Modeling study of the effects of overlapping Ca2+ microdomains on neurotransmitter release

Although single-channel Ca2+ microdomains are capable of gating neurotransmitter release in some instances, it is likely that in many cases the microdomains from several open channels overlap to activate vesicle fusion. We describe a mathematical model in which transmitter release is gated by single or overlapping Ca2+ microdomains produced by the opening of nearby Ca2+ channels. This model accounts for the presence of a mobile Ca2+ buffer, provided either that the buffer is unsaturable or that it is saturated near an open channel with Ca2+ binding kinetics that are rapid relative to Ca2+ diffusion. We show that the release time course is unaffected by the location of the channels (at least for distances up to 50 nm), but paired-pulse facilitation is greater when the channels are farther from the release sites. We then develop formulas relating the fractional release following selective or random channel blockage to the cooperative relationship between release and the presynaptic Ca2+ current. These formulas are used with the transmitter release model to study the dependence of this form of cooperativity, which we call Ca2+ current cooperativity, on mobile buffers and on the local geometry of Ca2+ channels. We find that Ca2+ current cooperativity increases with the number of channels per release site, but is considerably less than the number of channels, the theoretical upper bound. In the presence of a saturating mobile buffer the Ca2+ current cooperativity is greater, and it increases more rapidly with the number of channels. Finally, Ca2+ current cooperativity is an increasing function of channel distance, particularly in the presence of saturating mobile buffer.