Theoretical and Experimental DNA Computation (Natural ...

116 5 Physical Implementations
or even thousands. For example, a particular DNA-based algorithm may rely
upon repeated “sifting” of a “soup” containing many strands, some encoding
legal solutions to the given problem, but most encoding illegal ones. At
each stage, we may wish to extract only strands that satisfy certain criteria
(i.e., they contain a certain sequence). Only strands that satisfy the criteria
at one stage go through to the next. At the end of the sifting process, we are
hopefully left only with strands that encode legal solutions, since they satisfy
all criteria. However, assuming 95% efficiency of the extraction process, after
100 extractions the probability of us being left with a soup containing (a) a
strand encoding a legal solution and (b) no strands encoding illegal solutions
is about 0.006. Repetitive extraction will not guarantee 100% efficiency, since
it is impossible to achieve the conditions whereby only correct hybridization
occurs. Furthermore, as the length of the DNA strands being used increases,
so does the probability of incorrect hybridization.
These criticisms have been borne out by recent attempts [86] to repeat
Adleman’s experiment. The researchers performed Adleman’s experiment
twice; once on the original graph as a positive control, and again on a graph
containing no Hamiltonian path as a negative control. The results obtained
were inconclusive. The researchers state that “at this time we have carried
out every step of Adleman’s experiment, but have not gotten an unambiguous
final result.”
Although attempts have been made to reduce errors by (1) simulation of
highly reliable purification using a sequence of imperfect operations [90] and
(2) application of PCR at various stages of the computation [32], it is clear
that reliance on affinity purification must be minimized or, ideally, removed
entirely. In [12], we describe one possible error-resistant model of DNA computation
that removes the need for affinity purification within the main body
of the computation. It is proposed that affinity purification be replaced by a
new enzymatic removal technique.
In [93], Kurtz et al. consider the effect of problem size on the initial concentrations
of reactants and analyze the subsequent probability of a correct
solution being produced. They claim that, without periodic amplification of
the working solution, the concentration of strands drops exponentially with
time to “homeopathic levels.” One proposal to reduce strand loss during computations
is described in [100]. Rather than allowing strands to float free in
solution, the authors describe a surface-based approach, whereby strands are
immobilized by attachment to a surface (glass is used in the experiments
described in [100], although gold and silicon are other possible candidates).
The attachment chemistry is described in detail in [72]. This model is similar
to that described in [12], in that it involves selective destruction of specific
strands, although in this case Exonuclease is used to destroy unmarked rather
than marked strands. Preliminary experimental results suggest that strand
loss is indeed reduced, although the scalability of this approach is questionable
due to the two-dimensional nature of the surface.