468 9. INHIBITION IN CELLS AND TISSUES 



Whether a new steady state will be attained will depend not only on the 

 enzymic inactivation but possibly on the diffusion of the agonist from the 

 region. It will also depend on the rate at which the agonist is formed; when 

 it is synthesized in and released by nerve endings, its production will na- 

 turally depend on the frequency of impulses in the nerve. In some isolated 

 preparations, the rate of formation is apparently steady and inhibition 

 of the inactivating enzyme will cause a progressive accumulation of the 

 agonist, as in isolated atria (Webb, 1950b). 



The kinetics of such a multienzyme system will depend on the spatial 

 arrangement of the three basic elements — the receptor groups and the 

 loci for formation and inactivation of the agonist. These are probably 

 never distributed homogeneously within a region since all are intimately 

 related to certain cell structures. The agonist usually arises outside the 

 cell it affects and must diffuse to the receptors, which can be on the sur- 

 face of the cell, in the membrane, or inside the cell; the inactivating enzyme 

 can likewise be located in any of these regions. The effect of inhibiting the 

 inactivating enzyme will be much greater if this enzyme is so located that 

 the agonist must diffuse through a "screen" of it before it can react with 

 the receptors, because in this case the agonist concentration at the receptor 

 region will be strongly dependent on the activity of the inactivating en- 

 zyme. A certain fraction of the agonist will normally be destroyed before 

 it can produce an effect and an inhibitor will decrease this. Possible spatial 

 relations between acetylcliolinesterase and receptors in atrial tissue have 

 been discussed (Webb, 1950b) and evidence presented that such a "screen- 

 ing" effect is operative in this tissue, where the acetylcholine concentration 

 at the receptors may be only one-hundredth that of the concentration in 

 the medium. It is, therefore, difficult to develop a quantitative treatment 

 of such inhibition. Equations have been derived by Furchgott (1955) 

 for the situation in which the agonist must diffuse across a membrane to 

 a region where receptors and inactivating enzyme are homogeneously 

 distributed. It is unfortunate that such a direct treatment is probably not 

 justifiable in most cases but the validity must ultimately be determined 

 by accurate experimental data, which at present are lacking. It was also 

 assumed that the inactivation is first-order and did not follow enzyme 

 kinetics. Finally, the acetylcholinesterase is a good example of a mutual 

 depletion system (Chapter 3) and to what extent these more complex ki- 

 netics must be applied is unknown. 



Assuming a constant external concentration of agonist and a homogene- 

 ous distribution of receptors and inactivating enzyme within a membrane: 



+R^ AR 



A„;Ff^A,^^ (9-16) 



E7^ inactivation 



