Information Technology Reference
In-Depth Information
contamination as well as input data, as illustrated by Hopfield networks. Further-
more, we have shown how simulation of such phenomena in silico can also exhibit
similar characteristics while affording a digital implementation, when desired. In
summary, a Hopfield net with
n
neuronal units can be implemented as a DNA Hop-
field memory with up to 4
n
2
noncross-hybridizing (nxh) oligonu-
cleotides. The requirements on codewords increase linearly with the number of neu-
rons
n
(not of weights, which increase quadratically). The overall conclusion is that
Hopfield nets can be implemented in DNA in ways that preserve their fault tolerance
by mapping their energy landscapes to Gibbs landscapes using nxh sets [16], while
their implementation is very feasible and becoming easier with currently available
biotechnology.
The resulting neuronal ensembles can also be implemented on high-performance
digital clusters in silico, or in test tubes in vitro, in scales and densities fairly large in
comparison to other implementations. For example, we are in possession of the code
sets necessary to implement networks of order up to 100 K neurons on a standard
DNA chip of small dimensions (the order of a square inch) with current biotechnol-
ogy. The rapid progress in microarray design and manufacturing will make feasible
much larger arrays at relatively small prices. Other network architectures can be
implemented by similar methods. Furthermore, the technique can be easily general-
ized to other recurrent networks and it can be automated easily, even in microscales
using microfluidics [28]. This is a particularly interesting property for potential ap-
plications of the networks.
This type of models presented here can be called coarse grained because they
only capture critical aspects of the target phenomenon while ignoring most others
in order to preserve physical simulations of DNA chemistry. They offer a sharp
contrast to systems developed using more traditional methods that aim at physical
realism in the simulation of natural phenomena [31]. Thus, the advantages of fea-
sible implementation (both in vitro and in silico, as desired) on the one hand, and
the robustness and fault tolerance of neural networks and the optimality inherent in
DNA reactions, on the other, can be guaranteed in the design of these systems, at
least to a close degree of approximation. The universality properties of neural nets
as function approximators ( [19], Chapter 4), as well as their ability to even learn
certain dynamical systems [30], make them a promising tool in the design of robust
and nearly optimal complex systems. Similar efforts are underway to model other
complex systems such as biological cells, see, for example, [33, 34, 23].
+
2
n
=
2
n
(
2
n
+
1
)
Acknowledgments
We are thankful to Igor Beliaev and Mark Myers, students in Computer Sci-
ence at The University of Memphis, for their help in implementing various preliminary parts of this
project. We are also grateful to Sungchul Ji in Pharmacology and Toxicology at Rutgers Univer-
sity for useful conversations related to biological function, as well as to Art Chaovalitswongse in
Systems Engineering for inviting the lead author to participate in the computational neuroscience
conference 2008, from which the theme in this chapter was originally developed.
