Applications of kinetics to auxin-induced growth 



The reciprocal of equation (7) is convenient to use in testing the applic- 

 ability of our formulation to the coleoptile-auxin system : 



1 1 1 A',u^ 



growth rate (growth ratej^^^x (auxin) (growth ratej^^x 



The reciprocal of growth rate is expected to be a linear function of the 

 reciprocal of auxin concentration for a system which follows the formulation 

 of equation (8). The double reciprocal plot o^ Figure 3 shows that our Avena 

 growth rate data fulfil the expectations of equation (8) and are thus in agree- 

 ment with our formulation. We see further that although each individual 

 active auxin (indoleacetic acid, lAA; 2:4-dichlorophenoxyacetic acid, 



Reciprocal of growth against reciprocal of lAA concentration. 

 Slope = iCaux/t^max; intercept = l/F^ax 



S J-Or 



20 



^ 10 



20 W 60 80 100 



1/S-* Tag /I. 



Figure 3. Growth rate q/" Avena coleoptile sections as a function of auxin concentration. Reciprocal of 

 growth rate (V) is plotted as reciprocal of auxin concentration {S). After Foster, McRae, and Bonner 

 (1952). 



2:4-D) of those considered yield straight lines in agreement with the formula- 

 tion, none the less the parameters (growth rate)„,ax ^^^d A'^y^ ^^"^ different for 

 the different substances. These parameters afford us then a quantitative 

 method for expressing differences in activity as between different auxins. 



We have, in the paragraphs above, considered data on the concentration- 

 dependence of auxin-induced coleoptile growth and found that these data 

 suggest the hypothesis that auxin accomplishes its work by first interacting 

 with some entity of the coleoptile to form a complex, the concentration of 

 which determines growth rate. The relation between coleoptile growth rate 

 and auxin concentration is in fact formally identical to the relation between 

 rate of an enzymatic reaction and the concentration of substrate on which 

 the reaction subsists. Our formulation (equation (3)) and the derived rate 

 equation (equation (7)) are identical with those of Michaelis and Menten 

 (1913) for the enzymatic case. The purpose of the present discussion is to 

 show that we need not apply enzyme kinetics to the study of auxin-induced 

 growth. We might equally well develop growth kinetics for our own pi'oblem, 

 and the enzymologists might then try our growth kinetics and see how well 

 they fit enzymatic reactions. Enzyme kinetics have however been delved 

 into extensively already. They constitute a large body of lore. Our growth 

 kinetics turn out to be identical with enzyme kinetics and we naturally use 

 the prior experience of enzymologists in formulating our own problem. The 



298 



