Partial hydrodynamic screening of confined linear and circular double-stranded DNA dynamics

We performed experiments and simulations to investigate the influence of hydrodynamic interaction on the diffusion dynamics of circular and linear λ-DNA confined in nanoslits. Contrary to the common assumption that intrachain hydrodynamic interaction (HI) is completely screened when polymers are confined in channels with height $h$ smaller than the radius of gyration $R_{\mathrm{g}}$, it is found that the HI is partially screened and approaches complete screening only for $R_{\mathrm{g}}\ll h$. For λ-DNA, the HI becomes nearly completely screened only when the channel height is smaller than the Kuhn length. In addition, the dynamics of linear and circular λ-DNA in very strong confinement is shown to be independent of the chain topology.

Figure 1

The surface morphology of the $h$ = 20 nm nanofluidic chip. (a) The cross-sectional SEM image of the nanoslit. (b) The cross-sectional view giving the surface profile $h$($x$) of the unsealed nanoslit.

Figure 2

Fluorescent images of linear and circular λ-DNA confined in nanoslits with $h$ = 20–465 nm.

Figure 3

(a) Experimental results of $D$ vs $h$. The solid (dashed) line is the best fit to linear (square) and circular (circles) λ-DNA for $h$ = 110–765 nm. The dotted line is the fit using $D$ = β ln($h$/$w$). The inset shows $D_{\mathrm{C}}/$$D_{\mathrm{L}}$ vs $h$. (b) BD-LB results of $D/D_{\mathrm{mon}}$ vs α$h_{\mathrm{eff}}/$Δ$x$ for $N$ = 152, circular (circles) and linear (square) chains with σ = 0.5 (open symbols) and 1.0 (filled symbols) Δ$x$. $D_{\mathrm{mon}}$ is the single bead diffusivity. The lines are power-law scaling with exponents of 0.5 (dashed) and 0.7 (solid). α = 2 (σ = 0.5) and 1 (σ = 1.0) accounts for coarse-graining effects such that [$R_{\mathrm{g}}$(σ = 0.5)/(α$h_{\mathrm{eff}}$)] = [$R_{\mathrm{g}}$(σ = 1.0)/(α$h_{\mathrm{eff}}$)]. In the inset, $D_{\mathrm{C}}/$$D_{\mathrm{L}}$ vs $h_{\mathrm{eff}}/$Δ$x$ for $N$ = 100 (triangles), 200 (circles), and 300 (squares) are shown.

Figure 4

(a) BD-LB results of $D/D_{\mathrm{mon}}$ vs $N$ for linear chains with σ = 0.5Δ$x$ (open squares) in slits with confinement $h_{\mathrm{eff}}$ = bulk, 8.2, 5.2, 3.2, and 2.2Δ$x$ (from top to bottom), and with σ = 1.0 Δ$x$ (solid squares) for $h_{\mathrm{eff}}$ = bulk and 2.9Δ$x$ (top and bottom). The thin dashed (solid) line is the HI (screened HI) prediction. The thick dashed lines show where $h$ = $R_{\mathrm{g},\mathrm{L}}$. The inset shows ν${}_{\mathrm{N}}$ vs α$h_{\mathrm{eff}}/$Δ$x$ for α = 2 (σ = 0.5) and 1 (σ = 1.0) such that [$R_{\mathrm{g}}$(σ = 0.5)/(α$h_{\mathrm{eff}}$)] = [$R_{\mathrm{g}}$(σ = 1.0)/(α$h_{\mathrm{eff}}$)]. (b) Normalized chain diffusivity $D/D_{\mathrm{bulk}}$ vs $R_{\mathrm{g}}/$$h_{\mathrm{eff}}$ for linear (squares) and circular (circles) chains of simulation (open symbols) and experimental (filled symbols) data. Previous simulation results [46] are shown as open triangles. Experimental results from Ref. [11] rescaled to the relevant axes are shown as crosses.

Figure 5

Linear and circular λ-DNA relative extension vs $h$. The solid (dashed) line fit linear (circular) λ-DNA with (3).