GENERAL CHARACTERISTICS OF GROWTH-PROCESS 483 



i 



display regeneration when portions of their tissues are removed. 

 Even in the case of bacteria growing in a limited supply of culture- 

 medium, there is evidence which tends to show that in many cases the 

 accumulation of bacteria or bacterial products really sets the limit to 

 their multiplication rather than the exhaustion of the nutrients in their 

 culture medium. 



We infer, therefore, that the process of growth is governed by a 

 series (in mammals usually three) of autocatalyzed chemical reactions 

 in which the factor which determines the retardation and ultimate 

 equilibrium of the process is the accumulation of the products, i. e., 

 the growth itself. 



The constancy of the concentration of Growth-substrates in animals 

 affords a readily intelligible explanation of the extraordinary simplicity 

 of the quantitative relationship between growth and time, which, as 

 we have seen, so frequently obtains. The relationship in question is 

 that which characterises the progress of an autocatalyzed monomolecu- 

 lar reaction, and even admitting the probability that a single chemical 

 transformation may determine the speed and set the pace for the 

 whole of the multitudinous variety of chemical processes involved in the 

 growth of new protoplasm, yet it may seem strange that even this 

 single reaction should be of so simple a character, more especially since,, 

 as the construction of protoplasm involves synthesis of large out of 

 relatively small molecules, we would expect any reaction involved in 

 growth to be multimolecular. Now this may actually be the case, even 

 in the Master-reaction which determines the quantitative outcome of 

 all the growth-processes, for if the concentration of the substrates of 

 growth remains undiminished by the growth which occurs, then any 

 number of molecules of the substrates may participate in the synthesis 

 which constitutes the governing reaction, without involving any depar- 

 ture of the relationship between the time and extent of growth from 

 that which is expressed in the monomolecular autocatalytic formula. 

 If "n" molecules of the substrate combine to form one molecule of the 

 product, then the velocity of the forward reaction will be given by: ' 



while that of the backward reaction will be given, as before, by 



*L _ k 2 x* 

 dt 



hence the net effect, or actual growth, will be given by 



dx k xAn _ k x2 



"dT 



which, rearranging the terms, becomes: 



dx 

 = k 



dt 



