Physical Nature of Bacterial Cytoplasm

We track the motion of individual fluorescently labeled mRNA molecules inside live E. coli cells. We find that the motion is subdiffusive, with an exponent that is robust to physiological changes, including the disruption of cytoskeletal elements. By modifying the parameters of the RNA molecule and the bacterial cell, we are able to examine the possible mechanisms that can lead to this unique type of motion, especially the effect of macromolecular crowding. We also examine the implications of anomalous diffusion on the kinetics of bacterial gene regulation, in particular, how transcription factors find their DNA targets.

Figure 1

Motion of a tagged RNA molecule inside an E. coli cell [see also movie in 13 ]. Cells were grown and treated as described previously [10, 11, 12]. Cells were imaged with a Nikon Eclipse inverted epifluorescence microscope, under a 60X objective. Time-lapse movies were taken with a Cascade:512B (Roper Scientific) high sensitivity camera for 30 minutes at $1\mathrm{\text{frame}}/\mathrm{\text{second}}$, 200 msec exposure time. Each camera pixel covers a square of size $\sim 67\times 67{\mathrm{nm}}^2$, thus oversampling the optical resolution limit (Airy radius $\sim 200\mathrm{nm}$). (a) A series of epifluorescent images of the cell. Images are 100 sec apart ($\mathrm{\text{scale bar}}=1\mu \mathrm{m}$.) (b) A plot of the $x$ and $y$ coordinates (axis chosen arbitrarily) of particle position during the time covered in panel A. (c) A two-dimensional plot of the particle trajectory (same data as in panels A and B).

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 $\mathbf{r}(t)=\mathbf{(}x(t),y(t)\mathbf{)}$ for each RNA molecule, where $t=\{0,\Delta T,2\Delta T,3\Delta T\dots \}$ is discretized by the camera framing interval $\Delta T$. This vector was used to calculate the mean square displacement as a function of time interval: $⟨{\delta }^2(\tau )⟩$, where $\delta =|\mathbf{r}(t+\tau )-\mathbf{r}(t)|$ and averaging is performed over all pairs of time points $(t_1,t_2)$ obeying $|t_1-t_2|=\tau$, thus $\tau$ is also discretized by $\Delta T$. (a) The mean squared displacement $⟨{\delta }^2⟩$ of the molecule is plotted as a function of the time-interval between measurements $\tau$. Different markers and colors denote different trajectories (total of 23 trajectories from 3 different experiments). $\mathrm{\text{Solid lines}}=\mathrm{\text{slope}}0.7$. 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 $⟨{\delta }^2(\tau )⟩$ for an RNA particle diffusing in 70% glycerol. In this case the motion is normal diffusion ($\alpha =1.04\pm 0.03$, 4 trajectories), as demonstrated by the dashed line with slope 1. (b) Power spectrum $P(f)$ of RNA trajectories. The complete set of $x(t)$ and $y(t)$ trajectories were concatenated, and the power spectral density of the combined trajectory was calculated [see 12, 13 ]. $\mathrm{\text{Blue dots}}=\mathrm{\text{measured}}P(f)$; $\mathrm{\text{solid line}}=\mathrm{\text{linear fit}}$ yielding slope $-1.77\pm 0.03$. A calculation using only the $x(t)$ and $y(t)$ coordinates separately gave similar results. As an additional test for the validity of the spectral density calculation, the trajectory steps [$\Delta x(t),\Delta y(t)$] were randomly permutated and then reintegrated [27]. The resulting new trajectory should exhibit a random walk behavior, with $P(f)\sim f^{-2}$ [28]. The calculated spectral density (red dots) is in agreement with this prediction, yielding a slope of $-1.96\pm 0.04$.