Waves of DNA: Propagating excitations in extended nanoconfined polymers

We use a nanofluidic system to investigate the emergence of thermally driven collective phenomena along a single polymer chain. In our approach, a single DNA molecule is confined in a nanofluidic slit etched with arrays of embedded nanocavities; the cavity lattice is designed so that a single chain occupies multiple cavities. Fluorescent video-microscopy data shows fluctuations in intensity between cavities, including waves of excess fluorescence that propagate across the cavity-straddling molecule, corresponding to propagating fluctuations of contour overdensity in the cavities. The transfer of DNA between neighboring pits is quantified by examining the correlation in intensity fluctuations between neighboring cavities. Correlations grow from an anticorrelated minimum to a correlated maximum before decaying, corresponding to a transfer of contour between neighboring cavities at a fixed transfer time scale. The observed dynamics can be modeled using Langevin dynamics simulations and a minimal lattice model of coupled diffusion. This study shows how confinement-based sculpting of the polymer equilibrium configuration, by renormalizing the physical system into a series of discrete cavity states, can lead to new types of dynamic collective phenomena.

Figure 1

Schematic of the experimental system. (a) Diagram of the laboratory-on-a-chip device with the microfluidic reservoirs connected by nanofluidic slits. The slits are embedded with nanocavity lattices that act as entropic traps for the DNA. (b) Oblique view of the nanoslit and nanocavity lattice. (c) Side view of two cavities for definition of the geometric parameters of the system (typical values are $h=100\text{nm},d=200\text{nm},a=500\text{nm}$, and $\ell =1000\text{nm}$) (d) Electron micrograph of two adjacent nanocavity arrays with 400 and 300 nm cavity widths. Scale bar is $1 \mu \mathrm{m}$. (e) Cartoon of a contour overdensity propagating along a molecule spanning seven pits, demonstrating the case of a coherent direction of propagation. (f) Fluorescence micrograph and time-space kymograph of a contour overdensity propagating through the molecule, manifesting itself as a brighter-than-average cavity. Horizontal scale bar is $2 \mu \mathrm{m}$, vertical scale bar is 5 s. (g) Fluorescence micrograph and time-space kymograph of a contour underdensity propagating through the molecule, manifesting itself as a dimmer-than-average cavity. Horizontal scale bar is $2 \mu \mathrm{m}$, vertical scale bar is 5 s.

Figure 2

Raw forward-time correlation functions between the cavity at one end of a seven-cavity spanning molecule and the second, third, fourth, and fifth cavities. The correlation with the closer cavities rises from negative to positive before decaying to an uncorrelated floor, while more distant correlations are weaker and decay more slowly to the uncorrelated level. Data is shown for an experiment (a) and a Langevin dynamics simulation (b).

Figure 3

(a) The autocorrelation functions of the nine in-pit intensities of a single molecule. The end-pit autocorrelation functions decay more slowly. (b) The autocorrelation times of the individual cavities (red circles) as a function of their position in the array, normalized to the average of the interior correlation times of each molecule. The average of each position is shown (black squares). The average of the end-position autocorrelation times is twice that of the interior times, which are independent of position. Results for circular DNA (cyan hexagons) do not show the end effect.

Figure 4

(a) The averaged autocorrelation and neighbor correlation functions for circular DNA molecules in four-cavity rings. An exponential fit to the neighbor correlation data is shown, and used to predict the autocorrelation function. Results from Langevin dynamics simulations are also presented. (b) Comparison of the four-pit neighbor correlation functions for linear $\left(\lambda \right)$ and circular charomid DNA. There is no positive correlation peak seen in the circular data. Overlaid are the predictions of the lattice model

Figure 5

The averaged nearest-neighbor $\mathrm{\Delta }$-correlation functions of seven-cavity molecules, grouped according to their position relative to the end of the molecule. To form the $\mathrm{\Delta }$-correlation functions we subtract off the zero-time variance, so that the correlation at zero lag is normalized to zero. The time axis is normalized by the mean autocorrelation time of the interior pits. Overlaid are the output of the Langevin dynamics simulations (for 1-2 and 3-4) and the predictions of the lattice diffusion model (normalized in the same way).