Four independent lac⁻ mutants (mutants A to D) are isolated in haploid strains of E. coli. The strains have the following phenotypic characteristics:

Mutant A is lac⁻, but transcription1 of operon genes is induced by lactose.
Mutant B is lac⁻ and has uninducible2 transcription of operon genes.
Mutant C is lac⁺ and has constitutive3 transcription of operon genes.
Mutant D is lac⁺ and has constitutive3 transcription of operon genes.

A microbiologist develops donor and recipient varieties of each mutant strain and crosses them with the results shown below. The table indicates whether inducible, constitutive, or noninducible transcription occurs, along with  and  growth habit for each partial diploid. Assume each strain has a single mutation.

Mating             Transcription and Growth
A × B                 lac⁻
A × C                 lac⁺, inducible
A × D                 lac⁺, constitutive
B × C                 lac⁺, inducible
B × D                 lac⁺, constitutive
C × D                 lac⁺, constitutive

Use this information to identify which lac operon gene is mutated in each strain.

Verified step by step guidance

1. Step 1: Understand the lac operon system. The lac operon in E. coli is a set of genes involved in lactose metabolism. It includes structural genes (lacZ, lacY, lacA) and regulatory elements (promoter, operator, and the lacI gene encoding the repressor). Mutations in these components can affect transcription in different ways: inducible (normal regulation), constitutive (always on), or noninducible (always off).
2. Step 2: Analyze the phenotypes of the mutants. Mutant A is lac⁻ but inducible, suggesting a mutation in a structural gene (e.g., lacZ or lacY) that does not affect regulation. Mutant B is lac⁻ and uninducible, indicating a mutation in a regulatory element that prevents transcription entirely (e.g., lacP or lacO). Mutants C and D are lac⁺ and constitutive, suggesting mutations that disrupt repression (e.g., lacI or lacO).
3. Step 3: Examine the results of the partial diploid matings. For example, in the A × C cross, the phenotype is lac⁺ and inducible. This suggests that the mutation in A is complemented by the wild-type allele in C, and the mutation in C does not affect inducibility. This points to A having a structural gene mutation and C having a regulatory mutation (e.g., lacI or lacO).
4. Step 4: Use the complementation test results to assign mutations. For instance, in the B × C cross, the phenotype is lac⁺ and inducible. This indicates that the mutation in B is complemented by the wild-type allele in C, and the mutation in C does not prevent inducibility. This suggests B has a mutation in a regulatory element (e.g., lacP) and C has a mutation in lacI or lacO.
5. Step 5: Summarize the mutations. Based on the data, Mutant A likely has a structural gene mutation (e.g., lacZ or lacY), Mutant B has a mutation in the promoter (lacP), Mutant C has a mutation in the repressor (lacI), and Mutant D has a mutation in the operator (lacO). These assignments are consistent with the phenotypes and complementation test results.

Key Concepts

Lac Operon Structure and Function

The lac operon is a set of genes in E. coli that are involved in the metabolism of lactose. It consists of three structural genes (lacZ, lacY, and lacA) and regulatory elements that control their expression. The operon is typically off but can be induced by lactose, which binds to the repressor protein, allowing transcription of the genes necessary for lactose utilization.

Mutations and Their Effects

Mutations in the lac operon can lead to different phenotypes, such as lac⁻ (non-functional) or lac⁺ (functional). Specific mutations can affect the repressor's ability to bind to the operator or alter the promoter's activity, resulting in uninducible or constitutive expression of the operon. Understanding these mutations is crucial for determining the functional status of each mutant strain.

Partial Diploids and Complementation

In genetic studies, partial diploids are created by introducing a second copy of a gene into a haploid organism, allowing researchers to study gene interactions. In the context of the lac operon, crossing different mutants can reveal whether a mutation is dominant or recessive, and whether the mutations can complement each other to restore function, which is essential for identifying the specific mutations in each strain.