DNA computing-foundations and implications

Abstract

DNA computing is an area of natural computing based on the idea that molecular biology processes can be used to perform arithmetic and logic operations on information encoded as DNA strands. The first part of this review outlines basic molecular biology notions necessary for understanding DNA computing, recounts the first experimental demonstration of DNA computing (Adleman's 7-vertex Hamiltonian Path Problem), and recounts the milestone wet laboratory experiment that first demonstrated the potential of DNA computing to outperform the computational ability of an unaided human (20 variable instance of 3-SAT). The second part of the review describes how the properties of DNA-based information, and in particular the Watson-Crick complementarity of DNA single strands, have influenced areas of theoretical computer science such as formal language theory, coding theory, automata theory and combinatorics on words. More precisely, we describe the problem of DNA encodings design, present an analysis of intramolecular bonds, define and characterize languages that avoid certain undesirable intermolecular bonds, and investigate languages whose words avoid even imperfect bindings between their constituent strands. We also present another, vectorial, representation of DNA strands, and two computational models based on this representation: sticker systems and Watson-Crick automata. Lastly, we describe the influence that properties of DNA-based information have had on research in combinatorics on words, by enumerating several natural generalizations of classical concepts of combinatorics of words: pseudopalindromes, pseudoperiodicity, Watson-Crick conjugate and commutative words, involutively bordered words, pseudoknot bordered words. In addition, we outline natural extensions in this context of two of the most fundamental results in combinatorics of words, namely Fine and Wilf 's theorem and the Lyndon-Schutzenberger result.