Parameters characterizing confined diffusion are severely affected by time-averaging over the frame time. (

*A*) The

*MSD*-

*t* plots for particles trapped within a 120-nm length square compartment at frame times of 25

*μ*s (

*left*) and 33 ms (

*right*).

*MSD*s calculated from the trajectories shown in (single-molecule

*MSD*s), plotted as a function of the time interval.

*MSD* grows rapidly and then levels off. The theoretical plateau value is

which is 4800 nm

^{2} (because both

*L*_{x} and

*L*_{y} are 120 nm). At a frame time of 25

*μ*s (

*left figure*), this is very close to the observed value. However, at a frame time of 33 ms, the limiting plateau value is severely suppressed (

*right figure*; note the greatly reduced value in the

*y* axis, despite the expanded

*x* axis from the left figure by 1000-fold), corresponding to the centralized distribution of the observed points at this frame time. (

*B*) Apparent microscopic diffusion coefficient

*D*_{2–4}, plotted against frame time. The solid line is not a fitting, but the predicted apparent diffusion coefficient from (see the text). The set diffusion coefficient in the simulation was 9

*μ*m

^{2}/s. (

*C*) The compartment size determined by fitting the

*MSD*-

*t* curve (like those shown in

*A*) using displayed as a function of the frame time (at least 100 simulations at each frame time). Note that both the apparent diffusion coefficient and compartment size are severely underestimated at longer frame rates, as expected from the trajectories in and the

*MSD*-

*t* curves in

*A*. In

*B* and

*C*, error bars are mostly hidden by the data markers.

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