesicles to diffuse anisotropically, such that they move mostly vertically to the AZ, and perform mostly vertical fusions, a solely Ca²⁺ and geometrically controlled homotypic fusion process could explain the observed features of MQR. But in view of the complex and rich proteome of synaptic vesicles (Takamori et al., 2006), it appears likely that the homotypic fusion process is regulated even further by molecular means.