Chapter 26, Problem 1P

(a)

Interpretation Introduction

Interpretation: Calculate the approximate intracellular concentration of repressor if the average intracellular volume of E.coli cell is $0.13\times 13\text{m}\text{L}$ .

Concept introduction: Deoxyadenosine methylase is commonly referred to as DAM methylase. This is an enzyme that catalyzes the addition of methyl ( ${\text{CH}}_{\text{3}}$ ) group to the adenine of the sequence of $5^{\text{'}}-\text{GATC}-3^{\text{'}}$ in the DNA (Deoxyribonucleic acid) which is newly synthesized.

Explanation of Solution

Given that about $10$ molecules are in E.coli average intracellular volume if $\text{0}\text{.13×13}\text{m}\text{L}$

Also, we know that $1mol$ has $\text{6}{\text{.023×10}}^{\text{23}}\text{molecules}$

Thus, moles of molecules $\text{=}\frac{\text{10}}{\text{6}{\text{.023×10}}^{\text{23}}\text{molecules}}\text{=1}{\text{.66129×10}}^{\text{-23}}$

Concentration is given as follows

  $\text{M=}\frac{\text{1}{\text{.66129×10}}^{\text{-23}}\text{mol}}{\text{0}{\text{.13×13}}^{\text{-15}}\text{L}}\text{=5}{\text{.537×10}}^{\text{-8}}\text{M}$

Thus, Intracellular concentration of repressor is $=5.5\times {10}^{-8}M$

(b)

Interpretation Introduction

Interpretation:

Calculate the approximate intracellular concentration of operator if the average cell consists of two copies of lac operon.

Concept introduction: Deoxyadenosine methylase is commonly referred to as DAM methylase. This is an enzyme that catalyzes the addition of methyl ( ${\text{CH}}_{\text{3}}$ ) group to the adenine of the sequence of $5^{\text{'}}-\text{GATC}-3^{\text{'}}$ in the DNA (Deoxyribonucleic acid) which is newly synthesized.

Explanation of Solution

Given that average cell consists of two copies of lac operon.

Concentration of repressor is given as follows:

  $\mathrm{Concentration}=\frac{2LacOperon}{0.3\times 10^{-12}\text{mL}}$

  $Concentration=6.67\times {10}^{-12}lacoperon/ml$

Thus, Intracellular concentration is $6.67\times {10}^{-12}lacoperon/ml$

(c)

Interpretation Introduction

Interpretation:

Calculate the approximate intracellular concentration of free operators.

Concept introduction: Deoxyadenosine methylase is commonly referred to as DAM methylase. This is an enzyme that catalyzes the addition of methyl ( ${\text{CH}}_{\text{3}}$ ) group to the adenine of the sequence of $5^{\text{'}}-\text{GATC}-3^{\text{'}}$ in the DNA (Deoxyribonucleic acid) which is newly synthesized.

Explanation of Solution

Given that average cell consists free operators

Concentration of repressor is given as follows:

  $\text{Concentration}=\frac{\text{1 Lac Operon}}{\text{0}{\text{.3×10}}^{\text{-12}}\text{mL}}$

  $\text{Concentration=3}{\text{.33×10}}^{\text{-12}}\text{lac operon/mL }$

Thus, Intracellular concentration is $3.33\times {10}^{-12}\text{lac operon/mL}$

(d)

Interpretation Introduction

Interpretation:

Give the reason to explain how a cell with haploid chromosome could consists of an average of two copies of the lac operon.

Concept introduction: Deoxyadenosine methylase is commonly referred to as DAM methylase. This is an enzyme that catalyzes the addition of methyl ( ${\text{CH}}_{\text{3}}$ ) group to the adenine of the sequence of $5^{\text{'}}-\text{GATC}-3^{\text{'}}$ in the DNA (Deoxyribonucleic acid) which is newly synthesized.

Explanation of Solution

In the living organism, prior to the cell division, the amount of the DNA is doubled by the cells. This causes the cells to the possess double the amount of the DNA present in the cells and the haploid cells may have two copies of the genes at a same time, which is divided into two different daughter cells, later. In this way, the cell may possess two copies of lac operon at the same time.