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Am J Physiol Cell Physiol 294: C1096-C1102, 2008. First published February 20, 2008; doi:10.1152/ajpcell.00252.2007
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MEMBRANE TRANSPORTERS, ION CHANNELS, AND PUMPS

Dynamics of single potassium channel proteins in the plasma membrane of migrating cells

Volodymyr Nechyporuk-Zloy,1,* Peter Dieterich,2,* Hans Oberleithner,1 Christian Stock,1 and Albrecht Schwab1

1Institute of Physiology II, University of Münster, Münster; and 2Institute of Physiology, Medical Faculty Carl Gustav Carus, Technical University of Dresden, Dresden, Germany

Submitted 13 June 2007 ; accepted in final form 19 February 2008


   ABSTRACT
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Cell migration is an important physiological process among others controlled by ion channel activity. Calcium-activated potassium channels (KCa3.1) are required for optimal cell migration. Previously, we identified single human (h)KCa3.1 channel proteins in the plasma membrane by means of quantum dot (QD) labeling. In the present study, we tracked single-channel proteins during migration to classify their dynamics in the plasma membrane of MDCK-F cells. Single hKCa3.1 channels were visualized with QD- or Alexa488-conjugated antibodies and tracked at the basal cell membrane using time-lapse total internal reflection fluorescence (TIRF) microscopy. Analysis of the trajectories allowed the classification of channel dynamics. Channel tracks were compared with those of free QD-conjugated antibodies. The size of the label has a pronounced effect on hKCa3.1 channel diffusion. QD-labeled channels have a (sub)diffusion coefficient DQDbound = 0.067 µm2/s{alpha}, whereas that of Alexa488-labeled channels is DAlexa = 0.139 µm2/s. Free QD-conjugated antibodies move much faster: DQDfree = 2.163 µm2/s{alpha}. Plotting the mean squared distances (msd) covered by hKCa3.1 channels as a function of time points to the mode of diffusion. Alexa488-labeled channels diffuse normally, whereas the QD-label renders hKCa3.1 channel diffusion anomalous. Free QD-labeled antibodies also diffuse anomalously. Hence, QDs slow down diffusion of hKCa3.1 channels and change the mode of diffusion. These results, referring to the role of label size and properties of the extracellular environment, suggest that the pericellular glycocalyx has an important impact on labels used for single molecule tracking. Thus tracking fluorescent particles within the glycocalyx opens up a possibility to characterize the pericellular nanoenvironment.

calcium-activated potassium channel 3.1; quantum dot; single molecule tracking; cell migration

CELL MIGRATION IS AN ESSENTIAL PROCESS from unicellular organisms, such as amoeba, where its main function is search for food (46), to multicellular organisms, where it is crucial for embryonic development (18), inflammatory immune response (19), wound repair (25), and tumor formation and metastasis (20). In the last decade it was clearly shown that ion and water channels contribute to optimal cell migration. Inhibition or genetic ablation of channels leads to a marked impairment of migration (39). Volume regulation in migrating cells is one of the important functions of ion channels, particularly calcium-activated potassium channels (KCa3.1) (21). They are expressed in many migrating cells (39) and support the retraction of the uropod by mediating an intermediate local shrinkage of this cell pole (37). Hence, inhibition of KCa3.1 channels slows down cell migration, whereas its heterologous expression speeds up cells that do not contain endogenous KCa3.1 channels (26).

KCa3.1 channel proteins are found in the entire plasma membrane of migrating cells, but they are concentrated at the cell front. It was proposed that directed endocytic recycling of KCa3.1 channels could contribute to this characteristic subcellular distribution in migrating cells (26). Such recycling was shown for β2-integrins (9). Alternatively, KCa3.1 channels could be clustered by linkage to the cytoskeleton; KCa3.1 channel proteins should then be immobilized in the plasma membrane. However, so far there is no information available on the dynamics of K+ channel molecules in the plasma membrane of motile cells. We recently developed a microscopic technique that allows the identification of hKCa3.1 channels on the single-molecule level (26). We have adopted this technique to live cell imaging and can thereby track single hKCa3.1 channel molecules in the plasma membrane of migrating cells. To the best of our knowledge, this is the first report on the dynamics of ion channel proteins in motile cells. We provide evidence that hKCa3.1 channels are not immobilized at the front but move in a diffusive way throughout the plasma membrane of migrating cells.


   METHODS
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Channel construct and transfected cell line. Madin-Darby canine kidney focus (MDCK-F) cells (29) were transfected with a modified hKCa3.1 channel containing a hemagglutinin (HA) tag in the extracellularly located S3–S4 linker as described previously (40). They were maintained in CO2/HCO3–-buffered minimal essential medium (MEM; pH 7.4) (PAA, Pasching, Austria) supplemented with 10% FBS (Biochrom, Berlin, Germany) and 600 mg/ml geneticin (PAA) at 37°C. For experiments, cells were seeded on poly-L-lysine (Sigma-Aldrich, Taufkirchen, Germany)-coated glass coverslips.

Channel labeling. MDCK-F cells were cultured in Leibowitz medium L-15 (23) (pH 7.1; PAA) with FBS (10%) on poly-L-lysine-coated glass coverslips for 12 h before antibody labeling at 37°C. The cells were incubated with primary rat antibodies (3F10; Roche Diagnostics, Mannheim, Germany) against the extracellular HA tag of hKCa3.1 channels for 15 min (1:900), briefly washed (at 37°C), and then washed three times for 5 min in L-15 medium with FBS (10%). Thereafter, cells were incubated with quantum dot (QD) goat F(ab')2 anti-rat IgG conjugates (1:1,000) with emission maximum at 655 nm (QD655) (Invitrogen, Karlsruhe, Germany) for 15 min at 37°C (Fig. 1). Titers of secondary antibodies were chosen such that the total density of QDs was low enough to clearly track them individually. The cells were then washed again as described above, and the coverslip was positioned in a heated chamber (37°C) for microscopic observation.


Figure 1
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  		Fig. 1. Labeling of human KCa3.1 (hKCa3.1) channel proteins in the plasma membrane of migrating Madin-Darby canine kidney focus (MDCK-F) cells with quantum dots (QDs). Migrating cells contact the extracellular matrix with adhesion molecules that protrude up to 50 nm from the outer leaflet of the plasma membrane (8). Primary antibodies (Ab) and QD conjugates can diffuse to the entire "basal" plasma membrane and bind to the channel proteins. QD655, quantum dot labeling with emission maximum at 655 nm.

 
Alternatively, cells were incubated with an Alexa488-conjugated anti-HA antibody for up to 45 min at 37°C (1:150; Molecular Probes, Eugene, OR) and then washed and positioned on the microscope stage. We performed control experiments in which we omitted the primary antibody and incubated the cells only with QD655 goat F(ab')2 anti-rat IgG conjugates (1:500) in the same way as described above.

Microscopy and data acquisition. MDCK-F cells were kept in L-15 medium throughout the course of the experiment. They were observed with an inverted microscope (Axiovert 200; Zeiss, Oberkochen, Germany) equipped with a digital camera (Visitron, Puchheim, Germany, or Zeiss), a total internal reflection fluorescence (TIRF) slider (TILL Photonics, Gräfelfing, Germany, or Zeiss), and a x100 1.45 oil-immersion objective. Data acquisition was controlled by Metavue or Axiovision software (Visitron or Zeiss). Cell movement was monitored for 10 min before TIRF microscopy by acquiring brightfield images in 20-s intervals. The initial observation of migration was immediately followed by monitoring of the dynamics of KCa3.1 channels with TIRF microscopy. QDs that labeled individual KCa3.1 channels were excited with an argon laser (TILL Photonics) at a wavelength of 488 nm. We used the following filters for QD655: z488/10 (excitation; Chroma Technology, Rockingham, VT), 545DRLP (dichroic mirror; Omega Optical, Brattleboro, VT), XF305–1 (emission; Omega Optical). Stacks of 50 images were acquired in time intervals {Delta} = 600 ms with a shutter (exposure) time {eta} = 200 ms. The time interval was lowered to {Delta} = 300 ms and the shutter time to {eta} = 100 ms when unbound QD-conjugated antibodies or Alexa488-labeled KCa3.1 channels were tracked.

Analysis of cell migration. The boundaries of the cells were labeled by employing AMIRA software (TGS, San Diego, CA). The cell contours then served as the basis for analyzing cell migration. The migratory speed was calculated as the movement of the cell center from a three-point difference quotient by using self-made JAVA programs and the National Institutes of Health ImageJ software (http://rsb.info.nih.gov/ij/) (40). The displacement represents the distance covered by the cell center within a time period of 10 min.

Tracking of KCa3.1 channels and unbound QD-conjugated antibodies. The x and y coordinates of individual KCa3.1 channels were determined in each image of the stack with the ImageJ plugin Spot Tracker 2D (34). Trajectories constructed from these data sets were the basis of further analysis. We assessed the accuracy of the QD localization by tracing immobile QDs that were attached to the glass surface in cell-free areas during data acquisition (NQDimmobile = 11). This delivered an uncertainty of position measurement {epsilon} {approx} 0.03–0.04 µm for the x or y direction.

Analysis of KCa3.1 dynamics. We pooled all trajectories from all cells observed under a given labeling procedure and calculated the mean squared displacement (msd), which describes the mean of the squared distances between a common starting point at time t0 and a later position at time t. It is defined as

Formula 1(1)
where x and y denote the positions of the QDs at observation time t in the two-dimensional plane, and the term within angle brackets marks a combined average over all starting times t0 and all paths. The time-dependent behavior of the mean squared displacement characterizes the dynamic behavior of the hKCa3.1 channels. If the msd(t) shows a power-law scaling over a certain time range, it can be written as model equation

Formula 2(2)
for a two-dimensional process. D{alpha} represents the diffusion coefficient, and {alpha} corresponds to the slope of msd(t) in the double-logarithmic plot. The parameter {alpha} allows us to distinguish between normal diffusion ({alpha} = 1), subdiffusion ({alpha} < 1), and superdiffusion ({alpha} > 1). Freely diffusive proteins exhibit normal diffusion, whereas proteins transiently trapped for a variety of timescales, for example, by cytoskeletal linkages, would be expected to move in a subdiffusive way. When proteins become permanently trapped and thereby immobilized, msd(t) would saturate at a constant value (5). In the case of a collective drift (i.e., in our case due to directed transport, or movement of the entire cell), Eq. 2 may be modified by the additional term vdrift2t2.

As shown by Savin and Doyle (35), static and dynamic measurement errors modify the apparent experimental result. Accordingly, a modification of Eq. 2 has to be made to incorporate the dynamic measurement error that is due to the finite shutter time {eta} that is in the same order of magnitude as the time interval of image acquisition {Delta}. Values of {eta} and {Delta} were as follows: QD-labeled hKCa3.1 channels: {eta} = 200 ms, {Delta} = 600 ms; Alexa488-labeled hKCa3.1 channels and unbound QD-conjugated antibodies: {eta} = 100 ms, {Delta} = 300 ms.

Formula 3(3)
If shutter times {eta} are much smaller than the interval between two exposures ({eta} << {Delta}), msd(t)mod* will practically reduce to the simpler form of Eq. 2. However, in our case, the long shutter time {eta} generates a dynamic error that induces an apparent superdiffusive behavior for small times (35). This error can be eliminated by using Eq. 3.

The calculation of msd(t) provides an initial characterization of the nature of diffusion. However, an additional classification of the type of diffusion requires the determination of further parameters such as the so-called kurtosis {kappa}. The kurtosis is defined as

Formula 4(4)
where x denotes the positions of the particle at observation time t in the x direction. Equation 4 applies for y coordinates accordingly. The term within angle brackets marks a combined average over all starting times t0 and all paths, as in Eq. 2. The x and y coordinates of the paths of the channel proteins can also be used to calculate the probability that a particle is at a given time at a given position. This gives rise to probability distributions p(x,t) and p(y,t) that are usually more or less bell shaped. The shape (wideness, "peakedness") of these distributions is described by the kurtosis. A Gaussian distribution has a kurtosis of {kappa} = 3. This is typical for a normally diffusive process. {kappa} != 3 characterizes probability distributions that deviate from Gaussian distributions. They could either be flatter ({kappa} < 3) or steeper ({kappa} > 3). Any deviation from {kappa} = 3 is additional manifestation of anomalous diffusion.

Statistics and parameter estimation. Data are means ± SD unless stated otherwise. We applied Bayesian probability theory for fitting the msd function (Eq. 3) to the msd (Eq. 1) obtained from experimentally measured data as described previously (6). We used this approach (16) to estimate the values of the parameter {alpha} and the D{alpha} of the msd model.


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We showed in our previous study that individual KCa3.1 channels can be visualized with QD labeling technology. In fixed cells, each channel protein binds only one QD antibody conjugate (26). In this study we performed control experiments with living cells to rule out the possibility that the bivalent primary antibodies cause channel clustering and thereby induce the formation of large channel complexes with altered mobilities. To this end, we quantified hKCa3.1 channel labeling in MDCK-F cells after incubating them for 45 min at 37°C with Alexa488-conjugated anti-HA antibodies. hKCa3.1 channel density amounts to 1.63 ± 0.08 µm–2 (10 cells), which is identical to the density obtained in fixed cells (1.53 ± 0.15 µm–2) (26). If cross-linking had occurred in living cells, the apparent channel density would have been lower due to their accumulation in clusters in which the distance between two channel proteins would have been too small to be resolved optically. A lack of channel cross-linking by primary antibodies was also described by other groups studying single-channel dynamics in the plasma membrane (3, 13). Thus the movement of QDs can be taken as an approximation of the movement of single-channel molecules.

After the labeling procedure and before imaging of the dynamics of hKCa3.1 channels with TIRF microscopy, MDCK-F cells moved with a speed of 0.56 ± 0.06 µm/min (10 cells) (Fig. 2A; Supplemental Movie 1). (Supplemental data for this article is available online at the American Journal of Physiology-Cell Physiology website.) Figure 2B demonstrates that the channel proteins were labeled over the entire basal plasma membrane with no preference for the cell periphery (Supplemental Movie 2). That is, QDs had free access to the lower surface of MDCK-F cells so that they could be imaged with TIRF microscopy. The specificity of the hKCa3.1 channel labeling was verified by staining MDCK-F cells with secondary QD655-conjugated antibodies only or by using wild-type MDCK-F cells that do not express the modified hKCa3.1 channel. In both cases, we observed a maximum of only two to three QDs per visual field that were attached nonspecifically to the cell surface or to the glass coverslip. This number is negligible compared with the number of ~100 hKCa3.1 channels labeled with QDs in the plasma membrane of a MDCK-F cell under our experimental conditions with low antibody concentrations.


Figure 2
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  		Fig. 2. Imaging of hKCa3.1 channel dynamics in a migrating MDCK-F cell by QD labeling. A: bright field image of a MDCK-F cell. (See also Supplemental Movie 1). B: total internal reflection fluorescence (TIRF) image of QD-labeled hKCa3.1 channels in the plasma membrane of the cell shown in A. QDs are visible as white dots that are present throughout the entire basal plasma membrane. The cell border is indicated by a white line. (See also Supplemental Movie 2). C: trajectories of 2 hKCa3.1 channels in the plasma membrane of the cell shown in A and B. Channel movement was monitored for 30 s. (See also Supplemental Movie 3a and 3b). D: trajectories of all QD-labeled hKCa3.1 channels in the plasma membrane shifted to a common starting point from the same cell (A and B). The radius of the circle corresponds to the mean distance covered by QD-labeled channels within 25 s.

 
It is evident that the movement of hKCa3.1 channels is very heterogeneous. Some channels cover relatively long distances (up to 6.3 µm within 30 s), whereas some are less mobile. Figure 2C shows the typical paths of "stationary" and more mobile hKCa3.1 channel proteins in the plasma membrane of a migrating MDCK-F cell (Supplemental Movies 3a and 3b). The average distance covered by hKCa3.1 channels within 30 s is ~2.1 µm (given as square root of the corresponding msd value). The average displacement of the entire cell within the same time period amounts to ~0.3 µm. Hence, the movement of hKCa3.1 channels is almost one order of magnitude faster than the movement of MDCK-F cells. Figure 2D, which compiles the trajectories of all QD-labeled hKCa3.1 channels of one cell, reveals the absence of a preferential direction of motion of hKCa3.1 channels in the plasma membrane. A similar distribution of apparently stationary and more mobile potassium channels is obtained when their dynamics are simulated in silico with a constant set of parameters.

The dynamics of QD-labeled hKCa3.1 channels can be quantified by the time-dependent behavior of the mean squared displacement according to Eq. 1. Figure 3A shows the msd of NQDbound = 534 tracked hKCa3.1 channels. At first view, the double-logarithmic plot indicates a power-law scaling over the observed time range. However, at smaller times, the msd displays a larger inclination. The application of Eq. 3 shows that this is an error produced by the finite observation time (shutter time {eta} = 200 ms). In our case, the error of position measurement {epsilon} {approx} 0.03–0.04 µm makes only a marginal contribution of (2{epsilon})2 {approx} 0.0036–0.0064 µm2 to the msd (which has a value of ~0.15 µm2 at the smallest time, 0.6 s) and is thus negligible. Table 1 summarizes the numerical values of the parameters describing hKCa3.1 dynamics that were obtained with Bayesian data analysis. The diffusion coefficient D{alpha} amounts to DQDbound = 0.0673 ± 0.0005 µm2/s{alpha}. A threefold increase of the primary antibody concentration (titer of 1:300) has no effect on dynamics of QD-labeled hKCa3.1 channels (see Fig. 3A). However, the size of the label itself does influence channel dynamics. When we tracked hKCa3.1 channels marked with Alexa488-conjugated anti-HA antibodies, whose molecular weight is approximately one-third of that of QDs, we obtained a diffusion coefficient of DAlexa {approx} 0.139 ± 0.004 µm2/s (see Fig. 3B). However, it should be noted that the diffusion coefficients of QD- and Alexa488-labeled hKCa3.1 channels cannot be directly compared with each other, since they have different physical units. Nonetheless, the msd plot, which includes the contribution of {alpha}, clearly shows that Alexa488-labeled hKCa3.1 channels diffuse significantly faster.


Figure 3
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  		Fig. 3. A: mean squared displacement (msd) of QD-labeled hKCa3.1 channels in the plasma membrane of migrating MDCK-F cells. msd is proportional to the area of the circle shown in Fig. 2D that indicates the mean distance covered by the hKCa3.1 channels in a given time. Symbols indicate the results of the experimental measurements. Continuous curves represent the results of fitting the msd data to a power-law model of Eqs. 2 and 3. The msd of QD-labeled hKCa3.1 channels (QDs + channels) is in good agreement with a power-law scaling when corrected for the exposure time {eta} = 200 ms (fit to Eq. 3). The dotted line (fit to Eq. 2) shows the power-law fit without corrections. This fit does not describe the transition at smaller times. Small filled triangles (modified dilution) represent experiments with a threefold higher concentration of the primary antibody. Channel dynamics are not altered by variations of the antibody concentration. B: comparison of msd curves from hKCa3.1 channels labeled with QD-conjugated antibodies (QDs + channels) or Alexa488-conjugated antibodies (Alexa + channels) and from free QD-conjugated antibodies (free QDs). Lines indicate the fit to Eq. 3. The straight line ({alpha} = 1) illustrates the scaling for normal diffusion over the whole time range.

 

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  		Table 1. Parameters of hKCa3.1 channel protein dynamics

 
The movement of unbound QD-conjugated antibodies is much faster than the movement of hKCa3.1 channels. To allow reliable tracking, we had to reduce the time interval between two images and the exposure time to {Delta} = 300 ms and {eta} = 100 ms, respectively. The diffusion coefficient of unbound QD-conjugated antibodies is DQDfree = 2.163 ± 0.056 µm2/s{alpha}. The difference of almost two orders of magnitude between bound and unbound QD-conjugated antibodies indicates that the motion of bound QDs is mainly determined by the coupled channel dynamics.

We next analyzed the movement of KCa3.1 channels separately for each cell to test whether it follows a drift that may be generated by the movement of the cell or by directed transport processes of the channel protein itself. The estimated error of the drift velocity vdrift was always much larger than the corresponding mean value of ~0.006 µm/s. In addition, simulation of random walk processes with parameters similar to those obtained for hKCa3.1 channels from our experiments (D = 0.06 µm2/s, number of particles Nsim = 80, number of steps of the path L = 50, time interval {Delta} = 0.6 s) for a variety of drift values showed that vdrift had to be larger than ~0.1 µm/s to be detected with certainty. According to the work of Qian et al. (32), the contribution of a drift is only observable for times much larger than 4D/vdrift2, corresponding to vdrift >> Formula 4. With D = 0.067 µm2/s and tmax = 30 s for our experiments, the condition vdrift >> 0.1 µm/s had to be fulfilled to observe a directed drift. Since this is not the case, we could neglect the contribution of a possible drift to channel dynamics.

Finally, we wanted to obtain more information about the type of diffusion of hKCa3.1 channels. The coefficient {alpha} that classifies the mode of diffusion is smaller than 1 for QD-labeled hKCa3.1 channels. The average value for QD-labeled hKCa3.1 channels studied is {alpha}QDbound = 0.82 ± 0.003. To obtain a second line of evidence that QD-labeled KCa3.1 channels diffuse anomalously, we calculated their kurtosis according to Eq. 4. Table 1 displays mean values of the kurtosis of hKCa3.1 channels in the time range between 5 and 25 s. The kurtosis of QD-labeled hKCa3.1 channel saturates at a value of {kappa}QDbound = 4.17 ± 0.11, which is indicative of anomalous (non-Gaussian) dynamics.

To our surprise, hKCa3.1 channels labeled with Alexa488-conjugated antibodies have a coefficient {alpha}Alexa = 1.015 ± 0.0027 (see Fig. 3B). The mean value of the kurtosis of hKCa3.1 channels labeled with Alexa488-conjugated antibodies is {kappa}Alexa = 3.15 ± 0.33. Thus the size of the label not only modifies the value of the diffusion coefficient D but also the nature of diffusion. Whereas QD-labeled hKCa3.1 channels move subdiffusively, the dynamics of Alexa488-labeled channels correspond to normal diffusion. To solve this apparent discrepancy, we also determined {alpha}QDfree = 0.789 ± 0.023 and kurtosis {kappa}QDfree = 5.04 ± 0.24 of unbound QD-labeled antibodies. Both values are similar to those of QD-labeled hKCa3.1 channels, i.e., QD-conjugated antibodies diffuse anomalously. Together, these results indicate that diffusion of hKCa3.1 channels in the plasma membrane of MDCK-F cells is a normally diffusive process over the observed time scale (from 0.3 to ~30 s). Moreover, they show that the label used for single-molecule tracking experiments has to be chosen with great care. When single molecules are tracked at the interphase between the glass coverslip and the ventral surface of the cell, it can have a pronounced impact on the apparent dynamics of the molecule of interest. Given these reservations, we think that the diffusion coefficient of hKCa3.1 channels obtained with Alexa488-conjugated antibodies is more realistic than that obtained with QDs.


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Previous studies on the mobility of ion and water channel proteins gave different values of mean diffusion coefficients: 0.0002 µm2/s (KV1.3) (38), 0.02 µm2/s (KV2.1) (27), 0.005 µm2/s (CFTR) (13), 0.1 µm2/s (glycine receptor) (3), 0.15 µm2/s (L-type Ca2+ channels) (14), and 0.09 µm2/s (aquaporin-1) (2). Based on the diffusion coefficients, channels can apparently be divided into two groups: channels that are virtually immobile and channels that are mobile in the plasma membrane. hKCa3.1 channels investigated in the present study clearly belong to the second group of mobile ion channels. Their diffusion coefficient is of the same order of magnitude as that of L-type Ca2+ channels, glycine receptors, or aquaporins. The cellular context in which channels are studied appears to play an important role with respect to their mobility. KV1.3 channels are stationary in lymphocytes (Jurkat cells), whereas they are highly mobile when expressed in HEK-293 cells. On the other hand, KV1.2 channels are relatively immobile in their native environment (hippocampus neurons) and in HEK-293 cells (28). Aquaporins are mobile in two cell types, but the respective diffusion coefficients differ by a factor of 3. The immobility of ion channels was explained with clustering by binding to the actin cytoskeleton. Thus disrupting the COOH terminus-mediated binding to the actin cytoskeleton largely increased the mobility of CFTR molecules in the plasma membrane (13, 17). Conversely, diffusion dynamics of mobile aquaporins are not affected by disrupting the actin cytoskeleton (2).

It is interesting to note that two mobile channel proteins, hKCa3.1 channels and aquaporins (AQP1), are both concentrated at the leading edge of the lamellipodium of migrating cells (30, 40). The observation that both proteins are freely diffusible in the plasma membrane suggests that their characteristic subcellular distribution is not due to their restricted mobility at this cell pole, unless the ruffled membrane at the leading edge has different properties than the bulk plasma membrane. At least lateral mobility of lipids in the outer membrane leaflet of the plasma membrane is blocked at the leading edge (44). However, so far we have no experimental evidence that such a barrier for lipid diffusion would also apply to hKCa3.1 channels. Rat KCa3.1 channels were reported to be associated with lipid rafts (1) that may confine the diffusion of membrane proteins (7). However, it is unlikely that lipid rafts are found only in the ruffled membrane at the leading edge of MDCK-F cells and not in their bulk plasma membrane. Therefore, additional mechanisms must come into play to account for the concentration of freely diffusible channels at the leading edge of migrating cells. Future studies will have to show whether hKCa3.1 channels behave, for example, like integrins. Integrins have diffusivities similar to those of hKCa3.1 channels when their linkages to extracellular matrix and actin cytoskeleton are disrupted (15). Recycling of integrins by means of endocytosis and reinsertion into the plasma membrane toward the front of the cell importantly contributes to their concentration at this cell pole (31).

One crucial aspect of single-molecule tracking is the labeling procedure (24). We found a clear difference in K+ channel dynamics depending on the manner of labeling. Diffusion is slower with QD- than with Alexa488-labeled K+ channels, and QD-conjugated antibodies turn normal K+ channel dynamics into an anomalous process. hKCa3.1 channels are composed of four subunits that bind calmodulin as a "β-subunit" (10) and nucleoside diphosphate kinase as a "{gamma}-subunit" (41). This kinase is a regulator of KCa3.1 channels whose existence had been postulated but whose molecular identity remained obscure for some time (12, 47). The molecular masses of channel subunit, calmodulin, and nucleoside diphosphate kinase are ~50, 17, and 17 kDa, respectively. Thus the molecular mass of a functional KCa3.1 channel molecule can be estimated to be in the order of 300 kDa. The extracellular "load" imposed on the channel by primary and QD-conjugated secondary antibodies amounts to ~500 kDa (36). In the case of labeling the channel proteins with an Alexa488-conjugated antibody or fusing the channel subunits to green fluorescent protein, the load would be in the order of 150 kDa. For comparison, 40-nm gold particles or 100-nm polystyrene beads that are also frequently used for single-particle tracking (4, 15) constitute a load whose molecular mass is several orders of magnitude larger than the molecules of interest. Thus labeling hKCa3.1 channels with QDs appeared to be a reasonable compromise between fluorochrome stability and size of the external load, since the mass of the antibody/QD complex does not grossly exceed the mass of the K+ channel. Moreover, it was shown that the external load has only a small influence on the diffusion of membrane proteins in artificial membranes. The lateral mobility of a peptide consisting of 12 leucines was hardly changed by the attachment of streptavidin, although their diameters and molecular masses differed by a factor of 10 and 40, respectively (11). In contrast, in the present study, radius and mass of QD/antibody labels (as indicated by the manufacturer) are similar to those of hKCa3.1 channel complexes.

Nonetheless, our study showed that QD-conjugated antibodies left their own fingerprint on K+ channel dynamics. That the payload of a membrane protein has almost no effect on its diffusivity in an artificial membrane as opposed to our findings is most likely due to the glycocalyx surrounding the plasma membrane. The viscosity within this narrow space is ~50 times higher than that of water (22). Already, Saffman and Delbrück (33) pointed out in their hydrodynamic model that an increased viscosity of the surrounding medium can slow down diffusion. Accordingly, digestion of the glycocalyx led to a doubling of the diffusion coefficient of gold particles anchored in the outer leaflet of the plasma membrane, and the diffusion coefficient of FITC-labeled membrane lipids is more than five times larger than that of lipids labeled with gold particles (22). Along these lines, the different diffusivities of aquaporins in the plasma membrane of epithelial MDCK cells and fibroblasts (Chinese hamster ovary cells) (2) could also be due to different viscosities of the glycocalyces. An extension of these considerations is the characterization of the pericellular space by monitoring diffusion of free QDs. Such an approach was used for determining the width of the extracellular space within brain tissue (43). Interestingly, the diffusion coefficient of free QDs (QD655) within brain tissue is practically identical to that of QDs underneath MDCK-F cells. This is a strong argument for our interpretation that dynamics of QD-conjugated antibodies underneath MDCK-F cells are indeed modulated by the glycocalyx and not by interactions with the glass coverslip.

So far, we do not know why free QD-conjugated antibodies diffuse anomalously in the narrow space underneath migrating MDCK-F cells, i.e., in a space most likely occupied by the glycocalyx. First, we considered the geometric constraints that limit diffusion essentially to two dimensions. However, simulations of free diffusion with excursions in the z-direction limited to 40 nm yield a reduction of the diffusion coefficient but no anomalous diffusion. We therefore suggest that more "specific" interactions between QD-conjugated antibodies and components of the pericellular space have to occur. The characterization of diffusion dynamics within the glycocalyx and their modification by the pericellular nanoenvironment [for example, by the pericellular protons (42) or Ca2+ ions (45)] must be the focus of future experiments.


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 ABSTRACT
 METHODS
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 DISSCUSSION
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This work was supported by Deutsches Forschungsgemeinschaft Grants RE 1284/2-1,2 and SCHW 407/9-3 and 407/10-1.


   ACKNOWLEDGMENTS
 
We thank Drs. K. Greulich, R. Preuss, and D. Grünwald as well as Marianne Wilhelmi and Armin Kramer for fruitful discussions, and Sabine Mally for excellent technical support. We also thank Zeiss for providing a TIRF microscope.


   FOOTNOTES
 

Address for reprint requests and other correspondence: A. Schwab, Institute of Physiology II, Univ. of Münster, Robert-Koch-Str. 27b, D-48149 Münster, Germany (e-mail: aschwab{at}uni-muenster.de)

The costs of publication of this article were defrayed in part by the payment of page charges. The article must therefore be hereby marked "advertisement" in accordance with 18 U.S.C. Section 1734 solely to indicate this fact.

* V. Nechyporuk-Zloy and P. Dieterich contributed equally to this work. Back


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