5.  DNA from a bacterial strain with genotype at b⁺c⁺d⁺e⁺f⁺ was isolated and used to transform a strain of bacteria with genotype a^–b^–c^–d^–e^–f^–.The transformed cells were tested for the presence of co-transformed genes and the following types of co-transformants were observed:
a⁺ and c⁺           e⁺ and d⁺
d⁺ and b⁺           b⁺ and f⁺
c⁺ and e⁺

The correct order of genes will be:
(1) a b c d e f      (2) a c e b f d
(3) a c e d b f      (4) a b f e d c

Cotransformation in bacterial genetics occurs when DNA fragments from a donor strain (a⁺b⁺c⁺d⁺e⁺) are taken up by a recipient strain (a⁻b⁻c⁻d⁻e⁻), and closely linked genes on the same fragment are inherited together. The observed cotransformed pairs—a⁺b⁺, c⁺e⁺, d⁺c⁺, b⁺d⁺—indicate linkage, as only nearby genes appear on the same transforming DNA fragment (~2% of the genome). The correct gene order is a b d c e (option 4), deduced by linking overlapping pairs: a-b, b-d, d-c, c-e.​

Cotransformation Principle

Genes co-transform at higher frequencies if proximal on the chromosome, as random DNA fragments capture linked markers. Absent pairs (e.g., no a⁺c⁺ or b⁺e⁺) imply separation beyond fragment size. Mapping treats pairs as edges in a linkage graph: a-b, b-d, d-c, c-e form a linear path a-b-d-c-e without branches or contradictions.​

Option Analysis

• (1) a b c d e: Fails as b⁺d⁺ cotransform (skipping c), but c lies between; contradicts d⁺c⁺ linkage without b-d proximity.

• (2) a c b e d: Invalid—no a⁺c⁺ or c⁺b⁺ observed; d isolated from core linkages.

• (3) a b c e d: Wrong—d⁺c⁺ and b⁺d⁺ require d between/near b-c, not after e; no b⁺e⁺ support.

• (4) a b d c e: Matches all—fragments cover a-b-d, b-d-c, d-c-e, c-e; no unobserved pairs needed.​