A theoretical study of factors influencing calcium-secretion couplingin a presynaptic active zone model

A theoretical analysis of some of the relevant factors influencing the calciumtime course and the strength and timing of release probabilities of vesicles evoked by an action potentialin a calyx-type active zone is presented in this paper. In particular, our study focus on the comparison of cooperativevs non-cooperative calcium binding by the release site and the effect of the number of Ca$^{2+}$ binding siteson the calcium sensitivity for release.Regarding the comparison of cooperative and non-cooperative kinetic schemes, our simulations show that quitedifferent results are obtained when considering one or another: a reduction in the release probability of more than a $50\,\%$is obtained when considering the cooperative kinetic scheme. Also, a delay in the average time for releaseappears when using this model for the calcium sensor.
    Our study also shows thata non-cooperative kinetic binding scheme gives rise to a well defined average calcium level for release assumingthat thesame kinetic constants are considered for all the sites. Our results also suggest thatthe central value of the calcium sensitivity for release depends on the number of binding sites $N$ and the dissociation constant $K_{D}$ with a scaling law depending on $N K_{D}$.