Probabilistic secretion of quanta at somatic motor-nerve terminals: the fusion-pore model, quantal detection and autoinhibition.

The probability of detecting first, second, and later quanta secreted at release sites of a motor-nerve terminal during the early release period following a nerve impulse has been addressed. The possibility that early quantal release autoinhibits later quantal release during this period has also been ascertained. In this investigation, a model for the secretion of a quantum at a release site is developed in which, following the influx and diffusion of calcium ions to a release site protein associated with synaptic vesicles, kappa steps of association of the ions with the protein then occur at rate alpha. The release site protein then undergoes a conformational change which may not go on to completion if calcium ions dissociate from the protein at rate gamma. If this process does reach completion then a fusion-pore between the vesicle and the presynaptic membrane is created; this happens at rate delta. Key assumptions of this fusion-pore model are that the quantal secretions from each site are independent of each other, and that there is a large number of vesicles, each with a small probability of secretion, so that the number of secretions is Poisson in nature. These assumptions allow analytical expressions to be obtained for predicting the times at which first, second and later quanta are secreted during the early release period following an impulse. To test the model, experiments were performed in which the times of first, second and later quantal releases were determined at discrete regions along the length of visualized motor-terminal branches in toad (Bufo marinus) muscles. Estimates of model rate constants and of kappa from the times for first quantal secretions failed to give satisfactory predictions of the observed times of later secretions. Therefore, either the model fails, or the procedure used for detecting later quantal events as a consequence of their being masked by earlier quantal events is inadequate. To solve this detection problem, a two-dimensional analysis of the spread of charge following the secretion of a quantum at a random site on the motor-terminal branch has been done. This allows determination of the probability that later quanta will be detected following secretion of earlier quanta. The detection model was then incorporated into the fusion-pore model to predict the times at which second and later quanta occur during the early release period, based on the estimates of the model parameters derived from the analysis of first quantal releases. Good estimates were now obtained for the observed times of second and later quantal releases, indicating that appropriate procedures must be adopted for adequate detection of quantal secretions. Furthermore, the experiments provide support for the fusion-pore model. It has been suggested that the binomial nature of quantal release from the entire motor-nerve terminal may be explained if early quantal release inhibits later quantal release during the early quantal release phase (M. R. Bennett & J. Robinson 1990, Proc. R. Soc. Lond. B 239, 329-358). Although the fusion-pore detection error model gave good predictions of the observed times of first, second and later quantal releases, these may be improved if a model for autoinhibition is included. In this model the first quantum was taken as giving rise to an inhibition of secretion that propagates to surrounding release sites with a constant velocity, v. A combined model incorporating the fusion-pore detection error model and that for autoinhibition was then used to predict second and later quantal latencies, by using the first quantal latencies to determine the estimates for the parameters in the combined model. When this analysis was done on the times for quantal secretion at sites on thirteen different motor-nerve terminals, the value of v was estimated as zero in each case, so that no autoinhibitory effect was observed.