Diversity and Sampling

A heap of about fifty gumballs in a dozen flat colours — pink, green, yellow, blue, red, purple, orange, black and one white — piled on a white surface.

Theoretical Diversity

A three-by-six grid. The columns are numbered 1 to 6 and the rows are labelled Seq1, Seq2 and Seq3. Each cell holds one gumball, and the colours differ freely from cell to cell: Seq1 reads green, crimson, magenta, yellow, black, blue; Seq2 white, black, crimson, crimson, black, magenta; Seq3 black, black, black, blue, yellow, blue.

20*  20*  20*  20*  20*  20 = 20^6 = 6.4E7

Measuring library size

Oversampling

Six gumballs — green, crimson, magenta, yellow, black and blue — pressed into a row so that they touch, one glued hexamer.

Probability that a single member exists only once in a library:

p = number of hexamers chosen
      (library size)
n = theoretical diversity

P = 1 − e−p/n= 0.99

p = n · ln(0.01) = 4.6n

Nucleic Acids Res. 1998 Feb 15;26(4):879-86. PMID: 9461443

Library Quality issues:

Diversity/Bias

  • Synthesis-derived base bias
  • Cloning-derived base bias / biased annealing
  • Differential growth rates
  • Uneven spreading on plates

Non-canonical members

  • Parent vector bleedthrough
  • Deletions and insertions
  • Stop codons

Library Construction: Synthesis

A screenshot of a gene synthesis vendor's product page, headed Variant Libraries, under the breadcrumb Products / Variant Libraries, with a short blurb and an Explore Data button.
https://www.twistbioscience.com/products/libraries
Three kinds of variant library offered as products, each drawn as a row of coloured circles standing for residues. A combinatorial variant library mutates multiple sites, a stretch, or several stretches with length variation. A site saturation library changes one position to every residue in turn. A spread-out low diversity library changes scattered single sites.