12 A. C. R. Dean and Sir Cyril Hinshelwood 



That in certain examples the resistant forms, which 

 emerge from the process of "training" in the presence of the 

 drug, are not present at all in the original culture is strongly 

 supported by a study of the development as a function of 

 time of colonies on drug plates. Suppose a given number of 

 cells to be plated. Let aQ^ be the fraction which ever form 

 colonies and a^ the fraction which has done so at time t. 

 With a trained strain, a^^ will approach unity, while with an 

 untrained strain it may vary from near unity to a vanish- 

 ingly small value according to the drug concentration. Even 

 when aoo is very small countable numbers of colonies can never- 

 theless be obtained by the use of large enough inocula. If 

 these inocula contain preformed resistant mutants similar 

 to those in the trained strain, then clJol^, no matter how small 

 aQo may be, will be a function of time similar to that which 

 would be found in experiments with the trained strain itself. 

 In a number of examples tested, however, this consequence 

 was not verified. The time required for a given fraction of the 

 final number of colonies to appear was much longer for the 

 untrained strain. Thus it would seem that the nature as well 

 as the number of the resistant cells in the trained culture 

 differs from that of anything present in the original culture 

 (Dean and Hinshelwood, 1955). 



The only way of reconciling these observations with the 

 uncompromising mutation-selection theory is to postulate an 

 almost continuous series of minute mutational steps, and to 

 assume that the chance of a considerable number of successive 

 mutations is negligible unless cells that have already taken a 

 few of the steps are first selected and then given further 

 opportunities for taking subsequent steps. But in some ex- 

 amples aQQ may be not far short of unity (i.e., nearly all the 

 population consists of mutants) and yet the time of colony 

 formation is longer than for a trained strain. So it seems 

 (a) that there would have to be a very high proportion of 

 early step mutants and (b) that even these are not fully adapted 

 at first. If (a) is true then the complete absence of the more 

 profoundly mutated cells is strange, and if {h) has to be 



