A researcher wants to clone the human insulin gene (coding sequence 1,100 bp) into the plasmid vector pBR322 (size 4,363 bp). If 5 µg of the recombinant plasmid DNA is required for transformation, calculate the approximate number of plasmid molecules needed. (Assume average molecular weight of a base pair is 660 Da.)

Step-by-step solution

1. Find the total length of the recombinant plasmid: vector length $4,363\text{bp}$ + insert length $1,100\text{bp}=5,463\text{bp}$.
2. Calculate the molar mass of one plasmid molecule: $5,463\text{bp}\times 660{\text{g⋅mol}}^{-1}{\text{bp}}^{-1}=3,605,580{\text{g⋅mol}}^{-1}$.
3. Convert the required mass to grams: $5\mu \text{g}=5\times 10^{-6}\text{g}$.
4. Determine the number of moles of plasmid needed: $\text{moles}=\frac{5\times 10^{-6}\text{g}}{3,605,580{\text{g⋅mol}}^{-1}}\approx 1.386\times 10^{-12}\text{mol}$.
5. Use Avogadro's number to obtain the number of molecules: $1.386\times 10^{-12}\text{mol}\times 6.022\times 10^{23}{\text{mol}}^{-1}\approx 8.35\times 10^{11}$ molecules.
6. Round to one significant figure as required, giving approximately $8.3\times 10^{11}$ plasmid molecules.

Concept tested: Calculation of plasmid copy number

Published 18 September 2026 · How this solution was prepared and checked