Figure 2
Subdiffusive motion of RNA molecules in the cell. Movies were read into Matlab software (Mathworks). The fluorescent particles were automatically recognized and followed, to yield a time series of particle coordinates
for each RNA molecule, where
is discretized by the camera framing interval
. This vector was used to calculate the mean square displacement as a function of time interval:
, where
and averaging is performed over all pairs of time points
obeying
, thus
is also discretized by
. (a) The mean squared displacement
of the molecule is plotted as a function of the time-interval between measurements
. Different markers and colors denote different trajectories (total of 23 trajectories from 3 different experiments).
. Deviations from the 0.7 slope at longer times are due to the effect of limited cell size, and the averaging over a smaller number of position pairs. Also shown in the figure is a typical plot of
for an RNA particle diffusing in 70% glycerol. In this case the motion is normal diffusion (
, 4 trajectories), as demonstrated by the dashed line with slope 1. (b) Power spectrum
of RNA trajectories. The complete set of
and
trajectories were concatenated, and the power spectral density of the combined trajectory was calculated [see
12,
13 ].
;
yielding slope
. A calculation using only the
and
coordinates separately gave similar results. As an additional test for the validity of the spectral density calculation, the trajectory steps [
] were randomly permutated and then reintegrated [
27]. The resulting new trajectory should exhibit a random walk behavior, with
[
28]. The calculated spectral density (red dots) is in agreement with this prediction, yielding a slope of
.
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