Figure 1

(a) Pictorial description of a single particle diffusing in a harmonic potential applied by the DNA. Two different conformations are shown. (b) $P(x,\Delta t|x_0)$ for $x_0=-650\mathrm{nm}$. Dashed red line: for $\Delta t=0.01\tau$; solid blue line: for $\Delta t=0.1\tau$; and dotted black line: for $\Delta t=10\tau$. Solid green line: the steady-state (Boltzmann) distribution.Reuse & Permissions

Figure 2

Theoretical joint probability distribution $P(x\left(t\right),x(t+\Delta t))$ for two different time intervals: left: $\Delta t=0.01\tau$ and right: $\Delta t=0.5\tau$. The brighter the color, the higher the probability. (a) and (b) Assuming that $x\left(t\right)$ is uniformly distributed. (c) and (d) Taking into account that the initial position $x\left(t\right)$ is distributed according to a Boltzmann distribution. The dashed lines represent the linear fit.Reuse & Permissions

Figure 3

(a) Dashed blue line: the theoretical slope of the joint distribution $P(x\left(t\right),x(t+\Delta t))$ for different sample frequencies and asterisks: the simulation results. Three different frequency domains that correspond to different time-interval regimes are observed. At long time intervals (low frequencies), there is no correlation between the positions $\langle x\left(t\right)x\left(t+\Delta t\right)\rangle \approx 0$, and the steady-state distribution dominates. For short time intervals (high frequencies), the influence of the force field is negligible, and the diffusion dominates. In the intermediate regime, the force field, as well as the diffusion, affect the dynamics. (b) Solid red line: the theoretical Gaussian width as a function of the sampling frequency shown as ${\sigma }^2/\Delta t$ vs ${\left(\Delta t\right)}^{-1}$. Circles: simulation results. At high frequencies, the Gaussian width becomes identical to that of a one-dimensional freely diffusing particle, shown as a solid green line: ${\sigma }^2/\Delta t=2D$.Reuse & Permissions

Figure 4

Experimental results. (a) $x(t+\Delta t)$ vs $x\left(t\right)$ for $\Delta t=3\mathrm{ms}$. (b) For $\Delta t=30\mathrm{ms}$, notice the changes in both slope and width. Dashed line: fit of a linear curve for the slope. (c) Bars: steady-state distribution. Solid red line: fit to a Gaussian. (d) Circles: experimental results for the width of the distribution divided by the time interval as a function of sample frequency. Solid line: fit to the theoretical function.Reuse & Permissions