Error analysis of deep sequencing of phage libraries: peptides censored in sequencing

Next-generation sequencing techniques empower selection of ligands from phage-display libraries because they can detect low abundant clones and quantify changes in the copy numbers of clones without excessive selection rounds. Identification of errors in deep sequencing data is the most critical step in this process because these techniques have error rates >1%. Mechanisms that yield errors in Illumina and other techniques have been proposed, but no reports to date describe error analysis in phage libraries. Our paper focuses on error analysis of 7-mer peptide libraries sequenced by Illumina method. Low theoretical complexity of this phage library, as compared to complexity of long genetic reads and genomes, allowed us to describe this library using convenient linear vector and operator framework. We describe a phage library as N × 1 frequency vector n = ||ni||, where ni is the copy number of the ith sequence and N is the theoretical diversity, that is, the total number of all possible sequences. Any manipulation to the library is an operator acting on n. Selection, amplification, or sequencing could be described as a product of a N × N matrix and a stochastic sampling operator (Sa). The latter is a random diagonal matrix that describes sampling of a library. In this paper, we focus on the properties of Sa and use them to define the sequencing operator (Seq). Sequencing without any bias and errors is Seq = Sa IN, where IN is a N × N unity matrix. Any bias in sequencing changes IN to a nonunity matrix. We identified a diagonal censorship matrix (CEN), which describes elimination or statistically significant downsampling, of specific reads during the sequencing process.