Libraries & cloning formulas

DNA libraries, gene cloning and recombinant protein production. 2 formulas for GATE BT Recombinant DNA Technology and Tools, each with when to use it. Each is explained in the topic notes.

All 2 Libraries & cloning formulas

LIBRARY SIZE EQUATION (CLARKE–CARBON)

N = \frac{ln ( 1 - P )}{ln ( 1 - f )}

$N$ = number of independent clones required; $P$ = desired probability that a given sequence is present at least once. Genomic library: $f$ = average insert size / genome size, in the same units (bp). cDNA library: $f$ = the fraction of all mRNA molecules made up by the transcript of interest (its abundance). Assumes fragments are cloned at random and independently, with every fragment equally clonable. Always round $N$ up.

PROBABILITY THAT A GIVEN SEQUENCE IS PRESENT IN N CLONES

P = 1 - (1 - f)^{N}

The same relation solved for $P$ . For small $f$ , $ln (1 - f) \approx - f$ , so $N \approx \frac{- ln ( 1 - P )}{f}$ , which slightly overestimates $N$ .

Where this was asked: 2020 (4), 2025 (1). See the 5 previous-year questions on Libraries & cloning. This shows what was asked, not what will be asked.

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Libraries & cloning: the notes and 5 solved previous-year questions