The kinetics of auxin-induced growth 



fully occupied by auxin molecules. Let us see how we might formulate this 

 hypothesis, which has been suggested by the data oi Figure 2. Evidently 



auxin -(-coleoptile -> (auxin-coleoptile), .... (1) 



growth rate = A'(auxin-coleoptile), .... (2) 



or (auxin-coleoptile) > growth, .... (2a) 



where A: is a constant which relates growth rate to concentration of the auxin- 

 coleoptile interaction product. This formulation may be expanded if we 

 take note of the fact that reaction ( 1 ) is reversible, as is shown by the fact 

 that a coleoptile in an auxin solution at one concentration quickly adjusts 

 its growth rate to the appropriate level when transferred to a second auxin 

 solution of different concentration. Combining this fact with equations (1) 

 and (2a), we obtain 



k 



auxin -f coleoptile ^ (auxin-coleoptile) > growth. .... (3) 



This equation is, of course, nothing more than a description in words, and 

 not necessarily a unique description, of the relations oi Figure 2. Equation (3) 

 does, however, have certain attractive features. For one thing, its applic- 

 ability may be tested. The central feature of our formulation is that auxin 

 interacts with coleoptile to form something to which growth rate is pro- 

 portional. We have further seen that the formation of the interaction 

 product is a reversible reaction. Let us assign the dissociation constant 

 7iaux to the dissociation of the interaction product: 



(auxin) (coleoptile) 



(auxin-coleoptile) ~ *"^* ••••(, ) 



The total concentration of auxin-receptive interaction sites in the coleoptile 

 is at all times equal to the sum of the auxin-occupied sites and the sites not so 

 occupied : 



(coleoptile) total = (auxin-coleoptile) + (coleoptile) f^ge .... (5) 



From relations (4) and (5) we may solve for (auxin-coleoptile) in terms of 

 (auxin), (coleoptile) tot^b ^^divay^- Substituting the value of (auxin-coleoptile) 

 thus obtained into equation (2), we obtain an expression for growth rate of 

 the coleoptile as a function of auxin concentration : 



K. 



aux 



growth rate = AQ,,,,/ ^ 1 +^^^^ j • .... (6) 



It will be evident that as auxin concentration is increased, growth rate will, 

 according to expression (6), approach A:Q(,tai ^s a maximum value. Let us 

 therefore replace kC^^^^^x by (growth rate)niax5 the growth rate in non-limiting 

 auxin concentration: 



growth rate = (growth rate)„,ax / ( 1 +7 — ^ ) (7) 



(auxin) 



V_ 297 



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