Fundamental Bounds and Approaches to Sequence Reconstruction from Nanopore Sequencers

Motivation: Nanopore sequencers are emerging as promising new platforms for high-throughput sequencing. As with other technologies, sequencer errors pose a major challenge for their effective use. In this paper, we present a novel information theoretic analysis of the impact of insertion-deletion (InDel) errors in nanopore sequencers. In particular, we consider the following problems: (i) for given InDel error characteristics and rate, what is the probability of accurate reconstruction as a function of sequence length; (ii) what is the number of ‘typical’ sequences within the distortion bound induced by InDel errors; (iii) using repeated extrusion through the nanopore, what is the number of repetitions needed to reduce the distortion bound so that only one typical sequence exists within the distortion bound. Results: Our results provide a number of important insights: (i) the maximum length of a sequence that can be accurately reconstructed in the presence of InDel errors is relatively small; (ii) the number of typical sequences within the distortion bound is large; and (iii) repeated extrusion is an effective technique for unique reconstruction. In particular, we show that the number of repeats is a slow function (logarithmic) of sequence length – implying that through repeated extrusion, we can sequence large reads using nanopore sequencers. InDel errors are the primary error mode for nanopore sequencers. To this end, the results in this paper can be viewed as (tight) bounds on reconstruction lengths and repetitions for accurate reconstruction. Contact: [email protected]