LNCS 2950 - Aspects of Molecular Computing (Frontmatter Pages)

Digital Information Encoding on DNA 153
guarantee good performance in test tube protocols. Other than greedy “generate
and filter” methods common in evolutionary algorithms [8], the only systematic
procedure to obtain code sets for DNA computing by analytic methods is the
template method developed in [2]. An application of the method requires the use
of a binary word, so-called template, in combination with error-correcting codes
from information theory [26], and produces codewords set designs with DNA
molecules of size up to 32−mers (more below.)
This paper explores novel methods for encoding information in DNA strands.
The obvious approach is to encode strings into DNA strands. They can be stored
or used so that DNA molecules can self-assemble fault-tolerantly for biomolecular
computation [9,11,19,18]. In Section 2, a binary analog of DNA is introduced as
a framework for discussing encoding problems. Section 3.2 describes a new technique,
analogous to the tensor product techniques used in quantum computing
for error-correcting codes [29], to produce appropriate methods to encode information
in DNA-like strands and define precisely what “appropriate” means. It is
also shown how these error-preventing codes for binary DNA (BNA, for short)
can be easily translated into codeword sets of comparable quality for DNAbased
computations. Furthemore, two independent evaluations are discussed of
the quality of these codes in ways directly related to their performance in test
tube reactions for computational purposes with DNA. We also compare them to
code sets obtained using the template method.
Direct encoding into DNA strands is not a very efficient method for storage
or processing of massive amounts (over terabytes) of abiotic data because
of the enormous implicit cost of DNA synthesis to produce the encoding sequences.
A more indirect and more efficient approach is described in Section 4.
Assuming the existence of a large basis of noncrosshybridizing DNA molecules,
as obtained above, theoretical and experimental results are presented that allow
a preliminary assesment of the reliability and potential capacity of this method.
These new methods can be regarded as a different implementation of Tom Head’s
idea of aqueous computing for writing on DNA molecules [22,21], although only
hybridization is involved. Section 5 summarizes the results and presents some
preliminary conclusions about the technical feasibility of these methods.
2 Binary Models of DNA
DNA molecules can only process information by intermolecular reactions, usually
hybridization in DNA-based computing. Due to the inherent uncertainty
in biochemical processes, small variations in strand composition will not cause
major changes in hybridization events, with consequent limitations on using
similar molecules to encode different inputs. Input strands must be ”far apart”
from each other in hybridization affinity in order to ensure that only desirable
hybridizations occur. The major difficulty is that the hybridization affinity between
DNA strands is hard to quantify. Ideally, the Gibbs energy released in the
process is the most appropriate criterion, but its exact calculation is difficult,
even for pairwise interactions among small oligos (up to 60−mers), and using