The formula
copies = (mass in ng × 6.022 × 1023) ÷ (length in bp × 660 × 109)
660 g/mol is the average mass of one base pair of double-stranded DNA (about 330 per base for single-stranded DNA and 340 for RNA), 6.022 × 1023 is Avogadro's number and 109 converts nanograms to grams. The longer the molecule, the fewer copies a nanogram holds.
A worked example
How many molecules are in 1 ng of a 5,000 bp plasmid?
- Molar mass: 5,000 × 660 = 3.3 × 106 g/mol.
- Moles: 1 × 10−9 g ÷ 3.3 × 106 g/mol = 3.03 × 10−16 mol.
- Copies: 3.03 × 10−16 × 6.022 × 1023 = 1.8 × 108 copies.
A handy rule: 1 ng of a 1 kb fragment is about 9 × 108 copies, and 1 ng of 1 bp would be 9 × 1011, so divide by the length in bp.
From copies back to mass
Rearranged: mass (ng) = copies × length × 660 × 109 ÷ 6.022 × 1023. For 106 copies of the same plasmid that is 106 × 5,000 × 660 × 109 ÷ 6.022 × 1023 = 5.5 × 10−3 ng, or 5.5 pg.
A qPCR standard curve
Absolute quantification needs standards with a known number of copies. Measure the plasmid concentration, convert it to copies per µL, then make ten-fold serial dilutions from, say, 108 down to 102 copies per µL. Run them alongside the samples; a plot of Ct against log copies should be a straight line with a slope near −3.3 (100% efficiency). Linearized plasmid gives more accurate standards than supercoiled, and a carrier such as tRNA or yeast RNA stops low-copy dilutions sticking to the tube walls.
Calculators
The DNA Copy Number Calculator converts between nanograms and copies for DNA or RNA of any length. Get the concentration from an A260 reading with the DNA Concentration Calculator; for relative rather than absolute quantification, use the ΔΔCt Calculator.