Biomedical Engineering Reference
In-Depth Information
Fig. 7.1 Network of
synthetic peptides forming
agraph
T 5
T 3
T 7
T 1
T 4
paths which were too short, too long, or had wrong departure and arrival cities. The
remaining DNA molecules form the solution. The parallelism was ensured by the
large number of ssDNA strands in the reaction (3 10 13 copies of each).
An illustrative example of the statistical nature of biomolecular logic is the
Boolean functions implementation by segments of small network of synthetic
peptides that form a graph with 5 nodes and 15 directed edges ( Ashkenasy and
Ghadiri 2004 ). This graph is represented in Fig. 7.1 . The system operates in neutral
aqueous solutions and consists of synthetic peptides denoted by T i in Fig. 7.1 that
form a network and that differ from one another through amino acids. A peptide T i
can transform into another peptide T j in the presence of template-directed cross-
catalytic reactions consisting of condensation of nucleophilic N and electrophilic
E j fragments or can undergo autocatalytic reactions if T j D T i .
The transformation directions are represented by arrows in Fig. 7.1 ,theauto-
catalytic reactions by circles, and the reaction rates for transforming peptide T i
into peptide T j ; R ij , satisfy the following relation: R 77 D R 33 < R 47 < R 37 D
R 73 < R 31 D R 41 < R 35 D R 57 < R 14 < R 74 < R 51 < R 53 D R 75 < R 55 . Under these
circumstances, the subnetwork T 3 $ T 7 $ T 4 can implement an OR logic gate
with T 3 and T 4 as inputs and T 7 as output. More precisely, when T 3 and T 4 are
absent, the autocatalytic production rate of T 7 in the presence of N and E 7 is
low, while in the presence of either of the two inputs in the reaction mixture the
production rate of T 7 increases. A NOT gate can be implemented as the autocatalytic
reaction of T 3 in a mixture containing N and E 3 .WhenE 5 is added, the production of
T 5 is encouraged by the more efficient T 3 ! T 5 reaction, and thus the autocatalytic
reaction of T 3 is negatively affected. The NOR gate involves the circular subnetwork
T 3 $ T 5 $ T 7 , with T 3 as output. Its autocatalytic production rate in the presence
of N and E 3 is diminished if E 5 and/or E 7 is added since the transformation T 3 ! T 5
and/or T 3 ! T 7 are more efficient. Similarly, the NOTIF gate can be implemented
by the transformation T 3 ! T 1 , with T 3 as output. The strong autocatalytic reaction
of T 3 is inhibited by the presence of E 1 , which induces the T 3 ! T 1 reaction.
T 1 cannot back-catalyze to form T 3 and is not an autocatalyst.
An interesting approach to Boolean biomolecular computing was reported in
Frezza et al. ( 2007 ). It involves solid-supported DNA gates emerged in solution and
input and output ssDNA molecules. The solid-supported gates provide enhanced
modularity since the task of choosing suitable input and output DNA strands for
cascaded operation is much simplified. The device in Frezza et al. ( 2007 ) is based on
the strand displacement process in which a full-length input complementary strand
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