SEGREGATIONS IN ESCHERICHIA COLI 517 



matrix, and there occasionally occurs a gene-for-gene interchange. This is 

 equivalent to the "Konversion" theory once proposed by Winkler (1932), to 

 account for interchanges in Drosophila. While this type of arrangement would 

 account for a tendency to preserve the parental configuration, it fails to ex- 

 plain either quantitative linkage intensities, or the interaction of segregations 

 which is revealed by the data on Lac and V in table 5. Naturally, one could 

 further modify the "Konversion" theory to take these exigencies into account, 

 but in so doing one would be elaborating an exceedingly complicated theory 

 which would, in fact, be a re-expression of a mechanical theory of linkage. 



The interaction of the Lac and V segregations is perhaps the most critical 

 datum with which a genetic system for E. coli can be formulated. The inter- 

 action may be expressed as follows: the frequency of interchanges between 

 [BM] and Lac is dependent upon the interchanges between [BM] and V. Spe- 

 cifically, in the cross B+M+T'L-Br Lac-V 1 S XB-M~T+L+B 1 + Lac+VS, one 

 finds in the B + M + T + L+Bi + the following distribution of classes: Lac~Vi 9 23 

 percent, Lac + Vi r 29 percent (for the parental combinations) and Lac~V{ 46 

 percent, Lac + Vy s 2 percent (for the new combinations). With reference to 

 [B+M+], Lac~ is the parental, Lac + the interchange type. The proportion of 

 Vi T (representing an interchange between V\ and [BM]) is different in the Lac~ 

 and Lac + segregations: namely 46:23 = 2:1 and 29:2=14.5:1 respectively. 

 This interaction between interchanges is most simply explained by the assump- 

 tion that factors are located on a linear segment, so that interchanges between 

 proximal factors also lead to the crossing over of more distal factors, barring 

 the occurrence of additional interchanges. 



Additional support for the theory of linear arrangement has been found in 

 the segregation of V 6 , summarized in table 6. It will be noted that the segrega- 

 tions of Lac, Vi, and V 6 are quite congruous in the Bi~ and Bi + classes. In the 

 totals, one finds the ratios, for each factor separately, of Lac~ 78 percent; 

 PV 82 percent; Vi" 36 percent; indicating that the first two are both linked to 

 [BM] while the latter is linked to [TL]. V 6 cannot, however, be to the left of 

 [BM] because it does not interact with B\. If, therefore, there is a linear order 

 of genes, V 6 must be to the right of [BM], and because of its greater linkage 

 intensity, nearer [BM] than is Lac. This arrangement is indicated in the map 

 in table 6, and in fig. 2c. The agreement of the data with the hypothesis can 

 be examined at several points. In the first place, the single exchange types, as 

 indicated in the table, should be the most frequent. Secondly, barring multiple 

 exchanges, an interchange between V 6 and Lac should lead also to an inter- 

 change between V 6 and V\. That is to say, the Lac + Vf class should be more 

 often Vi r than V\*. Finally, in view of the similarity in linkage intensities to 

 [BM], Lac and V 6 must be closely linked. Although the "triple-interchange" 

 types would seem to be rather frequent, reference to the table may suggest that 

 these conditions are fulfilled. In particular, it will be noted that among the 

 Lac~, the ratio of V 6 r : V 6 * is 94:3, or 31:1, while among the Lac+, this same 

 ratio is 10:29, or 1:3. This difference is interpreted to mean that Lac and V 6 

 are linked to each other, as demanded by the theory of linearity. 



It is not, of course, proven that the gene order is not branched at some other 



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