Development of a Microfluidic Device for Single Cell Specific Membrane Capacitance Quantification

by

Qingyuan Tan

A thesis submitted in conformity with the requirements for the degree of Master of Applied Science

Department of Mechanical and Industrial Engineering University of Toronto

© Copyright by Qingyuan Tan 2012

ii

Development of a Microfluidic Device for Single Cell Specific

Membrane Capacitance Quantification

Qingyuan Tan

Master’s of Applied Science

Department of Mechanical and Industrial Engineering University of Toronto

2012

Abstract

The specific membrane capacitance (SMC) of biological cell membranes correlates with cells’

electrical activity and morphology, which are physiological markers for cellular phenotype and

health. Conventionally, SMC measurements are conducted using electro-rotation and Patch-

clamping, which entail long time training and stringent operation skills. Both techniques also

suffer from limited throughput and lengthy measurement time. In this study, a microfluidic

device, which enables impedance spectroscopy measurements, was developed to quantify the

SMC of single biological cells. The device has a testing speed of approximately one cell per

minute and is relatively easy to operate. Three-dimensional finite element simulations of the

microfluidic device confirm the feasibility of this approach. SMC measurement of two AML

(Acute Myeloid Leukemia) subtypes and two UCC (Urothelium Cell Carcinoma) subtypes were

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conducted. Measured SMC results were found to lie in the comparable range with previously

reported publications.

iv

Acknowledgments

I am sincerely grateful to my supervisor, Professor Yu Sun, for his support and guidance

throughout my Master’s studies at the University of Toronto. His enthusiasms for research have

inspired me to overcome every challenge I faced in research. Without his encouragement and

help this thesis would have been impossible.

I would like to give special thanks to Dr. Jian Chen, Haijiao Liu, Brandon Chen and Yi Zheng

for their patience in helping me to learn microfabrication, cell culture and sharing their valuable

knowledge with me. I would like to thank Dr. Graham Ferrier for working with me on FEM

simulation. I would like to thank all past and present members of Advanced Micro and

Nanosystems Laboratory for all the encouragement and support.

I would also like to thank Dr. Chen Wang from Mount Sinai Hospital, Dr. William Geddie from

Toronto General Hospital for their assistance in helping me with biological questions and their

valuable advices which helped me to complete my work.

In the end, I would like to express my deep appreciation to my parents’ continuous support of my

goals and aspiration in life.

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Table of Contents

Acknowledgments .......................................................................................................................... iv

Table of Contents ............................................................................................................................ v

List of Tables ............................................................................................................................... viii

List of Figures ................................................................................................................................ ix

Chapter 1 ......................................................................................................................................... 1

1 Introduction ................................................................................................................................ 1

1.1 Specific Membrane Capacitance ......................................................................................... 1

1.2 Motivation ........................................................................................................................... 3

1.3 Objectives ........................................................................................................................... 6

1.4 Thesis Organization ............................................................................................................ 7

Chapter 2 ......................................................................................................................................... 8

2 SMC Microfluidic Device .......................................................................................................... 8

2.1 Device Design ..................................................................................................................... 8

2.2 Device Fabrication ............................................................................................................ 11

2.3 Ag/AgCl Electrodes .......................................................................................................... 14

2.3.1 Electrical Double Layer ........................................................................................ 14

2.3.2 Polarizable and Non-polarizable Electrodes ......................................................... 17

2.3.3 Ag/AgCl Electrodes Fabrication ........................................................................... 17

2.4 Conclusion ........................................................................................................................ 21

Chapter 3 ....................................................................................................................................... 22

3 Equivalent Circuit Model and FEM Simulation ...................................................................... 22

3.1 Equivalent Circuit Model .................................................................................................. 22

vi

3.1.1 Equivalent Circuit Model ...................................................................................... 22

3.1.2 Complex Nonlinear least-squares curve fitting ..................................................... 23

3.1.3 SMC Determination .............................................................................................. 26

3.2 FEM Simulation ................................................................................................................ 27

3.2.1 COMSOL Simulation ........................................................................................... 27

3.2.2 Simulation Results Analysis ................................................................................. 30

3.3 Conclusion ........................................................................................................................ 32

Chapter 4 ....................................................................................................................................... 36

4 AML Subtypes SMC Quantification ........................................................................................ 36

4.1 Introduction ....................................................................................................................... 36

4.2 Material and Methods ....................................................................................................... 39

4.2.1 Materials ............................................................................................................... 39

4.2.2 Experimental procedures ...................................................................................... 39

4.3 Results and Discussion ..................................................................................................... 41

4.3.1 AML2 in different osmolality solutions ............................................................... 43

4.3.2 AML2 vs. NB4 ...................................................................................................... 46

4.4 Conclusion ........................................................................................................................ 48

Chapter 5 ....................................................................................................................................... 49

5 UCC Subtypes SMC Quantification ........................................................................................ 49

5.1 Introduction ....................................................................................................................... 49

5.2 Material and Methods ....................................................................................................... 51

5.3 Results and Discussion ..................................................................................................... 52

5.4 Conclusion ........................................................................................................................ 53

Chapter 6 ....................................................................................................................................... 56

6 Conclusion and Future Work ................................................................................................... 56

6.1 Conclusion ........................................................................................................................ 56

vii

6.2 Future Work ...................................................................................................................... 57

Bibliography ................................................................................................................................. 59

viii

List of Tables

Table 3.1: SMC values and variations versus membrane permittivity….……………………….33

Table 4.1: Different concentration sucrose/dextrose solutions used for making mediums of

different osmolality….…………………………………………………………………………..41

Table 4.2: AML2 cells diameter vs. SMC in hypertonic and isotonic mediums….....................43

ix

List of Figures

Figure 2.1: Top-view of the microfluidic device. Cell suspension and the exterior medium are

conducted from the inlet end to the outlet end. …………………………………………………10

Figure 2.2: Side-view of the microfluidic device. The loading channel is more spacious than the

tapered constriction channel, thus to preserve cell integrity before cell trapping………………..10

Figure 2.3: The force diagram for a single cell trapped inside the tapered constriction

channel...........................................................................................................................................11

Figure 2.4: Fabrication steps for forming the two-layer PDMS device. ………………………...12

Figure 2.5: Inside the dashed box: two PDMS microfluidic devices bonded on a glass

slide………………………………………………………………………………………………13

Figure 2.6: Schematic picture of an electrical double layer between an electrode surface and an

electrolyte solution. The polarity of the surface charge is determined by the nature of the solid

electrode and the electrolyte. ……………………..……………...………………………….…..16

Figure 2.7: From top to bottom: 99.9% silver wire, silver wire rinsed in bleach for 30mins,

Ag/AgCl wire…….………………………………………………………………………………18

Figure 2.8: Left: a Ag/AgCl wire soldered onto a SMC connector. Right: a Ag/AgCl electrode

sealed into a T-shaped fluid connector…………………………………………………..………19

Figure 2.9: Ag/AgCl electrodes plugged into the reservoirs on a microfluidic device. The dash

boxes marked the ports for medium passage…………………………………………………….20

Figure 3.1: (a)-(b): Circuit models used for fitting the impedance and phase spectra generated by

an empty channel (a), and a single cell trapped in the channel (b). A membrane-bound cell has a

cytoplasmic resistance, Rcell, and a membrane capacitance, Cm = C1C2 / (C1+C2). To account for

space between the cell perimeter and the channel walls, a seal resistance, Rgap, is introduced.

x

Experimental amplitude (d) and phase (e) spectra of one measured cell are fitted with the circuit

models in (a) and (b)………………………………………………………………………….….25

Figure 3.2: SEM images of the tapered channel: (a) top-view, and (b) view through the cross-

section……………………………………………………………………………………………26

Figure 3.3: (a) Three-dimensional geometry of the microfluidic chip. (b) A moderately-sized box

surrounding the cell and channel facilitated meshing between the large PDMS domain and the

much smaller channel domain. (c-d) For illustrative purposes, a side view of the microfluidic

channel reveals lines of current density colored according to their strength (blue = weak, red =

strong). Similarly, the background color represents electric potential. In this demonstration, the

membrane thickness, , is 100 nm and zgap = 250 nm. At low frequencies (Fig. 3.3(c) - 4 kHz),

current is redirected through the shunt pathways (zgap). At high frequencies (Fig. 3.3(d) - 1

MHz), current is permitted through the cell……………………………………………………...29

Figure 3.4: Specific membrane capacitances versus cell-to-channel gap, cell length, cell position

and seal resistance. The error bars represent the 95% confidence intervals for the fitted SMC.

……………………………………………………………………………………………………34

Figure 3.5: Current density versus position along the horizontal and vertical edges of the

membrane…………………………………………………………………………………......….35

Figure 4.1: Schematic of the experimental apparatus. Silver/silver chloride electrodes are

inserted into inlet and outlet ports for impedance measurements. In parallel with the electrodes

are fluid-filled tubes that route cells into the inlet port, through the loading channel, and finally

into the tapered channel. Screen captures of an AML2 cell illustrate its shape changes at two

different positions (P1 and P2). Cells are pressurized using a custom pumping system [1]........38

Figure 4.2: (a)-(d): Specific membrane capacitance (SMC) values for cells in solutions of

different osmolalities. Cells in isotonic or marginally hypertonic solutions yield essentially

xi

identical SMC values ( 0.34p ), while very-hypertonic solutions induced significant increase

( 0.01p ) in the SMC…………………………………………………………………...…….45

Figure 4.3: (a)-(c): Specific membrane capacitance values of 23 AML2 and 23 NB4 cells in

DMEM. Based on the SMC distributions across each cell population, the mean SMC values of

AML2 and NB4 cells are found to be significantly different ( 0.01p ). Cells initially parked at

a position, P1, are later parked at a more constrictive position, P2……………………………...47

Figure 5.1: Screen captures of the SMC measurement on one RT4 cell: (1). cell is aspirated into

the tapered channel via negative pressure. (2). The RT4 cell is trapped inside the tapered channel

for SMC measurement. (3). The RT4 cell is removed from the tapered channel by increasing the

negative pressure. (4). Cell is removed from the channel. The tapered channel is empty and is

ready for another measurement…………………………………………………………….....….50

Figure 5.2: SMC values of 20 measured T24 cells……………………………………………...53

Figure 5.3: SMC values of 19 RT4 cells………………………………………….……………..54

Figure 5.4: The more malignant UCC subtype T24 cells are found to have a larger mean SMC

than RT4 cells. (P<0.01) …………………………………..………………………………….…55

1

Chapter 1

1 Introduction

1.1 Specific Membrane Capacitance

The specific membrane capacitance (SMC) represents the ability of the plasma membrane to

store charges in the presence of an applied electric field. It is calculated through the standard

parallel-plate capacitance formula, 0m rC d , where is vacuum permittivity, r is the

relative permittivity of the plasma membrane and d is the thickness [2, 3]. These parameters are

largely determined by the lipid constituents of the cell membrane and influenced by the protein

content [4-6].

The fluid-mosaic model of plasma membrane indicates that proteins and other biomolecules are

incorporated into lipid bilayers [7]. Thus the capacitance of lipid bilayer functions in parallel

with the capacitance of the protein and other parts of the membrane [5][8]. For artificial

membranes, the typical SMC values is estimated to be 4-6 mF/m2 [9]. For real cells containing

brush layers and surface proteins, the SMC increases to 10-40 mF/m2 [5, 10-13].

SMC variations may represent evidence of physiological variations in biological cells. For

example, Bao et al. demonstrated that the SMC ramps significantly when the environment

temperature exceeds the physiological temperature (37 °C) [13]. In addition, Long and Xing

have monitored the time-dependence of apoptosis (programmed cell death) in Jurkat cells using

electro-rotation [14]. Their results showed that the SMC decreased significantly with time over a

48 hour timeframe after cells were treated with cytosine arabinoside.

Wang et al. [5], Irimajiri et al. [12] and Zimmermann et al. [6] have each shown that cell SMC

values would change according to the change of exterior medium osmolality. In general, the

higher the osmolality of the medium, the larger the SMC values of cells. When the same types of

cells are immersed in different osmotic medium, the constituents of the plasma membrane would

2

remain unchanged while cell would undergo volume change, i.e. shrinking or swelling. Jacobs

has pointed out that cell surface area would remain constant during this process [15], thus the

shrinking or swelling would result in cell surface morphology alteration while the total surface

area is unchanged. SEM imaging has confirmed that cell shrinking would make cell surface

microvilli thicker and more elongated, while cell swelling, on the other hand, would make the

cell surface somehow granular and is relatively free of microvilli [5, 12]. For a perfect smooth

spherical cell with radius R, the total surface area of the cell is 4R2. If the SMC of the cell is

Cspc then the total capacitance of the cell is 4R2Cspc. When the cell shrinks, the total surface

area would remain constant while R would decrease to R1. Therefore, the new SMC would

become 4R2Cspc / 4R12 which is larger than Cspc due to volume shrinkage [5, 12], the new

folds and ridges developed on the plasma membrane would increase its capability of charge

storage. In reality, blebs, microvilli, microridges, folds and ruffles would cover the cell surface,

thus cell swelling and shrinking would expand or reduce the density of cell surface structures

which lead to a SMC change.

Iyer et al. who used atomic force microscopy has shown that healthy and cancerous epithelial

cells have distinct membrane morphologies [16]. Healthy cells revealed a single surface brush

layer, while cancer cells revealed two brush lengths of significantly different densities. Peter et

al. demonstrated that healthy and cancerous mammalian cells have very distinct membrane

electric properties [17], i.e. their dielectrophoretic (DEP) crossover frequency vary significantly.

Since DEP crossover frequency reflect cell membrane relative permittivity, therefore, it is

possible that the SMC would also vary significantly between healthy and cancerous cells.

3

1.2 Motivation

Patch-clamping [18] and electro-rotation [2, 19, 20] are well known methods for measuring the

SMC of single cells. In patch-clamping, a single electrode conducts the electrical currents

flowing through ion channel molecules embedded in the plasma membrane [21, 22]. The

electrode is placed in a micropipette wherein a cell membrane region surrounding one or more

ion channels is aspirated. The suction pressure provides a gigaohm (GΩ) seal resistance, which

allows currents to be recorded with low electrical noise and good mechanical stability.

Using the appropriate equivalent circuit model, one can fit the transient current response of an

applied voltage pulse to extract the membrane capacitance of a cell [23]. However, in this rather

invasive approach, a patch of cell membrane is commonly removed from the cell surface.

Consequently, successful implementation requires laborious and skillful manipulation of the

electrode and micropipette. Furthermore, the relatively large parasitic capacitance of the glass

pipette limits the measurements to low frequencies (< 1 kHz), while on-chip patch-clamping

successfully reduces parasitic capacitance but often suffers from reduced seal resistance [21, 24-

28].

Electro-rotation is a non-invasive approach in which a cell is electrically rotated while suspended

in a low-conductivity medium. The entire cell is rotated by electric fields generated by applying

four sine waves in phase quadrature to an electrode array surrounding the cell [5, 29-32]. The

magnitude and direction of the electrical torque depend on the difference in dielectric properties

between an electrically heterogeneous cell and its surrounding medium. With recorded cell

rotation rate and direction versus frequency, the SMC is extracted by curve-fitting the dielectric

spectrum with a shell model. The low ionic strength of the medium used in electro-rotation may

compromise the integrity of the plasma membrane after an extended period of time (e.g., longer

than 10 minutes) [33]. This is a concern because automated electro-rotation systems require

approximately 10 minutes for testing one cell [34]. Multi-cell electro-rotation systems have the

additional challenges of precise cell positioning and spacing as the electrical interaction between

4

neighboring cells self-induce dipole moments, and non-centralized cells can experience lateral

dielectrophoretic forces due to field non-uniformities near the electrodes [35-39].

In comparison to patch-clamping and electro-rotation, impedance spectroscopy is a more

convenient approach for cellular electrical measurements [40] [41] [42]. The method provides

label-free, real-time and non-invasive biological detection of cell physiological state. Much

effort has been given to develop impedance spectroscopy based microfluidic devices for cellular

electrical property characterization.

Sun et al designed a high-throughput single cell impedance sensing chip which can record the

dynamic passing of single cell through the channel in a relatively short time (1ms for a single

measurement) [40]. However, due to electrode-polarization and large shunt current, the recorded

impedance spectrum is mostly sensitive to cell size. Thus the technique is unlikely to use for cell

SMC measurement (SMC is a size-invariant parameter).

Malleo et al demonstrated the dynamic variation of HeLa cells’ electrical impedances are subject

to chemical intervention [41]. The technique offers a promising and non-invasive approach to

observe the dynamic process of cell membrane pore-formation under a single frequency.

However, the existence of electrical-double layer and the poor contact between the electrode and

the trapped cell made the technique impossible for cell SMC quantification.

Han et al presented a SMC quantification technique which utilized impedance sensing and

hydrodynamic trapping of single cells [42]. The good seal between the cell and the cavity

perimeter decreased the shunt current therefore increased the measurement sensitivity of the

device. However, suffering from electrode polarization, the device was not able to present

impedance data below 10 kHz which sacrifice the accuracy of cell SMC quantification.

Bao et al. developed an approach to measuring the average SMC of a cell population using

electrical impedance spectroscopy [11, 13]. Briefly, AC signals (1 Hz – 1 MHz) are applied to

measure the impedance response of cells immobilized into numerous pores etched along a

polycarbonate filter. The impedance response of the cell batch is recorded and curve-fitted to an

equivalent circuit model to determine the capacitance of the cell membrane. Finally, with a

geometric model, they calculate the exposed surface area and subsequently the average SMC.

This technique is advantageous because cells can be measured noninvasively in physiological

5

buffers of high ionic strength. In addition, a sufficiently large seal resistance created by the cell-

to-pore interaction ensures that electric fields pass through the cell membranes. However,

because cells line up in a parallel configuration along the filter, high impedance sensitivity is

achieved only when cells fill the pore array completely, which is difficult to achieve in

experiments. Otherwise, current flows through the empty pores rather than the cell membranes.

In addition, it is difficult to ensure that cells form a monolayer along the filter. In general, cell

size heterogeneity and the formation of multiple cell layers would break down the geometric

model for calculating cell surface area. Furthermore, this approach reflects only the cell

population’s collective SMC characteristics. Hence, it is insensitive to SMC variations across

the cell population.

6

1.3 Objectives

There is an increasing drive toward developing microfluidic devices for detecting and

characterizing single cells. Rather than classify cells based on a bulk property, which represents

an averaged value over a cell population that disregards the presence of rare cells and

physiological variations, cell populations are better classified by analyzing individual cells [43-

48].

The specific objective of this study is to develop a microfluidic technique wherein the SMC

values of single cells are measured using impedance spectroscopy. Compared with previous

techniques described above, the device should be easier to use and be capable of measuring cells

under their normal physiological state. It would be more practical if a measurement of the full

impedance spectrum of a single cell can be completed within a minute (vs. 10 minutes/cell as in

electro-rotation).

7

1.4 Thesis Organization

This work is organized into the following chapters: Chapter 2 introduces the design of the device

and some knowledge about the electrical double layer. Chapter 3 introduces an equivalent circuit

model for extracting the SMC from the impedance spectrum of measured cells. Finite element

method simulations results are also provided for a better understanding about data interpretation.

Chapter 4 reports the SMC measurements and comparisons of two acute myeloid leukemia

(AML) cell line subtypes with different malignancies using the technique. Cells treated in

mediums with different osmolality are also measured and the results compared to the SMC

values reported in previous literatures. Chapter 5 reports the SMC measurements and

comparisons of two different grade urothelial cell carcinoma (UCC) bladder cell lines using the

new technique. Finally, Chapter 6 gives a summary of this research and possible future works.

8

Chapter 2

2 SMC Microfluidic Device

2.1 Device Design

One of the important functions of the device is to enable single cell trapping. There have been a

number of microfluidic designs that use impedance sensing system to measure/analysis single

cell electrical/physiological properties. Different cell trapping methods were applied in those

designs. Younghak et al, has reported a micro-device which applied hydrodynamic trapping of

single cells for cell impedance characterization [49]. Single red blood cells (RBC) were trapped

between a pair of cantilever electrodes for impedance recording. Normal RBC and alcohol

treated RBC were found to have distinct impedance spectrums in this research.

Malleo et al. have developed a microfluidic approach that focused on dynamic variations in

electrical impedance as HeLa cells are subjected to chemical variations [50]. Single cells were

trapped inside a den for impedance recording. By altering the medium constituents, they were

able to monitor the gradual lysis of cells under chemical treatment using dynamic impedance

changes.

Younghak et al [51], and Han et al [52], have each proposed a device which utilize negative

pressure to trap single cells for impedance characterization. Cells in different pathological states

were shown to own different impedance patterns.

For single cell impedance spectroscopy measurement, after the cell is trapped, a frequency

dependent signal is applied across the cell. By measuring the current response, the impedance

analyzer is able to generate the impedance spectrum of the measured cell. Shunt current is the

major issue that would affect the measurement results. If the shunt current is too large, then most

current would go around the cell rather than go through the cell, therefore, most of the

9

cell/exterior interaction rather than the cell electrical properties are reflected in the impedance

spectrum.

Thein et al, have used electrode surface modification to enhance the adhesion between cell and

the electrode, thus to diminish shunt current [53]. In addition, micro-hole based devices modified

from on-chip patch-clamping devices were demonstrated to address the shunt current issue by

forming tight seal between the aspirated cell and the wall of the micro-hole [54, 55].

Based on the experiences provided by the previous work, in order to achieve single cell trapping

and minimize the shunt current during cell measurement, a single tapered constriction channel

design is determined for cell trapping. (Fig. 2.1, Fig.2.2)

The microfluidic device consists of two levels of channels, the loading channel and the tapered

shape constriction channel. Two round reservoirs are in direct connection with the loading

channels while the tapered channel is sandwiched between the two loading channels. Culture

medium and cell suspension are injected into the inlet reservoir, and is conducted into the

loading channel by negative pressure. The entrance of the tapered channel is designed to be

larger than the cell, thus facilitating cell trapping. The wide opening would weaken the shear

stress that exerted on the cell surface by the channel wall, therefore, preserve cell membrane

integrity. Due to cell body elasticity, the constrictive design of the tapered channel would exert

larger normal stress on the cell membrane as the negative pressure drags it towards the narrow

end of the tapered channel. The increase of the normal stress would cause the friction force

exerted on the cell surface to increase. Eventually, both the friction force and the aspiration force

would reach an equilibrium state. Cell would then stop at a certain position inside the channel for

impedance measurement. (Fig.2.3)

Loading channels are designed to have a length of 0.48 cm, a height of 35 m and a width of

1000 m. For the tapered shape constriction channel, the height is 10 m and the length is 120

m. The seal created between the cell and the channel wall would become better as the cell is

dragged towards the narrow end of the channel by negative pressure. The outlet width (narrow

end) of the tapered channel is 4 m.

10

Tapered channels with different inlet widths (25 m and 15 m) were designed to accommodate

different cell sizes. For the AML cell subtypes, the 15 m wide devices were used, while for the

UCC subtypes, the 25 m wide devices were used.

Figure 2.1: Top-view of the microfluidic device. Cell suspension and the exterior medium are

conducted from the inlet end to the outlet end.

Figure 2.2: Side-view of the microfluidic device. The loading channel is more spacious than the

tapered constriction channel, thus to preserve cell integrity before trapping.

11

Figure 2.3: The force diagram for a single cell trapped inside the tapered constriction channel.

2.2 Device Fabrication

The microfluidic device is made of polydimethylsiloxane (PDMS) [56]. A mold master is

required for PDMS device replica molding. Fig. 2.4 shows the fabrication steps for constructing

the two-layer SU-8 mold master. Glass slides were cleaned in acetone, methanol, and de-ionized

water, and dried on a hot plate (20min at 175 ). The first layer of SU-8 was 10 μm thick (SU-8-

5) for forming the tapered constriction channel.

SU-8-5 is first spun on the glass slide at a speed of 500 rpm for 5 seconds, and then ramped up to

1,200 rpm for 30 seconds. The glass slide is then soft-baked (2 min at 65 °C and then 5 min at

95 °C) and UV exposed (6.2 sec, 16 mW/cm2, 365 nm) with the first photolithography mask.

The glass slide is then baked (1 min at 65 °C and then 2 min at 95 °C) to crosslink the exposed

SU-8-5 without development.

12

The second layer of SU-8 (25 μm thick) is made of SU-8-25 to form the cell loading channel.

SU-8-25 ias spun coated on the glass slide covered with the first layer of SU-8-5 (without

development) (500 rpm for 5 sec then ramp up to 2000 rpm for 30 sec), soft-baked (3 min at

65 °C and then 7 min at 95 °C), aligned, and UV exposed (12 sec, 16 mW/cm2, 365 nm) with the

second photolithography mask. The glass slide is then baked (1 min at 65 °C and then 3 min at

95 °C) to crosslink the exposed SU-8-25, developed in SU-8 developer for 60 sec, and finally

hard baked for 2 hours under 175 °C. PDMS devices are then replicated from the SU-8 mold

master and plasma bonded to a glass slide. (Fig. 2.5)

Figure 2.4: Fabrication steps for forming the two layer PDMS device.

13

Figure 2.5: Inside the dashed box: two PDMS microfluidic devices bonded on a glass slide.

14

2.3 Ag/AgCl Electrodes

2.3.1 Electrical Double Layer

The electrical double layer exists at the electrode/electrolyte interfaces (Fig. 2.6). When the

electrode is placed inside the electrolyte, there would be two layers of charges that cover the

solid. The first layer is the surface charge which are ions adsorbed onto the solid due to chemical

interactions. The second layer is composed of ions attracted to the solid by the first ion layers via

coulomb force [57].

The electrical double layer is traditionally characterized by an electrical capacitance [58-61].

Therefore, when measuring electrodes are placed inside a conductive medium for impedance

measurement, the capacitance of the electrical double layer is in series connection with the

measuring electrodes.

This would be a concern for single cell electrical characterization. When low frequency signals

are applied, the impedance contributed by the electric double layer would dominate, thus

overwhelm impedance contribution of the cell [49, 51, 53]. In previous research, in order to

overcome the issue caused by the double layer, multiple methods have been proposed:

Use differential measurement. Two pairs of electrodes are used in this condition. One

pair of electrodes is used to measure the cellular electric response, while the other pair of

electrodes is placed very close to the first pair and is used for measuring a reference

signal without the presence of a cell. One can eliminate the effect caused by the double

layer by differentiate the signals measured from the two pairs of electrodes [40, 46, 50,

62].

15

Use four electrodes setup for impedance measurement. Under this setup, two pairs of

electrodes are used for signal excitation and sensing respectively. One pair of electrodes

is used to apply the current signal across the cell. While another pair of probe electrodes

is placed far away from the current excitation electrodes and is used to sense the potential

change across the cell [11, 13]. Since the potential sensing electrodes are far away from

the excitation electrodes, the electrical double layer would have little influence on the

measured potential across the cell.

Use non-polarizable electrodes for cell measurement [44, 63].

16

Figure 2.6: Schematic picture of the electrical double layer between an electrode surface and an

electrolyte solution. The polarity of the surface charge is determined by the nature of the solid

electrode and the electrolyte.

17

2.3.2 Polarizable and Non-polarizable Electrodes

Perfectly polarizable electrodes are the type of electrodes which pass current between the

electrode and the electrolytic solution by changing charge distribution within the solution close

to the electrode. Thus, no actual current crosses the electrode-electrolyte interface. The electrode

acts like a capacitor [64]. Polarizable electrodes can create serious limitation when the

measurement includes low frequency or D.C. signals. Furthermore, when electrodes are

physically moved relative to the electrolyte, the charge distribution in the electrolyte which is

adjacent to the electrodes would also change. This will induce a voltage change on the electrodes.

Non-polarizable electrodes would allow current to pass freely across the electrode-electrolyte

interface without altering the charge distribution in the electrolytic solution adjacent to the

electrode. Non-polarizable electrodes also do not have over-potentials [64].

In order to diminish the influence caused by the electrical double layer, we choose to use non-

polarizable electrodes as our measuring electrodes. Ag/AgCl electrodes are the electrodes that

have characteristics which are very similar to non-polarizable electrodes [65].

2.3.3 Ag/AgCl Electrodes Fabrication

Ag/AgCl electrodes are made from 99.9% silver wires purchased from Warner Instruments. The

fabrication procedures are listed below (Fig. 2.7):

(1) Immerse the silver wire into bleach for half an hour.

(2) After the color of the wire turns to grey, take out the wire from bleach and rinse it in HCL.

(3) When the wire color turns to white, rinse it in DI water.

(4) Solder the Ag/AgCl wire on a SMC connector. (Fig. 2.8)

(5) Insert and seal the wire into a T-shaped fluid connector. (Fig. 2.8)

18

Figure 2.7: From top to bottom: 99.9% silver wire, silver wire rinsed in bleach for 30mins,

Ag/AgCl wire.

19

Figure 2.8: Left: a Ag/AgCl wire soldered onto a SMC connector. Right: a Ag/AgCl electrode

sealed into a T-shaped fluid connector.

20

Figure 2.9: Ag/AgCl electrodes plugged into the reservoirs on a microfluidic device. The dash

boxes marked the ports for medium passage.

21

2.4 Conclusion

This chapter introduces the design and fabrication of a PDMS microfluidic device for cell SMC

quantification. The tapered channel design of the microfluidic device facilitated single cell

trapping. The intimate contact created between the cell and the channel wall would provide good

sealing which would lead to better measurement accuracy. Ag/AgCl electrodes are used to

diminish the potential issue caused by the electrical double layer. The fabrication procedures for

the Ag/AgCl electrodes are also given in this chapter.

22

Chapter 3

3 Equivalent Circuit Model and FEM Simulation

3.1 Equivalent Circuit Model

3.1.1 Equivalent Circuit Model

In order to extract cell membrane capacitance from the measured impedance spectrums, we

devised equivalent circuit models to quantify the impedance behavior of the microfluidic device.

The two circuit models in Fig. 3.1a and Fig. 3.1b represent the situations when the tapered

channel is unplugged, and then plugged with a single cell respectively.

Ag/AgCl electrodes were used as measuring electrodes. These electrodes are considered to be

non-polarizable electrodes which diminish the effect of the electrical double layer [65].

Therefore, the capacitive influence caused by the electrical double layer can be neglected. When

the tapered channel is unplugged (Fig. 3.1a), the impedance is described by a parallel RC circuit.

Both the loading channel and the tapered channel are filled with conductive culture medium (1.5

S/m), thus a resistor Rchannel is used to represent the channel resistance. CPDMS represents the

capacitance of the fluid filled channel and surroundings (PDMS, air, glass) [11, 13, 26, 47, 53] .

When the tapered channel is plugged (Fig. 3.1b), it contains impedance contributions from both

the extracellular fluid and the trapped cell. Already in 1925, Fricke’s impedance measurements

proved that biological cells are covered by a thin insulating membrane [66]. In contrast, cell

cytoplasm is more conductive than the plasma membrane [26, 47, 62, 67]. Thus, the cell can be

modeled as a resistive cytoplasm, Rcell, in series with a capacitive plasma membrane. The cell

surface areas facing the channel inlet and outlet are approximated as two capacitors in series, C1

and C2.

23

When current is conducted into the tapered channel, it is split between entering the plasma

membrane and the shunt pathway between the cell and channel walls. Consequently, a gap

resistance, Rgap, represents the resistance created by the shunt current path [11, 13, 53].

3.1.2 Complex Nonlinear least-squares curve fitting

A complex nonlinear least-squares curve fitting algorithm is employed in a MATLAB program

to fit the measured impedance to the devised equivalent circuit models (Fig. 3.1a-b). In the curve

fitting, the impedance values of both the real and imaginary parts are taken into account. Both

parts are fitted simultaneously to the circuit model which ensures a complete fit.

To reduce the parameters in our circuit model and increase the curve-fitting accuracy, the

following procedures are used. The channel resistance (Rchannel) and capacitance (CPDMS) are

determined by curve-fitting the impedance spectrum from a fluid-filled channel without a cell

present.

a. After a cell is aspirated in the tapered channel, its volume replaces an equal volume of

extracellular fluid. Consequently, the resistance contributed by extracellular fluid in the

channel decreases. Eq. 1 is used to calculate the resistance loss due to cell trapping (Rloss).

Therefore, when a cell is trapped, the remaining channel resistance is calculated

using series channel lossR R R . The channel conductivity and height are channel and h ,

respectively. The cell widths facing the channel inlet and outlet are 1A and 2A , respectively,

and is the angle between a channel wall and the horizontal axis (Fig. 3.1c).

1

2

1ln

2 cotlosschannel

AR

h A

(1)

24

b. Rgap is the seal resistance. It is determined using the low frequency impedance value

obtained from the trapped cell impedance spectrum to subtract the Rseries value.

c. Finally, the total membrane capacitance, Cm, and cytoplasm resistance, Rcell, are extracted

after curve-fitting the impedance spectrum induced by a trapped cell.

A regression coefficient ρ quantifies the degree to which the derived parameters fit the

measurement data. Xest (fi) values are estimated from the devised equivalent circuit model, while

Xexp (fi) are experimental data. A value of ρ close to 1 means a good fit between the theoretical

model and the experimental data [5].

2

exp

2

exp

est i ii

ii

X f X f

X f

(2)

25

Figure 3.1: (a)-(b): Circuit models used for fitting the impedance and phase spectra generated by

an empty channel (a), and a single cell trapped in the channel (b). A membrane-bound cell has a

cytoplasmic resistance, Rcell, and a membrane capacitance, Cm = C1C2 / (C1+C2). To account for

space between the cell perimeter and the channel walls, a seal resistance, Rgap, is introduced.

Experimental amplitude (d) and phase (e) spectra of one measured cell are fitted with the circuit

models in (a) and (b).

26

3.1.3 SMC Determination

Once the membrane capacitance (C) is extracted, we calculate the cross-sectional membrane

areas (A) to calculate the specific membrane capacitance, SC C A . During the experiments,

we were able to observe at different focal planes the trapped cell inside the wedge-shaped

constriction channel. It was observed that for all the cells we tested, they all had highly intimate

contact with the channel walls. Therefore, the exposed membrane surface areas are approximated

to be the cross-sectional areas of the tapered channel (extracted from SEM imaging, shown in

Fig. 3.2) at the proximal and distal ends of the cell at its trapped position (see Fig. 3.1.c).

Figure 3.2: SEM images of the tapered channel: (a) top-view, and (b) view through the cross-

section.

27

3.2 FEM Simulation

3.2.1 COMSOL Simulation

(Collaborated with Dr. Graham Ferrier on this section)

To demonstrate the feasibility of our SMC quantification approach, a three-dimensional model of

the microfluidic device is built using COMSOL Multiphysics 4.2 (Fig. 3.3a). The 3D model

comprises the experimental channel dimensions. A zoomed-in portion of the tapered channel is

shown for clarity (Fig. 3.3b). The gap distance, zgap, is taken as the vertical distance between the

cell perimeter and a channel wall.

Due to Maxwell-Wagner interfacial polarization, the extent to which an electrically

heterogeneous cell stores and conducts electrical charge depends on frequency. As shown in

Figs. 3.3c and 3.3d, the insulating membrane redirects current toward the conductive shunt

pathway at low frequencies (4 kHz), and permits current flow at higher frequencies (1 MHz).

Before aspiration, the cell is assumed to be a single-shelled sphere. Consequently, we use a

single-shell model to evaluate the effective permittivity and conductivity of the sphere. In the

3D simulation results that follow, we model the cell as a trapezoidal block (conforming to the

local channel geometry minus a gap distance) having a complex effective permittivity, *eff , given

by:

* *3 3 2

* *3 2* *

2 * *3 3 2

* *3 2

22

2

eff

a

a

(3)

28

where outer innera R R (outer radius / inner radius) and the complex permittivities of the

cytoplasm and membrane are *3 and *

2 , respectively. From this, the frequency-dependent

permittivity and conductivity of the cell are *Reeff eff and *Imeff eff ,

respectively [68].

Terminal electrodes are placed at the far ends of the channel geometry. We solve the Laplace

equation for the potentials (V ) and electric fields ( E V ) between the terminals in the

frequency domain. By assigning a fixed voltage across the terminals, COMSOL solves for the

admittance, the reciprocal of which is the impedance, Z. The corresponding phase

is 1tan Im Re 180Z Z .

29

Figure 3.3: (a) Three-dimensional geometry of the microfluidic chip. (b) A moderately-sized box

surrounding the cell and channel facilitated meshing between the large PDMS domain and the

much smaller channel domain. (c-d) For illustrative purposes, a side view of the microfluidic

channel reveals lines of current density colored according to their strength (blue = weak, red =

strong). Similarly, the background color represents electric potential. In this demonstration, the

membrane thickness, , is 100 nm and zgap = 250 nm. At low frequencies (Fig. 3.3(c) - 4 kHz),

current is redirected through the shunt pathways (zgap). At high frequencies (Fig. 3.3(d) - 1

MHz), current is permitted through the cell.

30

3.2.2 Simulation Results Analysis

A single cell trapped inside the tapered channel has a specific length, position, and gap distance

between its perimeter and the channel wall. To investigate the dependence of these parameters

on the determined SMC, we measure the impedance responses from a simulated three-

dimensional channel geometry using finite element analysis. Variations due to a single

parameter (e.g., cell length) are effectively isolated by keeping the two remaining parameters

constant. In each simulation set, we vary the relative permittivity of the membrane (10, 20, and

30) while keeping the membrane thickness constant (10 nm). In this way, we tabulate theoretical

SMC values using 0m rC d (Table 3.1). For comparison, the simulated impedance and

phase spectra are recorded and curve-fitted using the procedures described in sections 2.3 and 2.4

to extract the SMC values using the equivalent circuit model. All the curve-fitted results have a ρ

value larger than 0.99.

Since the fitted membrane capacitance is an estimate parameter of the proposed equivalent

circuit model function. In order to produce error estimate of the fitted membrane capacitance,

non-linear regression analyses were applied to determine the uncertainties of the least-squares

(best-fit) coefficient of the membrane capacitance using Matlab programing [69]. The SMC

values were derived by dividing the membrane capacitance with the corresponding cross-section

area of the modeled cell.

The theoretical SMC values along with the derived SMC values vs. cell position, length, gap

distances and seal resistance are shown in Fig. 3.4. The dashed lines represent the theoretical

SMC values while the solid lines represent the SMC values derived from curve fitting. The error

bars represent the 95% confidence intervals for the SMC. When the relative permittivity of the

cell increases (10, 20, and 30), the derived SMC correspondingly increases (11.8 0.3 mF/m2,

21.6 0.6 mF/m2, and 31.4 0.8 mF/m2, the error ranges here represent the variation of the fitted

SMC variation across the cell-channel gap, cell length, cell position and seal resistance ranges),

giving a ratio close to 1:2:3. For the parametric simulation, the range of cell lengths is chosen

based on the minimum and maximum cell sizes observed using video microscopy (11.6 m -

31

13.6 m ). The range of cell positions is chosen from a typical range of positions observed in

experiments (52.6 m – 90.0 m relative to the tapered channel inlet). Finally, since the low-

frequency impedance has a strong dependence on the gap distance, the range of gap distances

(150 nm – 300 nm) is chosen using simulated impedance spectra that have comparable low-

frequency values to those in experimental impedance spectra.

Based on our seal resistance determination described in section 3.1, the largest and the smallest

seal resistance values are 0.91MΩ and 1.78MΩ respectively. Results shown in Fig. 3.4 suggest

that the derived SMC values do not significantly vary with cell length, position, or gap distance.

A maximum variance of 2 mF/m2 occurs vs. cell length for the 30 case (6.25% of the mean

value). In addition, since the cell volume changes as each parameter varies, we claim that the

SMC value obtained from curve-fitting is a size-independent parameter reflecting the electrical

properties of the plasma membrane. However, the curve-fitted SMC values are generally larger

than the theoretical values. Based on the device design, we believe there are three possible

reasons for these differences:

(1) The channel resistance, Rchannel, is calculated based on Ohm’s law for defining resistance,

i.e., R L A , which assumes a uniform current distribution inside the channel.

However, sharp geometric transitions in the microfluidic device induce the bending of current lines, which breaks down this assumption. In our device, such geometric variations occur at the loading-to-tapered channel interfaces, and at the exposed cross-sectional areas of the cell (current shunt pathway). The current distributions at these interfaces are generally non-uniform and frequency dependent (Fig. 3.3c-d).

(2) In the simulation, we apply the single-shell sphere model to define the effective permittivity and conductivity of the cell. Given that the sphere conforms more toward a trapezoidal shape in the tapered channel, the directional nature of the permittivity in the non-symmetric shape may play a role in determining the SMC. Indeed, the maximum SMC variations arise from changes in cell length, which would cause the cell to deviate progressively more or less from spherical symmetry. Variations in the effective permittivity due to geometric considerations may alter the membrane permittivity, and hence the specific membrane capacitance.

(3) As the frequency of the excitation signal increases, current lines begin to penetrate the cell perimeter sections that are parallel to the channel wall. Consequently, these

32

horizontally-aligned membrane sections may also contribute to the capacitance (Fig. 3.3c-d). When this occurs, the real surface area involved as a capacitor in the circuit is effectively larger than the assumed surface area (vertical membrane sections) used to calculate the SMC. Consequently, our underestimation of the membrane area may yield a SMC value that is larger than expected (Fig. 3.5).

Due to the reasons above, the curve-fitted SMC values are larger than the SMC values calculated

using the parallel-plate capacitance formula. Notwithstanding this upward shift, our simulation

has revealed a clear relationship between membrane permittivity and the curve-fitted

capacitance, which is not affected by variations in cell volume. Hence, the SMC values

determined from experimental data and curve-fitting reflect the cell membrane's electrical

property.

3.3 Conclusion

This chapter introduces the equivalent circuit model and FEM simulation we proposed for cell

capacitance extraction. Cell membrane SMC can be extracted by fitting the measured impedance

spectrum with the devised equivalent circuit model. FEM simulation results confirmed the

validity of our technique to bridge the derived SMC with cell membrane electrical properties. A

strong dependency between the membrane permittivity and the extracted SMC values is revealed

from the simulation results.

33

Table 3.1: SMC values and variations versus membrane permittivity. For three relative

membrane permittivities (10, 20, 30), the theoretical (based on parallel-plate (p.p.) capacitance

formula) and curve-fitted SMC values (units are mF/m2) are evaluated as a function of cell-to-

channel gap, cell length, cell position and seal resistance. The error ranges correspond to the

fitted SMC variations across the gap, length, position and seal resistance ranges in Fig. 3.4.

Relative

Permittivity

SMC

(p.p.)

SMC vs.

Gap

SMC vs.

Length

SMC vs.

Position

SMC vs.

Seal

Resistance

Mean

SMC

10 8.85 11.9 ± 0.2 11.8 ± 0.5 11.66 ± 0.08 11.9 ± 0.2 11.8 ± 0.3

20 17.70 21.8 ± 0.2 21.8 ± 0.9 21.3 ± 0.3 21.8 ± 0.2 21.6 ± 0.6

30 26.55 31.7 ± 0.1 32 ± 2 31.0 ± 0.5 31.7 ± 0.1 31.4 ± 0.8

34

Figure 3.4: Specific membrane capacitances versus cell-to-channel gap, cell length, cell position

and seal resistance. The error bars represent the 95% confidence intervals for the fitted SMC.

35

Figure 3.5: Current density versus position along the horizontal and vertical edges of the

membrane.

36

Chapter 4

4 AML Subtypes SMC Quantification

4.1 Introduction

In chapter 3, we have used FEM simulations to show the validity of our approach to bridge

derived SMC values with cell membrane electrical properties. In this chapter, the device is used

to quantify SMCs of two AML cell subtypes.

The following experiments are designed:

SMC measurement of AML2 cells treated in mediums with different osmolality

SMC measurement of AML2 and NB4 cells

When cells are treated in mediums with a different osmolality compared to their natural growing

condition, cell would undergo volume and surface morphological changes. Wang et al. [5], used

electro-rotation and scanning electron microscopy (SEM) imaging to demonstrate that Friend

murine cells (Ds-19) treated in mediums with higher osmolality would intensify cell membrane

intricacy which reflected in higher cell SMC values. (When the osmolality was increased from

210 to 450 mOsm/kg, the mean SMC of Ds-19 cells changed from 15.8 to 20.5 mF/m2)

Irimajiri et al. [12], shown that cultured rat basophilic leukemia (RBL-1) cells SMC increased

systematically from a hypotonic value of approximately 10 mF/m2 up to 50mF/m2 at 650

mOsm/kg. They have latter used SEM to confirm that the increase in SMC was due to the

increase of cellular ‘surface/volume’ ratios. (The total surface area of the cell would remain

constant while cell volume would decrease after cells treated in hypertonic solutions.)

Zimmermann et al. [6], have demonstrated that HEK293 cells revealed larger SMC values when

treated in isoosmolar mediums compared to those treated in hypoosmolar medium using both

37

electro-rotation and patch-clamping. Zimmermann et al. proposed that under hypotonic

conditions, cell swelling would leads to membrane flattening due to unfolding/retraction of

membrane surface microvilli which resulted in the SMC decrease.

Based on the above mentioned research results, we are highly interested to see whether our

microfluidic device can also reveal similar SMC changes when the cell exterior medium

osmolality is changed accordingly. If this phenomenon can be observed from our measurement,

we will have stronger support on the functionality of our device.

In the second experiment, SMC of two AML cell subtypes with different malignancies are

measured. The SMC values of two subtypes are compared and possible reasons are addressed for

the SMC differences between them.

38

Figure 4.1: Schematic of the experimental apparatus. Silver/silver chloride electrodes are

inserted into inlet and outlet ports for impedance measurements. In parallel with the electrodes

are fluid-filled tubes that route cells into the inlet port, through the loading channel, and finally

into the tapered channel. Screen captures of an AML2 cell illustrate its shape changes at two

different positions (P1 and P2). Cells are pressurized using a custom pumping system [1].

39

4.2 Material and Methods

4.2.1 Materials

All chemicals used in experiments were obtained from Sigma-Aldrich (Oakville, ON, Canada).

Cell-culture reagents were purchased from the American Type Culture Collection (ATCC,

Manassas, VA, USA). Materials used for device fabrication include SU-8 photoresist

(MicroChem Corp., Newton, MA, USA) and 184 silicone elastomer (Ellsworth Adhesives

Canada, Burlington, ON, Canada).

Acute myeloid leukemia cell lines (AML2 [70-72], and NB4 [73]) are cultured in Dulbecco’s

Modified Eagle’s Medium (DMEM) supplemented with 10% fetal bovine serum and 1%

penicillin (medium conductivity = 1.5 S/m). Before harvest, cells are incubated at 37°C in a

humidified 5% CO2 atmosphere for 2 days in a 25 ml culture flask. At harvest, we gently tap the

culture flasks to suspend the cells.

4.2.2 Experimental procedures

To investigate osmotic effects, AML2 cells are suspended in isotonic (269 mOsm/kg),

marginally-hypertonic (344 mOsm/kg), and very-hypertonic (489 mOsm/kg) solutions [74]. The

corresponding solution conductivities, as measured using a digital conductivity meter (Eutech

Instruments), are 1.24, 1.30, and 1.30 S/m, respectively. Hypertonic solutions are made by

mixing cell suspensions with a sucrose/dextrose solution in a 1:4 ratio, and isotonic solutions are

made by mixing cell suspensions with distilled water in a 1:3 ratio (Table. 4.1). Before each

measurement, cells are incubated in the sucrose/dextrose solution for 15 minutes. This allows the

cell adequate time to equilibrate with the new osmotic condition. To compare the SMC values of

AML2 and NB4 cells, both cell lines are suspended in DMEM during experiments.

40

Microfluidic devices are fabricated according to the steps listed in Chapter 2. After preloading

the microfluidic channel with an appropriate extracellular medium, a droplet of dilute cell

suspension is delivered into the microfluidic device. Before a cell is aspirated into the tapered

channel, a reference impedance spectrum is collected using Ag/AgCl electrodes located at the

inlet and outlet ports. The Ag/AgCl electrodes are specifically chosen to reduce secondary

impedance contributions from the electrical double layer bridging the electrode and electrolyte

[65]. The impedance spectrum is recorded using an impedance analyzer (Agilent 4292A). Cells

are then guided into the loading channel using negative pressure (-100 Pa), and a single cell is

drawn inside the tapered channel. Maintaining a small negative pressure (-50 Pa) afterward

establishes a good seal between the trapped cell and the channel walls. While recording the

impedance spectrum of the cell, microscope imaging (Nikon eclipse Te2000-S) is used for

observing and recording videos of the cell shape inside the tapered channel.

To test the device repeatability, we record the impedance spectra induced by a cell parked at two

different positions in the tapered channel. After recording the cell impedance spectrum at the

first position, we apply a larger negative pressure (-70 Pa) to aspirate the cell into a more

constrictive region of the tapered channel. After recording the second cell impedance spectrum,

we apply a -100 Pa pressure to aspirate the cell fully through the tapered channel. This

procedure is repeated sequentially for all cells.

41

Table 4.1: Different concentration sucrose/dextrose solutions used for making different

osmolality mediums. The mixing ratio between the sucrose/dextrose medium and the cell

suspension are stated in 4.2.2.

Osmolality

(mOsm/kg)

Sucrose

(g/L)

Dextrose

(g/L)

Conductivity

(S/m)

489 300 3 1.3

344 85 3 1.3

269 0 0 1.24

4.3 Results and Discussion

It is well known that the cell membrane acts as an efficient insulator in the low frequency range

(5 kHz – 100 kHz). Thus, in our device, current is forced to flow around the cell. Because of the

intimate cell/channel wall contact, the gap existing in between forms a very good seal which lead

to a relatively large resistance, thus a stable impedance plateau can be seen at the low frequency

range for the trapped cell impedance profile (Fig. 3.1d). In this case, more of the cell/channel

interaction rather than the cell property are revealed. As the frequency increases (100 kHz – 1

MHz), current flow across the cell membrane becomes more and more efficient. Since the

voltage applied is constant, the total current would increase inside the constriction channel. In

this case both cell membrane and cytoplasm electrical property are reflected.

42

A large seal resistance is important for cell membrane capacitance quantification [44, 53]. When

a cell is trapped inside the tapered channel, the continuously applied negative pressure would

drag the cell membrane close to the channel wall, creating a good seal. The low frequency

impedance amplitude measured at this moment is mostly contributed by the seal resistance Rgap

and the channel resistance Rseries (Fig. 3.1b). The plateau in the low frequency range (5 kHz – 10

kHz) of the amplitude spectrum reveals the sealing quality (Fig. 3.1d).

Experimentally, the smallest and the largest seal resistance values were 0.7 MΩ and 2.4 MΩ.

The reason for this range of seal resistance values was due to the variation of cell size. In

general, larger cells created a better seal resistance than smaller cells. Cells were placed at two

different positions inside the tapered channel, and SMC values derived at the two different

positions will be compared later in the paper.

In the next section, we present results from the two experiments. Through variations in the

SMC, the first experiment evaluates the response of AML2 cells to osmotic variations, and the

second experiment evaluates the differences between two leukemia cell lines having differing

levels of metastatic potential. In both experiments, all curve fitted results have a value larger

than 0.99.

We monitor the cellular integrity both by imaging and through impedance measurement. When

the cellular integrity is compromised, we observe the ejection of cytoplasmic contents from the

cell. At the same time, the low-frequency impedance dramatically decreases and no plateau is

formed. For all recorded data shown in Fig. 4.2 and 4.3, cell integrity is preserved as cells are

drawn further into the tapered channel. Consequently, the membrane properties are expected to

remain unchanged during cell aspiration and were confirmed by the constant SMC determined in

experiments.

43

4.3.1 AML2 in different osmolality solutions

AML2 cells exposed to different osmotic conditions were measured. Cells immersed in

hypertonic solutions experienced volume shrinkage compared with cells near or within the

optimal isotonic range (260-320 mOsm/kg) [74]. The corresponding cell diameters for cells in

isotonic, marginally-hypertonic, and very-hypertonic solutions are 11.1±0.6 m (n=12), 10.6 ±

0.8 m (n=13), and 9.6 ±0.7 m (n=12), respectively (Table. 4.2). Cells immersed in very-

hypertonic solutions also produce significantly larger ( 0.01p ) SMC values than cells in

isotonic or marginally-hypertonic solutions. The SMC values produced by isotonic, marginally-

hypertonic, and very-hypertonic solutions are 16.6 1.9 mF/m2, 16.8 1.9 mF/m2, and 20.5 1.8

mF/m2, respectively (Fig. 4.2d).

Table 4.2: AML2 cells diameter vs. SMC in hypertonic and isotonic mediums.

Osmolality

(mOsm/kg)

Cell diameter

(m)

SMC

(mF/m2)

489 9.6±0.7 (n=12) 20.5 1.8 (n=12)

344 10.6 ±0.8 (n=13) 16.8 1.9 (n=13)

269 11.1±0.6 (n=12) 16.6 1.9 (n=12)

44

In order to test the repeatability of the device and technique, impedance profiles were recorded at

two positions for each cell. Cells measured at two different positions (P1 and P2) in the tapered

channel are found to generate similar SMC values (Fig. 4.2a-d). As the cell moved from P1 to

P2, it elongated and formed a more intimate seal with the channel wall. However, as previously

confirmed by simulation, the SMC value does not significantly vary with cell length, position,

gap distance or seal resistance. Furthermore, as the cells tested were obtained from asynchronous

log phase cultures thus the population was a mix of cells from different cell cycle phase.

Therefore, the SMC variations of the cell population are likely due to heterogeneity among the

cells.

Occasionally, when a cell was aspirated into position P2, it began to slip through the channel

before the impedance spectrum was fully recorded. When this happened, we only plotted data

from P1.

Cell SMC is determined by the surface morphology and the dielectric properties of the plasma

membrane [8][5]. Intensive studies on artificial lipid bilayers have shown that the bilayer

membrane thickness would change in accordance to the varying length of the carbon chains [75].

Proteins which incorporated inside the lipid membrane would also change cell SMC by changing

the membrane morphology. The present of a protein would stretch or compress the bilayer, thus

evoke its capability for charge storage [76, 77].

Since all cell samples tested were descendants from the same cell type, the lipid bilayer

compositions of the samples should be similar. Therefore, the changes in cell surface

morphology are primarily responsible for SMC variations in different osmotic conditions [5, 6,

12].

This phenomenon is evident in our measurement results for AML2 cells immersed in different

osmotic solutions (Fig. 4.2a-d). In human blood plasma, cells normally present a wide tolerance

range (optimally, 260-320 mOsm/kg) to osmotic pressure [74]. Within the optimal tolerance

range, the cell morphology is not expected to vary significantly and indeed, the SMC varies

insignificantly (p=0.34) for cells in 269 and 344 mOsm/kg solutions. However, cells immersed

in a solution having an osmolality (489 mOsm/kg) that is well outside the optimal tolerance

range reveal significantly higher SMC values ( 0.01p ). Rich et al. note that the cell surface

45

area generally remains constant over a wide range of volume swelling and shrinking.

Consequently, very hypertonic solutions that cause cell volume shrinkage correspondingly

initiate membrane rippling which made the cell surface more villated [78]. Irimajiri et al. found

that cell volume shrinkage in hypertonic solutions can also induce the microvilli to increase in

thickness and elongation. Essentially, cells immersed in hypertonic extracellular media undergo

severe volume shrinkage, which leads to local cell membrane folding and surface area

enhancement that increase the charge holding capability of the membrane of a unit area [12].

Figure 4.2: (a)-(d): Specific membrane capacitance (SMC) values for cells in solutions of

different osmolalities. Cells in isotonic or marginally hypertonic solutions yield essentially

identical SMC values ( 0.34p ), while very-hypertonic solutions induced significant increase

( 0.01p ) in the SMC.

46

4.3.2 AML2 vs. NB4

Acute myeloid leukemia (AML) is characterized by the rapid growth of abnormal white blood

cells, which accumulate in the bone marrow and interfere with normal blood cell production

[70]. Acute promyelocytic leukemia (APL) is a subtype of AML, which is characterized by a

chromosomal translocation involving the retinoic acid receptor-alpha gene on chromosome 17

(RARα) [73]. APL can cause a life threatening coagulopathy [79].

Since APL cells are known to be a distinct and highly aggressive form of AML [79, 80], we

investigated how the corresponding SMC values vary between APL cells and cells from another

AML subtype. For this experiment, we characterized AML2 (AML cell line) and NB4 (APL cell

line) cells. Each cell was measured at two different positions in the tapered channel.

The SMC values for AML2 and NB4 cell lines are distinguishable ( 0.01p ) at 16.9 1.9

mF/m2 (n=23) and 22.5 4.7 mF/m2 (n=23), respectively. In addition, similar SMC values are

extracted from cells located at positions P1 and P2. Therefore, the membrane property for each

individual cell is considered to remain constant during each cell measurement at P1 and P2 (Fig.

4.3a-c).

Osmolality measurements performed previously show that our methodology has the potential to

extract SMC and correlate it with cell surface morphology. APL cells are known to contain more

membrane proteome than AML cells [80], which may suggest that additional membrane

proteome increases the surface complexity of NB4 cells. Although membrane thickness might

contribute to this SMC difference, the lack of related literatures made this assumption stay in

doubt. Compared to AML2 cells, the larger SMC values and variations of NB4 cells can be due

to their more complex membrane morphologies and suggest that NB4 cells could also have more

heterogeneity across their population.

47

Figure 4.3: (a)-(c): Specific membrane capacitance values of 23 AML2 and 23 NB4 cells in

DMEM. Based on the SMC distributions across each cell population, the mean SMC values of

AML2 and NB4 cells are found to be significantly different ( 0.01p ). Cells initially parked at

a position, P1, are later parked at a more constrictive position, P2

48

4.4 Conclusion

In this chapter, the microfluidic device is used to quantify the SMC for AML2 cells treated in

different osmolality medium and latter between two AML cell subtypes with different

malignancies. The similar SMC values measured from the same cell at two different positions in

the tapered channel showed the good repeatability of the technique. We also showed that cells

treated in hypertonic medium tend to own a larger SMC value than cells treated in isotonic

medium. We measured SMC of two AML subtypes. By comparing the results, we found that the

more malignant cell line NB4 has a larger SMC value than the less malignant cell line AML2.

49

Chapter 5

5 UCC Subtypes SMC Quantification

5.1 Introduction

It is estimated that over 141,140 people in the United States alone will be diagnosed in 2012 with

carcinoma of the urinary bladder [81]. Histopathologically, more than 90% [81, 82] of bladder

cancers are classified as Urothelial (Transitional) Cell Carcinomas (UCC or TCC). The

carcinoma occurs in cells lining the bladder and has a high recurrence rate.

T24, which is a poorly differentiated grade III bladder carcinoma [83], and RT4, which is a well

differentiated grade I bladder papilloma [84], are two bladder cancer cell lines of different

grades. They have been important models in bladder cancer research and have been extensively

studied.

These two cell lines are known to exhibit different human leukocyte antigen profiles (HLA) [85],

growth and migration characteristics [86], different receptor expressions, and different

membrane morphological features [82, 87, 88]. The two cell lines also revealed different

survival rates after MMC cancer drug treatment [89]. Compared to these biochemical findings,

the biophysical properties of these two bladder cancer cell lines and their differences are

understudied.

It is known that for a smooth lipid bilayer membrane, the SMC value is in the range of 4-6mF/m2

[9] . Biological cells’ SMC values are higher (e.g., 10-40 mF/m2) since their membranes contain

brush layers (microvilli, microridges and cilia) and surface proteins. Iyer et al. has shown that

healthy and cancerous epithelial cells possess different membrane brush layers using AFM

(atomic force microscopy) imaging [16]. Benign cells usually have a single-length brush layer

while cancerous cells have a brush layer with two characteristic lengths and higher grafting

50

densities (number of ‘molecules’ per μm2) than normal cells. Since RT4 and T24 are cancer cells

of different grades, we hypothesized that their SMC values would have measurable differences.

In this chapter, SMC of both RT4 and T24 cells are measured using the microfluidic device.

SMC results from both cell lines are compared and possible explanation are given to explain the

SMC difference.

Figure 5.1: Screen captures of the SMC measurement on one RT4 cell: (1). cell is aspirated into

the tapered channel via negative pressure. (2). The RT4 cell is trapped inside the tapered channel

for SMC measurement. (3). The RT4 cell is removed from the tapered channel by increasing the

negative pressure. (4). Cell is removed from the channel. The tapered channel is empty and is

ready for another measurement.

51

5.2 Material and Methods

T24 and RT4 cells were purchased from the American Type Culture Collection (ATCC,

Manassas, VA, USA). Cells were cultured in ATCC-formulated McCoy’s 5a modified medium

supplemented with 10% fetal bovine serum and 1% penicillin under 37°C in a 100% humidified

5% CO2.

The tapered channel used for SMC measurements has a larger entrance width (25 μm) compared

to the ones used for AML subtype testing (15μm), thus to accommodate the sizes of RT4 and

T24 cells. Cells were first trypsinized from the flask substrate and then mixed with fresh culture

medium in a 1 to 4 ratio.

After preloading the microfluidic channel with culture medium, the cell suspension mixture was

then added to the inlet reservoir of the device. Fig. 5.1 shows a cell trapped inside the tapered

microfluidic channel for SMC measurement.

Before a cell is aspirated into the tapered channel, a reference impedance spectrum is collected

using Ag/AgCl electrodes located at the inlet and outlet ports. The impedance spectrum is

recorded using an impedance analyzer (Agilent 4292A). Cells are then guided into the loading

channel using negative pressure (-200 Pa), and a single cell is drawn inside the tapered channel.

Maintaining a small negative pressure (-90 Pa) afterward establishes a good seal between the

trapped cell and the channel walls. While recording the impedance spectrum of the cell,

microscope imaging (Nikon eclipse Te2000-S) is used for observing and recording videos of the

cell shape inside the tapered channel. After recording the cell impedance spectrum, we apply a -

300 Pa pressure to aspirate the cell fully through the tapered channel. This procedure is repeated

sequentially for all cells.

52

5.3 Results and Discussion

The average diameters of RT4 and T24 cells in their suspension state were measured to be

13.6±1.3μm (n=19) and 13.1±2.0μm (n=20). The SMC values of RT4 and T24 were measured to

be 40.0±8.3mF/m2 (n=19) and 47.0±5.1mF/m2

(n=20), respectively (Fig. 5.4). Regression

coefficients for all measured cells were larger than 0.99.

Electrically, the capacitance of the cell membrane is contributed by the lipid bilayer in parallel

with proteins and other portions of the membrane [5]. RT4 cells are of lower grade than T24

cells, the two cell lines are also considered as representation for continuous progression of

urothelial cancer development [90]. Therefore, the hydrocarbon molecules which form the lipid

bilayer of the two cell lines are not expected to differ significantly. Hence, the capacitance

contribution of the lipid bilayer of both RT4 cells and T24 cells can be considered similar.

Thus the difference in SMC values of T24 cells and RT4 cells is likely due to their distinct

membrane structures. It is known that T24 and RT4 cells have different micro nanotube densities

[88, 90]. Membrane nanotubes grown on cell surface connect separate cells and offer an effective

way for intercellular transport and communication. T24 cells were reported to have denser

nanotube structures than RT4 cells [88]. Thus, the total membrane surface area per patch of a

T24 cell can be larger than the same sized RT4 cell patch. The extra surface area of the cell

increases its charge storage ability, resulting in a higher capacitance value. Consequently,

although the two cell lines have similar diameters, SMC values of T24 cells are significantly

larger than RT4 cells (P<0.01) due to their more complicated surface morphologies.

53

5.4 Conclusion

In this chapter, we measured SMC from two UCC cell subtypes. By comparing the results, we

found that though having similar cell diameters, the more malignant cell line T24 has a larger

SMC value than the less malignant cell line RT4.

Figure 5.2: SMC values of 20 measured T24 cells.

54

Figure 5.3: SMC values of 19 RT4 cells.

55

Figure 5.4: The more malignant UCC subtype T24 cells are found to have a larger mean SMC

value than RT4 cells. (P<0.01)

56

Chapter 6

6 Conclusion and Future Work

6.1 Conclusion

We developed a microfluidic device that performs SMC measurements of single cells using

impedance spectroscopy. The tapered shape constriction channel design made it possible to trap

and measure a single cell without the interference of the other cells. The Ag/AgCl electrodes

used for impedance sensing diminish the series capacitance influence caused by the electrical

double layer which made it possible to apply impedance measurement in conductive medium

(1.5 S/m). Three-dimensional FEM simulation confirms the validity of the equivalent circuit

model. Based on the impedance and phase traces from experimental and simulated geometries,

we demonstrated that four cell-lines are distinguishable based on their SMC values. The more

malignant cell lines all revealed a larger SMC values compared to their less malignant

counterparts. Additionally, compared with immersion in isotonic solutions, immersion of AML2

cells in hypertonic solutions caused volume shrinkage, leading to a relative decrease in the mean

SMC. The technique is easy to use and has a testing speed of approximately 1 minute/cell.

57

6.2 Future Work

The work presented in this paper only considered cell membrane surface morphology differences

as the primary reason for SMC differences among different cell lines. However, according to

SMC definition equations, membrane thickness and membrane permittivity are also two

important factors that would affect cell SMC. Therefore, one of our future goals is to try to

decouple the influence of each of these three parameters on cell SMC. Possible ways to

accomplish this is to use artificial lipid membranes for measurement or to use proper antigen to

identify measured cell membrane protein compositions.

From the simulation results, we discovered that the SMC values derived from our technique are

all larger than their theoretical values. Multiple possible explanations were given in chapter 3

that addressed the possible reasons for these differences. Thus in order to compensate the error,

the following methods might be useful to help bring down the extracted SMC closer to their

theoretical values.

(1) In our proposed equivalent circuit model, the channel is simplified as a frequency

independent resistance. However, in Fig. 3.3c-d, we can see that the current distribution

at the cell membrane/electrolyte interfaces is frequency dependent. A constant-phase-

angle element (CPA) is commonly used to address the frequency dependency of interface

electrical double layers. CPA is an empirical element that used to describe the process of

electric charges transfer across the interfaces between two substances with very

dissimilar properties. The impedance of this has the form of : ( )Z j , where is the

angular frequency and 1j , and 0 1 [91-93]. Though there is still no clear

physic-chemical explanation for this element [58], by including this element between the

channel series resistance and the membrane capacitance in our equivalent circuit model

might help better describe our experiment conditions.

(2) In order to simplify the FEM meshing process, we previously chose to use the shell-

model for cell property definition. Therefore, only a cell body is defined in the simulation.

58

However, given that the cell sphere conforms more toward a trapezoidal shape in the

tapered channel, the directional nature of the permittivity in the non-symmetric shape

may play a role in determining the SMC. Thus the theoretical SMC values might change

from its original values. In order to rule out this possible influence, it is better to make

and define a real cell membrane outside our simulated cell body instead of using the shell

model. Specific permittivity and conductivity properties should be assigned to these cell

regions (Cytoplasm, membrane etc.). By doing this, we can keep the theoretical SMC

values constant, and therefore facilitate us to understand the accuracy about our SMC

determination.

59

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