Single cell studies of mouse embryonic stem cell (mESC) differentiation by electrical impedance measurements in a microfluidic device

Biological populations of cells show considerable cell-to-cell variability. Study of single cells and analysis of cell heterogeneity are considered to be critical in understanding biological processes such as stem cell differentiation and cancer development. Recent advances in lab-on-a-chip techniques have allowed single-cell capture in microfluidic channels with the possibility of precise environmental control and high throughput of experiments with minimal usage of samples and reagents. In recent years, label-free techniques such as electrical impedance spectroscopy have emerged as a non-invasive approach to studying cell properties. In this study, we have designed and fabricated a microfluidic device that combines hydrodynamic trapping of single cells in pre-defined locations with the capability of running electrical impedance measurements within the same device. We have measured mouse embryonic stem cells (mESCs) at different states during differentiation (t=0 h, 24 h and 48 h) and quantitatively analysed the changes in electrical parameters of cells during differentiation. A marked increase in the magnitude of the cell impedance is found during cell differentiation, which can be attributed to an increase in cell size. The analysis of the measurements shows that the nucleus-to-cytoplasm ratio decreases during this process. The degree of cell heterogeneity is observed to be the highest when the cells are at the transition state (24 h), compare with cells at undifferentiated (0 h) and fully differentiated (48 h) states. The device enables highly efficient single cell trapping and provides sensitive, label-free electrical impedance measurements of individual cells, enabling the possibility of quantitatively analysing their physical state as well as studying the associated heterogeneity of a cell population.


Cell model
When an AC electric field is applied to a cell in suspension, the dielectric properties of the cell change as a function of frequency, known as Maxwell-Wagner dispersion. The dielectric behaviour of cell suspensions can be analysed using Maxwell's mixture theory. One basic model of a cell in suspension is the "single-shell" model (Fricke 1925), in which the cell membrane is modelled as a thin dielectric shell and the cytoplasm is modelled as a conducting homogeneous sphere. This model assumes only one spherical shell separating the cell inner from the ambient and also ignores the intracellular structures of cells thereby simplifying the analysis. The single-shell model showed a good agreement with experimental data for cells with negligible nucleus or organelles, however, it presented a partial disagreement with experiment for cells containing sizeable intracellular structures (Asami et al. 1989).
To effectively accommodate the actual cell's morphology (e.g., the presence of a sizeable nucleus within the intracellular space), Irimajiri et al. proposed a more comprehensive cell analogy -the "double-shell" model (Irimajiri et al. 1978;Irimajiri et al. 1979). In this model, the cell is composed of four phases, i.e., cell membrane, cytoplasm, nuclear envelope and nucleoplasm (Fig. 1D). The "double-shell" implies the thin cell membrane and nuclear envelope, with the membrane separating the cytoplasm from the ambient medium and the nuclear envelope separating the nucleoplasm from the cytoplasm. Each phase is modelled with its own electrical properties (conductivity ' ' and permittivity ' '). The conductivity and permittivity of the medium are and respectively. The dielectric properties of the membrane and cytoplasm are significantly different from those of the nuclear envelope and nucleoplasm (Pethig et al. 2010). The double-shell model is more appropriate than the single-shell model for studying cells with a high nucleus-to-cytoplasm (N/C) ratio such as stem cells, as the properties of the nuclear envelope and nucleoplasm are taken into account.
Assuming a spherical cell is suspended in a medium, the equivalent complex permittivity of the whole mixture (cell and medium) is given by the Maxwell's mixture theory for heterogeneous systems:
Based on the double-shell model (Fig. 1D), the equivalent complex permittivity of the whole cell, containing a spherical membrane, cytoplasm, nuclear envelope and nucleoplasm, can be written as:

̃=̃2
(1 − 1 ) + (1 + 2 1 )̃1⁄ where ̃ is the complex permittivity of the cell membrane, 1 is the fractional volume of cytoplasm sphere relative to the membrane sphere, i.e., 1 = ( − ) 3 . and are the outer radius of the cell and the thickness of the cell membrane, respectively. 1 is the equivalent complex permittivity of the inner part of the cell (including the cytoplasm, nuclear envelope and nucleoplasm) and is given by: where ̃ is the complex permittivity of the cytoplasm. 2 is the volume fraction of the nucleus relative to the cytoplasm, i.e., 2 = ( − ) 3 , where is the outer radius of the nuclear envelope. The equivalent complex permittivity of the nucleus (containing the nuclear envelop and nucleoplasm), 2, is given by: where ̃, ̃ are the complex permittivity of the nuclear envelope and nucleoplasm respectively, 3 is the fractional volume of the nucleoplasm sphere relative to the nuclear envelope sphere, i.e., 3 = ( − ) 3 , and is the thickness of the nuclear envelope. Fig. 1D presents the electrical model of a cell suspended in a medium inside a microfluidic system. The total complex impedance of a cell surrounded by a medium (i.e., cell-medium mixture) in the sensing volume is ̃ and the complex impedance of the medium in the reference volume is ̃. Coplanar electrodes are patterned on the bottom glass substrate. Between the electrode surface and the electrolyte forms an electrical double layer, of which the capacitance is notated as ̃. With double layer capacitance taken into account, the total impedance measured from the electrodes in sensing group is ̃ and the total impedance measured from the electrodes in the reference group is ̃.
The complex impedance of the cell-medium mixture can be written as : where ̃ is the complex capacitance of the cell-medium mixture.
For the coplanar electrode configuration, assuming the width and length of the coplanar electrodes are and respectively, and the spacing between them is 2 , the complex capacitance of the cell-medium mixture between the two sensing electrodes can be derived using Schwartz-Christoffel transformation : where ( ) is the complete elliptic integral of the first kind, and is given by: ; (S12) The electrical double layer formed at the interface of the electrode surface and the electrolyte can affect the electrical response of the measurement system. The electrical double layer is modelled as a capacitor ( ), and is in series with the total complex impedance of the cell-medium mixture (Fig.  1D). Therefore, the total impedance measured from the sensing electrodes, ̃, can be expressed as: For the reference group in Fig. 1D, the complex impedance of the medium between the two reference electrodes is given by: With double layer effects taken into account, the total impedance measured from the reference electrodes, ̃, is given by:

̃= 2 +̃
(S16) The differential spectrum of a cell can be obtained by normalising the impedance of the sensing group with regard to the impedance of the reference group (Malleo et al. 2010): where the magnitude, |̃|, and the phase, , of the differential impedance spectrum are,

Device fabrication details
Electrode fabrication. Electrodes were patterned on 2" Pyrex glass wafers by lift-off. AZ 5214E photoresist (MicroChemicals) was used in image reversal mode as the sacrificial layer for the lift-off process. First, the glass substrate was cleaned and dehydrated on a 200°C hot plate for 5 minutes. Photoresist spin coating was performed immediately after cooling down the substrate to avoid readsorption of water. AZ 5214E was spin-coated onto the wafer at 500 rpm for 5 seconds and then 4000 rpm for 45 seconds. The resulting film thickness was 1.6 um, calibrated by profilometer. After removing the edge bead by acetone, the substrate was pre-baked at 105°C for 60 seconds, and then rehydrated at room temperature for 10 minutes before exposure to allow a certain water content to be present in the resist during exposure, so that a reasonably high development rate and contrast could be achieved. UV exposure of the resist was done with the Karl Suss MJB4 mask aligner (exposure energy: 10 mJ/cm 2 ). After exposure, the sample was relaxed for 10 minutes to outgas the nitrogen formed during exposure from the exposed resist. Reversal bake of the resist was performed on a 116°C hotplate for 60s, after which a flood UV exposure was done using the mask aligner (exposure energy: 300 mJ/cm 2 ). The resist was developed in AZ 726 MIF developer (MicroChemicals) for 90 seconds, rinsed with DI water and blow-dried with nitrogen gas. The resist was slightly over-developed to create undercut and ease the lift-off process. Titanium (20 nm, as an adhesion layer) and gold (100 nm) were deposited on the sample by electron beam evaporation (Kurt J. Lesker e-Beam Evaporator PVD 75) at a deposition rate of 1Å/s. After metal deposition, the photoresist was removed in AZ 100 remover bath at 50°. After lift-off, the substrate was thoroughly rinsed with DI water and dried with nitrogen, and electrode patterns were inspected with microscope. The width of the electrodes at the sensing region of the chip is 15 µm, and the distance between two neighbouring electrodes is 15 µm.
Master wafer fabrication. The master moulds for the microfluidic trapping channels (geometric dimensions are listed in Table S1) were fabricated using negative photoresist SU-8 2015 (MicroChem) by standard photolithography process. SU-8 2015 was spin-coated onto a 3" silicon wafer at 500 rpm for 8 seconds and 3000 rpm for 60 seconds, resulting in a 15µm-thick film. Soft bake was performed at 65°C for 1 minute and 95°C for 4 minutes. Exposure was done with Karl Suss MJB4 mask aligner (exposure energy: 140 mJ/cm 2 ). After exposure, the wafer was post baked at 65°C for 1 minute, 95°C for 3 minutes. After cooling down, the resist was then developed in SU-8 developer (PGMEA) for 3 minutes (with gentle agitation), then rinsed thoroughly with propanol and dried with nitrogen. A hard bake step was performed at 200°C for 5 minutes to improve the mechanical properties and thermal performance of SU-8. Prior to PDMS moulding, the surface of the master wafer was rendered hydrophobic by vapour deposition of FDTS (1H,1H,2H,2H-Perfluorodecyltrichlorosilane, 96%, Alfa Aesar).
PDMS rapid prototyping. PDMS (Sylgard 184 silicone elastomer kit, Dow Corning) was prepared by mixing 10:1 base to curing agent. The mixture was degassed in a vacuum desiccator for 1 hour to remove all air bubbles. After degassing, the mixture was spun onto the master mould at 500 rpm for 8 seconds and then 1000 rpm for 60 s. This layer was cured on a 65°C hot plate for 2 minutes and on a 150°C hot plate for 5 minutes. The resulting PDMS layer (~ 60 um thickness) was thin enough that the shrinkage of PDMS, caused thermal expansion and contraction during the curing process, can be neglected. We found that this approach can effectively solve the shrinkage-induced PDMS registration problem during the alignment and bonding process of microfluidic channels and electrode patterns. A separate thick PDMS block, serving as a substrate for the thin PDMS layer for easy handling, was made by mixing the base and curing agent with 10: 1 ratio, degassing for 1 hour and then pouring onto a blank wafer. After curing, the thick PDMS substrate was peeled-off from the blank wafer, and bonded to the thin PDMS layer immediately after oxygen plasma treatment (Diener etcher, 100% power for 20 seconds at 1.0 mbar). The bonded sample was further baked in a 65°C oven for 1 hour to improve the bonding strength, after which the PDMS was peeled off from the master mould and cut into desired shape. After channel inlets/outlets (1 mm diameter) were drilled using a biopsy punch, the PDMS sample was ready for bonding with glass to close the channel. Before bonding, the PDMS sample (containing microfluidic channels) and the glass substrate (containing electrode patterns) were cleaned properly and activated by oxygen plasma. Immediately after the plasma activation, the two pieces were aligned and brought into conformal contact to form permanent bonding. A soft force was applied to remove any trapped air bubbles. The bonded sample was then baked in a 65°C oven for 1 hour to improve the bonding strength.
Device assembling and experiment setup. Surface mount connectors (0.1" surface mount terminal strip, Samtec TSM series) were used to make the connections between the electrode patterns on the fabricated chip and external measuring instrumentation. The connectors were bonded to the electrode pads on the chip using silver conductive epoxy (Fig. 1A). The microfluidic device was connected to a 1 ml syringe with PTFE tubing (0.59mm ID x 0.25mm Wall) and 23G needles. Fluid flow was controlled by syringe pumps. Before use, the channels were pre-treated with 1% BSA (in 1×PBS) for 30 minutes to block hydrophobic interactions between biological samples and PDMS surface. The chip was connected with an impedance analyser (Solartron SI 1260) for impedance measurements. Prior to cell characterisation, the device was first filled with PBS buffer, and a calibration experiment was performed for the device itself, serving as a baseline for further cell measurements. After the calibration, cells were loaded into the device at flow rate of 20 µl/hr. Once all traps were occupied by cells (inspected with microscope), the device was washed with buffer. Cell impedance measurements were then conducted with the impedance analyser. A 100 mV input single was used. The frequency range was from 100 Hz to 20 MHz, with 10 points being measured per decade. Analytical simulations based on the double-shell cell model were performed using Matlab. Numerical simulations were conducted using COMSOL 4.4 (AC/DC module).