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Fig. 14.1: Size of the PCR selection product obtained from the filtered input sets
(
left bars
) based on the polymerase chain reaction. The size of the resulting set
(
middle bars
) can be estimated by the subpower law (1.9n
0.6)
4
(
light bars on the
+
right
) [16].
14.4 Neural Nets in Biomolecules
In this section we use the results described in the previous sections to show how to
implement large sets of neuronal ensembles in DNA molecules. Although we will
use artificial neural nets as the prototype of such ensembles, we note that similar
techniques can be used to implement higher order structures of the type exemplified
by more complex ensembles known as brains (more in the discussion in the next
section). For a review of neural networks, the reader is referred to [19]. Hopfield
networks [21] will be used as a prototype to describe the design, but the techniques
readily extend to other types of neural nets and associative memories [19, 18]. We
will also omit technical details of the biotechnical implementation in a wet lab and
concentrate only on the simulation in silico.
Turberfield et al. [35] describe the first attempt to implement a specific type
of neural network in DNA, specifically, recurrent Hopfield nets. Their approach
showed the experimental possibility of using DNA as an almost direct replacement
of neurons with the hybridization affinity as the critical component to capture synap-
tic connections for associative retrieval. The model required the use of restriction
enzymes and high-quality nxh DNA codewords (unavailable at the time). The ex-
perimental implementation proved to have low reliability and speed in activation
updates of the neuronal units due to the use of restriction enzymes in many cycles of
PCR amplification [27] and the uncertainty of hybridization reactions, which we can
a posteriori recognize as due to cross-hybridization. Moreover, their work remained
untested for scalability since implementing large networks required the use of large
sets of nxh codewords, which were not readily available at the time. However, this
attempt provides a very good description and test of the experimental requirements
for their implementation, and much of it can be used in an appropriately updated
form in this implementation.
