IV 



GROWTH OF TISSUES 



167 



is limited by catabolic loss depending on volume. Then, omitting the initial 

 radius {r^} of the culture as small and negligible, an equation : 



E 







U'< 



will apply as found in experiment (Fig. 6). 



In contrast to assertions often made, Buch Andersen and Fischer emphasize 

 that the growth of tissue cultures is not unHmited; growth rate decreases and 



N/E" 



^0^4- 1 



/^ I I I I I I I I I I I I I I I I I I I I I I I 



2 4 

 Fig. 6. Growth of a tissue culture. After Buch Andersen and Fischer, 1929. 



8 10 12 14 16 18 20 22 24 26 28 30 

 Time in days 



eventually becomes zero if the experiment is sufficiently prolonged. In its first 

 part, however, a growth curve according to equation (4.1) is nearly a straight 

 line, the curvature becoming apparent only later. That is, growth rate of the 

 radius is approximately constant at first: 



(4-2) 



(4-3) 



dridt 



hence 



E 



- Et 



Therefore, the area reached by short-living cultures at time = t can be expressed by : 



a = {Ety (44) 



if the small initial radius r^ is neglected. 



Hence, the growth curve of the area of a tissue culture in this seemingly 

 "unlimited" growth is approximately a parabola. This is easily understood under 

 the assumptions mentioned because surface and hence intake of nutrients is large 

 at first compared to volume and loss; hence increase of the radius will be nearly 

 hnear {E), and only later on the term {-kr) will become manifest. This case is 

 important for two reasons : i. The first phases show that the growth rate of the 

 radius of a circular tissue culture would be constant if it were not eventually 

 counteracted by degradative volume-dependent processes. The fact that growth 

 of a tissue culture is a "marginal phenomenon" (Buch Andersen and Fischer, 

 1929) is a confirmation of the assumption that synthetic processes depend on a 

 surface. 2. In growth curves where only the first part is envisaged, a similar 

 constancy of the increase of linear dimensions and thus seemingly "unlimited" 

 growth may appear; therefore, equation (4.3) for the growth of tissue cultures is 

 identical with equation (6.1) for embryonic growth (p. 223). 



For residual growth of tissue cultures, i.e. growth without nutritive extract, an 

 equation (Ephrussi and Teissier, 1932) applies which can be written in the form: 



Literature p. 253 



