= Solution
A conceptual single-molecule measurement follows a labelled bound molecule along an independently mapped <DNA> contour. Project fitted positions onto contour distance and estimate the <Mean squared displacement>[mean-squared displacement] at several lag times. For unbiased <Diffusion>[one-dimensional diffusion],
$$
\langle[s(t+\Delta t)-s(t)]^2\rangle=2D_1\Delta t.
$$
Independent localization errors of <variance> $\sigma_{\rm loc}^2$ add an intercept $2\sigma_{\rm loc}^2$. Finite exposure adds motion blur, and <Drift velocity>[drift], binding transitions and the finite <DNA> contour must be distinguished from free <Facilitated target search>[sliding]. A slope fit with those limitations can estimate $D_1$; simply fitting all observed <Displacement>[displacements] to a noiseless line can bias it.
\b[Retain the printed coefficient.] The original PDF really prints $D_1=5\times10^{10}\,\mathrm{m^2\,s^{-1}}$, not a negative exponent. In <sliding diffusivity with per-step dissociation>, for a basepair step $a\simeq0.34\,\mathrm{nm}$, an <Random walk>[unbiased nearest-neighbour walk] has step interval $a^2/(2D_1)$. If the <Dissociation rate constant>[dissociation] <probability> per step is $P$, the mean number of steps is approximately $1/P$, giving
$$
\boxed{\tau_{\rm bound}\simeq\frac{a^2}{2D_1P},\qquad
\ell_{\rm rms}\simeq\frac a{\sqrt P}.}
$$
For the printed values, $\tau_{\rm bound}\simeq1.16\times10^{-24}\,\mathrm s$ and $\ell_{\rm rms}\simeq0.34\,\mathrm{\mu m}$. The latter is a random-walk <displacement>, not the contour distance travelled in a million steps. The step interval is about $1.16\times10^{-30}\,\mathrm s$, even shorter than the light-travel time across a basepair by many orders of magnitude. This is an unphysical extrapolation for a <protein>, not a meaningful experimentally measurable <Diffusion coefficient>[diffusivity].
Consequently no <fluorescence> camera could temporally resolve trajectories under the stated formal values, regardless of the spatial excursion's length. An actual corrected exponent cannot be inferred uniquely from the paper. If a physically plausible $D_1$ were supplied instead, resolving <Facilitated target search>[sliding] would require exposures substantially shorter than $\tau_{\rm bound}$ and <diffusion> <Displacement>[displacements] larger than <Measurement error>[localization error], with enough detected <Photon>[photons]. The dependence on $D_1$ is explicit above, so no guessed source correction is needed.
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