TRANS-SYNAPTIC DYNAMICS 5 



is the measure of the effective stimulus acting upon any neuron origi- 

 nating at the given neuron's terminus. If at any moment the o- due 

 to the activity of a particular neuron is positive, we shall speak of 

 the neuron as "exciting" or having an "exciting effect" at that mo- 

 ment, without, however, meaning to imply thereby that it then ex- 

 cites any neuron. It will do this provided only that a exceeds the 

 threshold of a neuron suitably placed. Neither do we imply that the 

 neuron which produced the a is at this moment acting, though it 

 must have been acting in the very recent past if a is still appreciable. 

 Likewise, we shall speak of the neuron as "inhibiting" or having an 

 "inhibiting effect" whenever its a is negative. Consider the case of a 

 constant 5 , so that <j> and y are themselves constant. Asymptotically 

 £ and j approach </> and \p , respectively, so that the neuron is asymp- 

 totically exciting or asymptotically inhibiting according to the rela- 

 tive magnitudes of <p and y> . However, the initial rates of increase of 

 £ and j are equal to a<}> and to by , respectively, so that an asymptoti- 

 cally exciting neuron — for which cf> > ip — would be momentarily in- 

 hibiting in case by> > a<j> , and vice versa. Thus the transient and the 

 asymptotic effects of such a neuron would be quite opposite. 



Furthermore, suppose, for definiteness, that the neuron is asymp- 

 totically inhibiting, \p > </> , and consider the effect following the cessa- 

 tion of its own stimulus, when the neuron, as a result, comes to rest. 

 We suppose for simplicity that the constant stimulus is maintained 

 long enough for the asymptotic state to be reached. Then, on re- 

 moval of the stimulus, <£ and y.> both drop to zero so that £ and j de- 

 cline exponentially to zero. If b > a , the decline of j is more rapid 

 than that of £ and a transient exciting effect may, and in fact always 

 does, ensue while the neuron is thus at rest. 



To summarize all possible cases of this sort: A neuron is 

 a) Asymptotically exciting whenever 



4> > ip . 



Figure 1 





