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Chunk #6 — Methods — Theoretical expectation of deconvoluting singlets

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Multiplexed droplet single-cell RNA-sequencing using natural genetic variation.
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The theoretical distribution of expected singlets with multiplexing (presented in Supplementary Fig. 2) is as follows. Let do (e.g. 0.01) be the proportion of true multiplets when xo (1,000) cells are loaded when multiplexing was not used. Then the expected multiplet rates when x cells are loaded can be modeled exponentially as d(x)=1−(1−d0)xx0. Let α be the fraction of true singlets incorrectly classified as non-singlets (i.e. doublet or ambiguous), and β be the fraction of multiplets correctly classified as non-singlets. When multiplexing x cells equally from n samples, the expected multiplet rates are d(x), and 1nd(x) are expected to be undetectable doublets mixed between the cells from the same sample. Therefore, the overall effective multiplet rate is [n−(n−1)βn]d(x). Similarly, the expected number of correctly identified singlets becomes (1−α)[1−d(x)]x0d(x)−log(1−d0). Given α, β the expected number of singlets can be calculated by fixing the multiplet rate d(x) = d0. We used d0 = 0.01, x0 = 1000 for the simulation in Supplementary Fig. 2.