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In-vitro study of monocytic THP-1 leukemia cell membrane elasticity with a single-cell microfluidic-assisted optical trapping system

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Abstract

We studied the elastic profile of monocytic THP-1 leukemia cells using a microfluidic-assisted optical trap. A 2-µm fused silica bead was optically trapped to mechanically dent an immobilized single THP-1 monocyte sieved on a 15-µm microfluidic capture chamber. Cells treated with Zeocin and untreated cells underwent RT-qPCR analysis to determine cell apoptosis through gene expression in relation to each cell’s deformation profile. Results showed that untreated cells with 43.05 ± 6.68 Pa are more elastic compared to the treated cells with 15.81 ± 2.94 Pa. THP-1 monocyte’s elastic modulus is indicative of cell apoptosis shown by upregulated genes after Zeocin treatment. This study clearly showed that the developed technique can be used to distinguish between cells undergoing apoptosis and cells not undergoing apoptosis and which may apply to the study of other cells and other cell states as well.

© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

1. Introduction

Chemical-based staining and detection protocols include sample preparation that requires histological dyes or immunolabeling that is costly, laborious, and may affect the cell’s integrity. Recently, the mechanical properties of a cell have shown promising outcomes as an alternative label-free biomarker assay that can differentiate cell state [1,2]. Moreover, studying cell’s mechanical properties can provide additional information about biological processes such as adhesion, proliferation, and migration [3]. Also, cell profiling of cells using mechanical properties has been tested for fibroblast cells using a dual-optical trap [4] and holographic optical tweezers [5], and for malignant and metastatic cells using optical stretcher [6]. This was supported by the work of Kaffas et al. in 2014 that mechanical property can differentiate normal cells from cancerous cells [7]. Typical mechanical properties of a cell include elasticity, deformability, adhesiveness, viscosity, and many others. Several techniques are currently available in elucidating these mechanical properties such as atomic force microscopy (AFM) [8], magnetic twisting cytometry [9], micropipette aspiration [10,11], and optical trapping [1215]. However, the atomic force microscopy technique uses a pointed cantilever that may damage the cells and requires dry sample preparation that cannot mimic the cell environment. Magnetic twisting cytometry and micropipette aspiration, on the other hand, are limited to larger cells. The current optical trapping technique makes use of vertical indentation to determine the mechanical properties of a cell [16]. However, this technique has a limited axial displacement range for the microbead handler due to the random background noise of the surrounding media arising from the Brownian motion of an aqueous solution. To address this limitation, we implemented a single-cell microfluidic-assisted optical trapping technique that uses spherical microbeads that can minimize cell damage and can accommodate wider space for cell movement. Moreover, the microfluidic platform has the advantage of holding and isolating single cells for easy location of the cells. This provides for faster elasticity moduli acquisition times suitable for a single-cell THP-1 monocyte that rapidly divides.

Cell membrane elasticity is one of the many ways to identify cytoskeletal cell alterations that has the potential of determining the treatment efficacy for terminal illnesses, such as cancer, which is one of the leading causes of death worldwide [17]. In the Philippines alone, leukemia has a five-year survival rate of 5.2% and accounts for the 4,270 new cancer cases in 2015 [18]. Some anticancer drugs inhibit the abnormal proliferation of cancer by targeting the specific pathway that will lead to apoptosis or cell death. Several studies suggest that apoptosis is associated with the upregulation of the cfos and cjun gene expressions [1921]. The early apoptotic cfos and cjun marker genes can be activated by drugs that stimulate the cAMP pathway or Ca2+ elevation. Moreover, cfos and cjun are known to be associated with the cytoskeletal functions of the cell that contributes to its mechanical properties. In addition, akt or protein kinase B is an important regulator for cell survival, growth, and more importantly in actin reorganization [2224]. Furthermore, actin cytoskeleton reorganization largely contributes to the mechanical properties of cells [25,26]. Thus, targeting signaling pathways that lead to the inhibition of akt gene expression and the induction of cfos and cjun gene expressions may have the ability to modify the mechanical properties of cells.

In this study, monocytic THP-1 leukemia cells were treated with Zeocin, an anticancer drug known to downregulate growth-promoting akt gene and upregulate early apoptosis-promoting cfos and cjun gene expressions cascading to cytoskeletal effects through actin filament reorganization. The expressions of these anti-apoptotic and pro-apoptotic genes were compared to the elasticity profile of THP-1 after the administration of the drug. Measurement of membrane elasticity modulus is a label-free biomarker that may not only address the high cost of medical tests, extensive procedures, and cell modification due to chemical staining but also an indicator for early apoptosis of cells—leading to the discovery of potential cancer treatments. Moreover, this study can be extended to profiling other types of cells.

2. Materials, experimental setup, and method

2.1 Cells and cell culture

The THP-1 human monocytic leukemia cell line (American Type Culture Collection, Manassas, VA, USA) was provided by the Molecular Science Unit Laboratory (MSUL), Center for Natural Science and Environmental Research (CENSER), De La Salle University, Manila. THP-1 cells were maintained and cultured following standard protocol in a complete medium composed of Dulbecco’s Modified Eagle’s Medium (DMEM, Invitrogen, USA), 10% fetal bovine serum (FBS), and 1x antibiotic-antimycotic. Growth was attained at 37°C in a humidified incubator supplemented with 5% CO2 until 90% confluence prior to harvesting. The cells were then harvested, and an aliquot was stained with trypan blue to determine viable cell counts under a hemocytometer.

2.2 Microfluidic device fabrication

The fabrication materials and equipment for the microfluidic chip was provided by Nanobio Engineering group at Osaka University, Japan. The fabrication consisted of two parts – the master mold (silicon wafer) lithography printing and the microfluidic chip (PDMS polymer) following the protocol of Lake et al. [27]. Initially, the diameter of THP-1 cells (n = 90, ø = 13.02 ± 2.15 μm) was measured using a DS-Fi3-L4 microscope (Nikon Corporation) to estimate the capture chamber. The microfluidic chip was designed using AutoCAD2019 (Autodesk Inc.). Subsequently, a master mold (4-inch silicon wafer) was coated with SU-8 negative photoresist (SU-8 3025, MicroChem Corp., Westborough, MA, USA). It was then exposed to ultraviolet light using the maskless lithography machine (NanoSystems Solutions, Inc.) following the design of the microfluidic platform. The UV-exposed molecules crosslinked to form the structure, while the unexposed molecules remained soluble and were removed using SU-8 developer (MicroChem Corp., Westborough, MA, USA). Afterward, metal eyelets were glued at the inlet and outlet of the channel to support the silicon tubes. The polydimethylsiloxane (PDMS) was mixed containing the PDMS base and curing agent (Silpot 184, Dow Corning Toray, Tokyo, Japan) with a 10:1 ratio. PDMS was chosen because it has a transparent, low auto-fluorescence, and biocompatible properties. The fabricated PDMS microfluidic chip has a thickness of 1.5 mm and has 468 trapping sites with 0.015 mm width, 0.010 mm length, and 0.025 mm height. The PDMS microfluidic chip was bonded to a micro cover glass slide with 50 × 70 × 0.1 mm (Matsunami Glass Ind, Ltd.) using a plasma surface treatment (PDC210, Yamato Scientific Co., Ltd.).

2.3 Cytotoxic treatment with Zeocin

A total of 100 µL aliquots containing 1 × 105 viable THP-1 cells per mL in complete DMEM were seeded into each well of a 96-well plate and incubated overnight in a humidified incubator at 37°C supplemented with 5% CO2. The cells were then exposed to two-fold serial dilutions of Zeocin at 100, 50, 25, 12.5, 6.25, 3.123, 1.56, and 0.78 µg/mL concentrations followed by further incubation for 24 hours. Wells with untreated cells served as the negative control. Ten µL of PrestoBlue viability reagent (Invitrogen, USA) was added into each well and incubated for a minimum of 4 hours at 37°C with 5% CO2 in a humidified chamber to allow the remaining viable cells to metabolically convert blue resazurin to red resorufin. Spectrophotometric measurements were performed at 570 nm (BioTek Instruments, USA) to obtain optical density readings from which cytotoxicity indexes (CI%) were calculated using Eq. (1) below:

$${\textrm{CI}}\% = 100 - \left( {\frac{{O{D_{570}}\; treated}}{{O{D_{570}}\; untreated}}} \right)100\; $$
where OD570 is the measured optical density at 570 nm. The CI% values of Zeocin were used to determine the optimum concentration that resulted in a 50% cell viability reduction (IC50). The IC50 value was extrapolated from dose-response curves via nonlinear regression analysis using GraphPad Prism v.7.01 (GraphPad Software, Inc., USA). The calculated IC50 value was used as the concentration for the treatment of THP-1 cells in subsequent experiments.

2.4 Reverse transcription quantitative polymerase chain reaction (RT-qPCR) of akt, cfos, and cjun transcripts

RT-qPCR was performed according to standard methods with a few variations [28]. Firstly, a T-50 flask containing 5 mL THP-1 cells (1 × 105 viable cells per mL) were treated with the IC50 of Zeocin and incubated for 24 hours. A similar T-50 flask without Zeocin treatment was prepared as the untreated control. The cells were harvested and total RNA was extracted from both untreated and Zeocin-treated cells using Trizol (Invitrogen, USA) following the manufacturer’s instructions. Reactions for RT-qPCR were prepared as 10 µL volumes each containing 1.0 µL RNA, 1x KAPA One-Step SYBR (Roche, Switzerland) Fast Buffer I, 1x KAPA reverse transcriptase, 0.3 µM of each primer (Table 1), and Diethyl Pyrocarbonate (DEPC)-treated water. The reactions were subjected to initial cDNA synthesis at 50 °C for 3 mins followed by the actual PCR profile consisting of 45 cycles of 95 °C for 1 min (denaturation), 55 °C for 1 min (annealing), and 72 °C for 1 min (extension). A melting curve was performed thereafter. The same reaction was independently performed using primers for gapdH, the endogenous housekeeping gene control. The critical cycle threshold (Ct) was obtained from the built-in Rotor Gene software (RGQ v. 2.3.1.49). From the Ct value data, the relative gene expression 2(−ΔΔCt) of akt, cfos, and cjun genes were calculated.

Tables Icon

Table 1. Primer sequence for the amplification of akt, cfos, cjun, and gapdH gene transcripts

2.5 Microfluidic-assisted optical trapping

The membrane elasticity of THP-1 cells was measured using the microfluidic-assisted optical trapping (Figs. 1(a)–1(b)) that consisted of optical trapping (Impetux Optics S. L.) and microfluidic technology. The continuous-wave laser beam (Thorlabs, Compact laser Diode, λ = 976 nm) was focused using an objective lens (Nikon Plan Fluor 100x, oil) with a numerical aperture of 1.30. The sample chamber is made of a microfluidic platform (0.17 mm thick glass slide) with a working distance of 0.33 mm above the objective lens. The microfluidic platform was mounted on a piezo stage (Thorlabs, 3-Axis NanoMax Stage) that provides nanometer resolution for three-dimensional positioning of the sample. The optical trapping stiffness was calibrated using the power spectrum method with a 1μm/step position resolution.

 figure: Fig. 1.

Fig. 1. a) Microfluidic-assisted optical trapping configuration; L: Lens, WP: waveplate, PBS: Polarizing beam splitter, M: mirror, DM: dichroic mirror, CCD: Charged-coupled device, PSD: Position sensitive detector. b) The actual microfluidic-assisted optical trapping setup. (c-f) Elasticity measurement of THP-1 cells. c) A mixture of THP-1 cells ($\color{green}{\textbf{green}}$) and 2 μm fused silica beads ($\color{yellow}{\textbf{yellow}}$) in DMEM is infused into the inlet which flows onto the trapping sites of the microfluidic chip. d) THP-1 cells are captured inside the trap site. e) The 976 nm laser ($\color{red}{\textbf{red}}$) is turned on at 200 mW to trap the beads. f) The piezo stage is moved towards the bead to deform the cells.

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There are two consecutive protocols in measuring the cell membrane elasticity: the optical trapping of the 2.06 µm non-functionalized silica microparticles (Bangs Laboratories) using a 976 nm laser diode with an incident power of 200 mW and the capturing of ∼13 µm sized single-cell THP-1 monocytes inside a PDMS microfluidic chip. Briefly, a mixture of 2.06 µm beads and THP-1 monocyte cells were injected at the inlet of the microfluidic chip. After 3-5 minutes of cell sieving inside the microfluidic chip, the THP-1 cells occupied all the capturing sites. Afterward, the 976 nm laser was activated to trap and control the nearest bead for cell indentation with a 24.72 pN trapping force. The XYZ piezo stage where the THP-1 monocytes are captured inside the microfluidic chip moved transversely towards the optically trapped bead to deform the moving incident cell. Figures 1(c)–1(f) shows the experimental setup of the sieving of cells using a microfluidic chip and trapping of the bead using an optical tweezer.

2.6 Membrane elasticity of THP-1

The modulus of elasticity or Young’s modulus was determined using the Hertz approximation model. This is a geometry dependent contact theory of two spherical surfaces considering that there are no adhesion and friction between the two materials [29]. The elasticity can be quantified by the following equation

$$E = \frac{3}{4}\; \frac{F}{{{d^{3/2}}\; {R^{1/2\; }}}}$$
where F is the indentation force, d is the depth, and R is the relative radii [30]. The relative radii R of the two materials are given by $1/R = 1/{R_1}\; + 1/{R_2}$, which can be rewritten into $R = ({{R_1}{R_2}} )/({{R_1} + {R_2}\; } )$. For two different elastic objects in contact, the effective elastic modulus of the system is $1/E = 1 - {v_1}^2/\; {E_1}\; + 1 - {v_2}^2/{E_2},\; $where ${E_n}$ is the elastic modulus, and ${v_n}$ is the Poisson’s ratio. Poisson's ratio is the degree of contraction or expansion of material perpendicular to the loading direction. The subscripts 1 and 2 denote the two different materials. The elastic modulus of the fused silica bead is around 70 GPa or 7 × 105 K/cm2, which is large compared to the cell, having the second term of effective elastic modulus will be assumed zero [31]. Thus, the elasticity of the cell ${E_1}$ becomes [32]:
$${E_1} = \frac{3}{4}\; \frac{{({1 - {v^2}} )\; F}}{{{d^{3/2\; }}\; {R^{1/2}}}}\; .$$

2.7 Statistical analysis

For the cytotoxicity and RT-qPCR experiments, all samples were assayed in triplicate. The gathered data are presented as mean ± standard error of the mean unless stated otherwise. A two-sample Students’ T-test was used to determine the statistical differences between the untreated THP-1 cells and Zeocin-treated THP-1 cells. In our analysis, a p-value of <0.05 was considered statistically significant.

3. Results

3.1 Trapping capability of PDMS microfluidic chip

The design of the microfluidic chip was based on a hydrodynamic microfluidic method that has a mechanism to sort and isolate single THP-1 cells. It consists of inlet, filter, trapping sites, and outlet as shown in Fig. 2. The single-cell 69% trapping efficiency of the microfluidic chip was determined by imaging and counting the trapped cells. Several parameters affect the trapping efficiency of the microfluidic chip, but in this study, we considered the flow rate, flow guide, and flow resistance between the main channel and the trapping channel in the design. The cells were loaded at a flow rate of 0.5 ml/min.

 figure: Fig. 2.

Fig. 2. Illustration showing the a) microfluidic chip parts, b) trapped THP-1 cells in a trapping site, and c) the fabricated microfluidic chip.

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3.2 Cytotoxicity of Zeocin on THP-1 cells

The cytotoxicity indices (CI%) were plotted against Zeocin concentrations (log10). Based on the cytotoxicity index (CI%) plots via nonlinear regression (Fig. 3), the IC50 of the anticancer drug, Zeocin was calculated. Based on the results, Zeocin is cytotoxic to THP-1 cells with an IC50 value of 9.17 μg/mL. According to the American National Cancer Institute (ANCI), the accepted criteria for the cytotoxicity activity for pure compounds is 10 μg/mL [33]. The measured IC50 value is below the accepted standard, hence we used Zeocin for the experiment to ensure that the cells will commit early apoptosis.

 figure: Fig. 3.

Fig. 3. Dose-response curve of THP-1 cells after treatment with two-fold serial dilutions of Zeocin.

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3.3 Regulation of akt, cfos, and cjun gene expression

Changes in the regulation of expressions of the anti-apoptotic akt gene and early proapoptotic cfos and cjun genes were determined to confirm apoptosis and to associate this with changes in cell membrane elasticity. RT-qPCR results showed that the akt, cfos, and cjun gene expressions (2-ΔΔCt) of THP-1 cells (2.18 × 104 ± 2.58×103, 8.47 ± 2.94, and 10.58 ± 1.42, respectively) changed significantly after administration of Zeocin (7.52 ± 3.18, 4.38 × 104 ± 5.80 × 103, and 2.97 × 104 ± 1.09 × 104, respectively) as shown in Fig. 4. The relative gene expression of the anti-apoptotic akt gene was significantly downregulated (p < 0.05), while the relative gene expression of cfos and cjun genes were significantly upregulated (p < 0.05) compared to untreated controls.

 figure: Fig. 4.

Fig. 4. Relative gene expression (2-ΔΔCt values) of anti-apoptotic marker Akt gene and early apoptotic markers cfos and cjun genes for untreated and treated THP-1 cells.

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3.4 Alteration of the cellular membrane of THP-1 cells

To determine the effect of akt inhibition, and cfos and cjun increased expression, we employed microfluidic-assisted optical trapping to determine the membrane elasticity. The results showed that the membrane elasticity of THP-1 cells (43.05 ± 6.68 Pa, n = 11) was altered after exposure to Zeocin (15.81 ± 2.94 Pa, n = 9) as shown in Fig. 5. This suggests that the decrease in expressions of the akt gene and an increase in expressions of cfos and cjun genes of THP-1 cells resulted in a decrease in membrane elasticity (p< 0.05). Thus, the administration of Zeocin onto the THP-1 cells could alter its elastic moduli.

 figure: Fig. 5.

Fig. 5. Cell membrane deformation of (a) THP-1 cell and (b) THP-1 + Zeocin (scale bar = 5 μm). c) The scatter plot of membrane elasticity modulus of THP-1 compared to THP-1 with Zeocin.

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4. Discussion

The elastic modulus of a material determines the material’s resistance to being deformed. The lower elastic modulus signifies that the cell can be easily deformed when force is applied. Microfluidic-assisted optical trapping was used to measure the membrane elasticity of monocytic leukemia cells treated and not treated with an anticancer agent, Zeocin. However, according to other research works, the 976 nm laser used can induce heat absorption and photodamage on cells after a long exposure, such as for greater than five minutes [34,35]. In this research, the optical tweezer trapped a highly transparent microbead that offered no direct near-IR radiation exposure and no thermal conduction on the single cell. In addition, the optical tweezer used a laser diode with a 200 mW incident power that had approximately 1 μm diffraction limited beam spot size and a 2 μm sized optically trapped microbead, where the microbead was larger than the focused beam spot. Thus, photodamage on a single cancer cell could be minimized under these optical trapping conditions.

The Zeocin-treated flask contained 99.95% non-viable cells as measured using the trypan blue assay. Counting was done 24 hours after Zeocin treatment. The relative percentage of non-viable cells was calculated by back-tracking from the transcript copy numbers in which each had a corresponding cycle threshold (Ct), and deriving the relative number of cells from the standard curve of the gapdh housekeeping gene assayed using known concentrations of 102, 103, 104, 105, 106, 107, and 108 copies/μL (7 orders of magnitude). Each concentration had a relative number of cells based on the copy number of the housekeeping gene per cell. At the same time, the Zeocin-treated cells showed the upregulation of the expression of the early apoptotic cfos and cjun genes and the downregulation of the expression of the anti-apoptotic akt gene. These substantiate that the THP-1 cells tested for membrane elasticity were mostly undergoing early apoptosis.

The RT-qPCR results showed that Zeocin treatment inhibited the expression of the anti-apoptotic akt gene and upregulated the expression of the pro-apoptotic cfos and cjun genes. The regulation of these genes is nominally an indication of the apoptosis of the cell. Moreover, it can be attributed to the alteration of actin filaments [12,36]. The actin filamentary structures are parts of the cytoskeleton that provides cell support and shape. Consequently, the disaggregation of actin filaments is always followed by a decrease in cellular membrane elasticity [37]. Other techniques have been used to investigate the alteration of mechanical properties and its relationship with actin reorganization [38,39]. The changes in the mechanical properties are associated with the activation of p38 mitogen-activated protein kinases (MAPK) pathway [38,40]. The deficiency of MAPK would lead to the cytoskeletal reorganization of the cell [41,42]. Furthermore, the activation of the MAPK signaling pathway regulates cjun gene expression [43,44], triggers cfos gene expression [44,45], and interplays with the akt signaling pathway [46]. Thus, the regulation of these gene expressions can be attributed to the decrease in cell membrane elasticity after the administration of Zeocin.

The current study demonstrated that the THP-1 cells undergoing apoptosis had lower elastic modulus and is highly related to the regulation of the gene expression of the akt (anti-apoptotic), and cfos and cjun (early pro-apoptotic) genes. The current findings are supported by the results of previous reports. The measured elasticity is within the typical elastic modulus of eukaryotic cells that ranges from 101 Pa to 103 Pa [47]. Moreover, the mechanical properties of cells may decrease or increase after the administration of drugs because of the distinct apoptotic pathways in the cell [11]. Chemotherapeutic drugs usually target the cytoskeleton of cells that will affect the stiffness or elasticity of cells [48].

Overall, this study demonstrated that the decrease in the elasticity of the cell membrane was related to the upregulation of the expression of early pro-apoptotic genes cfos and cjun and the downregulation of the expression of the pro-apoptotic gene akt. Interestingly, changes in membrane elasticity can provide information about the metabolic processes of the cells when exposed to anticancer drugs. Moreover, the use of the microfluidic-assisted optical trapping can be applied to other cell types, treatments of cells at varying concentrations, and treatments of cells over time.

5. Conclusion

In-vitro cell membrane elasticity analysis indicated that the THP-1 leukemia cells treated with Zeocin exhibited lower elastic modulus compared to the untreated cells. This alteration in the membrane elasticity can be attributed to the regulation of the gene expressions. Comparative gene expression analysis showed that the anti-apoptotic akt gene expression and pro-apoptotic cfos and cjun gene expressions in THP-1 cells were downregulated and upregulated respectively after Zeocin treatment. The reduction of membrane elasticity was largely attributed to the ongoing cell apoptosis of THP-1 leukemia cells due to Zeocin. Another technical highlight of this study is the integrated use of the microfluidic system and optical trapping system, a promising optical tool, and a novel microfluidic platform in performing elastic moduli measurements for rapidly dividing cells like THP-1 leukemia cells as a biomarker without using chemical staining to differentiate cell state.

Funding

Philippine Council for Industry, Energy, and Emerging Technology Research and Development (04125).

Acknowledgment

The authors wish to extend their sincerest gratitude to Prof. Eiichi Tamiya from Nanobioengineering Laboratory of Osaka University, Japan for the fabrication of the microfluidic chip.

Disclosures

The authors declare no conflicts of interest.

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Figures (5)

Fig. 1.
Fig. 1. a) Microfluidic-assisted optical trapping configuration; L: Lens, WP: waveplate, PBS: Polarizing beam splitter, M: mirror, DM: dichroic mirror, CCD: Charged-coupled device, PSD: Position sensitive detector. b) The actual microfluidic-assisted optical trapping setup. (c-f) Elasticity measurement of THP-1 cells. c) A mixture of THP-1 cells ($\color{green}{\textbf{green}}$) and 2 μm fused silica beads ($\color{yellow}{\textbf{yellow}}$) in DMEM is infused into the inlet which flows onto the trapping sites of the microfluidic chip. d) THP-1 cells are captured inside the trap site. e) The 976 nm laser ($\color{red}{\textbf{red}}$) is turned on at 200 mW to trap the beads. f) The piezo stage is moved towards the bead to deform the cells.
Fig. 2.
Fig. 2. Illustration showing the a) microfluidic chip parts, b) trapped THP-1 cells in a trapping site, and c) the fabricated microfluidic chip.
Fig. 3.
Fig. 3. Dose-response curve of THP-1 cells after treatment with two-fold serial dilutions of Zeocin.
Fig. 4.
Fig. 4. Relative gene expression (2-ΔΔCt values) of anti-apoptotic marker Akt gene and early apoptotic markers cfos and cjun genes for untreated and treated THP-1 cells.
Fig. 5.
Fig. 5. Cell membrane deformation of (a) THP-1 cell and (b) THP-1 + Zeocin (scale bar = 5 μm). c) The scatter plot of membrane elasticity modulus of THP-1 compared to THP-1 with Zeocin.

Tables (1)

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Table 1. Primer sequence for the amplification of akt, cfos, cjun, and gapdH gene transcripts

Equations (3)

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CI % = 100 ( O D 570 t r e a t e d O D 570 u n t r e a t e d ) 100
E = 3 4 F d 3 / 2 R 1 / 2
E 1 = 3 4 ( 1 v 2 ) F d 3 / 2 R 1 / 2 .
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