Transactions on Engineering Technologies pp 43-53 | Cite as

# Statistics of End-to-End Distance of a Linear Chain Trapped in a Cubic Lattice of Binding Centers

## Abstract

Two and three dimensional nanostructured substrates are widely employed in a variety of biomedically-oriented nanodevices as well as in functional devices created with the use of DNA scaffolding. In this context spatial arrangements of binding centers influence the efficiency of these substrates. Here, we concentrate on 3D substrates and we compute and analyze the distribution of distances (*q*) between binding centers in the case where the centers are localized in nodes of a cubic lattice. We find that for this particular lattice the exact node-to-node probability distribution is a fifth-degree polynomial in *q*. We merge this polynomial-shaped distribution with an end-to-end distance distribution of a linear chain and we find an excellent agreement between it and the corresponding distribution for a self-avoiding walk in 3D.

### Keywords

Distance distribution DNA scaffolding Micropatterned substrates Polymer adhesion Self-avoiding walks Zigzag path statistics### References

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