Gene Arrangement and Chiasmata 



131 



You should be dissatisfied, however, with 

 the abiHty of this model to represent reality, 

 in view of the fact, previously noted, that a 

 given tetrad usually contains more than one 

 chiasma. This complication prompts the fol- 

 lowing question: What is the relationship 

 between two chiasmata in the same tetrad? 

 Two possible relationships come to mind. 

 First, the frequency with which two chiasmata 

 occur simultaneously within a certain region 

 may be larger or smaller than that expected 

 by chance. Second, the frequency with which 

 the two chiasmata involve the same two 

 strands of the tetrad may be larger or smaller 

 than that which would be expected by chance. 

 Consider the second relationship first. 



Let us specifiy the strands in the tetrad of 

 the model as 1,2, 3, 4, where 1 and 2 are the 

 normal sister strands and 3 and 4 the mutant 

 sister strands (Figure 17-3). Suppose one 

 chiasma occurs between strands 2 and 3 in 

 the a-b region. There are six combinations 

 of strands possible for a second chiasma 

 which occurs in the b-c region, namely, 1 

 with 2, 3 with 4, 2 with 3, 2 with 4, 1 with 3, 

 and 1 with 4. These positions are indicated 

 in the Figure. Note, for this second chiasma, 

 that the first two combinations listed would 

 involve sister strands which are, naturally, 

 genetically identical. Since sister-strand 

 crossing over would have an effect upon the 

 production of new genetic combinations only 

 under other, very special, circumstances, such 

 crossing over need not be considered further 

 for our purposes. Each of the last four types 



of chiasma involves nonsister strands in the 

 b-c region, and together with the single 

 chiasma in the a-b region, forms double 

 chiasmata of three types, respectively: 2- 

 strand (thQ same two strands exchange in both 

 chiasmata), 3-strand (one of the two strands 

 of the first chiasma exchanges in the second; 

 there are two ways this can occur), and 4- 

 strand (the strands exchanging in the second 

 chiasma are those which did not exchange in 

 the first). 



Restricting our attention to the a-c region, 

 let us examine the genetic consequences of 

 the nonsister double chiasmata described. 

 Figure 17-4 shows, at the left, the configura- 

 tions of these four nonsister types of double 

 chiasmata. The middle column shows the 

 meiotic products of each, and the right col- 

 umn describes whether these products are 

 noncrossovers, single crossovers, or double 

 crossovers for the a-c region. Notice that 

 following 2-strand double chiasmata two of 

 the four meiotic products are genetic non- 

 crossovers (+ + + and a b c) and two are 

 double crossovers {-\- b -\- and a -\- c) recog- 

 nizable because the middle gene is switched 

 in position relative to the end genes. A 3- 

 strand double chiasmata produces one double 

 crossover, two single crossovers (recognizable 

 because each has one end gene switched), 

 and one noncrossover. The 4-strand double 

 chiasmata produces four single crossover 

 strands. Two things may be noted, namely, 

 that each type of double chiasmata produces 

 some strands with a new genetic combination. 



FIGURE 17-3, Chromatid combinations possible in a double chiasmata. {See text 

 for details.) 



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