# An Algorithm for Creating a Synaptic Cleft Digital Suitable for Further Numerical Modeling
## 2 Materials and Methods
### Synaptic Cleft  
The synaptic cleft is embedded between the first and second (\(\Omega_{1}\) and \(\Omega_{2}\)) 3D bodies from Voronoi diagram synapse phantom track and contained within the AZ (\(\partial\Omega_{\text{AZ}}\)) and PSD (\(\partial\Omega_{\text{PSD}}\)) membrane lacunae. The presynaptic \(\partial\Omega_{\text{AZ}}\) includes multiple plausible locations for vesicular fusion pore openings (\(\partial\Omega^{i}{}_{\text{fusion}}\)). The canonical vesicular release protein machinery can vary, with different isoforms expressed throughout CNS, but the underlying principle is always the same [32]. Instead of quantal vesicular release theory, intermediate release modes have been postulated, including a kiss-and-run mode which permits just a small amount of a released neurotransmitter to pass through the transient opening of a tiny fusion pore, and a partial release mode which corresponds to a more pronounced temporal and spatial span. Together with full fusion, the intermediate release modes provide clues for the characterization of synaptic plasticity. At present, partial vesicular neurotransmitterrelease is suggested as the dominant mode of exocytosis [40]. The vesicular partial fusion pore diameter is restrained by Dinamin 1 and reaches a maximum width of 9 nm with a timescale up to 10 ms [41]. Moreover, the binding of the vesicles appears as regularly spaced cone-shaped structures with a size of approximately 50 nm attached to the presynaptic membrane, which are known as dense projections (DPs) or, collectively, the \"presynaptic particle web\" or \"presynaptic grid\" [42]. Interestingly, the same structured localization of receptors is observed in PSD. For example, the PSD region of the glycinergic synapse features precise coordination of glycine receptors by gephyrin [30]. Thus, the collocation of \(\partial\Omega^{i}\)fusion on \(\partial\Omega_{\text{AZ}}\) complies with the plausible hexagonal grid pattern of tethering synaptic vesicles and Ca\({}^{2+}\)-channel-recruiting AZ scaffold proteins (DPs) on the presynaptic membrane with unit parameter of 70 nm [42], as well as matching up with rather small vesicles of 40 nm in diameter [41].  
For moderate synaptic clefts (about 100 nm in radius), the mean distance between presynaptic and postsynaptic membranes fell to 61 \(\pm\) 3% at the edge of the cleft, when compared to central part [39]. In our 3D model, this difference was 62%, 47%, 38%, and 32% for synaptic cleft areas designed with 130 nm radius and various heights of the synapse phantom (15 nm, 20 nm, 25 nm, and 30 nm, respectively). Apparently, this prominent difference is a direct result of the synapse phantom geometry for the distance between the adjacent surfaces of \(\Omega_{1}\) and \(\Omega_{2}\), defined as a sheet with given minimal thickness [38].  
According to the 3D EM reconstruction, the opposing \(\partial\Omega_{\text{AZ}}\) and \(\partial\Omega_{\text{PSD}}\) are very similar in surface estimation, varying from 0.006 to 0.445 \(\upmu\)m\({}^{2}\), with a mean distribution value of approximately 0.09 \(\upmu\)m\({}^{2}\)[43]. In our modeling environment corresponding to the synapse phantoms, \(\partial\Omega_{\text{AZ}}\) and \(\partial\Omega_{\text{PSD}}\) were in a good agreement with the experimental data indicated above. The modeling values are presented in Table 2.