VIII 

 FLUCTUATIONS OF THE THRESHOLD 



It has been assumed thus far that the threshold of a neuron is a 

 constant which does not depend on time. Actually it varies from 

 moment to moment and when we speak of the threshold as a constant 

 we must understand by this some mean value of a group of measure- 

 ments of the threshold. A more complete description would give also 

 a measure of the variability. The threshold may vary with many 

 changes in the organism. These variations would generally be rather 

 slow. But within the neuron and in its immediate surroundings there 

 occur rapid minute fluctuations in the concentrations of the various 

 metabolites. The work of C. Pecher (1939) indicates very strongly 

 that it is these fluctuations in concentration that are responsible for 

 the variations in the thresholds of the peripheral fibers with which 

 he experimented. His calculations showed that as few as some thous- 

 and ions was sufficient to produce excitation. From the kinetic theory, 

 one should then expect that the per cent variation in the threshold 

 should be one hundred divided by the square root of the number of 

 ions necessary for excitation (Gyemant, 1925). This value in terms 

 of the coefficient of variation is of the order of a few per cent and 

 is comparable with the values obtained experimentally. 



We may make the calculation of the variation as follows. In 

 order for excitation to occur, it is necessary to stimulate a minimal 

 region of a neuron. Suppose this to be a node of Ranvier. Let the 

 width of the node be d oo 10 4 cm, the radius of the fiber r oo 10- 4 cm. 

 The effect of an ion is small at distances of a few diameters. Thus 

 ions a few diameters removed from the cell surface will have little 

 influence on the surface. Let this distance of influence be d oo 10 7 cm. 

 Then the volume within which the ions affect the excitability of the 

 neuron is 2nrdd . If C oo 10- 5 is the molar concentration of the 

 ions, and if N is Avogadro's number, the total number of ions influenc- 

 ing the excitability is 2nrddCN and thus the per cent fluctuation 

 is given by 100 /\/2jirddCN oo 2%. Had we used the area of an end- 

 foot (c\3l0 -7 ), the same sort of result would have been obtained. But 

 because of the variations in these quantities one cannot exclude the 

 possibility that rather large variations may occur. The calculations 

 only indicate that the fluctuations about the threshold may be appre- 

 ciable. As long as the range in variation is not comparable with the 

 threshold itself, the kinetic theory requires that the fluctuations be 

 distributed normally to a high degree of approximation. That this 



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