THE ACTION-CONCENTRATION CURVES OF 



MIXTURES OF GROWTH-PROMOTING AND 



GROWTH-INHIBITING SUBSTANCES 



K. Kaindl 



Biologisches Laboratorium der Osterreichische Stickstoffwerke A.G., Linz, Austria 



As I was trying to show at the Botanical Congress in Paris last year (Kaindl, 

 1954), it is possible to calculate the action-concentration curves of growth- 

 promoting substances (it is irrelevant in principle by which method they are 

 obtained) by the formula 



z = A^{\—e-^-^'')+A^{\—e'-^'<^')-B^{\-e-^f^')-B^{\—e'^'K<=), 



wherein z denotes the percentage change of cell elongation, e.g. of an Avena 

 coleoptile under the action of an acting substance measured in percentage 

 concentration c. The A-values are a measure of the hit probability with which 

 the correlated sensitive areas, called gaps, of the living system will be hit by 

 the acting molecule entering into the coleoptile. Therefore, the A;-values are 

 measures of the affinity between the molecules of the acting substance and 

 the living system. 



The first term of the formula describes the extent to which molecules of 

 a growth regulator attach to such gaps (called w-gaps) so that an increase of 

 cell elongation results. A■^^ is proportional to the number of open tf-gaps 

 (n^g) of the living substance in question and to the effect c^^ which one 

 molecule of the growth regulator produces. The expression in brackets gives 

 the probability with which one w-gap will be occupied when a given number 

 of molecules defined by the concentration c enters into the living system. 



The second term describes the extent to which molecules of the growth 

 regulator oust the acting molecules of the growth regulators produced by the 

 coleoptile itself. A^ is proportional, therefore, to the number /7„,,^ of gaps 

 which are occupied by the natural growth regulators. When the effect of one 

 natural molecule is given by f,^, on an average, it is evident that the mole- 

 cular effect produced by one replacement has to be c,„ — r,,,. Generally, the 

 molecular effect of a foreign molecule (not prodviced in the coleoptile) will 

 be lower than that of the average effect of a molecule of the natural growth 

 regulators and therefore A^ has to be negative. On the other hand, however, 

 if a strong effective component of the natural growth regulators is applied, 

 e.g. indoleacetic acid and indoleacetonitrile, this molecular effect may exceed 

 the average effect of the mixture of natural growth regulators present in the 

 coleoptile, and, in consequence, A^ will be positive. The expression in 

 brackets shows the probability with which one gap occupied by a natural 

 molecule gets filled by the replacing foreign molecule. 



The third term is equivalent to the first and describes the event of molecules 

 of the acting substance attaching to such a gap (/(-gap), so that inhibition of 

 cell elongation growth results. B-^ is pi'oportional to the number of open 



V 159 



