90 The Physiology of Sense Organs 



stimulating substance with the free receptor sites on the membrane 

 can be written as follows: 



C + (S-N) ^ N (i) 



and KC = NI{S-N), (2) 



where N is the number of sites occupied by the stimulus at any 

 concentration, C, S is the total number of sites available, and K is 

 the equilibrium constant of the reaction. Neither S nor N was 

 known to Beidler, but by making the further assumption that 

 the maximum response of the sense organ, R^, and the response 

 at any lower concentration of stimulus, R, are directly proportional 

 to, respectively, the unknown values for total number and for occu- 

 pied sites, these experimentally determined parameters may be 

 appropriately substituted in the above equation which, rearranged, 

 gives the following relationship: 



CIR = C/R^ + i/KR^. (3) 



If none of the assumptions in the theory is violated by the 

 reaction of the sense cell with a stimulating substance, a plot of 

 C/R vs. C should yield a straight line whose slope is equal to i jR^. 

 Measurements made by Beidler, using data from mammalian 

 taste buds, fulfilled this criterion. The theory may also be 

 applicable to single salt sensitive primary sensory neurons in the 

 blowfly, Phormia.^^ Data from these cells are, for technical 

 reasons, easier to interpret than those obtained from second- 

 order neurons in the mammalian chorda tympanic nerve (the 

 preparation used by Beidler). Since the salt-sensitive neurons of 

 the blowfly are rather insensitive, fairly high concentrations (up 

 to six molal) of stimulating salt were used. To obviate any errors 

 due to solute self-interaction in these experiments, the effective 

 concentration (i.e. the mean thermodynamic activity) of the salt 

 was calculated and the numerical values (d^) used in plotting the 

 graphs of equation (3). The result of one such plot is shown in 

 figure 40. The curve is satisfactorily linear, the slope being 

 identical with the measured value for the maximum response of 

 the sensory neuron. Thus there seems to be sufficient evidence 

 for tentatively accepting Beidler' s ion-binding theory as a 

 reasonable representation of the observed reaction between 



