DNA Nano Devices as a Biased Random Walk Process: A Case Study of Isothermal Ratchet?

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.