PRINCIPLES OF EMBRYOLOGY 



dw 



280 



mathematicaUy by the equation ^ ^ = ^ constant (where w is the weight 



or mass of the system). This, of course, leads to the absolute size increasing 

 ever faster and faster, at an exponential rate. The equation is solved to give 



w = 11^ oe^^ or log n^ = log Wo + ^^ 

 when li^o is the initial size and fe is a constant. 



It is impossible to fmd a naturally occurring biological system which 

 behaves so simply, and it is difficult to make one experimentally, though 

 it can be done. If a smaU population of yeast cells, or bacteria, is moculated 

 into a large mass of nutrient medium, allowed to grow for a time, and a 

 new inoculum transferred to fresh medium after a fairly short period, the 

 growth rate per unit mass may be kept constant indefmitely. The essential 

 points are that neither lack of nutrient nor the presence of harmful excreta 

 are allowed to inhibit the system. If frequent transfers are not made, one 

 or other or both these are certain to occur, and the rate of growth will 

 slacken tih the growmg mass becomes stationary and eventuaUy begms 

 to dechne when the death-rate of cells overtakes the rate of mcrease. 

 Samples taken from such declining cultures usually take a httle ttme to 

 get going when transferred to fresh medium, so that m the typical 

 growth curve of a colony of cells (yeast, bacteria, tissue-cultures and the 

 like) the logarithm of size when plotted against time, is not a straight Ime, 

 but has the form shown in Fig. 13.1. 



Figure 13.1 



Typical growth curve of a population of isolated cells (e.g. yeast cells, bacteria, 

 etc ) If the population starts with a group of cells taken from a non-growing 

 colony, there is first a 'lag phase' (i) then a phase of exponential growth (2) 

 in which the growth rate per unit mass is constant, then a phase of retarda- 

 tion (3) when the medium is becoming exhausted and fmally a regression 

 phase (4) when the medium can no longer support the population. 



