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1. The relation between m.e.p.p. frequency (F) and [Ca] was studied at the mouse neuromuscular junction, at varied concentrations of K⁺ and at nerve terminals depolarized by focal depolarization.

2. Under all conditions the relation between log F and log [Ca] was sigmoid, with a maximum slope that increased with depolarization or raised [K⁺]. In addition, depolarization or raised K⁺ caused a progressive shift of the sigmoid curve upward and to the left (to reduced log [Ca]) and increased the range over which log F could be altered by [Ca].

3. Reduction of osmotic pressure changed the relation between log F and log [Ca] in the same way as increase of depolarization, while increase of osmotic pressure did the opposite.

4. Raised [Mg] acted in two ways: (a) to shift the curve of log F vs. log [Ca] to the right and (b) to reduce maximum log F/ log [Ca] without altering the range of log F sensitive to [Ca].

5. The relation between log quantal content of e.p.p.s and log [Ca] was similar to that between log m.e.p.p. frequency and log [Ca].

6. Individual nerve terminals varied in both Ca-dependent and Ca-independent fractions of log F; a large Ca-independent portion appears to be associated with a low Ca-dependent portion and vice versa. With large prolonged depolarization the Ca-independent portion was increased, apparently at the expense of the Ca-dependent portion.

7. The results of all experiments were summarized in terms of parameters found by fitting the observed log release —log [Ca] curves to two theoretical equations, each derived on the basis of a model: (a) all-or-nothing activation of release probability by Ca-complex(es) and (b) graded activation of release probability by Ca complex(es).

8. On the basis of the all-or-nothing model, from which follows alinear relation between F and amounts of Ca complex(es), the number of Ca²⁺ atoms that `cooperate' to mediate release appeared to increase progressively with presynaptic depolarization, to a value of 4 or more with a presynaptic action potential.

9. On the basis of the graded activation model, which predicts an exponential relation between F and amount of Ca complex, the number of Ca²⁺ atoms that combine with Ca receptor appears to be independent of presynaptic depolarization.

10. Various models which could account for the data are discussed. It was concluded that all the data are consistent with a model in which:

(i) quantal release probability is continuously graded with the amount of a simple Ca complex (CaX) inside the nerve terminal.

(ii) Ca entry is governed by presynaptic membrane potential (increasing exponentially with depolarization) and by the amount of a Ca complex (Ca₂Y) on or in the membrane.

(iii) Mg²⁺ competes with Ca²⁺ at both receptors, X and Y.

(iv) The internal Ca receptor X is also increased by presynaptic depolarization.