Reaction Temperature Constraints in DNA Computing

Using the thermodynamics of DNA melting, a technique is proposed to choose a reaction temperature for the DNA computation that minimizes the potential for mishybridizations. Adleman[Adleman, 1994] showed the computational potential of the hybridization reaction and other molecular biology protocols. A basic framework for a computation based on oligonucleotide template matching reactions, or hybridizations, consists of three steps: 1) encoding of the problem instance in DNA oligonucleotides such that solution is enabled with molecular biology protocols, 2) the basic processing of the pool of oligonucleotides with hybridization and ligation reactions, and 3) extraction of the result with separation techniques, such as polymerase chain reaction (PCR) or hybridization to probe sequences attached to magnetic beads. Ideally, oligonucleotide hybridizations occur only between Watson-Crick complements. Depending upon the conditions under which the hybridization is done, however, base pairs that are not WatsonCrick complements, or mismatched base pair, can occur[Sambrook et al., 1989]. In addition, olgionucleotides can hybridize in various alignments that are shifted from the designed one. These mishybridizations can produce false positives, or solutions to the DNA computation that appear to be correct, but actually are not, and false negatives, or the failure to produce a solution to a problem with DNA computation when one actually exists. The e ect of the reaction conditions is characterized as the hybridization stringency. In general, as the reaction temperature of the hybridization is increased up to a critical point, the stringency increases. The temperature at which half the population of perfectly matched oligonucleotide hybrids will have dissociated into single strands is called the melting temperature, Tm. The melting temperature is determined from curves of UV absorbance versus temperature, and can be interpreted as the fraction of single strands versus temperature[Wetmur, 1997]. Under conditions of low stringency, oligonucleotides can hybridize with more mismatched base pairs and over shorter lengths than under conditions of high stringency. Therefore, under assumptions of perfect Watson-Crick hybridization or perfect Watson-Crick complementation between oligonucleotides, an e ect of the hybridization stringency is to introduce a possibility of false positives and negatives through mismatched hybridizations and shifted hybridizations. These mishybridizations can occur either in the basic processing step (step 2 above) or in the extraction process (step 3 above). In this paper, a method based on the thermodynamics of DNA melting is used to estimate the reaction temperature for a given oligonucleotide encoding of a problem. The nearest-neighbor base stacking model[Borer et al., 1974] for the melting temperature of short oligonucleotides is used. The estimated reaction temperature should minimize the potential for mishybridizations. An upper limit on the reaction temperature is estimated from the melting temperature and half-width of the melting curve of the oligonucleotide with the lowest melting temperature. A lower limit is set by requiring that the oligonucleotide with the highest melting temperature have minimum potential for mishybridizing with its nearest neighbor, as measured by the Hamming distance. Based on a model of nearest neighbor stacking interactions, a formula for non-self complementary oligonucleotide melting temperature is given by[Borer et al., 1974],