54 CELL HEREDITY 



F(0) as the fraction of cultures which had no mutational events, and 

 from this calculate m. The assumption is that the mutational events are 

 distributed at random, and this has been amply demonstrated to be the 

 case. Experimentally, ^(O) niay be measured by plating cultures of 

 bacteria on agar media where mutants may be detected. The frequency 

 of mutants is usually so small (ca. 10~^) that the medium preferably 

 should be selective, allowing no growth of the parents. Thus, among 

 the milnv millions of the latter on the plate, only the mutants present 

 will form colonies. 



This method of measuring mutations has been adapted for use with 

 liquid cultures and also is conveniently employed in cases where mutants 

 form papillae on the surface of colonies. In this case some colonies may 

 have no papillae at all. Letting this fraction equal F(0), the average 

 number of papillae, m, can be calculated from equation 2.3. Since each 

 papilla represents one mutational event, the calculated m can be com- 

 pared with the m obtained by counting the number of papillae directly. 

 The two estimates are found to agree because mutation is random. 



Once m is known, the chance of mutation per cell per division, a, can 

 be estimated from the equation defining mutation rate: 



a = mid (2.4) 



where d is the total number of divisions that have taken place. The 

 term d cannot be measured directly but it is in some cases approximately 

 equal to N, the total number of cells present per culture. This can be 

 seen by considering the properties of a clone produced by repeated divi- 

 sion into two: 



Here one division gave rise to two, three divisions to four, and seven 

 divisions to eight cells. The number of divisions counted from the first 

 cell is one less than the number of cells produced. As a con.sequence, 

 when a large culture is started from a few cells, d^N, and N may be 

 substituted for (/ in equation 2.4. In this way one can measure the 

 rate of mutation of manv microorganisms which grow as separate cells; 

 the method can be adapted for the somatic cells of higher organisms 

 as well. 



