Theoretical prediction of assembly contiguity
Theoretical methods for predicting the performance of assembly algorithms have the potential to guide experimental design on a scale that simulations cannot. A fundamental question of experimental design is how deep to sequence in order to obtain an assembly with long-enough contigs. More precisely, given a certain read length and coverage, what is the expected contig length that an assembler would produce on a given genome? The foundational work of Lander and Waterman tackled this question, but their method is not applicable to modern high-throughput sequencing. In this paper, we derive what we call a Z-value, which is a formula that takes as input the read length, coverage, and basic properties of the genome, and returns a prediction of the mean contig length produced by a simple single-k assembler on error-free data. We show on a benchmark of 14 genomes that the Z-value is highly accurate, with a mean absolute prediction error of less than 2 percent. We further show how this formula can be used to determine the best choice of k for the assembler and how to choose a coverage level that gives contig lengths within a desired fraction of the optimal. Finally, we show how the Z-value can also predict the performance of a more complicated assembler like Velvet and how it can be used to guide the choice between instruments when there is a tradeoff between coverage and read length and the budget is limited.