Nanoscale

PAPER

Cite this: DOI: 10.1039/c7nr09483c

Received 20th December 2017,Accepted 31st January 2018

DOI: 10.1039/c7nr09483c

rsc.li/nanoscale

Tracking fast cellular membrane dynamics withsub-nm accuracy in the normal direction†

Hui Yu, *a Yuting Yang,a Yunze Yang,b Fenni Zhang,b Shaopeng Wangb andNongjian Tao*b,c

Cellular membranes are important biomaterials with highly dynamic structures. Membrane dynamics

plays an important role in numerous cellular processes, but precise tracking it is challenging due to the

lack of tools with a highly sensitive and fast detection capability. Here we demonstrate a broad bandwidth

optical imaging technique to measure cellular membrane displacements in the normal direction at sub-

nm level detection limits and 20 µs temporal resolution (1 Hz–50 kHz). This capability allows us to study

the intrinsic cellular membrane dynamics over a broad temporal and spatial spectrum. We measured the

nanometer-scale stochastic fluctuations of the plasma membrane of HEK-293 cells, and found them to

be highly dependent on the cytoskeletal structure of the cells. By analyzing the fluctuations, we further

determine the mechanical properties of the cellular membranes. We anticipate that the method will con-

tribute to the understanding of the basic cellular processes, and applications, such as mechanical pheno-

typing of cells at the single-cell level.

Introduction

Cellular membranes exhibit various function-related shapesthat are highly dynamic, fluctuating over a broad range oftimescales.1,2 Membrane fluctuations are small in amplitude(nanometers), but play an essential role in many cellular pro-cesses, including cell migration, adhesion, differentiation anddevelopment.3–6 Changes in cellular membrane dynamics mayserve as disease markers.7–10 For a living cell, the membranefluctuations are expected to be inherent to many membraneprocesses, such as ion pumps, vesicle budding and traffickingprocesses.11–13 Understanding the nature of active fluctuationsin cellular membranes and their modulation during the lifecycle of a cell will advance our knowledge on the mechanismof membrane processes.

Optical imaging is most suitable for detecting the cellularmembrane fluctuations, as a non-invasive, accurate and fastmeasurement technique. Several optical imaging techniqueshave been developed,14 including flickering spectroscopy,15–17

diffraction phase microscopy,18 reflection interference contrast

microscopy (RICM),19–21 and weak optical tweezers.22–25

Limited by the optical imaging capability with the sensitivityof a few nanometers and a time resolution of several milli-seconds, these techniques have mostly been applied in theexperimental quantification of membrane fluctuations ongiant unilamellar vesicles (GUVs)17 and red blood cells(RBCs).26,27 Quantifying membrane fluctuations at higher fre-quencies and smaller amplitude will help resolve membranedynamics of GUVs and RBCs at time and length scales notpossible previously,28–31 and enable the study of plasma mem-branes of stiff eukaryote cells associated with membrane pro-teins, membrane-to-cortex attachments (MCA), and the cyto-skeletal structures.32

Many efforts have been devoted to expand the bandwidth ofdifferent tracking technologies. Dynamic optical displacementspectroscopy (DODS) based on fluorescence correlation spec-troscopy (FCS) is capable of resolving the cellular membranefluctuations of GUV, RBC and macrophages at 10 μs, but thiswas achieved at the expense of the displacement detectionlimit (∼20 nm).29,30 Recent advances of the optical and mag-netic tweezers have been developed for high-bandwidthmeasurements, leading to an impressive shot-noise-limiteddisplacement sensitivity of 3 fm Hz−0.5 at high frequencies ofup to 50 MHz for tracking the micrometer-size dielectricmicrospheres.33,34 By removing the common low frequencysystem noise with a reference particle, dual optical traps35 andhigh speed camera-based magnetic tweezers36,37 have allowedångström resolution for low frequency tracking of the locationof a microsphere. However, the cellular membranes are

†Electronic supplementary information (ESI) available: Noise analysis and ahydrodynamic model. See DOI: 10.1039/c7nr09483c

aInstitute for Personalized Medicine, School of Biomedical Engineering, Shanghai

Jiao Tong University, Shanghai 200030, China. E-mail: hui.yu@sjtu.edu.cnbBiodesign Center for Bioelectronics and Biosensors, Arizona State University, Tempe,

AZ 85287, USA. E-mail: njtao@asu.educState Key Laboratory of Analytical Chemistry for Life Science, School of Chemistry

and Chemical Engineering, Nanjing University, Nanjing 210093, China

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different from dielectric microspheres in size, shape, dielectricconstants, and dynamics, and are also prone to light induceddamage, especially under the illumination of strong infraredlight. A technology that can track small and fast cellular mem-brane dynamics is still challenging.

Here we describe an optical imaging method to measurefast cellular membrane fluctuations in the normal direction.The method uses a two-point differential detection algorithmto reduce the system common noise at slow timescales, andoptimizes photon counts to minimize shot noise at fast time-scales, which allows us to achieve the sub-nm level detectionlimit over a wide frequency or time window (five orders of mag-nitude, from ∼20 µs to s). We first validate the system noiselevel with fixed microspheres, and then study the spontaneousmembrane fluctuations of live HEK 293 cells at nanometerscales, perform spectral analysis of the fluctuations, andcompare the data with a simplified hydrodynamic model. Theeffects of a cytoskeletal structure on the membrane fluctu-ations are shown with the cells under cytochalasin D (C-D) orparaformaldehyde (PFA) treatments.

Results and discussionOptical detection scheme

To image and track cellular membrane fluctuations, we built amechanically stable optical imaging system (Fig. 1) equippedwith a high numerical aperture objective (100×, NA = 1.3) anda fast CMOS camera (100 000 frames per second (fps)).Because optical imaging at fast timescales (high frequencies)is limited by shot noise related to the finite number ofphotons detected by each pixel of the camera,33,34 we used a5 mW red (637 nm) laser, instead of a lamp used in the con-ventional optical microscope or an infrared laser in opticaltweezers, to illuminate the cell for direct visualization of thecellular image. The laser was collimated and refocused,

spreading over a relatively large area (∼7 µm2), so that the lightintensity was comparable to the weak optical tweezer experi-ments,23,24,33,34 and did not lead to any visible effect on thecell.

To further reduce shot noise, we placed a zoom lens (1–20×)in front of the camera, which, together with the imaging objec-tive, provided a total amplification between 100–2000×. Thehigh amplification rate did not change the light intensity onthe cell, but it allowed a given region of interest (ROI) on thecell to be imaged with an increased number of pixels. Becausethe maximum photon number detected by each pixel is funda-mentally limited by the full well capacity, the increasednumber of pixels resulted in more photons detected by thecamera for a given ROI, and thus helped reduce the total shotnoise. The insets in the dashed area showed a typical mem-brane image recorded at 2000× (field of view (FOV): 1.28 µm ×1.28 µm), by zooming in on a single HEK-293 cell imagerecorded at 240× (FOV: 10.7 µm × 10.7 µm) with the setup. Thecellular membrane can be clearly resolved in both images.

Characterizing the system noise

We tested the performance of the optical imaging system bytracking the position of a 1 µm polystyrene bead (insets inFig. 2) at a 2000× amplification rate. Because the bead wasfixed on a glass slide (see Materials and methods), themeasured displacement reflected the noise of the opticalimaging system. We used a detection algorithm38,39 analogousto the approach of weak optical tweezers,22,23,25 to measure thesample displacement in the normal direction (Fig. S1, ESI†).The blue curve in Fig. 2a showed a typical 1 s-displacementprofile of the bead in the horizontal direction, with a root-mean-square (rms) fluctuation amplitude of ∼6.1 nm. Thecorresponding power spectrum density (PSD) profile (averagedfrom six 1 s displacement profiles) is shown as the blue curvein Fig. 2b.

At slow timescales (lower frequencies than 1000 Hz),various types of system noise dominated, including the lightsource, mechanical vibration, temperature instability, andambient sound. To overcome this limitation, a typical methodis to include another bead as a reference, and calculate thedifference between the displacement profiles of the two beads.However, under 2000× imaging conditions and for cellularmembrane measurements, introducing another microbead asa reference is not practical. Instead, here we minimized thenoise by splitting the particle image into two separate sub-images, each containing the image of a half-bead, and calcu-lating the difference between displacement profiles of the twohalf-beads (ESI†), shown as the red curve in Fig. 2a. This differ-ential measurement strategy reduced the rms fluctuationamplitude to ∼0.5 nm, and the corresponding PSD profile (redcurve in Fig. 2b) clearly indicated the effective suppression oflow frequency common noise. Meanwhile, at fast timescales(higher frequencies than 1000 Hz), shot noise dominated, andboth measurements resulted in similar PSDs. We further veri-fied the shot noise limited performance at high frequencies by

Fig. 1 Schematic illustration of the optical setup for tracking membranefluctuations. The key components include the zoom lens, and a fastCMOS camera to record fast cellular membrane dynamics.

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systematically changing the illumination intensity (Fig. S2†)and binning adjacent pixels within a given ROI (Fig. S3†).

To further understand the system noise, we calculated thecorresponding Allan deviation from the displacement profiles,which is a measure for the tracking error when smoothing theparticle displacement trajectory over a given timescale(Fig. 2c).36,37,40,41 With the differential measurement, for small

time τ (10 µs–100 µs), the Allan deviation decreases with τ(−1/2),again confirming uncorrelated shot noise. A minimum noiseof 0.07–0.08 nm is achieved at 0.2 ms. A stable noise of0.1–0.2 nm is achieved between 1 ms and 100 ms. Althoughthe noise level for the timescale over 1 ms is not as good asthat of the state-of-the-art camera-based system reported,36,37

we note that the reported system used a 3 µm bead for cali-bration, which greatly increased the positioning sensitivity asscattered light scales with the cubic power of a bead size.Meanwhile, for timescales shorter than 0.5 ms, the noise levelin our system is clearly much lower, due to the improvementin the shot noise level as described above. Therefore, oursystem enables measurements of displacements in both fastand slow timescales with an extremely high accuracy.

Tracking spontaneous membrane fluctuations of HEK 293cells

After the establishment of a high accuracy optical system, wemeasured the spontaneous membrane fluctuations of theHuman Embryonic Kidney (HEK)-293 cell line. The cells werecultured on a glass coverslip, and incubated for 30 minutes toallow the cells to be anchored to the glass coverslip prior tothe measurement. We first imaged a whole HEK 293 cell witha relatively low magnification (240×) to identify a region of thecell membrane (Fig. 1, insets), and then zoomed in on theregion with a higher magnification (2000×) (Fig. 1, insets), andrecorded the images of the membrane region at 100 000 fps.The membrane fluctuations of the HEK 293 cell detected at asingle membrane area were overwhelmed by the system noise(Fig. S5†) at slow timescales. Thus, similar to the differentialmeasurement strategy for microbeads, we determined the dis-placement difference between two adjacent membrane areas(550 nm long) (Fig. 3b, insets).

Fig. 3a (red curve) shows a typical 1 s long membrane fluc-tuation profile, which reveals large fluctuations compared tothe time trace of the system noise (Fig. 2a, red curve). The rmsmembrane fluctuation amplitude of the HEK 293 cells wasfound to be 2.2 ± 0.5 nm (mean ± SD, N = 10 cells). This fluctu-ation amplitude is one order of magnitude smaller than themembrane flickering amplitude (>20 nm) of RBCs reported inthe literature,15,16,23 which is thus difficult to measure by thetraditional flickering spectroscopic analysis. The PSD profile isplotted in Fig. 3b (red curve), showing a continuous decreasefrom 1 Hz to 50 kHz without a shot noise dominated region.In the Allan deviation, the fluctuations are relatively stablebetween 0.3–0.6 nm for the timescale from 10 µs to 100 ms,which is well above the system noise level.

Effect of actin cytoskeleton on membrane fluctuations

Membrane fluctuations depend on the cell mechanical pro-perties, which are largely determined by the actin cytoskeletonstructure of the cell. HEK 293 has much smaller membranefluctuations than RBCs, reflecting the difference in their cyto-skeletal structures. To examine the effect of the cytoskeletonon the membrane fluctuations of HEK 293, we modified theactin filament structure of HEK 293 by cytochalasin D (C-D)

Fig. 2 System noise characterization with 1 µm polystyrene beads. Realtime signal (a), power spectrum density (b), and Allan deviation (c) of thedisplacement profiles of a bead attached to the glass surface, as calcu-lated by displacement of the whole bead (blue curves) shown in thedashed blue box, or difference between displacements of the twohalves of a bead (red curves) shown in the dashed red box.

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and paraformaldehyde (PFA) treatment. Cytochalasin D is aninhibitor of actin polymerization, and it induces the depoly-merization of actin filaments,42 while PFA causes covalentcross-linking between protein molecules and anchors proteinsto the cytoskeleton.43

Typical time traces of the HEK 293 membrane fluctuationsafter cytochalasin D (blue curve) and PFA (black curve) treat-ment are shown in Fig. 3a. The PFA treatment reduces themembrane fluctuations of the HEK 293 cells to 0.9 ± 0.3 nm(mean ± SD, N = 10 cells), close to the system background

noise level. This is also reflected in the PSD (Fig. 3b) and Allandeviation (Fig. 3c) of the membrane fluctuations of the PFAtreated cells, both showing identical features to that of thesystem noise profiles (Fig. 2). We attribute the drastic decreasein the membrane fluctuations by the PFA treatment to thecrosslinking between actin cytoskeleton and the cellular mem-brane, which led to a large increase in the rigidity of the cellu-lar membrane. In sharp contrast, treatment of the HEK 293cells with cytochalasin D led to an increase in the membranefluctuations to 4.9 ± 0.9 nm (mean ± SD, N = 10 cells) (Fig. 3a–c). The observed increase in the membrane fluctuations indi-cates that actin depolymerization softens the membrane byinhibiting the interaction between actin filaments and the cellmembrane, which is consistent with the report in theliterature.44

Determining the mechanical properties of HEK 293 cells

Membrane fluctuation profiles contain rich information aboutthe cellular membrane processes and properties. For example,the mechanical properties of GUV or RBC membranes can bedetermined from time resolved membrane fluctuation profilesusing a hydrodynamic model.24 The high accuracy tracking ofmembrane fluctuations of HEK 293 cells provides the possi-bility to determine mechanical properties of the cellular mem-brane. We modified the hydrodynamic model into a differen-tial form to fit our differential measurement profiles of themembrane fluctuation (eqn S11, ESI†). We note that the hydro-dynamic model assumes thermal equilibrium and a simplifiedcytoskeleton structure, so the analysis provides only a quanti-tative comparison of HEK 293 cells with membranes modifiedwith different chemical treatments, comparison of HEK 293cells with RBCs and macrophages analyzed with similarmodels (Fig. 4).

We fitted the PSD profiles of membrane fluctuation withthe model to extract mechanical properties including bending

Fig. 3 Spontaneous membrane fluctuation dynamics of HEK 293 cellsupon different treatments on cellular cytoskeleton structures. Typicaltime traces (a), PSDs (b) and Allan deviation (c) of membrane fluctuationswithout (red curves), with cytochalasin D (blue curves), and paraformal-dehyde (PFA) (black curves) treatment. The insets in (b) show the differ-ential measurement scheme.

Fig. 4 Mechanical properties of HEK 293 cells determined from themembrane fluctuation profiles. Bending modulus κ (a), surface tension σ

(b) and effective viscosity of cell cytoplasm η (c) of HEK 293 cell mem-brane (mean ± SD, N = 10 cells). Significance levels, P, were evaluated bythe t-test with P < 0.001 (**), and P < 0.05 (*). Error bars denote standarddeviations.

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modulus κ, surface tension σ and effective viscosity of cell cyto-plasm η (see Materials and methods). For normal HEK 293cells, we found that κ = 28.6 ± 13.3 × 10−18 J (∼8000 kBT ), σ =4.8 ± 1.1 × 10−5 N m−1, and η = 0.36 ± 0.21 Pa s. This κ isseveral times larger than those of macrophages20,45 anddictyostelium46 measured at adherent states (∼1000kBT ). A pre-vious AFM study44 reported that HEK-293 cells in suspendedstates were 4–5 fold stiffer than those in adherent states, andattribute the observation to the actin cytoskeleton structure.For C-D treated cells, we determined that κ = 3.8 ± 2.6 × 10−18 J(∼1000 kBT ), σ = 6.7 ± 1.5 × 10−6 N m−1, and η = 0.12 ± 0.06 Pa s.Both κ and σ of the C-D treated cells are nearly an order ofmagnitude smaller than those of the untreated HEK 293 cells.This finding is in good agreement with those reported in theliterature.44,47 The η was found to vary over a wide range from0.001–1000 Pa s for different cells,45,48,49 depending on thetechnique used. In the present case, we found that η of HEK293 cells is ∼10 times larger than that of the RBCs measuredby the weak optical tweezer technique.23 We attribute the largeeffective viscosity to a confinement effect by stronger associ-ation of the complex actin cytoskeleton with the membrane inHEK 293 cells than the spectrin in RBCs.50 Upon C-D treat-ment, the η decreased. These findings correspond well to theAFM study47 and the poroelastic model.51

The statistical significance of the mechanical parametersdetermined above was evaluated by a two sample t-test,showing a high confidence level for κ (P < 0.001), and relativelylow for σ and η (P < 0.05). The data in the present work wereanalysed by assuming thermal equilibrium. A recent studyshows that the thermal equilibrium assumption for live RBCbreaks down at low frequencies, but still holds at high frequen-cies.28 Because σ dominates PSD at low frequencies, while κ

dominates PSD at high frequencies,24 we may expect a lessreliable determination of σ with the equilibrium thermo-dynamics analysis.

Frequency-scaling relation

The optical detection method presented here allows the studyof cell membrane fluctuations over a wide frequency range(1 Hz to 50 kHz), which may reveal unknown mechanismsassociated with the membrane processes. We examinedfrequency-scaling relations predicted by the hydrodynamictheory (Fig. 5). For a free membrane, the theory predicts thatPSD ∝ f−5/3 at high frequencies23,24 (ESI†). However, for amembrane confined by a rigid wall,11,27 the predicted scalingof PSD with frequency is PSD ∝ f−4/3. In the present case, weobserved that at high frequencies, the PSD follows a frequencyscaling relation of ∝ f−n, with n = 1.35 ± 0.06 for normal HEK293 cells, which agrees with that for a membrane confined bya rigid wall. The PSD for C-D treated cells also follows ascaling relation in the PSD, with n = 1.64 ± 0.07, close tothat for a free membrane. These observations are consistentwith the fact that the membrane fluctuations are confined bythe cytoskeleton in the untreated normal HEK 293, and theyare less confined by the cytoskeleton after cytochalasin Dtreatment.

Conclusions

We have developed an optical imaging method to track cellularmembrane fluctuations with sub-nm level detection limits in thenormal direction over a broad time window (20 μs to s). The newdetection capability makes it possible for us to study the smallspontaneous fluctuations of a rigid cellular membrane, adifficult task by previous methods. We have measured the mem-brane fluctuations of HEK 293 cells, and found that the fluctu-ations are highly dependent on the cytoskeleton structure underdifferent chemical treatments. Using a modified hydrodynamicmodel, we determined the mechanical properties of HEK 293cells from the time-resolved membrane fluctuations, whichcorrespond well to the theory and reported values. The broad fre-quency range and high accuracy of the optical detection methodalso enable the study of the frequency scaling relation of themembrane fluctuations. We anticipate that the optical detectionmethod can be applied to study membrane protein activitiesand other processes taking place on cell membranes.52–55

Materials and methodsSample preparation

Dulbecco’s modified Eagle’s medium (DMEM), cytochalasin D,and PFA were purchased from Invitrogen (Carlsbad, CA, USA).PBS and fetal bovine serum (FBS) were purchased from Gibco(Grand Island, NY, USA). Human Embryonic Kidney cells 293(HEK-293) were purchased from ATCC (ATCC® CRL-1573™,Manassas, VA, USA).

Glass coverslips were rinsed twice with deionized water, fol-lowed by ethanol, prior to cell culture. For system noise cali-bration, 1 µm polystyrene particles (Nanocs, Boston, USA) werediluted in PBS at 1 : 10 000. A 10 µL droplet of the particle solu-tion was deposited on a clean glass coverslip, and dried in anoven at 50 °C overnight. The coverslip with particles wasrinsed with deionized water before observation to remove un-attached particles.

Fig. 5 Frequency-scaling relation of HEK 293 cellular membranefluctuation of PSD with/without cytochalasin-D treatment. The scalingof f−4/3 refers to a membrane confined by a rigid wall, while that of f−5/3

refers to a free membrane.

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The cells were recovered from cryopreservation and seededon a cleaned glass coverslip at ∼105 cells per cm2. Cell experi-ments were divided into three groups, a control group(untreated), a group treated with cytochalasin D, and a grouptreated with PFA. For the control group, HEK 293 cells wereincubated in DMEM with 10% FBS for 30 minutes. For the cyto-chalasin D-treated group, the HEK 293 cells were incubated inDMEM with 10% FBS and 5 µM cytochalasin D, for 30 minutes.Finally, for the PFA-treated group, the HEK 293 cells were firstincubated in DMEM with 10% FBS for 30 minutes. Then themedium was replaced with 4% PFA in PBS and incubated for15 minutes. Prior to imaging, the sample was first rinsed gentlywith PBS to remove the floating cells in the medium, and thenthe cellular membrane fluctuations were recorded in a live cellimaging solution (Thermal Fisher, MA, USA).

Data acquisition and analysis

The measurements were carried out with a home-built inverseoptical microscope with a fiber pigtailed laser (λ = 637 nm,OBIS 637 LX, Coherence) and a fast CMOS camera (V310,Vision Research). Incident light was collimated by using a con-denser, and focused at the sample plane by using a super longworking distance objective (50×, NA = 0.42, Mitutoyo). Cellsamples were cultured on a clean glass coverslip and mountedon a motorized sample stage. A homemade chamber filledwith a live cell imaging solution (Thermal Fisher, MA, USA)was sealed with another clean coverslip to keep the fluid stableduring image recording. Scattered light by samples andunscattered transmitted light were collected by using an oilimmersion objective (100×, NA = 1.3, Nikon) for high-resolu-tion imaging. The camera was operated at 100 000 fps with 128× 128 pixels (exposure time = 9.2 µs). Two adjacent regions ofinterest (ROI) were chosen along the cell membrane, each with55 × 110 pixels, and the membrane displacement in each ROIwas then determined using the differential algorithm.

For cellular experiments, the membrane fluctuations at eachlocation were continuously recorded for 6 s, and repeated 3times. For each cell, the fluctuation profiles were acquired atfour or more different locations on the membrane. For consist-ency, only cells with a radius between 6–8 µm were selected formeasurements and statistical analysis. For hydrodynamic modelfitting, the PSD was first smoothed by binning the data logar-ithmically into 10-data point per decade, and then fitted by aminimal norm least squares method performed in MATLAB.

Conflicts of interest

There are no conflicts to declare.

Acknowledgements

We thank Prof. T. C. Li for helpful discussions, and theNational Natural Science Foundation of China (#2137008 and#2137902), the Gordon and Betty Moore Foundation (#3388),

and National Institute of Health (#1R01GM124335-01) forfinancial support.

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