DIFFERENTIAL GROWTH 165 



d{R-\-D) R R 



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growth rate will be smaller than the true growth rate by an amount vary- 

 ing inversely with the unknown constant D. Consequently, of two cells 

 with different proportions of R and D but identical fundamental growth 

 rates of the portions R, the one with the larger D will appear to grow 

 more slowly. The fraction D is itself heterogeneous, including water, in- 

 organic compounds, and all organic compounds that have either not yet 

 been incorporated in the reproductive systems or have become detached 

 from them as metabolites and differentiation products. Accordingly the 

 ratio between D and R will be significantly different in different cell 

 types, and hence different actual growth rates must be expected simply 

 as a corollary of differentiation. Whether there is also a concurrent 

 change in basic growth rate remains undecided. 



Moreover, the ratio R/D does not remain constant for a given cell 

 strain over its whole ontogenetic history. As differentiation proceeds, the 

 proportion of "differentiated" terminal products, making up a large frac- 

 tion of D, increases progressively at the expense of R. This increasing 

 drain on the reproductive fraction of the cell is reflected in the well- 

 known decline of measured overall growth rate with age. After our 

 earlier discussion of differentiation it seems hardly necessary to reiterate 

 that the Z)- fraction in question includes not merely the formed cell prod- 

 ucts (pigments, secretions, fibrils, etc.) but also that part of their forma- 

 tive apparatus that is not self-reproductive. Even after the loss of the 

 formed products, as in tissue culture, cells of different strains of differen- 

 tiation exhibit different growth rates (31). 



Comparative evaluation of differential growth rates among different 

 cell types is further complicated by the fact that in some cells the formed 

 differentiation products stay within the cell and are therefore included 

 in all measurements, while in other cell types they are extruded and lost. 

 For instance myofibrils, neurofibrils, most pigment granules, mem- 

 branes, and the like stay with the protoplasms from which they arose, 

 while formed secretions, intercellular ground substances, and the like do 

 not. Comparisons based on visible increments are therefore quite de- 

 ceptive. 



Not until most of these matters have received much more precise 

 formulation and investigation will it be possible to develop a rational 

 theory of differential growth. Attempts have been made to account for 

 differential growth rates by different partition coefffcients in the appro- 

 priation of nutrients, by competition for "growth substrate," by differ- 



