Figure 1

(a) Schematic diagram of experiment. A single DNA molecule is held stretched between two optically trapped microspheres and suspended in a concentrated solution of entangled DNA. (b) Reptation models postulate that collective intermolecular interactions give rise to a tubelike confining field (dashed lines). We measure the confining force per unit length ($F_x$ and $F_y$) in response to an imposed displacement $\Delta x$ or $\Delta y$ (see text). (c) Average force induced by a displacement $\Delta y$ at $13\mu \mathrm{m}/\mathrm{s}$ (gray) vs a displacement $\Delta x$ at $65\mu \mathrm{m}/\mathrm{s}$ (black). Arrows mark the maximum displacements. The inset graph shows the displacement profiles. (d) $F_y$ vs ${\Delta }_y$ at rates of $65\mu \mathrm{m}/\mathrm{s}$ (red), $25\mu \mathrm{m}/\mathrm{s}$ (blue), $13\mu \mathrm{m}/\mathrm{s}$ (green), $0.52\mu \mathrm{m}/\mathrm{s}$ (cyan), and $0.10\mu \mathrm{m}/\mathrm{s}$ (orange). (e) Results for $\Delta y=15.5\mu \mathrm{m}$. (f) Confining potential per unit length $U(y)$ determined by integration of force data in plot (d). The dashed line indicates the theoretically predicted tube radius. (g) $U(y)$ determined by integration of force data in plot (e).Reuse & Permissions

Figure 2

Relative probability for a transverse displacement $y$ from the primitive path determined by $P(y)=e^{-U(y)/kT}$, where $U(y)$ is the confining potential [Fig. 1f]. Colors indicate displacement rates as in Fig. 1. Tube radius defined as the distance where $P(y)=l/e$, indicated by the dashed line. Measured tube radii are: 0.65, 0.82, 0.94, 1.0, and $1.8\mu \mathrm{m}$ for the $65\mu \mathrm{m}/\mathrm{s}$, $25\mu \mathrm{m}/\mathrm{s}$ ($a/{\tau }_e$), $13\mu \mathrm{m}/\mathrm{s}$, $0.52\mu \mathrm{m}/\mathrm{s}$, and $0.10\mu \mathrm{m}/\mathrm{s}$, respectively.Reuse & Permissions

Figure 3

Force relaxation following transverse displacements of 2.6 or $15.5\mu \mathrm{m}$. Colors indicate displacement rates as in Fig. 1. The solid lines are fits to sums of decaying exponentials (see text).Reuse & Permissions