98 Growth and Form 



To return to our bacterial culture, the above statements mean (1) 

 that during the exponential phase each bacterial cell gives rise to two, 

 the two to four, the four to eight, etc., and (2) that it takes the same 

 amount of time for one to yield two as for two to yield four, etc. Suppose 

 the generation time were one hour. Then the population would, on the 

 average, double once every hour. If we draw a graph in which the number 

 of cells is plotted against time, we get the curve shown in Fig. 45. This is 

 the first part of the S-shaped curve. If now the period of active growth 

 draws gradually to a close— cells begin to die rather than reproduce and 

 those that can reproduce take longer than an hour to do so— the second 

 part of the S-shaped curve appears. 



If growth were unlimited, the growth curve would simply go up 

 and up at an ever increasing rate, and it is interesting to speculate about 

 what would happen to our planet if the growth of, say, bacteria were 

 unlimited. One species of bacteria, Escherichia coli, can divide every 20 

 minutes in an optimal environment. Thus, if at time zero there were one 

 cell, at 20 minutes there would be 2, at 40 minutes 4, at 60 minutes 8, and 

 so on. The series 1, 2, 4, 8 can be expressed as 2° (=1); 2^ (=2); 2- 

 (=4); 2^ (=8); note that the exponents represent the number of genera- 

 tions of growth that have occurred. Therefore, the number of cells present 

 after n generations of growth would be 2". Since the generation time of 

 Escherichia coli is 20 minutes, there could be 3 generations per hour, or 

 24 X 3 = 72 generations per day. In other words, were growth not 

 limited, one bacterial cell would give rise in 24 hours to 2'^^ = 40,000,000,- 



Fig. 45. The first part of 

 the S-shaped curve is gen- 

 erated when every organ- 

 ism gives rise to progeny 

 (in this case by binary fis- 

 sion) and the generation 

 time is constant. 



