Fig. 3

Design of code elements and probabilistic features of optimal Lox cassettes. a Numerically determined maximal size of sets of elements that are separated by a minimal Hamming distance of 1 bp (black), 3 bp (gray), and 5 bp (blue). In order to be robust to two sequencing errors, the minimal distance needs to be 5 bp, which requires m to be larger than 4 bp. b Upper bound for the expected proportion of misclassified elements as a function of empirical DNA sequencing mismatch error rates [52] for three common sequencing platforms (Illumina, Ion Torrent, Pacific Biosciences) and different sequence data (P. falciparum (∙), E. coli (\(\blacktriangle \)), R. spha. (■), H. sapiens (+)). The minimal distance that separates the elements is 1 bp (solid), 3 bp (dotted), and 5 bp (dashed). c Ranked probabilities of the 1022 size-stable barcodes from a cassette with 13 elements generated under constitutive Cre expression. While a few codes are relatively frequent, the majority of codes are rare. d Scatter-plot showing barcode probabilities against the average number of excisions (black) and the number of inversions (blue) that are needed to generate from an initially 13 element optimal cassette a size-stable barcode. e Maximum number of cells in which a barcode can be induced versus the number of cells that produce 99 %-unique codes, for one to four sequential cassettes. The color represents the percentage of discarded codes relative to the total code diversity, which can be adjusted to experimental conditions post acquisition. Inducing barcodes in a target population of 10⁸ (circle) and 10¹² (square) cells yields a proportion of 10 % and 0.1 % of 99 %-unique barcodes respectively. f Although code diversity grows as O(n ³), the expected number of recombination events that are needed to generate a size-stable code increases linearly with the number of elements in the initial cassette