Encoding Cooperative DNA Codes

Abstract

Abstract : The primary goal of this research was the development of an enabling technology for DNA computing. It is focused on the construction of a biomolecular architecture designed to employ new algorithmic paradigms based on the massively parallel computational power of DNA hybridization. The intent is to develop a computing basis to eventually overcome the exponential time complexity of many discrete math problems so that they can be solved in linear real time. Many of these computationally hard (NP) problems are critical to logistics scheduling and security. In this way, this research addresses computational, national security and knowledge acquisition challenges of the Air Force. DNA code words are structural and information building blocks in biomolecular computing and other biotechnical applications that employ DNA hybridization assays. Thermodynamic distance functions are important components in the construction of DNA codes. We introduce new matrices for DNA code design that captures key aspects of the nearest neighbor thermodynamic model for hybridized DNA duplexes. One version of our metric gives the maximum number of stacked pairs of hydrogen bonded nucleotide base pairs that can be present in any secondary structure in a hybridized DNA duplex without pseudo knots. We introduce the concept of (t-gap) block isomorphic subsequences to describe new string metrics that are similar to the weighted Levenshtein insertion-deletion metric. We show how our new distances can be calculated by a generalization of the folklore longest common subsequence dynamic programming algorithm. We give a Varshamov-Gilbert like lower bound on the size of some of codes using our distance functions as constraints. We also discuss software implementation of our DNA code design methods.