A high throughput microfluidic system with large ranges of applied pressures for measuring the mechanical properties of single fixed cells and differentiated cells

Abstract

The mechanical properties of cells are of great significance to their normal physiological activities. The current methods used for the measurement of a cell’s mechanical properties have the problems of complicated operation, low throughput, and limited measuring range. Based on micropipette technology, we designed a double-layer micro-valve-controlled microfluidic chip with a series of micropipette arrays. The chip has adjustment pressure ranges of 0.03–1 and 0.3–10 kPa and has a pressure stabilization design, which can achieve a robust measurement of a single cell's mechanical properties under a wide pressure range and is simple to operate. Using this chip, we measured the mechanical properties of the cells treated with different concentrations of paraformaldehyde (PFA) and observed that the viscoelasticity of the cells gradually increased as the PFA concentration increased. Then, this method was also used to characterize the changes in the mechanical properties of the differentiation pathways of stem cells from the apical papilla to osteogenesis.

INTRODUCTION

The mechanical properties of cells, such as elastic modulus and viscosity, are critical for cell and tissue functioning. The alteration of mechanical properties is closely related to numerous physiological activities, such as stem cell differentiation,^1,2 embryonic development,^3,4 wound healing,^5,6 and cancer metastasis.^7,8 Meanwhile, recent findings have recognized cellular mechanical properties as vital status characteristics and potential noninvasive biomarkers for cancer diagnosis,^9,10 rare cell detection,^11,12 and mechanical phenotyping.^13,14 Related tools have been developed to measure the deformability of single cells from the local through global scales, including micropipette aspiration,¹⁵ atomic force microscopy,¹⁶ magnetic twisting cytometry,¹⁷ and optical tweezers.¹⁸ In a recent study,¹⁹ most of these methods were compared and analyzed in detail. Studies in Refs. 19 and 20 revealed that mechanical properties measured by means of different methods vary by two to three orders of magnitude even though these cells are cultured in the same environments. Furthermore, there are significant differences among these methods in terms of time consumption, measurement speed, and specialized technician needs. For each method, one or two of these factors limit its extensive application in scientific research and clinical diagnosis.

As one of the earliest developed tools, micropipette aspiration is still regarded as the gold standard for the measurement of cellular mechanical properties and is widely used in the field of biomechanics, such as mechanosensing mechanisms,²¹ cytoskeleton dynamics,²² and cell–cell communication.²³ The micropipette aspiration system is simple and affordable in most cases. Through heating and stretching of glass pipettes, operators cut and create customized micropipettes. However, there is no guarantee that the shapes and sizes of those micropipettes are exactly the same every time. Moreover, even for skilled operators, the micropipette aspiration system could be used to measure only one single cell at a time. As a result, the measurement speed is limited to up to 20 cells/h.²⁴ Insufficient sample size may not have adequate statistical power to obtain meaningful conclusions. Integrating with the micropipette aspiration system, several innovative microfluidic devices^25–27 have been engineered to enable measurement with better accuracy, higher throughput, and in an automated manner. Single cells are trapped in designated regions, and specific forces are exerted on these cells. Compared with traditional micropipette aspiration, these microfluidic chips integrated with micropipette aspiration can measure more than 100 cells^25–27 in an experiment.

However, the pressure range of current microfluidic chips that based on micropipette aspiration is still not sufficiently wide to characterize the mechanical properties of a heterogeneous population that consists of several cell types. The applied pressure on cells also depends on the occupation rate of the cell trapper in some of these methods. The development of microfluidic devices with a wider measuring range is necessary.

In this study, we developed an easy-to-use microfluidic device based on a micropipette array to measure the time-dependent mechanical properties of cells in a high-throughput manner. The microfluidic device also contains a pressure stabilization design and a pressure modulation design, thus achieving stable applied pressure over a wide range. In this way, we achieved the measurement of the cellular heterogeneity of different conditions and could provide a potential clinical method without fluorescent dyes or genetic engineering.

MATERIALS AND METHODS

Cell culture and differentiation

The human breast cancer cell line MCF-7 was purchased from the American Type Culture Collection (ATCC) and cultured in Dulbecco's modified Eagle's medium (DMEM; Gibco) supplemented with 10% fetal bovine serum (FBS; HyClone), 100 U/ml insulin (Gibco), and 100 U/ml penicillin and streptomycin (Gibco) at 37 °C and 5% CO₂.

Apical papilla tissues were obtained from normal human impacted third molars (18–24 years of age) with informed consent and under dental clinic guidelines as approved by the ethics research committee of Capital Medical University of Medical Sciences (Ref. No. CMUSH-IRB-KJ-PJ-2019-02F). One tooth was used in this study.²⁸ The stem cells from this apical papilla tissue were provided by Dr. Xiaoqiang Sun of Capital Medical University of Medical Sciences. Then, stem cells from the apical papilla (SCAPs) were cultured in a growth medium for adipose-derived stem cells (Cyagen; HUXXC-90011). SCAPs were passaged when the cells covered approximately 80% of the area of the whole dish.

SCAPs between the third and fifth passages were used throughout the study. These cells were inducted into osteogenic lineages in vitro with corresponding differentiation kits (Cyagen; HUXXC-90021) for 21 days. Meanwhile, the mechanical properties of these cells were measured using the microfluidic system on the 1st, 7th, 13th, and 20th days.

Cell sample

For cancer cells, the cell samples on a 60 mm diameter cell culture Petri dish were detached at 37 °C using prewarmed trypsin solution (Gibco) until >90% of cells were rounded and separated from the Petri dish. Suspended cells were washed with phosphate-buffered saline (PBS; Sigma–Aldrich) three times and then treated with different paraformaldehyde (PFA) solutions (0.2% and 0.5%) for 10 min. Meanwhile, suspended cells without PFA treatment were used as the control group. Before microfluidic experiments, the treated cell samples were again washed three times with PBS and resuspended in MCF-7-cell culture media to cell densities of 1 × 10⁵/ml.

For stem cells or differentiated cells, after removal from Petri dishes, they were resuspended using the growth medium for adipose-derived stem cells or an osteogenic differentiation medium and loaded into the microfluidic system directly. Compared with MCF-7 cells, stem cells were not treated with PFA solutions and were resuspended in the growth medium or the osteogenic differentiation medium. The other operations were exactly the same for both.

The design and fabrication of the microfluidic device

The design principle of our microfluidic device could be simplified as the equivalent electrical circuit, as shown in Fig. 1(a). The system comprises three functional zones, i.e., a resistance controller, a pressure stabilizer, and a cell trapper. The resistance controller contains two resistors in parallel, R₁ and R₂. The resistance of this zone could be adjusted by flipping switch S. The applied pressure of the other zones would be changed accordingly. The cell trapper is constituted by a series of microfluidic pipettes. The resistance of one microfluidic pipette is denoted as R_MA, and the total resistance of the cell trapper is denoted as R_c. Obviously, R_c would increase to R_c′ when cells are trapped in the micropipette array, and the applied pressure on the cell trapper would increase. To reduce this effect, we introduced a pressure stabilizer into this circuit. The resistance of the pressure stabilizer R_s is sufficiently small to ensure that the relative change in the applied pressure on the cell trapper is small or even negligible. In our experiments, we designed and fabricated microfluidic chips to meet three criteria: R_c/R_s= 12, R₁/R_s= 9, and R₂/R_s= 99. Using a pneumatic pump with a pressure range of 3–100 kPa, our system could be used to measure the mechanical properties of single cells over two measuring ranges, 0.03–1 kPa (switch off) and 0.3–10 kPa (switch on). Compared with the fully occupied system, the relative change in the applied pressure could be limited to <7.5% for the fully unoccupied system.

FIG. 1.

(a) The equivalent electrical circuit of the microfluidic chip. Three functional zones are marked using dashed boxes with different colors. (b) The design of the two-layer microfluidic device. Zoomed-in view: The inlet and filter show the design used to block the debris. The microfluidic pipette array shows how the cells were captured and measured. Detailed geometric parameters: R₁, 5400 μm (L) × 100 μm (W) × 20 μm (H); R₂, 19 000 × 40 × 20 μm³; R_s, 23 000 × 100 × 60 μm³ (for both branch channels); R_MA, 150 × 4 × 5 μm³. Region heights are listed on the bottom. (c) A photograph of the microfluidic chip. Zoomed-in view: The bright field image of a fractal tree-like branched network.

Based on the aforementioned design principle, our blueprint of the whole system is shown in Fig. 1(b). The microfluidic system included two PDMS layers, one control layer (bottom) and one flow layer (top). The control layer contained only a pitchfork structure to operate the valve, corresponding to switch S in Fig. 1(a). The flow layer included two microchannels in parallel corresponding to R₁ and R₂ in Fig. 1(a), a fractal tree-like branched network corresponding to R_c, and two side microchannels in parallel corresponding to R_s. In addition, as indicated by the orange dashed box in Fig. 1(b), next to the inlet, the filter structure comprised an array of posts, which could be used to block cell clusters and debris. In the zoomed-in view of the purple dashed box, microfluidic pipettes were constructed along the horizontal central line of the fractal tree-like branched network, yielding a total of 128 micropipettes. Specifically, the geometrical parameters of the main flow resistances of each part in the microfluidic chip are listed in Fig. 1(b). Obviously, the microfluidic pipettes in parallel could be regarded as a dominant part of the flow resistance in the fractal tree-like branched network. The master molds of the two functional layers were constructed using a photolithography technique. The mold of the control layer was constructed by SU8 with a height of ∼25 μm. The mold of the flow layer was also constructed by SU8 with three heights, as listed at the bottom of Fig. 1(b). A photograph of the whole microfluidic device is shown in Fig. 1(c). Through an air-plasma treatment, two layers were bonded to each other. Then, as a whole, they were bonded with a glass cover slide using the same treatment. The blue dashed box is the bright field image of the fractal tree-like branched network under an optical microscope.

Experimental setup

For the operation of this system, the inlet of the flow layer was connected to a pneumatic pump (MesoBioSystems, MBS-PR-200E1), and the inlet of the control layer was connected to a syringe pump (Longer Precision Pump Co., Ltd., TS-1B/4 W0109-1B) after the microfluidic chip was degassed in vacuum for 30 min. Then, the liquid was injected into the whole pitchfork microchannel until the entire microchannel was filled. At the same time, the cell suspension was adjusted to 1 × 10⁵ cells/ml and loaded into the microfluidic device. Then, the predefined pressure signal was input into the entire microfluidic device, and the dynamic behaviors of the cells were recorded under a Nikon Ti inverted microscope (Nikon, ECLIPSE Ti-E).

Chip testing

To test the microfluidic system, polystyrene fluorescent microspheres were loaded as indicators to measure the velocity field of the flow in microchannels, and the applied pressure on the cell trapper was further calculated. In our experiments, two sizes of fluorescent microspheres were used, 5 μm (Bangs Laboratories; FCDG008) and 1 μm (Invitrogen; F13083). The former was used to mimic cells to clog the cell trapper and block the small channels. The latter was used to measure the flow velocity with long exposure photography. The surfactant (Liby Dishwashing Liquid, with 0.5% volume fraction) was added to prevent adhesion of these fluorescent microspheres. It should be emphasized that the surfactant was only applied to bead measurements.

From the perspective of fluidic dynamics, the fluid flow within microfluidic channels is laminar, and an analytical solution could be deducted for the velocity field of flow. The velocity field of pressure-driven liquid flow through the rectangular cross section in R_s is shown in Fig. 2(a). The inset of Fig. 2(a) displays the x–y–z axes in the microchannel. Figure 2(b) shows the projection of this velocity field onto the x-axis. The fitted envelope curve was obtained from the experimental results to derive the applied pressure using the following formula:

$$\begin{array}{rl}u(x,y)& ={\displaystyle \frac{G}{2\mu }x(W-x)-{\displaystyle \frac{4G{W}^2}{\mu {\pi }^3}\sum _{n=1}^{\mathrm{\infty }}{\displaystyle \frac{1}{{(2n-1)}^3}}}}\\ & \times {\displaystyle \frac{\sinh ({\beta }_{n}y)+\sinh ({\beta }_n(H-y))}{\sinh ({\beta }_{n}H)}\sinh ({\beta }_{n}x),}\end{array}$$ (1)

where μ is the viscosity of the fluid in the microchannel and H and W are the height and width of the microchannel, respectively. G is the derivate of pressure along the flow (the z direction), i.e., $G=-dp/dz$. ${\beta }_n$ is the coefficient of the infinite series, ${\beta }_n=(2n-1)\pi /W$ in this formula. In our study, the infinite series was truncated after the top ten items. Because the pressure difference on R_s and R_c is the same, we can use $G=-dp/dz$ in the channel of R_s to calculate the pressure difference on R_c by $\int Gdz$. As a test, the pneumatic pump was used to generate a hydraulic pressure of 45 kPa on the whole microfluidic system in our experiments. As depicted in Figs. 2(c) and 2(d), under this condition, the applied pressure was 4.33 kPa when the micropipettes were unoccupied fully and 4.51 kPa when occupied fully. The relative change was lower than 5%. This suggests that the applied pressure on the cell trapper was nearly immune to the occupied rate of cells. In subsequent experiments, the pneumatic pump was used to generate a series of different hydraulic pressures ranging from 3 to 100 kPa, and the corresponding applied pressures on the cell trapper were calculated, as illustrated in Figs. 2(e) and 2(f). These results indicated that the applied pressure on the cell trapper displayed excellent linearity with respect to the predefined input pressure regardless of the valve position. More importantly, the measuring range was 0.03–1 kPa when the valve was closed and 0.3–10 kPa when the valve was open. This suggests that our microfluidic system could measure the mechanical properties of cells over a wide pressure range in a robust manner and has potential application in noninvasive cell phenotyping.

FIG. 2.

(a) The velocity field of the pressure-driven liquid flow through a rectangular cross section in theory. The inset of Fig. 2(a) displays the x–y–z axes in the microchannel. (b) The projection of the velocity field onto the x-axis in theory. (c) The velocity field in the channel of pressure stabilizer R_s measured in experiments when the cell trapper was fully unoccupied. (d) The velocity field in the channel of pressure stabilizer R_s measured in experiments when the cell trapper was fully occupied. (e) The applied pressure on the cell trapper as a function of input pressure when the valve was open. (f) The applied pressure on the cell trapper as a function of input pressure when the valve was closed.

Statistical analysis

Kolmogorov–Smirnov test: The two-sample Kolmogorov–Smirnov (K–S) test is used to test whether two samples come from the same distribution. The null hypothesis is that both samples come from a population with the same distribution. Compared with the Wilcoxon rank sum test, the K–S test is sensitive to any differences in the two distributions. In our experiments, the K–S test was used to judge whether two sampled populations could be merged into one.

Wilcoxon rank sum test: As a nonparametric test, the Wilcoxon rank sum test is used to test whether two samples are likely to have been derived from the same population. Compared with the K–S test, the Wilcoxon rank sum test is mostly sensitive to changes in the median. In our experiments, the Wilcoxon rank sum test was used to compare the medians between the two populations.

RESULTS

Modeling of cell mechanical properties

The mechanical properties of mammalian cells are vital for their normal physiological activities. Since the beginning of the last century, numerous tools have been developed to measure these mechanical properties. In our experiments, the MCF-7-cell line was used to verify the feasibility of the whole microfluidic system. In view of the fact that the mechanical properties of MCF-7 cells alone were not sufficient to demonstrate the unique characteristics of this system, a wide adjustable measuring range, paraformaldehyde, was added to fix these cells and alter the viscoelastic properties of these cells. As shown in Fig. 3(a), under the predefined pressure signal, single cells entered the micropipettes, clogged the flow, and elongated or shortened their protrusions with the change in applied pressure. In our experiments, the protrusion length L was defined as the distance from the micropipette entrance [indicated by blue lines in Fig. 3(a)] to the leading edge of a single cell [indicated by red lines in Fig. 3(a)] in the micropipette. When the pressure signal, as demonstrated in Fig. 3(b), was input into the whole microfluidic system, the dynamic behaviors of single cells were recorded using a time-lapse microscope. Figure 3(c) depicts the dynamic behavior of a typical cell. It is not difficult to observe that this typical dynamic behavior has obvious patterns, and to a certain extent, it could be described well by a Maxwell model.²⁰ To calculate the viscoelastic properties of cells, the Maxwell model was introduced. As shown in the inset of Fig. 3(d), the Maxwell model can be illustrated using the combination of a linear elastic spring E and a purely viscous dashpot η. Considering that a constant stress ${\sigma }_0$ is applied, the creep response can be deducted,

$$\epsilon ={\sigma }_0\left({\displaystyle \frac{1}{E}+{\displaystyle \frac{1}{\eta }t}}\right).$$ (2)

FIG. 3.

(a) Phase contrast microscopy images taken from a time-lapse series at 20 s intervals. Red lines mark the micropipette entrance, and blue lines mark the leading edge of a single cell. (b) The pressure signal inputted into the microfluidic system. (c) Time sequence of the protrusion length extracted from the time-lapse series shown in (a). (d) Blue dashed box Time Window 2 in (c) was magnified to show the calculation of mechanical properties. Inset: The schematic diagram and simulation result of the Maxwell model.

Under this model, when a constant stress is applied, the ideal elastic spring stretches instantaneously, and the viscous dashpot extends with time until the stress is removed. Upon release of the stress, the spring contracts immediately. However, the dashpot would not recover, and the viscous component of the previous strain remains.

Assuming that the elastic component and the viscous component contribute the same in a specific time interval T under a given applied pressure, then, as shown in the inset of Fig. 3(d), the strain curve in the simulation is similar to the strain curve in the experiment. The Maxwell model cannot perfectly describe the behavior when the stress is removed. The Maxwell form of the Zener model might be used to solve this problem by introducing an additional ideal spring. However, it would increase the complexity of the calculation. In this study, we hope to distinguish cell phenotypes as simply as possible, and two parameters are sufficient to achieve this goal (see the supplementary material for more information).

To calculate Young's modulus and the apparent viscosity of a single cell, a specific time window with a descending part and an ascending part is selected from the strain curve and magnified, as demonstrated in Fig. 3(d). Next, the second half of the ascending part is used for linear fitting. Then, the straight line obtained by the linear fitting is extended backward until it intersects with the vertical line where the descending part ends. Using the fitting slope k and the instantaneous strain δ, Young's modulus can be calculated according to the following formula:²⁹

$$\delta ={\displaystyle \frac{3r{\mathrm{\Phi }}_p\mathrm{\Delta }p}{2\pi E},}$$ (3)

and the apparent viscosity can be calculated according to the following formula:²⁰

$$k={\displaystyle \frac{\mathrm{\Delta }p\times S}{6\eta \pi r},}$$ (4)

where r is the radius of the micropipettes. Φ_p is the coefficient related to the structure of the micropipettes and Φ_p = 2.1 in our experiments.³⁰

Δp is the pressure difference on a single cell. E and η are Young's modulus and the viscosity coefficient of a single cell, respectively. For the strain response obtained in the experiment, as shown in Fig. 3(d), four time windows are available for calculating the viscoelastic properties of cells. To explore whether there are differences among these calculated viscoelastic distributions, all viscoelastic distributions of MCF-7 cells without PFA treatment are drawn in Figs. 4(a) and 4(b). It is easy to find that the differences are not obvious. Using hypothesis testing, we find that the Kolmogorov–Smirnov test does not reject the null hypothesis at the 1% significance level; that is, there is no significant difference among these distributions. Therefore, the viscoelastic distributions of different time windows can be aggregated to increase the sample size. This also indicates that the system could obtain ∼300 samples in one measurement, which has certain advantages in practical applications in contrast to previous studies.³⁰

FIG. 4.

(a) Distributions of Young's modulus of MCF-7 cells without PFA treatment (Time Window 1–4 and total). (b) Distributions of apparent viscosity of MCF-7 cells without PFA treatment (Time Window 1–4 and total). n_i = 77, 71, 60, and 46 for the ith time window, and n_total = 254 for (a) and (b).

In addition, for the MCF-7 cell line without any special treatment in our experiments, the median and quartiles (25%, 75%) of Young’s modulus were 6.94 × 10² Pa (3.61 × 10² Pa, 1.375 × 10³ Pa), and the values of apparent viscosity were 4.77 × 10³ Pa s (2.10 × 10³ Pa s, 9.82 × 10³ Pa s). These results were comparable with previous research.^19,31–33 Thus, our microfluidic system could be considered reliable. However, even on a logarithmic scale in Fig. 4, a dramatic divergence of mechanical properties was caused by heterogeneity at the single-cell level. The variation in these mechanical properties could reach up to two orders of magnitude. Considering previous studies, it can be concluded that cellular heterogeneity is intrinsic for single cells. It is neither reasonable nor comprehensive to neglect the heterogeneity in discussing the mechanical properties of single cells.

Cancer cells with PFA treatments

To characterize the measuring range of this system, we measured the mechanical properties of MCF-7 cells treated with different concentrations of PFA. Typical examples of MCF-7 cells without PFA treatment and exposed to PFA at a concentration of 0.5% are shown in Figs. 5(a) and 5(b), respectively. The MCF-7 cells without PFA treatment denoted the control groups. The changing trend of the 0.5% PFA treatment group under the higher-pressure input was similar to that of the control group. However, Young’s modulus and the apparent viscosity of PFA-treated cells increased dramatically. Meanwhile, Figs. 5(c) and 5(d) reveal that a low concentration of PFA might increase Young's modulus and the apparent viscosity of cells only slightly. A threshold concentration that would remarkably change these mechanical properties may exist. Similar evidence has appeared in previous research. With treatment with 0.5% PFA, the cells should be much harder than the untreated cells.³⁴ Moreover, even though the difference with or without treatment could be a multiple of ten, it would become only one on a logarithmic scale. In our experiments, the median and quartiles (25%, 75%) of Young’s modulus and the apparent viscosity were 8.17 × 10² Pa (5.07 × 10² Pa, 1.72 × 10³ Pa) and 6.46 × 10³ Pa s (3.76 × 10³ Pa s, 1.49 × 10⁴ Pa s) for the 0.2% PFA treatment group and 2.26 × 10³ Pa (1.33 × 10³ Pa, 4.60 × 10³ Pa) and 3.87 × 10⁴ Pa s (1.81 × 10⁴ Pa s, 8.00 × 10⁴ Pa s) for the 0.5% PFA treatment group, respectively.

FIG. 5.

(a) Typical examples of MCF-7 cells exposed to 0.0% PFA. (b) Typical examples of MCF-7 cells exposed to 0.5% PFA. (c) Violin plot of Young's modulus of MCF-7 cells exposed to 0.0%, 0.2%, and 0.5% PFA. (d) Violin plot of apparent viscosity of MCF-7 cells exposed to 0.0%, 0.2%, and 0.5% PFA. n = 477, 197, and 164, for 0.0%, 0.2%, and 0.5% PFA in (c) and (d), *p < 0.05, **p < 0.01, and ***p < 0.001 compared with untreated MCF-7 cells for the Wilcoxon rank sum test.

The differentiation of SCAPs

Recently, chemical or physical approaches to induce the differentiation of stem cells have been a current research focus. Based on these emerging studies, stem cell therapies such as stem cell transplantation are becoming a potential alternative to conventional medicine in the treatment of many diseases. Determining the differentiation processes of stem cells is crucial for stem cell therapies. Related protein expression levels have been used as markers to test the status of differentiating cells in previous studies. The physical properties of stem cells might be regarded as a valuable supplement to characterize the stages of cell differentiation.

In our experiments, this system was used to measure the mechanical properties of stem cells from the apical papilla (SCAPs) during osteogenic differentiation. Figures 6(a) and 6(b) are bright field images of differentiating cells on the 1st and 20th days. We measured the mechanical properties of these cells, as shown in Figs. 6(c) and 6(d). It is obvious that the apparent viscosity of cells grew significantly in the late stage of osteogenic differentiation after 7 days. However, there were no noteworthy changes in Young’s modulus of the cells during osteogenic differentiation. Only a slight increase was observed on the 13th day. Therefore, our results show that osteogenic differentiated cells had a higher apparent viscosity than undifferentiated cells rather than a higher Young's modulus. Because the cells were discrete from the dish, the cover calcified material was removed from single cells, and the measured mechanical properties of the cells were much different from those of teeth. On the other hand, although bone-like nodules were observed in the experiments, they were distributed randomly and discretely, indicating that there may also be many undifferentiated cells. If the proportion of differentiated cells could be increased, the mechanical properties would be more significant than currently.

FIG. 6.

(a) Bright field image of undifferentiated SCAPs before osteogenic differentiation (scale bar: 100 μm). (b) Bright field image of SCAPs during osteogenic differentiation on the 20th day (scale bar: 100 μm). (c) Bar chart of Young's modulus of SCAPs during osteogenic differentiation. (d) Bar chart of the apparent viscosity of SCAPs during osteogenic differentiation. n = 1392, 117, 74, 108, and 179 for Stem (baseline), day 1, day 7, day 13, and day 20 for (c) and (d); *p < 0.05, **p < 0.01, and ***p < 0.001 compared with stem cells for the Wilcoxon rank sum test.

CONCLUSION AND DISCUSSION

The mechanical properties of cells obtained using different methods might differ by two or three orders of magnitude. On the one hand, the mechanical properties of the subcellular compartments are highly heterogeneous, such as the cell nucleus and cytoplasm. On the other hand, phenotypic heterogeneity among cells leads to a wide variation in the mechanical properties of cells. Developing an easy-to-operate and reliable microfluidic system that could provide a wide measuring range could be a considerable advancement for related fields.

Our system could use a microvalve to adjust the pressure range from 0.03–1 to 0.3–10 kPa, making it possible to characterize cellular heterogeneity, even across cell types. Unlike previous microfluidic systems with the same design principle, the introduction of the pressure stabilizer reduced the influence of the cell capture rate on the applied pressure. This design enhanced our system robustness and made it more reliable than other similar systems. The improvement of the experimental procedures ensured that the operator obtained ∼300 samples via a single measurement. Nevertheless, this system also has some problems to be addressed. Many cells bypassed the trapper and flowed out of the system because of the pressure stabilizer. Modeling of the mechanical properties was also simplified to reduce computational complexity. Overall, our system achieved the original purpose. This was confirmed by subsequent measurements of the mechanical properties of MCF-7 cells treated with different concentrations of PFA.³⁴ For untreated MCF-7 cells, the measured values approximately coincided with those of previous studies. In the experiments depicting stem cell differentiation pathways, we did not observe dramatic changes in Young’s modulus, as expected.³⁵ However, the apparent viscosity of some SCAPs increased noticeably in the late stage of differentiation. Perhaps the incomplete differentiation needed to be responsible for it. Compared with traditional micropipette techniques, our microfluidic system cannot screen out specific types of cells in experiments. Future research should focus on adding these features to this system.

SUPPLEMENTARY MATERIAL

See the supplementary material for the comparison of fitting methods for our data.

AUTHOR DECLARATIONS

Conflict of Interest

The authors have no conflicts to disclose.

Author Contributions

X.L., Y.J., and C.L. designed the research; X.L., Y.J., and X.S. performed the research; X.L., Y.J., J.S., C.L., and Q.O. analyzed the data; and X.L. Y.J., and C.L. wrote the paper.

DATA AVAILABILITY

The data that support the findings of this study are available from the corresponding author upon reasonable request.