208 



CELL HEREDITY 



From pump controlling 

 input from reservoir 



Overflow 



FIGURE 8.1. A chemostat in operation. 



overflow. In this steady state the total number of bacteria in the chamber 

 remains constant in accordance with the concentration of Hmiting 

 nutrient in the input; the rate of growth is also constant and equal to 

 the rate of turnover of the medium which is a function of the rate of in- 

 put. In a closed system such as a test tube, the concentration of nu- 

 trients falls during growth while the concentration of waste products 

 rises. In the open system of the chemostat, since the bacteria im- 

 mediately use up the incoming nutrient and since waste products are 

 continually lost in the overflow, a steady state of the chemical environ- 

 ment is maintained. In this way, then, the conditions of growth may be 

 accurately controlled and varied at will. 



When a mutant arises in the chemostat, it may multiply at the same 

 rate as the parents. If so, its proportion in the population will not in- 

 crease through growth alone because mutants as well as parents are lost 

 as fast as they are formed. But the proportion of mutants will increase 

 as new mutations occur, and in a linear fashion as long as the number of 

 mutants, M, is so small that it is unnecessary to take back mutation into 

 account. If the growth rate of the mutants is equal to that of the parents, 

 whose number is N, then so long as N is very large relative to M, the rate 

 of increase of mutants will be: 



dM 

 dt 



aN 



(8.1) 



where a is the chance of mutation per parent bacterium per generation. 



