Applications of kinetics to auxin-induced growth 



auxin activity. Evidently an active auxin molecule contains two functional 

 groups. If we remove one but leave the other intact, we have a competitive 

 inhibitor of auxin activity. But a competitive inhibitor inhibits by competing 

 with auxin for the auxin-receptive site. We may conclude therefore that the 

 auxin-receptive site contains two points of interaction, one suited to binding 

 of the reactive ortho position, the other suited to binding of the carboxyl group. 

 In the active auxin-receptor complex, a single auxin molecule would appear 

 to be simultaneously bound at both points. Competitive inhibitors, which 

 are capable only of single-point binding, may combine with either point but 

 not with both. 



The concept of the bifunctionality of the auxin molecule, of the growth- 

 active auxin-receptor complex as consisting of a doubly attached auxin 

 molecule, has been derived on the one hand by Muir and Hansch (1951) from 

 the consideration of structure and activity among the auxins and on the other 

 hand from the consideration of the chemical structure of competitive 

 inhibitors of auxin action (McRae and Bonner, 1953). This concept has 

 several corollaries which are of interest. The first has to do with the inhibi- 

 tion of growth which is induced by high auxin concentrations. If the growth 

 functional form of auxin consists of a two-point attached auxin-receptor 

 complex, then we must anticipate that at sufficiently high auxin concentra- 

 tions, two molecules of auxin will simultaneously bind to the receptor entity, 

 each remaining bound through but a single attachment point. This possi- 

 bility is expressed by 



E+2S ^ ES^S^ (growth inactive) . (12) 



Thus, as auxin concentration is increased, we should expect growth rate 

 first to increase owing to the interaction, first order in auxin, between auxin 

 and receptor, and then at still higher concentrations to decrease owing to 

 the formation, second order in auxin, of inactive complexes. The kinetic 

 consequences of eqviation (12) have been considered by Foster et al. (1952), 

 who have shown that the concept of two-point attachment of auxin leads 

 to the rate equation, 



V S 



jT '' max'-' (\'X\ 



^- Ks+S+S^IC ....(1^; 



This equation is similar in principle to the rate expression of equation (7) 

 with the addition that growth rate is now decreased as auxin concentration, 

 S, increases, by a term in S"^. It has been shown by Foster et al. (1952) that 

 the formulation of equation (13) fits the experimental data for coleoptile 

 section growth with considei'able precision over a concentration range of 

 one hundred thousand-fold. Inhibition of growth by high auxin concentra- 

 tion would appear to be a natural and indeed an inescapable consequence of 

 two-point binding of auxin to receptor at lower auxin concentrations. 



Let us now turn to a further phenomenon which we can effectively 

 describe in kinetic terms. This is the experimental fact that chemically 

 different auxins elicit different maximum growth rates in the coleoptile 

 system. The data of Figure 1 show for example that if we supply 2 : 4-D in 

 optimum concentrations, the growth rate or F^^^x which is elicited is only 

 about two-thirds that elicited by an optimal concentration of lAA. Other 



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