Theoretical and Experimental DNA Computation (Natural ...

114 5 Physical Implementations
Stage 2: PCR was first used to massively amplify the population of oligonucleotides
encoding paths starting at v1 and ending at v7. Next, strands that
do not encode paths containing exactly n visits were removed. The product of
the PCR amplification was run on an agarose gel to isolate strands of length
140 b.p. A series of affinity purification steps was then used to isolate strands
encoding paths that visited each vertex exactly once.
Stage 3: Graduated PCR was used to identify the unique HP that this
problem instance provides. For an n-vertex graph, we run n−1 PCR reactions,
with the strand representing v1 as the left primer and the complement of the
strand representing vi as the right primer in the i th lane. The presence of
molecules encoding the unique HP depicted in Fig. 5.2 should produce bands
of length 40, 60, 80, 100, 120, and 140 b.p. in lanes 1 through 6, respectively.
This is exactly what Adleman observed. The graduated PCR approach is
depicted in Fig. 5.6.
α β λ δ
α β λ δ
α β λ δ α β λ δ α β λ δ
Long
Short
Run strands through gel
to sort them on length
Fig. 5.6. Graduated PCR
Add primers
PCR produces
many copies
of strands
Adleman’s experiment was remarkable in that it was the first to demonstrate
in the laboratory the feasibility of DNA computing. However, we note that
it was performed on a single problem instance with just one HP. No control
experiments were performed for cases without Hamiltonian Paths. The final
detection step is problematic, due to reliance on the error prone PCR procedure.
In addition, the use of affinity purification is also error prone, which may