One-Parameter Scaling Theory for DNA Extension in a Nanochannel.

Experiments measuring DNA extension in nanochannels are at odds with even the most basic predictions of current scaling arguments for the conformations of confined semiflexible polymers such as DNA. We show that a theory based on a weakly self-avoiding, one-dimensional "telegraph" process collapses experimental data and simulation results onto a single master curve throughout the experimentally relevant region of parameter space and explains the mechanisms at play.

Electrophoretic separation of DNA in gels and nanostructures.

The development of nanostructure devices has opened the door to new DNA separation techniques and fundamental investigations. With advanced nanotechnologies, artificial gels (e.g. nanopillar arrays, nanofilters) can be manufactured with controlled and ordered geometries. This contrast with gels, where the pores are disordered and the range of available pore sizes is limited by the level of cross-linking and the mechanical properties of the gel. In this review, we recall the theories developed for free-solution and gel electrophoresis (extended Ogston model, biased reptation and entropic trapping) and from this perspective, suggestions for future concepts for fast DNA separation using nanostructures will be given.

Distribution of label spacings for genome mapping in nanochannels.

In genome mapping experiments, long DNA molecules are stretched by confining them to very narrow channels, so that the locations of sequence-specific fluorescent labels along the channel axis provide large-scale genomic information. It is difficult, however, to make the channels narrow enough so that the DNA molecule is fully stretched. In practice, its conformations may form hairpins that change the spacings between internal segments of the DNA molecule, and thus the label locations along the channel axis. Here, we describe a theory for the distribution of label spacings that explains the heavy tails observed in distributions of label spacings in genome mapping experiments.

Hairpins in the conformations of a confined polymer.

If a semiflexible polymer confined to a narrow channel bends around by 180°, the polymer is said to exhibit a hairpin. The equilibrium extension statistics of the confined polymer are well understood when hairpins are vanishingly rare or when they are plentiful. Here, we analyze the extension statistics in the intermediate situation via experiments with DNA coated by the protein RecA, which enhances the stiffness of the DNA molecule by approximately one order of magnitude. We find that the extension distribution is highly non-Gaussian, in good agreement with Monte-Carlo simulations of confined discrete wormlike chains. We develop a simple model that qualitatively explains the form of the extension distribution. The model shows that the tail of the distribution at short extensions is determined by conformations with one hairpin.

Exact lattice calculations of dispersion coefficients in the presence of external fields and obstacles.

We present a study of the field-dependent dispersion coefficient of point-like particles in various 2D overdamped systems with obstructions (periodic, percolating, and trapping distributions of obstacles). These calculations profit from the synthesis of a newly proposed Monte Carlo algorithm--the first such algorithm that correctly reproduces the free dispersion coefficient in the presence of finite external fields--and an asymptotically exact calculation technique. The resulting method efficiently produces algebraic and numerical results without the need to actually perform Monte Carlo simulations. When compared to such simulations, our exact method features a negligible computational cost and exponentially small errors. Utilizing the power of this numerical method, we engage in comprehensive parametric analysis of several model systems, revealing very subtle effects that would otherwise be swamped by statistical errors or incur prohibitive computational costs. The unified framework presented here serves as a template for further applications of lattice random-walk models of biased diffusion.