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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
iii
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.
v
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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