Extension of Lander-Waterman theory for sequencing filtered DNA libraries

Abstract

Background: The degree to which conventional DNA sequencing techniques will be successful for highly repetitive genomes is unclear. Investigators are therefore considering various filtering methods to select against high-copy sequence in DNA clone libraries. The standard model for random sequencing, Lander-Waterman theory, does not account for two important issues in such libraries, discontinuities and position-based sampling biases (the so-called "edge effect"). We report an extension of the theory for analyzing such configurations.

Results: The edge effect cannot be neglected in most cases. Specifically, rates of coverage and gap reduction are appreciably lower than those for conventional libraries, as predicted by standard theory. Performance decreases as read length increases relative to island size. Although opposite of what happens in a conventional library, this apparent paradox is readily explained in terms of the edge effect. The model agrees well with prototype gene-tagging experiments for Zea mays and Sorghum bicolor. Moreover, the associated density function suggests well-defined probabilistic milestones for the number of reads necessary to capture a given fraction of the gene space. An exception for applying standard theory arises if sequence redundancy is less than about 1-fold. Here, evolution of the random quantities is independent of library gaps and edge effects. This observation effectively validates the practice of using standard theory to estimate the genic enrichment of a library based on light shotgun sequencing.

Conclusion: Coverage performance using a filtered library is significantly lower than that for an equivalent-sized conventional library, suggesting that directed methods may be more critical for the former. The proposed model should be useful for analyzing future projects.

Figure 1

Schematic of the covering process for the conventional continuous library (top) versus the filtered discontinuous library (bottom).

Figure 2

Coverage evolution for both the discontinuous island model and the LW "super-island" (LWSI) model.

Figure 3

Evolution of gap census for both the discontinuous island model and the LWSI model.

Figure 4

Evolution of average contig length for both the discontinuous island model and the LWSI model.

Figure 5

Comparison of Thm. 5 to experimental gene-tagging results in sorghum and maize.

Figure 6

Tail probabilities for tagging various fractions of the gene space in Sorghum bicolor [14].

Figure 7

Island coordinate system and nomenclature.