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1. A quantitative description of facilitation in the crayfish claw opener muscle is presented. The facilitation of a test response following one or more conditioning stimuli, and the growth of facilitation during a tetanus, are measured.

2. In superficial central fibres facilitation following one or more impulses can be described as the sum of two components which are both maximum at the end of the conditioning train and decline simultaneously and exponentially with different time constants thereafter.

3. During a tetanus, facilitation to successive stimuli grows more rapidly than is predicted by assuming that each impulse adds a constant facilitative effect to an accumulating total state of facilitation.

4. Sufficiently large values of tetanic facilitation are predicted by a model which assumes that transmitter release is proportional to the nth power of a substance or factor accumulating in nerve terminals. But no single value of n predicts the correct rise of facilitation in a tetanus and the time course of its subsequent decline from the facilitation following a single spike.

5. A model which assumes that the facilitative effects of successive spikes multiply in a tetanus predicts responses that are larger than those observed.

6. The effects of varying the calcium concentration ([Ca²⁺]) on transmitter release and facilitation were studied. When a magnesium-EDTA buffering system is used to vary [Ca²⁺], transmitter release is found to be nearly linearly related to [Ca²⁺] in the range 0·1-13·5 mM.

7. The magnitude and time course of facilitation during and following a tetanus are unaffected by varying [Ca²⁺] between 1·0 and 40 mM.

8. The relation between `steady-state' facilitation and stimulus frequency is also unaffected by changing [Ca²⁺], except that in high [Ca²⁺] transmitter release appears to saturate at high frequencies (above 30 Hz).

9. The results are discussed in terms of the `calcium accumulation' hypothesis of facilitation. The findings in crayfish appear to be qualitatively consistent with this hypothesis if certain modifications are made in the hypothesis.

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