GROWTH IN TIME OF THE TOTAL ORGANISM 



209 



sition from "generative" to '"differentiated mass", and progressive differentiation 

 is one factor checking unlimited growth. 



J. Protoplasmic reproduction or growth is essentially based upon cell-specific 

 catalysts or "templates'" which reproduce living mass of the same kind. Besides, 

 each cell also produces specific, freely diffusibly compounds antagonistic to the 

 former ("antitemplates") which can block and thus inhibit the reproductive 

 activity of the corresponding "templates". 



^. Hence, a second growth-regulating and limiting factor is a negative feedback 

 in the way that an increasing population of "antitemplates " checks a corresponding 

 proportion of "templates", so leading to a decline of growth rate. 



5. Attainment of a terminal size is an expression of a steady state between 

 incremental and decremental growth components, and between self-reproducing, 

 intracellular "templates" and inhibiting, freely diffusible "antitemplates". 



6. Both "generative" and "differentiated mass" (including "antitemplates") 

 undergo continual metabolic degradation and replacement, but catabolic loss 

 of generative mass is, in first approximation, negligible in comparison with the 

 other growth-inhibiting components. 



Hence, the model is indicated by the scheme (Fig. 19). A system of differential 

 equations expressing these processes and interrelationships was formulated and 

 solved. 



Growth Component 



dG = 



Change in 

 generative 

 mass 



Basic rate of 

 reproduction 

 of generative 

 mass ( I A) 



Generative 

 feedback 

 term ( i B) 



d; 



Generative mass formed (dG^) 



dD 



Initial rate 

 of conversion of 

 generative mass 

 into differen- 

 tiated mass 



Differen- 

 tiation 

 feedback 

 term 



(I) 



dt 



Generative mass lost (dG,^ = i C) 



Change in 



differentiated 



mass 



Rate of gain of 

 differentiated mass by 

 conversion from G (2A) 



dt 



Rate of catabolic 

 loss of differen- 

 tiated mass (2B) 



dt (2) 



Differentiated mass produced 

 Feedback Component 



Differentiated mass lost 



d/ 



Change in number 

 of inhibitor 

 molecules 



Rate of 



production of dt 

 inhibitors (3A) 



Inhibitors formed 



Rate of cata- 

 bolic loss of 

 inhibitors (3B) 



Inhibitors lost 



dt (3) 



Fig. 19. Growth model after Weiss and Kavanau, 1957. The numbers (lA, etc.) refer to a 

 system of growth equations expressing the individual terms. 



Literature p. 253 



