Abstract
Objectives
The aim of the project was to numerically study DNA molecule conformations when confined in nanochannels with triangular cross section. Recently this geometry was used to confine biopolymers, (e.g. long DNA strands). At our knowledge, no predictions on the elongation of molecules inside nanostructures with such a geometry are present in the scientific literature. An algorithm based on Monte Carlo techniques was devoloped to perform numerical analysis. Off-Lattice methods were used and DNA molecules were described by a coarse grained model. Polymers were modelled as real chains and their rigidity was taken into account by means of a bending potential. The first goal of the project was to check the algorithm by simulating a real semiflexible chain free in solution and then to fit simulation parameters compairing the resulting radius of gyration with that measured experimentally by Tang et al. [1] for a DNA molecule in bulk solution. Then, the second objective was to simulate DNA molecule static behavour in triangular nanochannels and in particular to readapt the scaling behavior of square channels to the case of triangular ones.

[1] J. Tang, S. L. Levy, D. W. Trahan, J. J. Jones, H. G. Craighead, P. S. Doyle, Macromolecules, 43, 7368–7377 (2010).

Achievements
Numerical calculations of a real semiflexible chain in bulk solution were performed in order to obtain simulation parameters. By comparing the resulting radius of gyration with the one measured by Tang et al.[1] for DNA molecules in buffer solution, it was possible to fit the bending parameter, a value related to the rigidity of the chain.

Then, numerical simulations for DNA chains confined by triangular nanochannel were performed.

At first, the elongation of biopolymers in a channel with equilateral triangular cross section was studied as a function of the dimension of the channel and the polymer length. Under high confinement, e. g. for channel width a smaller than the polymer persistence length P, aP the behavior of the chain strongly depends on its length. Under moderate confinement, chains smaller than 300 nm tend asymptotically to their bulk conformation, whilst longer chain elongation follows the same trend observed by [2] and [3]. These results were compared with simulations of polymers in rectangular nanochannels (same base and height), and it was observed that chain elongation depends strongly on the area of the cross section and weakly on its geometry. Thus, it is possible to get information on polymer statics in an equilateral triangular nanochannel by considering the effect of a rectangular one with the same cross section area.

This behavior was not observed for channels with high aspect ratio a/h where h is the channel height. Numerical simulations revealed that triangular channels are more confining than rectangular ones having the same aspect ratio and cross section area. This fact can be explained by polymer depletion near the triangle corners formed by sides and base. This phenomenon observed only for triangular channels clearly depends on their aspect ratio a/h.

Obtained numerical results will be compared with experimentally observed DNA elongation in triangular nanochannels, structures that we fabricate in our labs.

[1] J. Tang, S. L. Levy, D. W. Trahan, J. J. Jones, H. G. Craighead, P. S. Doyle, Macromolecules, 43, 7368–7377, (2010);

[2] P. Cifra, Z. Benkova, T. Bleha, J. Phys. Chem. B, 113 (7), 1843-1851, (2009);

[3] Y. Wang, D. R. Tree, K. D. Dorfman, Macromolecules, 44 (16),6594–6604, (2011).