Fundamental Bounds for Sequence Reconstruction From Nanopore Sequencers

Abstract

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) using replicated extrusion (the process of passing a DNA strand through the nanopore), what is the number of replicas needed to accurately reconstruct the true sequence with high probability? Our results provide a number of important insights: (i) the probability of accurate reconstruction of a sequence from a single sample in the presence of indel errors tends quickly (i.e., exponentially) to zero as the length of the sequence increases; and (ii) replicated extrusion is an effective technique for accurate reconstruction. We show that for typical distributions of indel errors, the required number of replicas is a slow function (polylogarithmic) of sequence length – implying that through replicated extrusion, we can sequence large reads using nanopore sequencers. Moreover, we show that in certain cases, the required number of replicas can be related to information-theoretic parameters of the indel error distributions.

An Overview of Capacity Results for Synchronization Channels

“…In particular, if Ch is a BSC, we recover (39). As another example, if Ch is a BEC with erasure probability , we conclude that…”

“…We note that the multi-use setting for sticky channels has been considered by Magner, Duda, Szpankowski, and Grama [39]. This is motivated by nanopore sequencing, which, as mentioned before, has recently found connections to DNA-based data storage [12,13].…”

“…Sticky channels and run-length encoding Repeat channels that do not introduce deletions (i.e., Pr[R = 0] = 0) are called sticky channels. In a sense, sticky channels are the easiest type of repeat channels to analyze, and they are also connected to practical applications (e.g., see [38,39]). Widely studied examples of such channels include the duplication channel, which independently duplicates each input bit with probability p (i.e., R = 1 + Ber p ), and the geometric sticky channel, which independently replicates each input bit according to R = 1 + Geom p .…”

“…This inequality immediately leads to improved capacity lower bounds when compared to (39), both numerical (by using the state-of-the-art lower bounds from [66]), or analytical (since there are better analytical lower bounds on C(d) than 1 − h(d), see [46,83]). Rahmati and Duman [82] successfully apply the observation above to obtain lower bounds beyond what we present here.…”

Models and Information-Theoretic Bounds for Nanopore Sequencing

“…We believe that several of the techniques and results could also be of independent interest, beyond its application to nanopore sequencing. In [23], a nanopore sequencer is modeled at a hard-decision level by a simplified insertion-deletion channel, where no run of DNA bases is deleted (similar to [24]) or inserted, to understand how to combine multiple reads. Our channel model, however, is aimed at designing base-callers (algorithms for decoding DNA from current trace) and therefore operates at fine-grained signal level.…”