ISSN 1998-0124 CN 11-5974/O4

2019, 12(1): 000–000 https://doi.org/10.1007/s12274-021-3357-4

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Quantifying 3D cell–matrix interactions during mitosis and theeffect of anticancer drugs on the interactions

Yongman Liu1,§, Jianye Wang2,3,§, Yong Su1, Xiaohai Xu1, Hong Liu4, Kainan Mei1, Shihai Lan1, Shubo Zhang1,

Xiaoping Wu1, Yunxia Cao2,3 (), Qingchuan Zhang1 (), and Shangquan Wu1 ()

1 CAS Key Laboratory of Mechanical Behavior and Design of Material, Department of Modern Mechanics, CAS Center for Excellence in

Complex System Mechanics, University of Science and Technology of China, Hefei 230027, China 2 Reproductive Medicine Center, Department of Obstetrics and Gynecology, The First Affiliated Hospital of Anhui Medical University, Hefei

230022, China 3 Anhui Province Key Laboratory of Reproductive Health and Genetics, Anhui Medical University, Hefei 230022, China 4 Department of Chemical Physics, University of Science and Technology of China, Hefei 230026, China § Yongman Liu and Jianye Wang contributed equally to this work.

© Tsinghua University Press and Springer-Verlag GmbH Germany, part of Springer Nature 2021

Received: 5 November 2020 / Revised: 20 January 2021 / Accepted: 21 January 2021

ABSTRACT

The mechanical force between cells and the extracellular microenvironment is crucial to many physiological processes such as

cancer metastasis and stem cell differentiation. Mitosis plays an essential role in all these processes and thus an in-depth

understanding of forces during mitosis gains insight into disease diagnosis and disease treatment. Here, we develop a traction

force microscope method based on monolayer fluorescent beads for measuring the weak traction force (tens of Pa) of mitotic cells

in three dimensions. We quantify traction forces of human ovarian granulosa (KGN) cells exerted on the extracellular matrix

throughout the entire cell cycle in three dimensions. Our measurements reveal how forces vary during the cell cycle, especially

during cell division. Furthermore, we study the effect of paclitaxel (PTX) and nocodazole (NDZ) on mitotic KGN cells through the

measurement of traction forces. Our results show that mitotic cells with high concentrations of PTX exert a larger force than those

with high concentrations of NDZ, which proved to be caused by changes in the structure and number of microtubules. These

findings reveal the key functions of microtubule in generating traction forces during cell mitosis and explain how dividing cells

regulate themselves in response to anti-mitosis drugs. This work provides a powerful tool for investigating cell–matrix interactions

during mitosis and may offer a potential way to new therapies for cancer.

KEYWORDS

cell division, traction force, paclitaxel, nocodazole

1 Introduction

Cancer has a high mortality rate because of cancer cell’s uncontrolled and relentless division and has become a leading cause of death worldwide. An increase in mitosis increases cancer risk, especially for endometrium and ovary cancer [1]. To find more effective treatments for cancer, studying cancer cell division is clearly of great importance. The mechanical forces between cells and their surroundings play a vital role in controlling cell structure and functions [2–6]. Cancer formation, cell proliferation, and stem cell differentiation are regulated by mechanical forces [5, 6]. Mitosis is involved and plays a significant role in all the processes above. Therefore, a more comprehensive understanding of the force of the mitotic cell potentially yields insights into mechanical mechanisms during cell division, as well as informs the development of new anticancer drugs to disrupt cancer cell’s mitosis. Anticancer drugs, such as paclitaxel (PTX) and nocodazole (NDZ), are potent inhibitors of cell proliferation and are commonly used in clinical cancer treatment. However, the mechanical mechanism how mitotic cells interact with the extracellular

microenvironment (ECM) when they are treated with anticancer drugs remains unclear.

Various methods have been developed to study cell forces: deformable substrates [7], laser tweezers [8], atomic force microscopy [9], and pillar devices [10]. Traction force microscopy (TFM) [11], one of the most common methods, is widely used in fields of cell mechanics and biology [12–15]. Typical TFM uses flexible biocompatible substrate with fluorescent beads to track deformations generated by cells. Traction forces of migrating cells, both in two dimensions and three dimensions, have been well studied [4–8, 10–16]. However, studies on traction forces of the mitotic cell remain rare and the three- dimensional (3D) mitotic cell force remain unclear. Several works have measured two-dimensional (2D) traction forces during interphase [17–19]. Some researchers measured 2D traction forces of the dividing Dictyostelium cells [20, 21]. While these studies provide insight into cell division, they remain inherently limited to two dimensions. Using typical 3D TFM by embedding cells and beads in fibrous matrices, Lesman et al. measured one moment of mitotic cell force rather than the whole cell division process [22]. However, the detailed

Address correspondence to Shangquan Wu, wushq@ustc.edu.cn; Qingchuan Zhang, zhangqc@ustc.edu.cn; Yunxia Cao, caoyunxia6@126.com

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traction forces in three dimensions for the whole mitosis process with high spatiotemporal resolution is still unclear, and how mitotic cells interact with the ECM in three dimensions remains unknown. As mapping 3D traction forces for mitotic cells has been challenging, current studies on cell division are restricted to 2D interactions of cells and the ECM. However, cells exert forces in three dimensions in a native environment and the out-of-plane (normal) force plays an important role in investigations on cell behavior and mechanotransduction [23, 24]. Thus, a convenient and sensitive method for investigation on 3D traction forces during mitosis is highly sought.

Here, we develop a method to study traction forces of the mitotic cell. We use monolayer fluorescent beads to track the deformation of the substrate and develop an IC-GN2 (the inverse compositional Gauss–Newton algorithm combined with second-order shape function) algorithm for high-resolution deformation fields. The method is capable of acquiring 3D stacks rapidly and enables us to calculate the weak force exerted by dividing cells. Herein, we investigate the 3D traction stress map during a single cancer cell division and study the effect of two anti-mitosis drugs, PTX, and NDZ, on cancer cell mitosis, which may inspire strategies for cancer treatment. Our results reveal the mechanism of force generation during mitosis.

2 Experimental

2.1 Materials and reagents

3-Aminopropyltrimethoxysilane (APTES) and N-hydroxysuc-cinimide (NHS) were purchased from Sigma-Aldrich (St. Louis, MO, USA). Glass-bottom culture dishes were from Nest Biotechnology Co. Ltd. (Wuxi, China). Phosphate-buffered saline (PBS; 0.1 M phosphate buffer containing 0.9% sodium chloride, pH 7.5) and N-(3-dimethylaminopropyl)-N’-ethylcarbodiimide hydrochloride (EDC) were provided by Sangon Biotech Co. Ltd. (Shanghai, China). Carboxylate-modified green fluorescent beads (0.49 m in diameter, 505/515 nm, F-8813, Molecular Probe) were obtained from Life Technologies (USA). Rat- tail tendon collagen type I was purchased from Shanghai Canspec Scientific Instruments Co. Ltd. (Shanghai, China). Sulfosuccinimidyl 6-(4 -azido-2-nitrophenyl-amino) hexanoate and Hoechst 33258 were obtained from Thermo Fisher Scientific (sulfo-SANPAH, Waltham, MA, USA). Paclitaxel and nocodazole were purchased from ApexBio (Houston, USA). SiR-Tubulin was purchased from Cytoskeleton (USA). All other chemicals were from Beijing Chemical Reagents Co. Ltd. (Beijing, China). The circular quartz plate (12 mm diameter) was acquired from www.taobao.com.

2.2 Substrate fabrication

The glass-bottom culture dish was pretreated with 2 mL of 4% (v/v) APTES solution in deionized water for 15 min. The Petri dish was washed 3 times with ethanol before it was immersed in 2 mL of 0.5% glutaraldehyde solution in PBS for 30 min. Finally, the Petri dish was washed thoroughly with a stream of deionized water and dried in the air.

The polyacrylamide (PAA) hydrogel was prepared using a protocol according to previous reports [25, 26]. Solutions of 5% (w/v) acrylamide, 0.1% (w/v) N,N-methylene-bis-acrylamide, 0.5% N,N,N',N'-tetramethylethylenediamine, and 0.05% ammonium persulfate were mixed to form the pre-gel solution. The pre-gel solution was spread onto the surface of a pre- cleaned circular quartz plate. Subsequently, the activated Petri dish was slowly inverted onto the top of the droplet from one side of the quartz plate. The acrylamide droplet between

the Petri dish and the quartz plate became flat under gravity and polymerized for 60 min at room temperature. After removal of the Petri dish, the PAA gel was immersed in deionized water to remove the non-polymerized solution. The PAA gel, which was about 60–80 m in thickness, was linked to the Petri dish along the bottom surface. The Young’s modulus of the PAA gel is 3.8 KPa [27]. Next, 22 L of green fluorescent beads (2% (w/v), carboxylate-modified) together with 200 L of deionized water was added to the modified PAA films for 40 min. To activate the carboxylic acid groups, a mixture of 0.5% NHS and 2% EDC in water was added to the Petri dish. The solution was left undisturbed in the dark light for 2.5 h. The beads were uniformly distributed on the surface of the substrate at a density of ~ 1.5 beads/m2, as shown in the illustration in Fig. 1(a).

To promote cell adhesion on the gel surface, type I collagen was conjugated to the PAA film using the hetero-bifunctional cross-linker sulfo-SANPAH. 1 mg/mL solution of sulfo-SANPAH in water (200 L) was pipetted onto the gel surface to activate PAA. The Petri dish was irradiated with ultraviolet (UV) light (10 W) for 10 min before it was covered with 200 L of 0.6% (v/v) solution of collagen I in 6 mM aqueous acetic acid and incubated overnight at 4 °C.

2.3 Cell culture

Human ovarian granulosa (KGN) cells (Life Technologies, USA) were cultured in Dulbecco’s modified Eagle medium (DMEM) (Hyclone, Logan City, USA) supplemented with 10% fetal bovine serum (Gibco, Thermo Fisher Scientific Inc., UK), 100 U/mL penicillin G (Life Technologies, USA), and 100 g/mL streptomycin (Life Technologies, USA). They were incubated at 37 °C in a humidified 5% CO2 atmosphere. Cells were detached from culture flasks by the addition of 0.25% trypsin solution (Gibco, USA) containing ethylenediamine-tetraacetic acid (EDTA). The cells were centrifuged at 100 g for 5 min and resuspended in the culture medium. We then plated cells onto the gel substrate and incubated them for 4 h before imaging. For cells treated with drugs, drugs were added to Petri dishes before imaging.

2.4 Time-lapse acquisition of images

All confocal images were collected with a Zeiss 100×, NA 1.40 (numerical aperture) oil objective (Plan-Apochromat 100× Zeiss DIC M27) in an inverted Zeiss LSM 800 confocal microscope equipped with a Zeiss CCD camera. An argon laser (488 nm) was used to image the green fluorescent beads. 3D image stacks were acquired every 5 min for 20 h at a resolution of 512 × 512 × 8 voxels, which corresponds to voxel dimensions of 0.4 m × 0.4 m × 0.3 m in both horizontal planes and the axial plane. The time for volumetric image acquisition was 4 s, and stacks for our digital volume correlation (DVC) required 8 layers. After the acquisition of the time-lapse images, trypsin was used to remove cells from the substrate. And then the volumetric images of the beads were taken at the same place as un-deformed images. Cells were maintained in an incubation chamber (Tokai Hit, Shizuoka, Japan) at 37 °C with 5% CO2. Cells stained were imaged using a 40×, NA 0.95 objective at excitation wavelengths of 577 nm for microtubules (MTs) and 348 nm for nuclei.

2.5 Calculations for displacements, stress, and forces

Much work has been done in improving the efficiency and precision of digital image correlation (DIC) in our previous study. For example, the IC-GN2 algorithm was induced to DIC for local deformation with a high strain gradient [28]. In addition, we have studied the quality assessment of the speckle

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pattern for DIC [29]. Also, we have assessed systematic errors and the effect of shape functions and subset size on local deformation using DIC [30, 31]. In this work, we proposed the IC-GN2 for DVC based on our previous studies to calculate the displacements from the 3D images. The detailed process is available in the Electronic Supplementary Material (ESM) (Section “The proposed IC-GN2 algorithm for DVC”). The newly developed algorithm enables us to obtain displacements with a resolution of 0.02 m (see Section “Simulation analysis of the accuracy of IC-GN2 algorithm for DVC” in the ESM). The forces are reconstructed from the displacements and the constitution relation of the substrate on the basis of elastic mechanics theory in ABAQUS software. The resolution of force in our method reaches tens of Pa (see Section “Simulation of resolution of stress” in the ESM). The force in Figs. 5(b) and 5(c) represents the average force of cells and is obtained from the 3D stress map.

3 Results and discussion

Since dividing cells were sensitive to laser intensity and duration, cells were unable to divide under long time laser scanning during volumetric image acquisition [22]. It’s difficult for traditional methods to measure traction forces exerted by cells during mitosis. Therefore, we proposed a method to quantify mitotic cell traction forces by using monolayer beads to track 3D tractions information. Instead of embedding numerous beads inside the hydrogel substrate, we scattered fluorescent beads on the surface of the substrate in Fig. 1 and thus shortened our sampling time (4 s) to 1/50 of traditional methods which take about 3–7 min [23, 32]. Using monolayer fluorescent beads, we managed to track traction forces in three dimensions during cell mitosis by shortening the sampling time of stacks and

reducing phototoxicity. The PAA hydrogel was linked to the surface of the glass of the Petri dish in Fig. 1(a), serving as the substrate. Cells were cultured on the substrate with collagen I covering its surface for 4 h before imaging. The beads were conjugated onto the surface of the substrate and the reliability of this bond has been confirmed by previous work [26]. The beads were used to track the deformations of the substrate during the migration of cells, and their movement was recorded in volumetric images (Fig. 1(a)) by laser scan confocal microscope (LSCM). We chose a cell without additional cells around it. In the experiment, image stacks of the beads were taken every 5 min for 20 h, which were treated as speckle images in the calculation. The time-lapse volumetric images were converted to displacements through DVC. Since the deformation gradient exerted by the cells was large (see Fig. S5 in the ESM), we proposed the IC-GN2 algorithm for DVC to improve the calculation precision (a detailed method was available in the ESM). The region of interest (ROI) was 512 × 512 pixels, and the grid step size was 3 × 3 × 1. The IC-GN2 algorithm with subvolume size of 29 × 29 × 7 voxels was used in DVC to calculate the 3D dis-placement field (Fig. 3(b)). According to the elastic theory [33], traction forces were reconstructed from the displacements and constitutive relation of the substrate in ABAQUS software. The detailed process of calculation of displacements and stresses are discussed in the ESM.

3.1 3D traction forces of a single migrating cell

We quantitatively mapped the 3D traction force field induced by a migrating KGN cell. Figure 2 presents 3 images of the motile KGN cells on the PAA substrate captured for 40 min (complete data were supplied in Movie S1 in the ESM). The location and morphology of the motile cell were shown in Fig. 2(a), followed by a series of high-resolution 3D displacement and

 Figure 1 Traction force microscope platform and confocal images. (a) Schematic of the traction force microscope platform. Motile cells induced

deformations of the substrate with a single layer of fluorescent beads (green, 0.5 m in diameter). Typical 3D confocal image stacks of the single layer of

fluorescent microspheres along the z-axis were acquired every 5 min at a resolution of 512 × 512 × 8 voxels. Scale bar, 10 m. (b) Schematic of cell division

and the resulted 3D traction forces.

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force maps in Figs. 2(b) and 2(c). Comparison of the series of images affords insight into the

migration directions of the motile cell (Movie S1 in the ESM). Cells undergo cycles of extending protrusions, assembling and disassembling adhesions and contraction during migration [34, 35]. In accordance with previous reports [34, 35], the direction of the migration kept changing over time in this work, which suggested that cells migrated in a natural state in this experiment. In Fig. 2, the colored contours showed the normal deformations at the cell–gel interface and the vectors demonstrated tangential deformations. Both the magnitude and direction of the displacement (Fig. 2(b)) matched well with the shape of the moving cell obtained from a series of differential interference contrast images (Fig. 2(a)). For example, at the 20th min, the cell extended pseudopodia and moved toward the left. The maximum in-plane (tangential) displacement was about 1.8 m for this cell. Notable forces were presented over large areas beneath the cell in Fig. 2(c), indicating that the areas of interaction between cells and the substrate were large. In addition, the tractions were unevenly distributed on the substrate and changed along with the motion of the cell. The time-lapse analysis clearly showed how the magnitude and direction of the traction forces changed with the movement of the cell. Prior studies indicated that the traction of a single migrating cell was about 600 Pa [36]. In line with previous studies, the maximum normal cellular traction detected in the migrating cell was 500 Pa, and the maximum in-plane traction was 1,000 Pa. Also, the analysis of in-plane deformations showed that large forces were generated at the edge of the cell (Fig. 2(a)), which was consistent with previous reports [36, 37]. Additionally, we conducted numerical simulation (in the ESM) to verify the accuracy of our algorithm. Simulation results showed that the

resolution of displacement reached 0.05 pixels. Therefore, both the numerical simulation results (in the ESM) and experimental results (Fig. 2) showed the proposed method used to investigate cellular tractions was reliable. Time-lapse forces maps may explain the migration mechanism in which the cell’s leading edge is anchored on the substrate, providing the required fixed friction, and also may explain the mechanism in which parts of the cells are sloughed off from the substrate during migration [34].

3.2 3D traction forces during the cell cycle

Humans suffer from cancer for the uncontrolled cancer cell migration and proliferation. Studies on cancer cell mitosis flourish because it is involved in many vital physiological process. However, traction forces of mitotic cells in three dimensions are barely investigated. Prior study shows that the forces generated by the cytoskeleton proteins have a dominant influence on many intracellular activities involved in cell division, such as the generation of the spindle and the contractile ring, chromosome motility, and cytokinesis during the mitosis process [38–40]. The mechanical forces between cells and the ECM play a vital role in regulating cell behaviors and cell functions. For example, the change of extracellular mechanical environment affects stem cell differentiation [6]. Also, mechanical force may be used as an indicator of disease according to the force difference between the diseased cells and normal cells. A more in-depth understanding of cellular tractions during cell mitosis might offer better ways toward cancer treatment, disease detection as well as stem cell differentiation. Additionally, quantifying the forces during cell mitosis might provide a better tool for studying cell mitosis mechanics.

Cells transmit mechanical forces exerted by acto-myosin cytoskeleton onto the substrate through integrin and the

 Figure 2 3D stress maps of a KGN cell during its migration. (a) A series of confocal images captured for 40 min under differential interference contrast

mode. The images were captured every 5 min for a total of 90 min. (b) Successive 3D displacement contours exerted by the motile cell in (a). The arrows

represented the tangential component of the displacement, and the color bar represented the magnitude of the normal component of the displacement.

Scale bar, 1 m; color bar, m. (c) 3D traction force field obtained from displacements in (b). The arrows represented the tangential components of force,

and the color represented the normal components of force. Scale bar, 1,000 Pa; color bar, Pa.

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adhesion complexes. Although most of the cell–matrix adhesions disassemble before entering the M phase, recent research points that cell–matrix adhesions remain existing throughout the mitosis and guide the re-spreading of the daughter cells [41]. Another research also points out that peripheral adhesions are found in G1, S, G2, and M phases [42]. Since the traction forces are intensely related to the adhesion, the adhesions support the existence of forces. Therefore, the mechanical interactions between cells and matrix exist in the whole cell cycle including mitosis and regulate many intracellular activities involved in mitosis. We quantified the traction stress generated by a mitotic cell and analyzed the stress variations during the cell cycle in three dimensions (Figs. 3–5, Movie S2 in the ESM). These measurements unveil the mechanical interactions between a single mitotic cell and the matrix during cell mitosis.

To measure the forces generated by mitotic cells, 3D images of fluorescent beads (4 s for 8 layers) were taken every 5 min for 20 h. A series of 4 representative images of KGN cells during the cell cycle were shown in Fig. 3(a), and the resulting 3D displacement maps and 3D stress maps were shown in Figs. 3(b) and 3(c), respectively (complete data were supplied in Movie S2 in the ESM). The detailed traction forces during the whole mitosis process for PTX-treated cells and the control group were shown in Fig. 4. Variations of traction forces of cells under different anti-cancer drugs during the cell cycle were shown in Fig. 5. Mean traction forces during the cell cycle

 

 Figure 3 Four consecutive displacement and force contours during the cell

cycle. (a) A series of four representative images of a single mitotic KGN cell

were captured every 5 min for 20 h under differential interference contrast

mode. (b) Successive 3D displacement contours exerted by the mitotic cell

in (a). The arrows represent the tangential component of the displacement,

and the color represents the magnitude of the normal component of the

displacement. Scale bar, 1 m; color bar, m. (c) 3D stress maps calculated

from displacements in (b) The arrows represent the tangential components

of force, and the color represents the normal components of force. Scale bar,

500 Pa; color bar, Pa.

 Figure 4 Traction forces of a single KGN cell treated with PTX during

mitosis. Control: 3D stress maps of a KGN cell without drug treatment

during mitosis. 10 nM PTX: 3D stress maps of a KGN cell with 10 nM

PTX treatment during mitosis. Scale bar, left: 500 Pa; right: 800 Pa. The

interval between each frame is 5 min.

(Fig. 5) were obtained by the algebraic average of the total force. For in-plane mean traction forces,

2 2

1

( ) ( )n

x y

i

F i F i

F Sn

=

+=å

(1)

where F is the average in-plane force of the cell, xF and yF denote traction stress in plane, and S is the area of the cell. For out-of-plane traction forces,

1

( )n

z

iz

F i

F Sn

==å

(2)

where zF is the average out-of-plane force of the cell, and zF is traction stress out of plane.

Traction forces varied during the cell cycle, especially before and after mitosis (cell division: 50–85 min of the control group in Fig. 5 or Movie S2 in the ESM). Through analysis of variations of tractions, we found that the in-plane and normal traction forces manifested the same variation trend. At first, the cell exerted large forces on the matrix as large areas of the cell adhered on the substrate (Fig. 3: 25 min, control group in Fig. 5: 0–30 min). Before entering mitosis, cells began with the

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de-adhesion process during which cells detached from the substrate in preparation for cell division [42]. Both in-plane and normal traction forces exhibited a decrease in this process (the control group in Fig. 5 and Movie S2: 30–45 min in the ESM). After de-adhesion, cells rounded up (Fig. 3: 50 min) under the contractile force exerted by acto-myosin, supplying the space for the mitotic spindle and allowing correct spindle positioning [43]. The forces sharply decreased to tens of Pa at 50 min (Fig. 3: 50 min), followed by maintaining a low value (Fig. 4, Movie S2: 50–80 min in the ESM) until the mitotic cell divided into two nascent daughter cells (Fig. 3: 85 min). Finally, tractions increased gradually as two daughter cells re-spread on the substrate and migrated toward the opposite direction (Fig. 3: 110 min). In addition, cells exerted larger in-plane forces than those out of plane during the cell cycle except for the M phase where in-plane forces were almost as small as normal forces (the control group in Fig. 5). As for traction forces during the M phase (Fig. 4: control), the cell center generated downward forces while the peripheral region of the cell exerted upward forces. Both normal and in-plane forces of M-phase cells were small and had only a little change, which means cells exerted a stable and small force on the matrix during the M phase. The maximum traction force in plane was about 470 Pa and located at the leading and trailing edge of the two daughter cells (Fig. 3: 110 min).

The normal traction forces during mitosis are investigated for the first time. The magnitude of the forces during mitosis is tens of Pa out of plane, which is comparable to the in-plane force and should not be ignored. Some studies focus on 2D forces during the cell cycle without mitosis [17–19]. A few researchers measure 2D traction stress of dividing Dictyostelium cells [20, 21]. Common 3D TFM embed fluorescent beads inside elastic substrate to track deformations induced by cells cultured on the substrate surface [12, 23] or embedded in the substrate [32]. These methods take a few minutes (about 3–7 min) to acquire volumetric images of the beads in the entire substrate (from dozens of microns [23] to hundreds of microns [32]). Cell morphology is continuously changing during the process of image stack acquisition. As the scanning processes are long in duration, the top and bottom layers of the stacks may be not at the same moment. What’s more, since dividing cells are sensitive to laser intensity and duration [22], a long time of image acquisition causes strong phototoxicity which may prevent cell division. Thus, traditional 3D TFM is not appropriate for investigation on cell division. Besides common 3D TFM, confocal reference free TFM (cTFM) based on quantum dots can also measure the 3D traction field for cell migration. But they require complicated quantum dots printing technique because the precision of the un-deformed images highly depends on the accuracy print of each quantum dot on the substrate, which increases experiment cost and requirement of the experimental technique [44]. What’s more, since the optimal precision of force measurement in this method is hundreds of Pa [44], the cTFM may be not suitable for the weak force during mitosis. Hence, traditional methods are incapable of investigating 3D traction forces during cell division. Some researchers use traditional 3D TFM to measure the 3D displacements of mitosis [22]. To reduce the phototoxicity brought by laser scanning during 3D stacks acquisition (required 276 layers for 100 m in their experiment), they prolong the intervals of image acquisition to 30 min to ensure the undisruption of cell division. Since the M phase lasts about 1 h or shorter, their method could only capture one moment of mitosis but is not capable of revealing 3D traction forces during the whole mitosis process. Furthermore, since mitotic

cells change their morphology fast during mitosis, the top and bottom layers of the stacks (276 layers) may be not at the same moment in their experiment.

In the present study, by using monolayer beads and digital volume correlation algorithm, which was easier and had a high spatiotemporal resolution, we reduced experiment difficulty and improved precision to tens of Pa to make the method capable of calculating forces of mitotic cells in three dimensions.

3.3 Detection of the effects of anticancer drugs on cell

mitosis

Ovarian cancer and breast cancer occupy one-third of all cancers in females and the former is the most lethal cancer among women [45]. Since studying traction forces generated by drug- treated cells may offer better ways toward inhibition of cancer cell proliferation, we investigated traction forces exerted by cancer cells with drug treatment. PTX is chosen as the drug because it is a potent inhibitor of cell proliferation and is commonly used as a standard and effective chemotherapy drug in treating cancers, especially ovarian cancer and mammary cancer. In addition, we investigated the effect of another anticancer drug NDZ, which blocks mitosis in a different way, on traction forces of mitotic cells.

To investigate the influence of PTX on cancer cell mitosis, we quantified the 3D traction forces during the cell cycle for control cells and for cells treated with different concentrations of PTX. According to previous studies, PTX inhibits 70%–80% of cell proliferation at a concentration of 10 nM [46]. And our experiment showed that cells treated with 10 nM PTX lost their ability to divide. We therefore chose 1, 5, and 10 nM PTX to study their effects on mitosis. Cells were cultured for about 4 h before imaged and then they were taken to the confocal microscope for imaging after treated with PTX. After sampling, cells were treated with trypsin to acquire the reference images. 3D stress maps of cells treated with 0, 10 nM PTX during mitosis were shown in Fig. 4 (cells treated with 0, 1, 5, and 10 nM PTX were available in Fig. S2 in the ESM). Since the start of mitosis is marked by cell rounding, we chose the moment that cells rounded up as the starting point of the comparison of cells treated with drugs and those in the control group. From the moment of cell rounding, we compared the force exerted by cells treated with drugs and those in the control group every 5 min, as shown in Figs. 4 and 5. Results showed that cells treated with PTX lower than 10 nM (Fig. S2 in the ESM) exerted little or no traction force changes during M phase in this experiment. The reason for this phenomenon may be that cells transmit force on the matrix through adhesions and only a few focal adhesions that anchor cells to the substrate are left in M phase because most focal adhesions disassemble in G2 preparing for cell rounding [47]. Thus, mitotic traction forces were small and exerted little changes. In addition, cells with 0, 1, and 5 nM PTX exerted small normal and in-plane forces. However, cells with 10 nM PTX treatment exerted large downward normal force and center-orientated in-plane force on the substrate during mitosis (Fig. 4).

To further study how PTX affects traction forces during the cell cycle, we presented mean traction forces exerted by KGN cells treated with different concentrations of PTX during the cell cycle (Figs. 5(a)–5(d)). Results showed that cell mitosis completed at low concentrations of paclitaxel (below 10 nM) and failed at high concentrations (Fig. S2 in the ESM). The in-plane forces (Fig. 5(a)) and normal forces (Fig. 5(d)) of cells treated with PTX below 10 nM exhibited the same changing trend as the control group. At the beginning, cells exerted large in-plane and normal forces (hundreds of nN) before entering

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mitosis. Then, the mean force reduced rapidly as the cell rounded up to prepare for cell division. The time for cell rounding elongated with the increasing concentrations of PTX (0 nM: 15 min; 1 nM: 20 min; 5 nM: 25 min), indicating that longer time was required for cells to change their shape when treated with high-dose PTX. After cell rounding, cells entered mitosis and exerted forces of dozens of Pa during mitosis (Movie S2 in the ESM) when treated with 0, 1, and 5 nM PTX. Finally, forces gradually increased as two daughter cells re-spread on the substrate and then fluctuated in a range as two daughter cells migrate. For cells treated with 10 nM PTX, mean forces continued to decrease after cell rounding until cells gradually detached from the substrate. Compared with cells without PTX treatment, the mitotic time was prolonged for cells treated with 1 and 5 nM PTX. In particular, cells were unable to divide at 10 nM PTX (Movie S3 in the ESM) or higher concentration PTX. The results also showed that cells exhibited forces of dozens of Pa during mitosis with PTX below 10 nM (Fig. S2 in the ESM). No explicit difference of traction forces was detected at different concentrations of PTX in this experiment, which may attribute to the reduction of adhesion areas between cells and substrate during mitosis and the fact that adhesions played a leading role in transmitting forces to substrate. While the normal forces were smaller than those in plane during interphase, the normal force was comparable to the in-plane force during mitosis. Thus, to investigate traction forces during mitosis comprehensively, the normal force should be con-

sidered. Compared with cells treated with PTX below 10 nM, 10 nM PTX-treated cells exhibited a different and interesting phenomenon that cells were unable to divide and exerted large forces after cell rounding (Figs. 5(a) and 5(d)).

Then we investigated the effect of another anticancer drug NDZ, which prevents mitosis by affecting the dynamics of MTs and depolymerizing MTs, on mitotic traction forces. NDZ was added to cells before moving the culture dish onto the microscope platform. Figures 5(b) and 5(e) showed mean traction forces of KGN cells treated with different concentrations of NDZ (33, 60, and 120 nM) during the cell cycle. Concentrations of NDZ were chosen according to tests in Fig. S4 in the ESM. At 120 nM, cell division was significantly inhibited. Like paclitaxel-treated cells, cells treated with low concentration of NDZ (below 120 nM) still have the ability to complete mitosis, but cells with high concentration of NDZ (120 nM) lose their ability to divide. As shown in Fig. S4 in the ESM, for KGN cells with 10 nM PTX and 120 nM NDZ, mitotic cells accounted for 32% and 23% of total cells, and cytokinesis failure cells accounted for 84% and 86% of total mitotic cells, respectively, which suggested that the two drugs exhibited similar inhibitory effects on cell division. Therefore, the normalized concentrations for the study of the effect of these two drugs on mitotic cell tractions were 10 nM (PTX) and 120 nM (NDZ), respectively. For cells treated with 33 and 60 nM NDZ, cells enable complete mitosis and the variation of traction forces exhibited a similar trend as those in the control group. Additionally, with the

 Figure 5 Effect of PTX and NDZ on 3D traction forces of mitotic cells. (a)–(c) Mean in-plane traction forces of mitotic KGN cells (n = 3) treated with

PTX of 0, 1, 5, and 10 nM and with NDZ of 33, 60, and 120 nM. (d)–(f) Mean out-of-plane traction forces of cells in (a)–(c). (g) MTs and nuclei of KGN cells.

KGN cells MTs (SiR-Tubulin) and nuclei (Hoechst 33258) were shown in red and blue color. Scale bar: 10 m.

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increase of the concentration of NDZ, while the in-plane traction forces decreased during interphase (0–40 min in Fig. 5(b)), both the in-plane and normal traction forces exhibited no explicit difference during mitosis (50–80 min in Figs. 5(b) and 5(e)). This phenomenon may result from the situation that only a few adhesions are left during mitosis and the mitotic force is too small to distinguish, as discussed in Section “3D traction forces during the cell cycle”. NDZ induces abnormal spindle and depolymerizes MT. The proportion of abnormal cells and the organization of MTs and chromosomes depend on the concentration of the NDZ. At 33 and 60 nM NDZ, only a few MT depolymerizations are detected and many blocked spindles are similar to the normal metaphase spindles [48]. This phenomenon may be another possible reason for the results that cells with 33 and 60 nM NDZ complete mitosis and generate indistinguishable force compared to those in control. As for 120 nM NDZ, cells were arrested in metaphase (Fig. 5(g)), and mitosis was inhibited. The traction forces decreased to a value near zero and then fluctuated in a small range as cells enter mitosis. Mitotic cells treated with high concentration of NDZ showed the same morphological characteristics as those with high concentration of PTX: cells were unable to complete mitosis. However, their traction forces were very different (Figs. 5(c) and 5(f)). Both in-plane and normal traction forces of cells treated with 10 nM PTX were significantly higher than those with 120 nM NDZ during the cell cycle. PTX and NDZ affect MTs in different ways though both drugs block mitosis. The number and structure of MTs in cells treated with two different drugs were different (Fig. 5(g)). While PTX stabilizes MTs, NDZ depolymerizes MTs and induces abnormal spindle. Therefore, more MTs are left inside cells treated with PTX and fewer MTs are left inside cells with NDZ. The significant difference in forces of cells treated with PTX and NDZ suggests that the structure of MTs may have an important effect on the mitotic force. In addition, our results showed that there is a significant difference in force magnitude between cells retaining their ability to divide and those whose mitosis is inhibited. Therefore, the efficacy of new anti-cancer

drugs on cancer cell division could be assessed by measuring the traction forces.

Figure 5(g) showed MTs and nuclei of KGN cells without drug treatment. Cells treated with high concentration of PTX (10 nM) exerted bundles of MTs accumulating around nuclei. Prior work states that 100 nM NDZ induces 90% metaphase accumulation and depolymerize about 30% MTs. And cells treated with NDZ change their spindles and chromosomes to an abnormal type [48]. In accordance with previous reports, cells treated with high concentration of NDZ (120 nM) exhibited metaphase accumulation and showed abnormal MTs and chromosomes (Fig. 5(g)).

Our study presented insight into how traction forces exerted by a single cell varied during mitosis in three dimensions, and how traction forces changed when anticancer drugs interact with mitotic cancer cells. We found that mitotic cells treated with high concentrations of PTX failed to complete mitosis and exerted large normal forces after cell rounding. Although both PTX and NDZ enable block mitosis, cells with PTX exerted larger forces than those with NDZ during the cell cycle.

4 The mechanism of force generation during

mitosis

To illustrate the normal force during mitosis and elucidate the large force upon 10 nM PTX after cell rounding, we proposed a possible mechanism (Figs. 6(a) and 6(d)). As shown in Figs. 6(b), 6(e), and 6(h), previous studies show the distribution of MTs in mitotic cells without drugs [49], with PTX [49] and with NDZ treatment [48]. Figures 6(c), 6(f), and 6(i) showed the 3D traction force map of cells without drugs, with PTX and with NDZ treatment, respectively. Figure 6(g) was the schematic illustration of the explanation of the force in Fig. 6(f), showing the generation and distribution of forces on the substrate.

For mitotic cells without drugs, bipolar interpolar MTs exert sliding forces (F1 and F2 in Fig. 6(a)) resulting from MT-MT sliding and elongation. The sliding forces have component forces that are perpendicular to the substrate (Fy and Fy in

 Figure 6 Mechanism of traction forces during mitosis for KGN cells. Mechanism (a), MT polymer distribution in the mitotic spindle (b) [49] and 3D

traction forces (c) for a mitotic cell without drugs. Mechanism (d), MT polymer distribution in the mitotic spindle (e) [49] and 3D traction forces (f) for a

mitotic cell treated with PTX. Schematic of the normal force (red) and the in-plane force (blue) on the substrate generated by cytoskeleton during mitosis (g).

MT polymer distribution in the mitotic spindle (h) [48] and 3D traction forces (i) for a mitotic cell treated with NDZ. Scale bar 10 m. (b) and (e) Reproduced

with permission from Ref. [49], © American Society for Cell Biology 2009. (h) Reproduced with permission from Ref. [48], © Company of Biologists 1992.

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Fig. 6(a)). The downward forces (blue arrow 3 in Fig. 6(a)) are transmitted onto the substrate, which may explain the large downward forces detected in the cell center during mitosis (Figs. 4 and 6(c)). Since cells adhere on the substrate and the cell center exerts pushing force, parts of the substrate that linked with cells are pulled up (black arrows 1, 2 in Fig. 6(a)). The small in-plane force (Fig. 6(c)) may be due to the fact: tangential force (Fx and Fx in Fig. 6(a)) generated by interpolar MTs canceled out and those generated by astral MTs is small due to the small number of astral MTs inside cells in this stage (Fig. 6(b)) [49].

For cells treated with 10 nM PTX, larger forces are detected (Figs. 4 and 6(f)) than those with lower concentrations of PTX (0, 1, and 5 nM). Compared with cells without PTX, the distribution and number of the MTs change for PTX-treated cells: with the increase of concentrations of PTX, more astral MTs accumulate in the red box (Fig. 6(d)) and spindle length reduces [49]. The forces on the substrate mainly attribute to the increase of astral MTs. Also, a few polar MTs exert small forces on the substrate. The astral MTs in the red box exert pushing forces (F and F in Fig. 6(d)) on the substrates. The pushing forces produce downward normal component forces (Fy and Fy in Fig. 6(d)) and exert tangential component forces toward the center of the cell (Fx and Fx in Fig. 6(d)), corresponding to the normal force and in-plane force in Fig. 6(f), respectively. Since PTX inhibits cell mitosis by preventing MTs depolymerization, more MTs are left in cells with the increase of the PTX concentration, which means producing larger forces. Therefore, cells with high concentrations of PTX treatment exert larger forces (both in-plane and normal) on the substrate during mitosis. Additionally, the periphery region of cell–substrate adhesion is pulled up (black arrows 1, 2 in Fig. 6(d)) owing to the tension produced by the cell. Since cell membrane tension (about tens of Pa) [50] is not sufficient to provide such a large force (the maximum of force is about 150 Pa) during cell mitosis, the tension attributes to cytoskeletal tension rather than cell membrane tension. Cytoskeletal tension is caused by the downward pressure of the cells and adhesion to the substrate.

To verify the proposed mechanism above, we study the effect of NDZ on cell traction forces during mitosis. Results show high concentration of NDZ inhibits mitosis and low concentration of NDZ treatment couldn’t block mitosis. Interestingly, we find that, although two drugs block mitosis at high concentration, traction forces of cells with NDZ treatment are remarkably lower than those with PTX during mitosis. In other words, when the number of MTs increases due to the treatment of high concentration of PTX, the mitotic force becomes large. When MTs are depolymerized or disrupted by the high concentration of NDZ, the mitotic force becomes small. Therefore, mitotic traction forces are closely related to the MTs. NDZ inhibits cell division without increasing traction forces at high concentration, suggesting that the increase of traction forces in cells with high concentration of PTX is indeed caused by the specific effect of PTX on MTs. Thus, the increase of force exerted by cells with high concentration of PTX results from the change of MTs. Additionally, traction forces of cells with 10 nM PTX are obviously larger than those with 120 nM NDZ prior to mitosis onset (Figs. 5(c) and 5(f)), which may also attribute to the effect of drugs on MTs.

5 Conclusions

In summary, we track mitosis with high sample acquisition frequency for a long time (every 5 min for 20 h) and investigate the relatively small tractions (tens of Pa) during mitosis in

three dimensions. We quantify the 3D traction forces exerted by a cancer cell during the cell cycle and our investigations unveil how 3D forces vary during the cell cycle: decrease dramatically (entering mitosis), and then maintain a low value (from rounding to divide) for 30–40 min and finally increase progressively (two daughter cells re-spread) followed by fluctuation around a constant value (two daughter cells migrate). Our results suggest that the normal forces exerted by cells are as large as those in plane during mitosis.

Different from cell migration where traction forces reduce with the increase of PTX concentration [51], we find that although low concentrations of PTX have no explicit effect on traction forces during cell mitosis, cells treated with high concentrations of PTX fail to complete mitosis and exert large forces during mitosis. The large force caused by PTX is explained by the MT stabilizing behavior of PTX. In addition, our results show that high concentrations of MT destabilizing drug NDZ can also block mitosis and produce smaller force than high concentrations of PTX, which agrees well with our explanation. The mechanical difference between cells completing mitosis and those undergoing mitotic failure may serve as a criterion for speculating whether cancer cells are able to divide during drug therapy. Our study may provide further insight into the mechanical mechanism of drug–cell interaction during mitosis. Furthermore, our work highlights its potential applications in biology, as well as disease diagnosis and disease treatment.

Acknowledgements

The authors gratefully acknowledge financial support from the National Natural Science Foundation of China (Nos. 11872355, 11627803, 12072339, and 11872354) and the Strategic Priority Research Program of the Chinese Academy of Science (No. XDB22040502).

Electronic Supplementary Material: Supplementary material (complete data of 3D forces of cells during cell cycle; complete data of 3D stress maps exerted by mitotic cells treated with different concentrations of PTX; the proposed IC-GN2 algorithm and the traction reconstruction method; simulation analysis of the accuracy of the IC-GN2 algorithm for DVC; simulation analysis of the resolution of stress) is available in the online version of this article at https://doi.org/10.1007/s12274-021-3357-4.

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