Information Theory of DNA Shotgun Sequencing

TL;DR

This paper establishes fundamental limits on DNA sequence reconstruction using shotgun sequencing, revealing a phase transition based on read length and sequence entropy, and analyzing the effects of noise.

Contribution

It introduces an information-theoretic framework for DNA sequencing, identifying critical thresholds for successful assembly based on read length and sequence statistics.

Findings

Reconstruction is impossible below a critical read length threshold.

Above the threshold, sufficient coverage guarantees reconstruction.

Noise impacts the minimum read length needed for reliable assembly.

Abstract

DNA sequencing is the basic workhorse of modern day biology and medicine. Shotgun sequencing is the dominant technique used: many randomly located short fragments called reads are extracted from the DNA sequence, and these reads are assembled to reconstruct the original sequence. A basic question is: given a sequencing technology and the statistics of the DNA sequence, what is the minimum number of reads required for reliable reconstruction? This number provides a fundamental limit to the performance of {\em any} assembly algorithm. For a simple statistical model of the DNA sequence and the read process, we show that the answer admits a critical phenomena in the asymptotic limit of long DNA sequences: if the read length is below a threshold, reconstruction is impossible no matter how many reads are observed, and if the read length is above the threshold, having enough reads to cover the DNA sequence is sufficient to reconstruct. The threshold is computed in terms of the Renyi entropy rate of the DNA sequence. We also study the impact of noise in the read process on the performance.