VII 



THE DYNAMICS OF THE SINGLE SYNAPSE: 

 SEVERAL NEURONS 



When a pair of afTerents, instead of the single one assumed in 

 the preceding chapter, form a common synapse with a single efferent, 

 the resultant a at this synapse is capable of varying with time in a 

 much more complicated manner. We shall consider briefly two pos- 

 sible applications of such a mechanism, one in which both afferents 

 are supposed to be affected by the same stimulus, one in which the 

 stimuli are assumed to be different. 



Consider first the very special case in which both afferents are 

 stimulated by the same constant stimulus. Let one of the afferents 

 be of the simple inhibitory type with the associated yu and 6 T . Let 

 the other be of the mixed type with </> 2 , xp 2 , a 2 and b 2 . Let a 2 > > b x 

 or b 2 and let </> 2 — y\ — y^ = h , the threshold of the efferent. These 

 assumptions are made to reduce the number of parameters. We em- 

 ploy equation (8) of chapter i, with its analogue for j . Then, a 2 be- 

 ing large, the term e- a * [ quickly dies out so that except for very 

 small t , 



a - h = ?/>! e~ bit + y< 2 e^ 1 . (1) 



But the frequency v of response (chap, i) in the efferent neuron is 

 proportional to a — h when this is not too large. Since y, and y> 2 are 

 arbitrary, w e may replace a — h by v . We can then attempt to inter- 

 pret equation (1) as giving the variation with time of the frequency 

 of the response of an efferent neuron when a constant sustained stim- 

 ulus is applied to its afferents. Equation (1) is shown in Figure 1 

 (curve) for particular values of the constants while in the same figure 

 are shown the results of experiments by Matthews (1931) (points). 

 In these experiments the stretch receptors in muscle were stimulated 

 by means of attached weights and the variation with time of the fre- 

 quency of discharge was determined. Since experimentally the 

 weights tend to sink with time, one might separate the stimulus into 

 two parts, a constant part acting on the second neuron and a variable 

 part acting on the first, making this one excitatory with large a. The 

 variable part would presumably be roughly an exponentially decreas- 

 ing function whose decay-constant must be equal to 6, of equation 

 (1). This, also, would lead to equation (1). Whether or not the ac- 

 tual rate of decay corresponds sufficiently with the experimentally 

 determined decay-constant is then a question of fact. Formally, we 



49 



