Reliability and Efficiency of a DNA-Based Computation

Abstract

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 ...

Efficiency and Reliability of DNA-Based Memories

“…Later work on error-prevention has confirmed that the reduction will be orders of magnitude smaller [6]. Based on combinatorial constraints, [14] combinatorially obtained some theoretical lower bounds and upper bounds of the number of equilength DNA strands.…”

Development of DNA Based Active Macro–Materials for Biology and Medicine: A Review

“…As we have discussed in the properties of DNA, the primary structure, i.e., the sequence or the order of nucleotides, of DNA primarily determines its secondary and tertiary structures, thus it is of significance to design sequence which gives the desired bulk material properties. Meanwhile, although two complementary DNA strands achieve their minimum energy state when they hybridize in the perfectly aligned configuration, DNA hybridization does not occur without error (Deaton et al 1998). In addition, undesired interactions can occur between two strands as well as within a single strand.…”

“…Design of a pair of equal-length sequences is essentially an optimization problem with the minimization of undesirable (e.g., off-alignment) interactions as the objective function. For instance, in the work by Lin et al (Lin et al 2004b), DNA sequence was generated by incorporating into the algorithm the following considerations: minimization of undesired interactions among strands and potential secondary structures, thermodynamic stability of the hybridized sequence pairs (e.g., GC content, terminal sequences, and hairpin structures (Lin et al 2004b, SantaLucia & Hicks 2004), and initiation of branch migration (e.g., length of sticky ends) (Deaton et al 1998, Felsenfeld & Miles 2003. C-rich domain can be incorporated where it is desirable to have pH responsiveness (Cheng et al 2009).…”

“…This is also of interest to the community of synthetic chemistry . The scope of the current and potential applications of DNA based materials ranges from DNA based electronics (Berashevich & Chakraborty 2008) and computing (Deaton et al 1998) to novel material design (Dong Liu et al 2007, Um et al 2006a). The similar interest in using other three major types of macromolecules, namely, protein, lipids, carbonhydrates, as structural component for synthetic materials is also increasing (Ball 2005).…”

Biomolecular computing: Is it ready to take off?

“…Several error detection and fault tolerance methods have been established to increase the accuracy of computation [14][15][16][17][18]. Among them, Deaton et al [19] studied the errors associated with imperfect hybridization (i.e., false positive and false negative ligations). The authors pointed out that these errors depended largely on the reaction conditions of the hybridization, in particular on temperature.…”