Information Theory of DNA Sequencing

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 any assembly algorithm. By drawing an analogy between the DNA se-quencing problem and the classic communication problem, we formulate this question in terms of an information theoretic notion of sequencing capacity. This is the asymp-totic ratio of the length of the DNA sequence to the minimum number of reads required to reconstruct it reliably. We compute the sequencing capacity explicitly for a simple statistical model of the DNA sequence and the read process. Using this framework, we also study the impact of noise in the read process on the sequencing capacity.