A recombinant plasmid of 9 kb is isolated from E. coli culture. The purified plasmid DNA has a concentration of 150 µg ml⁻¹. How many copies of the plasmid are present in one millilitre of this preparation? (Use 1 bp = 660 Da and Avogadro's number = 6.022 × 10²³ mol⁻¹.)

medium 3 marks Class 12 · Biology · Biotechnology and Its Applications

Answer

1.5 \times 1 0^{13}

plasmid copies per ml

The correct answer is $1.5 \times 1 0^{13}$ plasmid copies per ml — Round to two significant figures: ≈ 1.5 × 10¹³ plasmid copies per ml.

Step-by-step solution

Convert plasmid size to base pairs: 9 kb = 9 000 bp.
Calculate molecular weight of one plasmid molecule: 9 000 bp × 660 Da bp⁻¹ = 5.94 × 10⁶ Da = 5.94 × 10⁶ g mol⁻¹.
Convert the DNA concentration to grams: 150 µg ml⁻¹ = 150 × 10⁻⁶ g ml⁻¹.
Find the number of moles in 1 ml: moles = mass / molecular weight = (150 × 10⁻⁶) g / (5.94 × 10⁶ g mol⁻¹) = 2.53 × 10⁻¹¹ mol.
Convert moles to number of molecules using Avogadro's number: 2.53 × 10⁻¹¹ mol × 6.022 × 10²³ mol⁻¹ ≈ 1.52 × 10¹³ molecules.
Round to two significant figures: ≈ 1.5 × 10¹³ plasmid copies per ml.

Common mistake: Forgetting to convert µg to grams or using 650 Da per base pair instead of 660 Da

Concept tested: Calculating plasmid copy number from DNA concentration