508 10. EFFECTS OF MORE THAN ONE INHIBITOR 



Summation: t'l 2 = ^ + H — hh 



Antagonism: ii^a < ii + 12 — iii^ (10-26) 



Synergism: ^l^2 > ^i + H — ii'h 



when the inhibitors do not influence each other's actions. Stated in another 

 way, antagonism occurs when a second inhibitor produces less effect in 

 the i^resence of the first inhibitor than it does alone, and synergism 

 occurs when the effect is greater. It should be evident that when antag- 

 onism or synergism is observed, it does in no way indicate the mecha- 

 nism involved nor imply that the two inhibitors act on the same system. 

 Isobolograms have been used pharmacologically to illustrate antago- 

 nism, summation, and synergism (Loewe, 1957). Let us consider the nature 

 of isobols derived from inhibition studies on complex metabolic systems 

 such as respiration. It may be assumed that each inhibitor alone acts ac- 

 cording to the equations: 



(I)i (I.) ^jQ_27) 



di) + K, (I2) + K2 



where K^ and K2 are simply constants of no physical significance. Combin- 

 ing these equations with the summation Eq. 10-26, the inhibition to be pre- 

 dicted from both inhibitors would be given by: 



Relationships between (I^) and (I,) may now be obtained for any desired 

 degree of inhibition i-^o and such have been plotted in Fig. 10-7. Summation 

 is therefore represented by a curve concave upwards and not by a straight 

 line. This is actually quite similar to the results on simple enzymes (Fig. 

 10-4, curves 2,5, and 8 where a = 1). Synergism then would be represented 

 by a curve with greater upward curvature and antagonism by curves of 

 lesser curvature and particularly by curves approaching linearity or con- 

 cave downwards (Fig. 10-8). A corollary to these considerations is the non- 

 additivity of inhibitor concentrations: thus if a certain degree of inhibition 

 is produced by (Ij) and (I2), the two inhibitors together at half their con- 

 centrations will not give the same inhibition. 



The possibility of antagonism or synergism occurring when two inhibitors 

 are introduced is particularly important in medical applications, as it is 

 in the combined use of any drugs. Many of the results on combination ther- 

 apy reported in the medical and jiharmacological literature are pertinent 

 to inhibition studies, but a thorough and quantitative theoretical approach 

 has never been made. In the pharmacological field, the treatments of Ariens 



