Dynamics of the Serine Chemoreceptor in the Escherichia coli Inner Membrane: A High-Speed Single-Molecule Tracking Study

Abstract

We investigated the mobility of the polar localized serine chemoreceptor, Tsr, labeled by the fluorescent protein Venus in the inner membrane of live Escherichia coli cells at observation rates up to 1000 Hz. A fraction (7%) of all Tsr molecules shows free diffusion over the entire cell surface with an average diffusion coefficient of 0.40 ± 0.01 μm² s⁻¹. The remaining molecules were found to be ultimately confined in compartments of size 290 ± 15 nm and showed restricted diffusion at an inner barrier found at 170 ± 10 nm. At the shortest length-scales (<170 nm), all Tsr molecules diffuse equally. Disruption of the cytoskeleton and rounding of the cells resulted in an increase in the mobile fraction of Tsr molecules and a fragmenting of the previously polar cluster of Tsr consistent with a curvature-based mechanism of Tsr cluster maintenance.

Introduction

Large-scale inhomogeneous distributions of proteins are found in many cell systems and specifically in the membranes of many widely differing cell types such as in neurons (1,2), cancer cells (3), and even bacteria such as Escherichia coli (4). It is of great interest to probe the fine structure of such distributions in live cells to understand the interactions possible. Techniques such as superlocalization microscopies allow for snapshots of such assemblies (5–7) including measuring stoichiometries of multicomponent clusters (8,9) but due to technical aspects, the fast dynamics of molecules in such assemblies cannot be accessed. The technique of single-molecule imaging has recently been applied to study gene expression (10,11) and diffusion in the membranes (12–14) and cytoplasm (15–19) of bacteria. In this report, we apply high-speed single-molecule tracking to observe the short time dynamics of individual Tsr molecules labeled with a variant of yellow fluorescent protein (Venus) inside and outside of their well-known polar cluster (4) in live E. coli cells.

The serine chemoreceptor protein, Tsr, is a member of the methyl-accepting chemoreceptor proteins (MCPs) of the E. coli chemotaxis sensing system (20,21). MCPs, including Tsr, can form heterotrimeric membrane complexes that have been shown to mostly cluster at the poles of the cell (4), and this clustering has been proposed to be important for signal amplification (22,23). It has been proposed that Tsr clusters at the highly curved poles of the cell, due to the splay of the Tsr-containing heterotrimeric complexes (24). Signal propagation occurs from the MCPs through controlling a phosphorylation/dephosphorylation cascade involving the Che proteins that, in turn, controls rotation of the flagellar motor.

Here, we find that the majority of Tsr molecules imaged are found in the polar regions of the cell, as expected. A small fraction (7%) is free to diffuse around the entire inner membrane. Surprisingly, when imaged at frame rates of 1000 Hz, all molecules showed similar diffusion coefficients to those free at slower frame rates, implying that all molecules are freely diffusing on short length-scales, whether they are contained within the polar cluster or not. Modification of the cell’s native curvature through disruption of the MreB cytoskeleton revealed a breakup of the polar cluster and an increase in the fraction of Tsr molecules freely diffusing throughout the membrane.

Materials and Methods

E. coli cells

E. coli K-12 BW36931 has the CRIM plasmid (25) pYY37 (attλ kan phoAp-tsr-venus) integrated into a single copy in BW36010 (MG1655 Δ(lacZp4105(UV5)-lacY)638(DElacZ) rph⁺ DE(araBAD)567). A sample of BW36931 was revived from a frozen stock on TYE agar, serially propagated on glucose M63 and glucose MOPS 2.0 mM Pi agar, then inoculated into 0.04% glucose MOPS 2.0 mM Pi broth and grown overnight, essentially as described in Haldimann and Wanner (25). A portion was reinoculated into fresh 0.4% glucose MOPS 2.0 mM Pi broth and incubated at 37°C until the sample chamber was readied (∼40 min).

To decrease the time delay from the protein expression to the detection, we used fast-maturing Venus fluorescence protein as a monitor. Tsr-Venus fusion protein under the control of phoA promoter (phoAp) from a CRIM plasmid was integrated into a single copy on the E. coli chromosome during growth in media with excess phosphate, in which phoAp expression is turned off. Under these conditions, phoAp is transcribed at a low enough rate such that a slow stream of individual Tsr-Venus protein molecules can be imaged at the single-molecule level in time-course image sequences. Therefore, we can decrease the possibility of finding molecule trajectories crossing over each other and also increase the identification accuracy of single molecules (10–45 nm corresponding to video rate of 30–1000 fps; see Fig. S4 in the Supporting Material) in the small-sized E. coli cell.

Sample chamber preparation

Bottom cover glasses (18 mm diameter) of glass bottom fluorodishes were immersed in pure sulphuric acid (H₂SO₄) for 5 min, washed in deionized water, sonicated in methanol, and then rewashed in deionized water for 20 min. Residual liquid was dried with a stream of nitrogen gas. The coverglass was then coated with 100 μL of 1% poly-l-lysine for 10 min. Cells were concentrated by gentle centrifugation (4000 rpm, 1 min), resuspended, and placed into the chamber and then allowed to immobilize for 20 min on the poly-l-lysine layer. Free-floating cells were washed off with 0.4% glucose MOPS 2.0 mM Pi medium and 3 mL of fresh medium was added to the chamber before observation. The final cell concentration was set so that ∼10 cells were visible in the field of view.

In experiments testing cell-curvature effects on Tsr localization, A22 (1.6% S-(3,4-Dichlorobenzyl)isothiourea) was added to the chamber with the media before observation. A22 is known to disassemble the MreB cytoskeleton of E. coli (24,26). After ∼3 h incubation in A22, the bacterial cells become spherical, losing all original polarity and removing the differential curvature originally found at the poles of the cell.

Preparation of chamber for purified Venus experiment

Square cover glasses (18 mm) were cleaned as above and purified Venus was overlaid onto the 50 μL of 1% polyethyleneimine-coated coverglass. A sample chamber was created on the glass cover slide using two strips of vinyl tape. A quantity of 100 μL of 10% polyacrylamide gel was added to the chamber and allowed to set for 20 min. Final concentration of purified Venus was set to give ∼100 single spots in the field of view.

Single-molecule fluorescence video microscopy

Oblique angle fluorescence imaging was used to excite single-molecule fluorescence in the entire cell while still reducing the background signal. The excitation laser (Argon ion, 488 nm emission; Newport Instruments, Newport Beach, CA) was expanded, filtered (488/10-nm line-width bandpass filter; Chroma Technology, Bellows Falls, VT), and directed toward the microscope objective (100×, NA 1.4 oil immersion; Carl Zeiss, Jena, Germany) parallel but off the optical axis through a dichroic mirror (500 nm cutoff, Chroma Technology). The resultant fluorescence image was projected through the dichroic mirror and an emission filter (525/50 nm bandpass; Chroma Technology) and collected on a dual MCP-intensified, cooled charge-coupled device camera (XR/Turbo-120z Turbo; Stanford Photonics, Palo Alto, CA). The excitation beam was set such that it is just outside of the condition for total internal reflection, thus allowing for a deeper excitation while still reducing background due to excess fluorescent matter in solution. The initial fluorescence synthesized overnight was completely photobleached by using 10-fold higher laser power (0.3–3 w/cm²). Either right after photobleaching, or after a 1-min wait, the laser was turned on for data acquisition.

Single-molecule tracking and mean-squared deviation calculation

An area local to the fluorescent spot is cropped from the video. To determine the position of center of the fluorescent spot, a cross-correlation was performed between the image and a Gaussian kernel created to approximate the point-spread function of a single fluorophore (27). The position of the fluorophore was determined from the centroid of the peak of the calculated cross-correlation, above a threshold that was set to remove background noise. This was repeated throughout the video until the spot bleaches to determine the trajectories of the molecule. For each molecule’s trajectory, the mean-square displacement (MSD) over time delay nδt was calculated as

$$\langle r^2\left(n\delta t\right)\rangle >={\left(N-1-n\right)}^{-1}\sum _{j=1}^{N-1-n}\left({\left[x\left(\left(j+n\right)\delta t\right)-x\left(j\delta t\right)\right]}^2+{\left[y\left(\left(j+n\right)\delta t\right)-y\left(j\delta t\right)\right]}^2\right)$$

where δt is the time between frames, (x(jδt), y(jδt)) is the position of the particle in frame j, N is the total number of frames in the trajectory, and n and j are positive integers.

Trajectory classification and diffusion analysis

While one expects a protein undergoing free Brownian motion to have an MSD that grows linearly in time delay, the MSD for a protein walking in a confined area displays a subdiffusive character where the MSD is δt^α and 0 < α < 1. Here we have used the slope of log(MSD/δt) versus log(δt) plot for each molecule’s trajectory, which measures the value of α − 1, to classify each trajectory into either mobile or immobile fractions. It was found that trajectories were either nearly horizontal or highly sloped in this representation. A value of α = 0.5 was chosen to distinguish these two fractions. Fig. S7 shows the log(MSD/δt) versus log(δt) for those trajectories classified as either mobile or confined. Shown in Fig. S7 c is the same plot for simulated free Brownian walkers on a typical cell surface (consisting of a 1-μm-long, 1-μm-radius cylinder capped by a 500-nm-radius hemispheres). The average slope was calculated as −0.14, −0.65, and −0.06, resulting in an average value of α of 0.86, 0.35, and 0.94 for mobile, immobile, and simulated trajectories, respectively.

To confirm these classifications, a further analysis of the mobility proceeded through calculation of the probability density P(r², n) of square displacement r², as function of time-lag n, where n = iδt and δt is the time increment per frame, and i is an integer. P(r², n)dr is then the probability of finding a molecule between a circle of radius r and a circle of radius r+dr at time n (28). Trajectories can be classified as confined if this probability reaches a stationary distribution over time. Fig. S2 displays normalized Gaussian fits of the calculated probability distributions of r² summed over all trajectories in each classification as a function of time (mobile N = 30, confined N = 402, on glass N = 175), showing the progression over time of n = 2–30 frames. The peak of P(r², n) for the mobile fraction (including 30 individual trajectories of Tsr-Venus) shifts to the right with increase in time, implying a circle size in which molecules are to be found increasing with time (see Fig. S2 a).

In comparison, no such shift in the probability is observed in the confined fraction of molecules (see Fig. S2 b), implying confinement is restricting long-range displacements. For completeness, purified Venus molecules immobilized on the cover glass were also tracked and analyzed as above. As expected, they also show a restricted maximum excursion, due to the finite accuracy of the tracking method (see Fig. S2 c). Molecules in the central fraction were further classified by their mobility into either confined or mobile fractions. To determine the position of molecules, each cell was outlined, the cell’s long and short axes were determined, and the molecule’s position was recorded relative to the long and short axis lengths. The coordinates of a molecule could then be transferred to an idealized cell (a 1-μm-long, 500-nm-wide rectangle capped by 500-nm-radius semicircles) by using a simple transformation matrix (see Fig. S1). Molecules were defined as being polar if they resided in a polar cap region (i.e., the semicircular caps on the idealized cell) throughout the trajectory.

It should be noted that we are measuring the projected, two-dimensional diffusion coefficient for molecules moving on the three-dimensional membrane of the E. coli cell. We have performed simple simulations of random walkers on an idealized E. coli shell and found the two-dimensional diffusion coefficient to be, on average, 70% of the three-dimensional diffusion coefficient set in the simulation for diffusion coefficient and trajectory lengths similar to those observed in this study.

Calculation of velocity autocorrelation

The velocity autocorrelation function was calculated for the polar confined and mobile fractions of the Tsr-Venus population (see Fig. S3). The velocity autocorrelation function G(τ) is defined through

$$G\left(\tau =j·\Delta t\right)=\langle {\overrightarrow{v}}_{i+j}·{\overrightarrow{v}}_i\rangle ,$$

where the velocities are found through ${\overrightarrow{v}}_i=\left({\overrightarrow{x}}_{i+1}-{\overrightarrow{x}}_i\right)/\Delta t$ and the $\overrightarrow{x}$ -values are the vector positions of the molecule in a trajectory, the subscripts i and j index frames of duration Δt, and the average 〈…〉 is over all measured positions in all trajectories in a given fraction. No correlations are found for positive values of time, implying that the molecules move through random motion.

Normalization process of coordinates of molecules

The x and y coordinates of the molecules in each video frame are transferred to a normalized cell (a 2-μm-long and 1-μm-width rod shape) by constructing a transformation matrix (see Fig. S1). To begin, the original fluorescence image is Fourier-transformed to remove the background. Thresholding the Fourier-transformed image by setting the threshold gray value of 80 out of 255 from the intensity distribution creates a binary image. This is used for particle analysis of characteristics such as cell area, length of the long and short axes, center of mass, and angle with respect to the horizontal axis, using the IMAGEJ software (open source from the National Institutes of Health, Bethesda, MD). Transformation from the camera coordinates (x, y = center of mass of the cell) to the model cell coordinates (x′, y′) was performed through a transformation matrix,

$$\begin{array}{ccc}\left(\begin{array}{l}{x}^{\prime }\\ y^{\prime }\end{array}\right)=\left[\begin{array}{l}\cos \varphi ,-\sin \varphi \\ -\sin \varphi ,-\cos \varphi \end{array}\right]\left(\begin{array}{l}x\\ y\end{array}\right),& x=r\cos \theta ,& y=-r\sin \theta \end{array},$$

where the polar coordinates r and θ of the molecule, and the angle between the cell’s horizontal axis, and the camera’s x axis and φ, are provided from the particle analysis. With this transformation, the locations of all newly emerged individual Tsr-Venus molecules are redistributed in the model cell to classify the polar and central fraction.

Results and Discussion

We expressed the Tsr-Venus protein under the control of phoA promoter (phoAp) from a CRIM plasmid (25) integrated in single copy on the E. coli chromosome during growth in media with excess phosphate in which phoAp expression is turned off. Under these conditions, phoAp is transcribed at a low-enough rate such that a slow stream of newly synthesized individual Tsr-Venus protein molecules can be imaged at the single-molecule level (see Movie S1, Movie S2, Movie S3, and Movie S4 in the Supporting Material). Initial observation of the Tsr-Venus containing E. coli cells confirms the well-known polar distribution of Tsr (Fig. 1, a and b). Fluorescence in the cell is concentrated at the poles, due to previously translated Tsr-Venus molecules, with a faint background throughout the cell, presumably due to cellular autofluorescence. Under these conditions, the cells showed expected growth rates (see Fig. S6) and recovery or fluorescence at the poles after photobleaching (see Fig. S8). Before imaging newly expressed Tsr-Venus molecules, this initial fluorescence is photobleached. After photobleaching, individual Tsr-Venus molecules appear sharply in the video image of the cell (after maturation of the Venus fluorophore). Tracking of each molecule, imaged as above, was then performed offline using a standard cross-correlation method (27,29).

Figure 1.

Single-molecule imaging of Tsr-Venus in live E. coli cell at 30 Hz. (a) Bright-field and (b) corresponding fluorescence image showing Tsr molecules localized at the poles in steady state. (c) Selected images from a video and (e) the corresponding trajectory of a confined Tsr-Venus molecule. (d) Selected images from a video and (f) the corresponding trajectory of a mobile Tsr-Venus molecule. Scale bars are 2 μm. (g) Typical fluorescence intensity of an individual Tsr-Venus molecule showing single-step activation and photobleach. The sharp dips in fluorescence intensity during the trace are due to fluorophore blinking. (h) Fluorescence lifetime of the Tsr-Venus molecules under our illumination conditions. This corresponds to a distribution of observed trajectory lengths. To see this figure in color, go online.

Initial imaging was done at 30 Hz to classify the motion of Tsr at long timescales. Analysis of 432 individual trajectories over six frames long (out of 2356 imaged molecules total) revealed two types of motion: confined and highly mobile (Fig. 1 and see Movie S2 and Movie S3 in the Supporting Material). Confined Tsr-Venus molecules mostly diffused within a small area near the pole(s) (Fig. 1, c and e), although a small fraction was found in the central region of the cell. Highly mobile molecules (Fig. 1, d and f) diffused throughout the whole cell area including the polar regions. The black background fluorescence image in the first and the last position in Fig. 1, c and d, shows the single-step maturation and photobleach of the imaged molecule implying that a single molecule was being observed, and the cell boundary is roughly outlined with green to aid the eye. Also shown in Fig. 1 g is a typical intensity trace from an individual Tsr-Venus molecule showing single-step activation and photobleach as well as blinking. Only molecules showing such a trace were tracked. Fig. 1 h displays the distribution of fluorescence lifetimes found under our illumination conditions. The average fluorescence lifetime was found to be 1.8 s, which corresponds to the average length of trajectory tracked during this study.

We defined the confined fraction of Tsr-Venus molecules as those molecules exhibiting a maximum excursion over time much smaller than the cell size or displaying the same mobility as the purified Venus molecules immobilized on the cover glass (see Fig. S2). Tsr-Venus molecules were also classified according to whether they were found within the polar region throughout the observation period (termed the “polar fraction”), or whether they were found elsewhere or escaped from the polar region (termed the “central fraction”).

For all trajectories that were tracked over at least six frames before photobleaching or loss of the track, the diffusion coefficient was determined through a linear fit to the MSD over points 2–4 (at 30 fps, this amounts to a diffusion coefficient over a time range of 66–133 ms, called D_100ms), as defined by Kusumi et al. (30). The distribution of calculated D_100ms for each of these cases is given in Fig. 2 a. The mobile fraction, which constitutes 7% of all molecules observed, exhibits a 15–20-fold larger average diffusion coefficient compared to the restricted polar (82% of the molecules) and restricted central (11% of the molecules) fractions. For comparison, the distribution of measured diffusion coefficients for Venus immobilized directly on the cover glass is also given. To further analyze these types of different behaviors, the averaged MSD of all trajectories in the mobile and confined polar fractions was calculated as a function of time-lag. Fig. 2, b and c, shows plots for the averaged MSD-t for the confined polar and mobile fractions. Whereas the mobile fraction displays the linear dependence expected for random Brownian motion, the plot for the motion of the polar fraction displays a distinct leveling-off, indicative of diffusion within a finite-sized domain. Data were fitted with the expected MSD for confined diffusion within an area of linear size L (Eq. 1) (30,31), or free diffusion (Eq. 2),

$$\langle {\left(\Delta r\right)}^2\rangle =\frac{L^2}{3}-\frac{32L^2}{{\pi }^4}\sum _{n=1\left(\text{odd}\right)}^{\infty }\frac{1}{n^4}\exp \left[-\frac{1}{2}{\left(\frac{n\pi 2D}{L}\right)}^{2}t\right],$$ (1)

$$\langle {\left(\Delta r\right)}^2\rangle =4Dt,$$ (2)

where L is compartment size, and D is diffusion coefficient. Note that the diffusion coefficient in Eq. 1 refers to the diffusion coefficient the molecule would have within the confined region (i.e., the diffusion coefficient that would be measured if the confinement did not exist). The fits above give diffusion coefficients of 0.40 ± 0.01 μm² s⁻¹ (N = 30) for the mobile fraction and 0.012 ± 0.002 μm² s⁻¹ (N = 402) for the polar confined fraction. Diffusion values are in agreement with the values recently measured by FRAP data for the cytoplasmic membrane proteins in E. coli ranging from 0.01 to 0.2 μm² s⁻¹ (9,32,33).

Figure 2.

Trajectory analysis of individual Tsr-Venus molecules on the inner membrane of live E. coli. (a) Distribution of diffusion coefficients for Tsr-Venus molecules classified as confined in the polar and central regions, and for those molecules classified as mobile. Also shown is the measured diffusion coefficient for Venus molecules immobilized on glass. (b and c) The MSD, averaged over all trajectories, for (b) confined polar and (c) mobile fractions of Tsr-Venus. To see this figure in color, go online.

Because one might expect that the mobile fraction of Tsr molecules would be actively driven toward the poles, we performed an autocorrelation on the velocities determined from the trajectories. Positive correlations at nonzero times would imply that the molecules were being directed (through either a ballistic- or drift-type motion) to move in a specific direction. The velocity autocorrelation function was determined for all fractions found above (see Fig. S3). There was no correlation found for positive times, implying that molecules of Tsr-Venus move through random diffusion (15) and, specifically, the mobile fraction is not driven toward the poles.

The asymptotic value of the MSD at long times for the confined fraction, 〈r²〉 = L²/3 in Eq. 1, of 0.024 μm² (0.036 μm² minus the y-intercept of 0.012 μm², which reflects the error in the MSD measurement), implies confinement within a domain ∼270 nm in diameter.

We examined the fine structure of E. coli inner membrane, which may underlie the 270-nm compartment found above, by increasing the observation rate up to 1000 Hz (see Fig. S4, Fig. S5, and Movie S1, Movie S2, Movie S3, and Movie S4 in the Supporting Material). Due to the link between timescale and spatial scales in diffusive motion, high spatial resolution requires high temporal resolution (34). Of course, there can be a simultaneous loss of spatial precision of the measurement at higher frame rates due to reduced photon emission. In this work, to maximize spatial precision, the full MSD-t curve was created by determining the MSD-t curve at four different frame rates (1000, 400, 260, and 30 Hz) and combining the four results into a single curve. As such, the laser excitation powers were chosen at each frame rate to maximize spatial precision within the boundary condition that the fluorophore could be imaged for 15 frames on average at that frame rate. All trajectories of six or more frames were then used in the analysis at each frame rate. The reduction in measurement precision under these conditions is measured (see Fig. S4).

Fig. 3 a shows a typical trajectory of an individual Tsr-Venus molecule imaged at 1 kHz. Fig. 3 b shows the complete MSD curve over time, averaged over all trajectories obtained by different camera rates (1000, 400, 260, and 30 Hz indicated by green, blue, red, and black, respectively). The inset in Fig. 3 b shows the higher magnification of the short time region. The vertical position of the raw curves is convoluted with the spatial precision of the measurement at each rate. As such, to set the vertical position of each curve to stitch together the entire curve, the following procedure was used: The 1000 Hz curve was set such that the intercept of a linear regression through points 2–4 of the curve vanished. At rates slower than 1000 Hz, the vertical position of the curve was set to be consistent with the MSD determined at similar time delays at the higher imaging rates.

Figure 3.

Inner membrane structure of E. coli visualized by single-molecule imaging. (a) Example trajectory of a Tsr-Venus molecule imaged at 1000 Hz. (b) Complete MSD-Δt plot observed over the full range of video rates (30 – 1000 Hz). Data are fitted with linear regressions in the three distinct linear regions. (c) Same MSD-Δt plot fitted with analytical solutions given by Eq. 3. (d) Fitting of a general fractional power law for anomalous subdiffusion fails to fit the curve at long times. (Data subsets: green, 1000 fps; blue, 400 fps; red, 260 fps; and black, 30 fps.) To see this figure in color, go online.

Note that at the faster frame rates, clear distinction between mobile and confined molecules was lost so all molecules tracked are combined into this single plot. Two clear crossovers occurred at τ₁ = 0.004 s and τ₂ = 0.07 s, differentiating three linear regions. The crossovers imply that the diffusion of Tsr-Venus is hindered by nested barriers at two different length-scales as has been seen in lipid diffusion in eukaryotic cells (35). Fitting a linear regression to each of these linear regions yields a short (1–4 ms, D_μ), intermediate (5–70 ms, D_int) and long (70–330 ms, D_∞) time-diffusion coefficient: D_μ = 0.43 ± 0.1 μm²s⁻¹, D_int = 0.037 ± 0.0015 μm²s⁻¹, and D_∞ = 0.008 ± 0.0003 μm²s⁻¹, respectively. Note that the diffusion coefficient at shortest times here agrees well with the diffusion coefficient found at long times for the mobile fraction, implying that at the shortest times all Tsr-Venus molecules undergo unrestricted Brownian motion, The fraction of molecules that are confined then see an inner barrier which slows their diffusion at intermediate time- or length-scales. At longer times or lengths, a second barrier to motion is found that severely restricts their motion and presumably keeps the confined fraction (93% of all molecules tracked at 30 Hz) confined.

We fitted the above MSD-t curve with the expected MSD for molecular diffusion through an equally space-semi-permeable barrier located periodically at a separation distance L (31). For this model, the exact analytical solution for the MSD is

$$\langle x^2\rangle =\frac{L^2}{2}\left(c_1+c_2\tau -\sum _n\underset{z\to z_n}{\lim }\frac{e^{-z^2\tau }}{z^3}\left[\frac{z+\left(\frac{D^{\text{'}}}{1-D^{\text{'}}}\right)\tan z}{\frac{1}{1-D^{\text{'}}}-z·\tan z}\right]\right),$$ (3)

where D′ = D_∞/D_μ, c₁ = 1/3(1−D′)², c₂ = D′, and τ = 4Dt/L² (dimensionless time), in which D_μ is the microscopic, or short-time diffusion coefficient; and D_∞ is the macroscopic, or long-time diffusion coefficient, and z_n is a solution of

$$f\left(z_n\right)=z_n+\left(\frac{D^{\text{'}}}{1-D^{\text{'}}}\right)\tan z_n,$$

provided by Kenkre et al. (36). To fit the two crossovers seen in this data, the MSD was split into two regions—short-to-intermediate times and intermediate-to-long times, where the intermediate times overlapped, and Eq. 3 was applied to each section independently. As a result, the fitted diffusion coefficients for the intermediate times were not expected to be accurate because the intermediate times are neither truly short nor truly long times. As such, we characterized this motion by the compartment sizes at the two cutoffs, L₁ and L₂, the microscopic diffusion coefficient from the shortest time region D_μ, and the macroscopic diffusion coefficient from the longest time region D_∞. The fitted curves are shown in Fig. 3 c, resulting in D_μ = 0.84 μm² s⁻¹, D_∞ = 0.016 μm² s⁻¹, L₁ = 170 ± 10 nm, and L₂ = 290 ± 15 nm. For comparison, a fit to the data for an anomalous diffusion model 〈r²〉 ∼ t^α, where α < 1 signifies a general anomalous subdiffusive process, is shown in Fig. 3 d with $\alpha =0.43$. Note that whereas the curve fits well at early times, it does not fit the entire curve, implying as before that there is a change in mobility at certain specific length-scales. A similar analysis was performed on Venus immobilized on glass to determine whether the inner domain found may be an artifact of the measurement on short length-scales (see Fig. S5). The results show strong confinement of the immobilized Venus in a domain of size 60 nm, much smaller than the smallest domain seen here.

To investigate the effect of membrane curvature in maintaining the polar Tsr cluster, we have tracked individual Tsr molecules on A22-treated E. coli cells. The effect of A22 treatment is a rounding of the cells over time. Shown in Fig. 4, a and b, are images of cells during an ∼3 and 4 h incubation in 1.6% A22 in media, respectively. After 3 h incubation, cells are rounding but still maintain a small polar cap, which contains most of the Tsr molecules. After 4 h incubation, the polar cap is disrupted and small Tsr clusters are found throughout the membrane.

Figure 4.

Effect of A22 treatment on Tsr clusters and individual Tsr molecular mobility. Image of the Tsr-Venus localization after (a) ∼3 h and (b) ∼4 h incubation in 1.6% A22 in media. Note the rounding of the cells and the dispersion of the large polar cluster over time. (c) Distribution of diffusion coefficients determined for the restricted and mobile fractions of Tsr-Venus in A22-treated cells after ∼4 h incubation. (d and e) The MSD, averaged over all trajectories, for (d) restricted and (e) mobile fractions of Tsr-Venus in panel c. To see this figure in color, go online.

Observation of the motion of individual Tsr molecules under A22 treatment at 30 Hz shows that there is an increase in the mobile fraction from 7 to 27% (25 out of a total of 91 trajectories) after rounding of the cells (Fig. 4 c). Due to the spherical symmetry of the A22 cells, the mobility of Tsr was divided only into mobile and restricted fractions. The average diffusion coefficients, determined as for the untreated cells above, were found to be 0.12 and 0.054 μm² s⁻¹ for the mobile and restricted fractions, respectively. The general reduction in the diffusion coefficients may be due to the gross morphological changes to the cell under A22 treatment. Further, asymptotic value of the MSD for the restricted fractions implies confinement in a domain of size 170 nm after A22 treatment, which is consistent with the smaller, inner domains found in untreated cells at high time resolutions.

Conclusion

Through application of high-speed single-molecule tracking techniques, we have shown that individual Tsr-Venus molecules in the inner membrane of line E. coli cells are not rigidly fixed in the polar cluster of chemoreceptors, but instead are free to diffuse in a relatively large area (on a molecular scale) measuring 170 nm in diameter. Beyond this domain, most molecules are severely restricted for motions over longer distances, >290 nm, which presumably keeps the maintenance of the polar cluster. A small fraction (7%) of all Tsr-Venus molecules was found to be free from the polar cluster. These molecules had the same diffusion coefficient at long times as that found for all the Tsr-Venus molecules at the highest observation rates and could traverse the entire cell membrane during observation.

The size of the domains found in this study correlates well with recent work on clustering in E. coli membranes. Lenn et al. (37) observed the dynamics of membrane patches by tracking individual immobile clusters (each containing 76 cytochrome bd-I molecules) labeled by GFP. They found a mean patch diameter of 160 nm in the E. coli inner membrane and that the patch diameter was independent of the number of cytochrome bd-I complexes. Even more recently, superresolution microscopy measurement revealed a continuous spectrum of Tsr cluster sizes ranging from 50 to 1750 nm (5).

After disruption of the MreB cytoskeleton, and the subsequent rounding of cells, the mobile fraction of Tsr molecules increased approximately fourfold and the previous polar cluster was found to fragment into smaller clusters throughout the membrane. This implies that the curvature of the membrane in the polar region is favorable to the Tsr heterotrimer complex and/or MreB has a direct interaction that helps stabilize the Tsr cluster.

Our results are consistent with the recent model of Endres (26), which takes into account the intrinsic curvature of a trimer of dimers. Where individual molecules and even individual dimmers have are approximately cylindrical in shape, the basic signaling unit of the chemoreceptor is a splayed trimer-of-dimers. Here we expect the small fraction of Tsr molecules found free in the membrane is composed of individual Tsr molecules that have not bound into a trimer of dimers complex. Those found at the poles may have bound into a trimer-of-dimers complex and thus now strongly favors the polar region. The mobility of these molecules at high time resolution implies they are not trapped in the polar region because of direct binding into a larger cluster but are free to move in a restricted region that comprises the polar region. Disruption of the curvature fragments the cluster and disperses it, as there is no longer a preferred location in the now-spherical cell. Further, a larger fraction of freely diffusing Tsr molecules are also found, perhaps due to the lack of an energetically favorable region to aggregate.