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Chandran, H., Gopalkrishnan, N., Phillips, A. and Reif, J. (2011) Localized Hybridization Circuits. In: Cardelli, L. and Shih, W., Eds., Proceedings of the 17th International Conference on DNA Computing and Molecular Programming, Pasadena, 19-23 September 2011, 64-83.
has been cited by the following article:
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TITLE:
DNA Nano Devices as a Biased Random Walk Process: A Case Study of Isothermal Ratchet?
AUTHORS:
Jean-Pierre Aimé, Juan Elezgaray
KEYWORDS:
DNA Nanotechnology, Isothermal Ratchet, Confined Chemical Reactions, DNA Logical Gate, DNA Origami, Modular Algorithm
JOURNAL NAME:
Materials Sciences and Applications,
Vol.6 No.5,
May
15,
2015
ABSTRACT: Computation and amplification processes based on Networks of Chemical Reactions are at the
heart of our understanding of the regulation and error correction of life systems. The recent advances
in DNA nanotechnology, with the creation of the modular structures origamis and the development
of dynamical networks using the toe hold mediated strand displacement, open fertile
areas to construct Hierarchical Cascades of Chemical Reactions with an increasing complexity inspired
from systems in biology. DNA strands have the great advantage to design autonomous and
homogeneous Networks of Chemical Reactions leaving aside companion chemical reactions as it
occurs in biological systems. In the present paper, we use the Fokker Planck equation to extract
predictions that address a wider class of systems beyond the case of diluted solutions. We introduce
the concept of toehold strength and output strength that leads to an exponential square dependence
of the toehold strength divided by the output strength on the escape rate and the probability
for the output strand to leave the gate. We highlight the influence of the boundary conditions
that may have an important consequence in confined environment when modular structures like
origamis are employed.