Chapter 16.2, Problem 20AQP

Summary Introduction

To determine:

The genotype of a lac operon that produces, or fails to produce, $\text{β-}\text{galactosidase}$ and permease under the following given condition.

Introduction:

An operon is defined as a group of genes that have a common promoter and regulator and also transcribed as a single unit. This transcription results in the production of single $\text{mRNA}$ which encodes several types of proteins. The gene of lac operon gets activated in the presence of lactose sugar.

Explanation of Solution

Tabular representation: Table 1: Transcription of a gene in the present or absent of lactose.

Genotype of strain	Lactose absent		Lactose present
	$\text{β-Galactosidase}$	Permease	$\text{β-Galactosidase}$	Permease
$lac{I}^{+}lac{P}^{+}lac{O}^{+}lac{Z}^{+}lac{Y}^{+}$	-	-	+	+
$lac{I}^{+}lac{P}^{+}lac{O}^{+}lac{Z}^{-}lac{Y}^{+}$	-	-	-	+
$lac{I}^{+}lac{P}^{+}lac{O}^{+}lac{Z}^{+}lac{Y}^{-}$	-	-	+	-
$lac{I}^{-}lac{P}^{+}lac{O}^{+}lac{Z}^{+}lac{Y}^{+}$	+	+	+	+
$lac{I}^{+}lac{P}^{+}lac{O}^{+}lac{Z}^{-}lac{Y}^{-}$ or $lac{I}^{-}lac{P}^{-}lac{O}^{+}lac{Z}^{+}lac{Y}^{+}$	-	-	-	-
$lac{I}^{-}lac{P}^{+}lac{O}^{+}lac{Z}^{+}lac{Y}^{-}$	+	-	+	-
$lac{I}^{-}lac{P}^{+}lac{O}^{+}lac{Z}^{-}lac{Y}^{+}$	-	+	-	+

Table 1: Transcription of a gene in the present or absent of lactose.

Lac operon is defined as an operon which is required for lactose metabolism and its transport. Lac operon is an example of the negative inducible operon. This operon contains three types of a structural gene which are designated as lac Z, lac Y, and lac A, that contain a common promoter and an operator region. Lac operon also contains regulator gene which is designated as lac I. Lac I gene encodes a repressor protein and inhibit transcription of a gene. Mutation in any genes presents in operon cause the change in gene expression.

The possible genotypes of given strains are listed below:

(i) The presence of both $\text{β-}\text{galactosidase}$ and permease enzyme inside the cell in presence of the substrate determines that the genotype of a strain is wild type. Thus, the genotype of the given strain will be $lac{I}^{+}lac{P}^{+}lac{O}^{+}lac{Z}^{+}lac{Y}^{+}$.

(ii) The presence of permease enzyme in the given strain and presence of the substrate determines that the gene for $\text{β-}\text{galactosidase}$ enzyme is mutated. Thus, the genotype of a strain will be: $lac{I}^{+}lac{P}^{+}lac{O}^{+}lac{Z}^{-}lac{Y}^{+}$.

(iii) The absence of permease enzyme after the presence of the substrate determines that gene for permease enzyme is mutated. Thus, the genotype of a strain will be: $lac{I}^{+}lac{P}^{+}lac{O}^{+}lac{Z}^{+}lac{Y}^{-}$.

(iv) The presence of both enzyme at the present or absent of substrate determines that the regulator gene is mutated. Thus, the genotype of the given strain will be: $lac{I}^{-}lac{P}^{+}lac{O}^{+}lac{Z}^{+}lac{Y}^{+}$.

(v) The absence of both enzyme at the present or absent of genotype determines either mutation occur at promoter and regulator gene region or mutation occur at both enzyme-coding gene regions. Thus, the possible genotype of a given strain will be: $lac{I}^{+}lac{P}^{+}lac{O}^{+}lac{Z}^{-}lac{Y}^{-}$ or $lac{I}^{-}lac{P}^{-}lac{O}^{+}lac{Z}^{+}lac{Y}^{+}$.

(vi) The presence of an enzyme $\text{β-}\text{galactosidase}$ only either in present or in absent of substrate determines that mutation occurs in both regulator gene region and the gene encoding for permease enzyme region. Thus, the genotype of a given strain will be: $lac{I}^{-}lac{P}^{+}lac{O}^{+}lac{Z}^{+}lac{Y}^{-}$.

(vii) The presence of an enzyme permease only either in present or in absent of substrate determines that mutation occurs in both regulator gene region and the gene encoding for $\text{β-}\text{galactosidase}$ enzyme region. Thus, the genotype of a given strain will be: $lac{I}^{-}lac{P}^{+}lac{O}^{+}lac{Z}^{-}lac{Y}^{+}$.

Conclusion

The enzyme synthesized by the structural gene will depend on the presence or absence of a substrate. If lactose is present, then the gene for lac operon will turn on and if lactose is absent then gene for lac operon will turn off. Mutation in any of the lac operon gene will change the gene expression.