The amplitude distribution of release events through a fusion pore

Neurotransmitters, hormones, or dyes may be released from vesicles via a fusion pore, rather than by full fusion of the vesicle with the plasma membrane. If the lifetime of the fusion pore is comparable to the time required for the substance to exit the vesicle, only a fraction of the total vesicle content may be released during a single pore opening. Assuming 1), fusion pore lifetimes are exponentially distributed (tauP), as expected for simple single channel openings, and 2), vesicle contents are lost through the fusion pore with an exponential time course (tauD), we derive an analytical expression for the probability density function of the fraction of vesicle content released (F): dP/dF=A (1-F)(A-1), where A=tauD/tauP. If A>1, the maximum of the distribution is at F=0; if A<1, the maximum is at F=1; if A=1, the distribution is perfectly flat. Thus, the distribution never has a peak in the middle (0