Normal and Compound Poisson Approximations for Pattern Occurrences in NGS Reads

Next generation sequencing (NGS) technologies are now widely used in many biological studies. In NGS, sequence reads are randomly sampled from the genome sequence of interest. Most computational approaches for NGS data first map the reads to the genome and then analyze the data based on the mapped reads. Since many organisms have unknown genome sequences and many reads cannot be uniquely mapped to the genomes even if the genome sequences are known, alternative analytical methods are needed for the study of NGS data. Here we suggest using word patterns to analyze NGS data. Word pattern counting (the study of the probabilistic distribution of the number of occurrences of word patterns in one or multiple long sequences) has played an important role in molecular sequence analysis. However, no studies are available on the distribution of the number of occurrences of word patterns in NGS reads. In this article, we build probabilistic models for the background sequence and the sampling process of the sequence reads from the genome. Based on the models, we provide normal and compound Poisson approximations for the number of occurrences of word patterns from the sequence reads, with bounds on the approximation error. The main challenge is to consider the randomness in generating the long background sequence, as well as in the sampling of the reads using NGS. We show the accuracy of these approximations under a variety of conditions for different patterns with various characteristics. Under realistic assumptions, the compound Poisson approximation seems to outperform the normal approximation in most situations. These approximate distributions can be used to evaluate the statistical significance of the occurrence of patterns from NGS data. The theory and the computational algorithm for calculating the approximate distributions are then used to analyze ChIP-Seq data using transcription factor GABP. Software is available online (www-rcf.usc.edu/∼fsun/Programs/NGS_motif_power/NGS_motif_power.html). In addition, Supplementary Material can be found online (www.liebertonline.com/cmb).