Chemical structure and biological activity 



this function is the comparatively high limits of errors which are inherent in 

 biological experiments. But apart from this, there is no doubt that the theory 

 expounded here would be confirmed if the calcvdation of action-concentra- 

 tion curves which arise from a mixture of two growth regulators was feasible. 

 It should be possible to calculate the function of the mixture curve providing 

 that the functions of the single acting substances are given and useful 

 considerations of probability are employed. In fact, this idea can already be 

 verified for six different mixture series and the considerations leading to the 

 derivation of the mixture function may be set forth here briefly. 



The function of a growth-promoting substance may be given by the 

 formida mentioned above: 



and 



Zj_^ = C^{\-e-'>^-)-D^{\-e-h<^2)-D^{\-e<''2) 



gives the function of an inhibiting substance. When the two substances are 

 simultaneously applied to the coleoptile the following competing actions take 

 place : 



1. The probability that the 11^-molecule enters into a w-gap and that an 

 //-molecule does not enter into this gap is given by 



P^ := (1 — e~^'«'''i)e'^«'''2, 

 assuming that the probability of replacement 4, valid for the ousting process 

 of a natural molecule holds approximately true for this corresponding 

 ousting process too. 



2. There is competition between H'- and //-molecules for the ousting of a 

 natural molecule from a w-gap. The probability of the occupation of the 

 !:f;-gap by a M'^-molecule is given then by 



Pg = (\—e-^-:r'^i)e-'>2 

 and for an //-molecule by 



2^= (1— ^-/;/2)^-^->i. 



3. For the IT-molecule competition of the two partners for an A-gap leads 

 to the probability 



P3 = (^\—e-^-n<'i)e-hc2; 



for the //-molecule to 



4. Finally, competition regarding the ousting process of a natural molecule 

 from an A-gap leads to the two probabilities 



P^ = (^l—e-K<-i)e-^'>.'^2 

 for the py-molecule and 



4P = (1— h;^2)^-^-a'-i 



for the //-molecule. 



The function of the mixture curve, therefore, has to be 



^u,+^H = A,P,+A,P,-B,P,-B,P,^C, . ,P-D, . ,P-D., . ,P. 



The results calculated by this formula show a good agreement with the 

 experimental data obtained in our biological laboratory. For Figures 4-6, I 

 have singled out one curve of the mixture series indoleacetic acid (10~^) 



162 



