476 



9, INHIBITION IN CELLS AND TISSUES 



ciprocal equations derived for saturating and subsaturating substrate con- 

 centrations (the second equation appears to be written incorrectly in the 

 original publication): 



(S) 



(S) 



>1 



<1 



1 



K, 



F,„ (S) - F, 



2k,, ^ 8D] 



K, 



V a K, 



2VJ8) 



rIo(V a r) Dj 



(9-22) 



(9-23) 



where r is the radius of the cylinder, k^ is the permeability constant, D^ 

 is the diffusion constant inside the cylinder, a = V„JD^K„ and the /'s 



k 



Fig. 9-9. Double reciprocal plot for an en- 

 zyme reaction occurring within a membrane 

 of permeability constant kg. 



are Bessel functions. Furthermore, it follows that in the general case the 

 substrate concentration is not the same throughout the cell, but decreases 

 from the membrane inward in an approximately exi^onential fashion. Con- 

 centration profiles for cylindrical cells were calculated for specific cases 

 and it is seen that they depend on all the various permeability, diffusion, 

 and enzymic factors. The measured rate will be an average of the varying 

 rates in the cell. 



Cylinders, spheres, and flat sheets are kinetically analyzed by Blum and 

 Jenden (1957) and equations are given for calculating the concentration 



