Information Theory of DNA Sequencing

Abstract

DNA sequencing is the basic workhorse of modern day biology and medicine. Shot- gun sequencing is the dominant technique used: many randomly located short frag- ments called reads are extracted fromthe DNA sequence, and these reads are assembled to reconstruct the original sequence. A basic question is: given a sequencing technol- ogy 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 minimumnumber 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.