⇦Chinese Physics Letters, 2020, Vol. 37, No. 7, Article code 078701Express Letter Quasi-Two-Dimensional Diffusion in Adherent Cells Revealed by Three-Dimensional Single Quantum Dot Tracking Chao Jiang (江超)1,2, Bo Li (李波)1, Shuo-Xing Dou (窦硕星)1,2, Peng-Ye Wang (王鹏业)1,2,3*, and Hui Li (李辉)1,4* Affiliations 1Beijing National Laboratory for Condensed Matter Physics and Laboratory of Soft Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China 2School of Physical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China 3Songshan Lake Materials Laboratory, Dongguan 523808, China 4School of Systems Science, Beijing Normal University, Beijing 100875, China Received 2 June 2020; accepted 5 June 2020; online 12 June 2020 This work was supported by the National Natural Science Foundation of China (Grant Nos. 11674383, 11874415, 21991133, and 11774407), the National Key Research and Development Program (Grant No. 2016YFA0301500), the Youth Innovation Promotion Association of CAS (Grant No. 2019006), and the Fundamental Research Funds for the Central Universities (Grant No. 2019NTST26).
*Corresponding author. Email: huili@bnu.edu.cn; pywang@iphy.ac.cn Citation Text: Jiang C, Li B, Dou S X, Wang P Y and Li H et al. 2020 Chin. Phys. Lett. 37 078701    Abstract Intracellular diffusion is critical for molecule translocation in cytoplasm and mediates many important cellular processes. Meanwhile, the diffusion dynamics is affected by the heterogeneous cytoplasm. Previous studies on intracellular diffusion are mainly based on two-dimensional (2D) measurements under the assumption that the three-dimensional (3D) diffusion is isotropic. However, the real behaviors of 3D diffusion of molecules in cytoplasm are still unclear. Here, we have built a 3D single-particle tracking (SPT) microscopy and studied the 3D diffusion of quantum dots (QDs) in adherent A549 cells. Notably, we found that the intracellular diffusion of QDs is quasi-2D, with the axial motion being severely confined. Further investigations demonstrated that disrupting the cytoskeleton component or endoplasmic reticulum (ER) does not alter the quasi-2D diffusion pattern, although ER reduces the diffusion rates and slightly relieves the constraint in the axial diffusion. The preferred quasi-2D diffusion is quite robust and attributed to the complex cytoarchitectures in the flat adherent cells. With the aid of 3D SPT method, the quasi-2D diffusion in cells was revealed, shedding new light on the physical nature of cytoplasm. DOI:10.1088/0256-307X/37/7/078701 PACS:87.15.A–, 66.30.Lw, 87.16.Wd © 2020 Chinese Physics Society Article Text Cytoplasm is the site where mostly cellular biochemical activities take place, and is also a complex environment crowded with macromolecules, cytoskeletons and membrane-enveloped organelles.[1,2] Intracellular diffusion is an essential way for macromolecule translocation in cells, which is tightly correlated with the cytoplasmic crowdedness and intracellular structures.[1,3] Since intracellular diffusion constitutes the physical basis for molecular interactions and functions, its characterization is critical for understanding the regulation of intracellular activities. Moreover, diffusion dynamics provide information about the intracellular crowding and microstructures that cannot be directly observed, offering us the opportunities to study the physical nature of cells.[3–6] Many studies have been made on intracellular diffusion in the past 30 years. Typical subdiffusive motions have been observed for proteins and particles with sizes from several to tens nanometers, and their diffusion rates are also obviously reduced compared to those in water, due to the intracellular crowding.[1] Compared with the fluorescence recovery after photobleaching (FRAP) and the fluorescence correlation spectroscopy (FCS) methods which yield ensemble-averaged results, the single-particle tracking (SPT) method can directly visualize the movement of single particles in living cells and generate new insights about the heterogeneity of intracellular environment from the dynamics of particle motions.[7,8] This advantage renders SPT a powerful tool for investigating not only diffusion dynamics on cell membranes, but also intracellular transport dynamics such as protein diffusion, endocytic trafficking and directed transport by motor proteins.[9,10] Meanwhile, semiconductor quantum dots (QDs) have become the ideal probes for measuring intracellular diffusion by SPT in living cells, because of their high quantum yields, moderate physical sizes comparable to intracellular macromolecules, and more importantly, biological compatibilities endowed by surface coating.[11] Recently, we have introduced a method for mapping the intracellular diffusion distribution by using single-QD tracking, and revealed a heterogeneous and compartmentalized distribution defined by endoplasmic reticulum (ER).[3] It should be noted, however, that current SPT studies are mainly performed in 2D. In other words, the observed particle trajectories are only lateral plane projections of actual 3D movements, thus the dynamical information in the axial direction is missed. In fact, it is recently realized that 2D dynamical studies cannot well characterize the complex behaviors of molecular motions in cells. For example, single-nanoparticle tracking in 3D revealed new hidden mechanistic steps in uptake process,[12] and another study of mRNA by 3D tracking discovered their directed motions in the axial direction, which would otherwise be mistakenly regarded as being confined in 2D.[13] Adherent cells belong to one of the most common types of cells, which includes the epithelial cells of skin and other organs, and are also the model cells in various cellular studies.[1] In such adherent cells spreading on a substrate, organelles and cytoskeletons tend to distribute laterally, constituting a heterogeneous and anisotropy environment.[14,15] Until now, the 3D diffusion dynamics in adherent cells or any other types of cells are still unclear. Technically, it is still a challenge for 3D SPT to achieve nanometer spatial and millisecond temporal resolutions, especially for tracking fast diffusing particles in living cells. Although several methods, such as active feedback tracking,[16] multiplane imaging,[17] and astigmatic 3D detection,[18] are available to measure the axial positions of the particles, they have certain limitations in the axial detection depth, temporal resolution, or instrument cost.[9] The diffraction ring formed by an off-focused particle provides a convenient way for detecting the axial position of the particle, as being used in longitudinal magnetic tweezers and multifocal imaging.[19–21] However, the vertical drift of the microscopy objective brings much difficulty to the detection, which needs to be resolved. In this Letter, we build a 3D SPT setup on a microscopy, by adding a focus-locking apparatus to eliminate the vertical drift and a two-focal imaging apparatus to measure the axial positions of particles from diffraction rings. Then, we deliver single QDs into living A549 (human lung carcinoma) cells and track the 3D intracellular diffusion of the QDs. Interestingly, we find that the QDs prefer to diffuse laterally in quasi-two-dimensional (quasi-2D) space rather than isotropically in the 3D space. The axial diffusion is remarkable constrained, with a diffusion rate five times lower than that for the lateral diffusion. Next, we examine the role of cytoskeleton and ER structures in the preferred quasi-2D diffusion. Our results show that the pattern of quasi-2D diffusion still remains after disrupting these intracellular structures, and only ER has an obvious influence on the diffusion rates of QD in both lateral and axial directions. Our results suggest that the preferred quasi-2D is an intrinsic feature of intracellular transport, which is likely shaped by the morphology of adherent cells.
cpl-37-7-078701-fig1.png
Fig. 1. Schematic of the setup and the localization accuracy. (a) Setup of the 3D SPT. (b) In-focused (left panel) and off-focused (right panel) images of QDs immobilized on the coverglass. Scale bar, 10 µm. (c) Calibration data between the $z$ coordinate and the measured radius ($r$) of diffraction rings. The red line is a linear fit of the data, yielding $z = -885.9 + 207r$. Inset: sample data of stage positions in the $z$ direction (red line) and the radii of diffraction rings (black circles). (d) Typical 3D trajectory of an immobilized QD. (e) MSD plots of 10 immobile QDs in the $x$ and $z$ directions. Error bars indicate SEM.
The 3D SPT platform was built on an inverted fluorescence microscope (Olympus IX73) equipped with a $60\times$ oil TIRF objective (1.45 N.A.) and a back-illuminated EMCCD camera (DU-897, Andor Technology). To realize 3D single-particle imaging, we added focus-locking and two-focal imaging apparatuses, as shown in Fig. 1(a). In the focus-locking part, a far-red laser (940 nm) is totally reflected by the interface between the specimen and coverglass and then detected by the CCD. The vertical drift of the objective, which causes position shift of the far-red spot, is continuously detected and compensated by a piezoelectric stage. In the two-focal imaging part, the fluorescence signal from the QDs is split into two beams with a $3\!:\!7$ intensity ratio, and sent to each half of the EMCCD camera. A lens ($f = 300$ mm) is inserted into the path of the beam with a higher intensity, to produce diffraction rings by shifting the focus. As shown in Fig. 1(b), the in-focused image of QDs from the channel with 30% intensity (left panel) is used for detecting their $x$ and $y$ positions, while the off-focused image from the channel with 70% intensity (right panel) is used for detecting their $z$ positions through the diffraction rings. To determine the 3D trajectories of QDs, we analyzed the images by using a custom-written Matlab algorithm. Firstly, we determined their 2D trajectories from the in-focused images, as usually done before.[3,22] The $x$, $y$ coordinates of the QDs were determined by Gaussian fitting. Next, their $z$ coordinates were determined from the off-focused images according to the outermost radii of the diffraction rings.[23] By selecting three QD spots from an in-focused image and measuring their centers in the corresponding off-focused image, we can determine the transpose matrix between images from the two channels. With the transpose matrix and the $x$, $y$ coordinates of each QD determined from the in-focused images, we could easily define a square region of interest (ROI) containing the diffraction image of that QD in the off-focused images. The ROI is then fitted with the following equation, which is a Gaussian peak surrounded by a ring of radius $r$: $$\begin{alignat}{1} I =\,&c_{0 }\!+\! c_{1}{\exp}[- c_{2}((x\! -\!x_{0})^{2}\!+\! (y\! -\!y_{0})^{2})]\\ & +\! c_{3}{\exp}[- c_{4 }(((x \!-\!x_{0})^{2}\!+\!(y\!-\!y_{0})^{2})^{1/2 }\!-\!r)^{2} ],~~ \tag {1} \end{alignat} $$ where $I$ is intensity matrix of the sub-image (ROI), $x_{0}$ and $y_{0}$ are the ring center coordinates, and $r$ is the ring radius. All diffraction images were checked manually to ensure that the fitting works well. To obtain the calibration between the $z$ position and ring radius, immobilized QDs on coverglass were imaged, while the objective was displaced along the axis in 50 nm steps by a piezoelectric stage (Fig. 1(c), inset). By linearly fitting the piezoelectric stage displacement ($z$) with the corresponding ring radius ($r$), we obtained the calibration between $z$ and $r$ as $z = c + Kr$ with $c =-885.9$ and $K = 207$ nm/pixel (Fig. 1(c)). It should be noted that, compared with the off-focused images, the in-focused images with higher signal-to-noise ratio provide a better determination of $x$, $y$ coordinates. Together, based on the accurate 2D trajectories constructed from the lateral positions of QDs by using the in-focus images, the out-focus images provide the additional axial position and complete the 3D trajectories. To evaluate the localization accuracy of our experimental system, QDs immobilized on coverglass were imaged under the same conditions as that for living cells (i.e., temperature, culture medium, CO$_{2}$ injection). By determining the $x$, $y$, and $z$ coordinates of the QDs from the images, we obtained their 3D trajectories (Fig. 1(d)). The mean square displacements (MSD) of more than 10 immobile QDs indicate that the fluctuation in the axial direction is slightly larger than in the lateral direction (Fig. 1(e)). The localization accuracy was calculated to be around 27 nm in the lateral directions ($x$ and $y$) and 35 nm in the axial direction ($z$), which are comparable to that of super-resolution fluorescence microcopy and 10 times better than that of convention confocal microscopy.[13,18,24] Note that, additionally, our experimental system could provide a better temporal resolution for single fluorescence particles in milliseconds, which is critical for studying intracellular diffusion. Next, we used QDs as the probe to study 3D intracellular diffusion. QDs were internalized in the cytoplasm of cultured A549 cells by the osmotic lysis of pinocytic vesicles,[3,25] as done before (Fig. 2(a)). Compared with our previous 2D SPT experiment,[3] here we decreased the amount of introduced QDs to reduce the overlapping of their diffraction rings. Highly inclined and laminated optical sheet imaging of intracellular QDs was performed with a 561 nm laser for excitation.[3] Continuous videos were acquired at 33 Hz for a total of 2000 frames (1 min), under the condition of serum-free and phenol red-free DMEM at 37 ℃ with 5% CO$_{2}$. Figure 2(a) shows the maximum projection of videos for QDs in an A549 cell. The corresponding 3D trajectories of the QDs are displayed in Fig. 2(b), exhibiting widely dispersed QDs in the 3D intracellular environment. Then we took a close look at one QD trajectory, and applies a local MSD window algorithm to analyze the temporal diffusion rate $D_{\rm temp}$ along the trajectory (Figs. 2(c) and 2(d)). Interestingly, we found that the QD movement in the axial direction is obviously suppressed compared with that in the lateral direction (Fig. 2(d), upper panel), and the temporal diffusion rate $D_{\rm temp}$ also shows great differences between the two directions (Fig. 2(d), lower panel). By totally analyzing 205 trajectories in 10 cells, the averaged MSD results further demonstrated that the axial diffusion is constrained compared with the lateral diffusion in cells. The MSD curve for each QD trajectory was calculated by the equation MSD($\tau$) = |r($t + \tau$)$- r(t)$|$^{2}$, where $r$ is the 3D coordinates and $\tau$ is the time lag. Then we could determine the diffusion rate $D$ by a linear fitting of the first 3 points with MSD$(t)=2dDt+c$, where $d$ is the dimension (1, 2 and 3 for 1D, 2D and 3D, respectively). Moreover, the motion mode of a QD could also be determined, by fitting the MSD with the power law MSD$(t)=At^{\alpha}$, where the exponent indicates the nonlinear relation between MSD and $t$. It is known that $\alpha$ centered around 1 indicates free Brownian motion; $\alpha < 1$ indicates sub-diffusion; $\alpha < 0.5$ indicates confined motion.[3,26–28] The active transport by molecular motors manifests as directed motion and would have an $\alpha$ over 1.5, which was not observed in our QD diffusion experiments. Here, we found that the MSD curves for diffusing QDs in the $x$ and $y$ directions are overlapped (Fig. 2(e)), indicating the lateral diffusion is homogeneous. The lateral diffusion of QDs with $\alpha_{xy} = 0.86$ indicates a sub-diffusive motion, which is consist with previous reports of 2D studies. However, the diffusion of QDs in the $z$ direction has a remarkably smaller exponent ($\alpha_{z} = 0.32$), indicating a confined motion in the axial direction. Note that the averaged MSD curves in the log–log plot have slight deviations from a straight line, because of the heterogeneous environments in different cells in which the QDs diffuse. As shown in Fig. 2(f), the diffusion rate for the axial direction ($D_{z} = 0.031$ µm$^{2}$/s) is five times smaller than that for the lateral direction ($D_{x}=D_{y} = 0.16$ µm$^{2}$/s). These results suggest that the intracellular diffusion in A549 adherent cells prefers to be in the lateral plane, i.e., a quasi-two-dimensional diffusion. That is, with the new capability of observing the axial diffusion by 3D SPT, it is revealed that the 3D intracellular diffusion of QDs is actually anisotropic, rather than isotropic that was generally taken as granted in all previous 2D experiments. By comparing the 2D and 3D dynamical parameters (Figs. 2(e) and 2(f)), it can be seen that both the 3D exponent $\alpha$ and diffusion rate ($\alpha_{xyz} = 0.79$, $D_{xyz} = 0.11$ µm$^{2}$/s) are smaller than the 2D ones ($\alpha_{xy} = 0.86$, $D_{xy} = 0.16$ µm$^{2}$/s). As in an isotropic medium, the 2D and 3D diffusion rates are identical,[16,29] the above differences imply that 2D SPT experiments may overestimate the diffusion rates in the 3D intracellular environment in adherent cells.
cpl-37-7-078701-fig2.png
Fig. 2. 3D tracking of QDs in A549 cells and dynamical analysis of their trajectories. (a) Bright-field image of an A549 cell (left panel) and superimposed fluorescence images of QDs in that cell (right panel). Scale bar, 10 µm. (b) 3D plot of all the trajectories longer than 50 frames in the cell. (c) A typical trajectory indicated by the red box in (a). (d) Temporal positions, and temporal diffusion rates of the single QD along its trajectory in the $x$, $y$ and $z$ directions. (e) Comparison of MSD plots for all trajectories in one dimension ($x$, $y$ and $z$), 2D ($xy$), and 3D ($xyz$). Error bars indicate the SEM. (f) Distributions of the diffusion rates in one dimension ($x$, $y$ and $z$), 2D ($xy$), and 3D ($xyz$).
Next, we investigated the roles of cytoarchitecture in the quasi-two-dimensional diffusion observed above. We firstly studied the influence of cytoskeletons. Microtubules and actin filaments are two major components of cytoskeleton that are distributed within cells. They are also reported to impose influences on the diffusive movements of micron-scale beads or vesicles.[1,2,10,29] We treated the cells with nocodazole to depolymerize microtubules, and with latrunculin A to inhibit the actin polymerization and destroy actin filaments. Obvious change in MSD curves of intracellular QD diffusion is observed in both lateral and axial directions (Fig. 3(a) and Fig. S1 in Supplementary Materials). The diffusion rates without microtubules ($D_{xy} = 0.13$ µm$^{2}$/s, $D_{xy} = 0.028$ µm$^{2}$/s) or actin filaments ($D_{xy} = 0.16$ µm$^{2}$/s, $D_{xy} = 0.031$ µm$^{2}$/s) are similar to the normal cells (Fig. 3(b)). These observations suggest that these cytoskeletons are not involved in the 3D diffusion of QDs in cells. ER is a continuous membrane system containing tubule network across the cell cytoplasm. Our past study by 2D SPT has demonstrated that ER tubules act as physical barriers slowing down the QD diffusion rate.[3] To examine the influence of ER on quasi-two-dimensional diffusion, we treated the cells with ionomycin, a calcium carrier, to fragment and eliminate the ER networks (Fig. S2). We found both the lateral and axial diffusions are remarkably increased by about three times ($D_{xy} = 0.45$ µm$^{2}$/s, $D_{z} = 0.11$ µm$^{2}$/s), suggesting that ER not only plays a role in regulating the lateral diffusion of QDs as we found before, but also impacts the axial diffusion.
cpl-37-7-078701-fig3.png
Fig. 3. Dynamical analysis of diffusing QDs in cells under different treatments. Averaged MSD curves (a) and diffusion rates (b) of QDs in control cells (Ctrl, 205 trajectories in 10 cells), nocodazole-treated cells (Noc, 145 trajectories in 7 cells), latrunculin A-treated cells (LatA, 194 trajectories in 5 cells), and ionomycin-treated cells (Ion, 31 trajectories in 4 cells). Error bars indicate the SEM.
cpl-37-7-078701-fig4.png
Fig. 4. Density map for diffusion rates in $D_{xy}$ and $D_{z}$ plane (a), and for the exponents $\alpha$ in $\alpha_{xy}$ and $\alpha_{z}$ plane (b) of diffusing QDs in cells under different conditions. The colors represent the normalized local density of trajectories between 0 (blue) and 1 (red). The sample sizes are the same as those in Fig. 3.
To further investigate the diffusion behaviors of QDs under different conditions, the distributions of the diffusion rates $D_{xy}$ and $D_{z}$ are presented in density maps (Fig. 4(a)). The density maps for the control, microtubule- and actin-disrupted cells are similar, with a symmetric distribution centered at one peak around $D_{xy} =0.15$ µm$^{2}$/s and $D_{z} = 0.01$ µm$^{2}$/s. For the ER-disrupted cells, however, the distribution is elongated and moves towards the upper right corner, with a major population peaking at $D_{xy} = 0.75$ µm$^{2}$/s and $D_{z} = 0.5$ µm$^{2}$/s. This obvious increase of diffusion rates for QDs in ER-disrupted cells is consist with our previous study. In the density maps of $\alpha_{xy}$ and $\alpha_{z}$, more information on the motion types of QDs is revealed (Fig. 4(b)). Under the first three conditions, there are two subpopulations with a dominant one peaking at $\alpha_{xy} = 0.95$ and a minor one peaking at $\alpha_{z} = 0.5$. The former represents the sub-diffusive QDs, whereas the latter represents the confined QDs. However, for ER-disputed cells, the major distribution peaking at $\alpha_{xy} = 0.95$ shifts upward, from $\alpha_{z} = 0.2$ to 0.5. It suggests that the confinement of QD diffusion in the axial direction is slightly relieved after the ER structures are removed. Even so, the axial diffusion is still obviously constrained, whereas the lateral diffusion remains subdiffusive. Together, these results indicate that ER decreases the intracellular diffusion rates of QDs, but it has limited impact on their overall diffusion modes in both lateral and axial directions. One might easily think that the above-mentioned quasi-2D intracellular diffusion that is constrained in the axial direction is actually the diffusion of QDs on cell membranes rather than inside the cells, but there are three factors which can exclude this possibility. Firstly, we used the method of osmotic lysis of pinocytic vesicles to load QDs into cells, which is a standard way to deliver QDs and other nanoparticles.[25,30] And the lateral diffusion of the QDs is consistent with previous studies of intracellular diffusion.[3] Secondly, it was reported that the on-membrane diffusion dynamics is slowed by the actin filaments beneath membranes.[31] Here the QD diffusion remains the same in actin-disrupted cells. Besides, we found that the axial diffusion range of QDs within one second is about 170 nm in control, as well as in microtubule- and actin-disrupted cells, whereas it expands to 340 nm in ER-disrupted cells (square roots of MSD values at 1 second, Fig. 3(a)). The range of axial diffusion is affected by the ER structures located in cytoplasm. Thirdly, we added the PEG to the cell culture medium and compressed the cell volume by increasing osmotic pressure. The QD diffusion rate was found to be decreased due to the increased intracellular macromolecule crowding (Fig. S3). Together, these results demonstrate that the QD diffusion takes place inside the cells and the constrained lateral motion is attributed to the intracellular environment. In summary, we have built a 3D SPT setup achieving 25-nm precision in the $x$ and $y$ directions and 35-nm precision in the $z$ direction in living cells, and studied the 3D diffusion of single QDs in living adherent cells. For the first time, an intracellular quasi-2D diffusion was discovered, in which the axial motion is strikingly constrained. Further, we carefully explored the roles of cytoarchitecture in the quasi-2D diffusion, and found that ER reduces the diffusion rates of QDs in cells. However, no obvious difference in the modes of axially confined diffusion was observed after eliminating the microtubules, actin filaments, or ER. The quasi-2D diffusion in the lateral direction is likely to be an intrinsic feature of adherent cells. The physics underlying this quasi-2D diffusion may be attributed to the entire cytoarchitecture of adherent cells.[1,2,29] It is well-known that the shape of adherent cells is inherently anisotropic like a fried egg. In our case, A549 cells spread generally over an area of 50 µm in diameter but the height at the periphery is less than 3 µm (Fig. S4). Note that the cell height could not result in the constraint in axial diffusion, as the height is actually ten times larger than the axial diffusion range of QDs. From the quasi-2D diffusion behaviors, it is inferred that planar structures exist in the cytoplasm, which provides a platform for rapid and efficient transport of molecules by diffusion in cells. Our supposition is supported by the cell images from scanning electron microscopy and super resolution fluorescence microscopy showing that layers of organelles and cytoskeletons stack up and laterally distribute in the cytoplasm.[14,15] The QDs are apt to diffuse laterally along these intracellular structures whereas their axial diffusion is blocked by layers of intracellular structures. Further studies are required to directly explore the relationship between the quasi-2D diffusion and the cytoarchitectures through the combination of the 3D SPT with dynamical subcellular imaging. Many bio-macromolecules with sizes comparable to QDs are diffusing in the cytoplasm for distinct functions, such as mRNA and actin oligomers.[9,11,24] The quasi-2D diffusion with constrained axial movements effectively promotes the translocation and shortens the searching time of these molecules in cells. A typical example is that the lamellipodia of keratocytes with only 200-nm thickness yields extremely rapid intracellular flow in 2D, enhancing the transport of actin monomers from the rear to leading edges during cell migration.[32] Our finding suggests that cells may utilize the cytoarchitecture to control the intracellular diffusion dynamics and regulate macromolecule transport. 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