414 8. INHIBITOR DISTRIBUTION IN LIVING ORGANISMS 



the exponential factor will disapper at large values of t. When (I^) does 

 not remain constant, integration of d (i^jdt = — k^ (I^) gives: 



(IJ = (IJo e-*i' (8-4) 



where (Io)o is the initial external concentration. For very approximate 

 results, this value may be substitued in Eq. 8-3. Such expression have been 

 applied to drugs but they are too inaccurate for further consideration and 

 it is necessary to turn to a more realistic system. 



Variation of Intracellular Inhibitor Concentration with Time: Complete 



System 



In most cases of interest, the entrance of the inhibitor into the region 

 of interest is reversible and the external inhibitor concentration is not 

 constant. 



I<,^I,^X (8-5) 



The differential equations for this situation are: 

 ddo) 



dt 



dih) 

 dt 



= k_Ah) - kAlo) (8-6) 



= kAlo) - krih) - k.iU (8-7) 



These simultaneous equations may be solved to give both external and in- 

 ternal inhibitor concentrations at any time. 



Ho) = (Io)o ^ , [{k^ + «)e^' - {k, + li)e-*] (8-8) 



a — p 



(I.) = (Uo -^^ [e^' - e^q (8-9) 



a — p 



where (Io)q is the initial concentration of external inhibitor and a and /3 

 have the values: 



a = 1/2 [- (2^1 + k,) - V ik\ + k\] (8-10) 



/S = 1/2 [ - m. + k^) + V 4^; + k^ (8-11) 



It has been assumed here that A;_i = ^'^ since in most instances the entrance 

 of an inhibitor into a cell is a diffusion process with equivalent rates in 

 each direction. 



