DNA-based computing uses the tendency of nucleotide bases to bind (hybridize) in preferred combinations to do computation. Depending on reaction conditions, oligonucleotides can bind despite noncomplementary base pairs. These mismatched hybridizations are a source of false positives and negatives, which limit the efficiency and scalability of DNA-based computing. The ability of specific base sequences to support error-tolerant Adleman-style computation is analyzed, and criteria are proposed to increase reliability and efficiency. A method is given to calculate reaction conditions from estimates of DNA melting. [S0031-9007 (97)04987-9] PACS numbers: 89.70. + c, 87.15.By, 89.80. + h Adleman [1] introduced a way to do computations with DNA, and applied the technique to the solution of an NPcomplete problem, the Hamiltonian path problem (HPP) [2]. In general, a DNA-based computation involves three steps. First, the problem instance is encoded in a collection of DNA oligonucleotides. Second, template matching reactions, or hybridizations, between oligonucleotides produce double-stranded molecules, which ligase forms into longer molecules. These long molecules potentially represent the result of the computation. Third, the results are extracted with techniques, such as polymerase chain reaction (PCR) and gel electrophoresis. The basic processing power of a DNA-based computation, as suggested by Adleman [1], is in the massive number of string comparisons that occur during the template matching reactions between DNA oligonucleotides. Thus, a fundamental step in a DNA computation is the hybridization between oligonucleotides. Other proposals for DNA computation [3][4][5] continue to rely on the mechanism of the template-matching hybridization reaction. Most assume that the hybridizations between oligonucleotides occur error free. Nevertheless, errors, i.e., double strands which are not fully Watson-Crick complementary, are a consequence of the cooperative and uncertain nature of the chemistry on which the technique is based, and cannot be eliminated entirely.To make DNA-based computing a reliable technique, the first step is to ensure that false positives and negatives occur with negligible probabilities. If many incorrect or mismatched hybridizations are possible, then false positives (i.e., DNA strands which appear to be valid solutions, but actually are not) can occur. Likewise, if DNA oligonucleotides are used up in unproductive mismatches, there will be fewer available for formation of the result, and a false negative, or the failure to detect a correct answer when one is present, is possible. The probability of a less than perfect hybridization depends on the reaction conditions of the hybridization, with temperature being the most significant [6,7]. In this paper, the Hamming distance between oligonucleotides is explored as a criterion for reliable DNA solution of HPP. As a first estimate for a reliable encoding, the required distance can be estimated from the melting temperature, which is the temperature at which ...
