Specific membrane capacitance, cytoplasm conductivity and instantaneous Young’s modulus of single tumour cells

As label-free biomarkers, biophysical properties of cells are widely used for cell type classification. However, intrinsic biophysical markers, e.g., specific membrane capacitance (Cspecific membrane), cytoplasm conductivity (σconductivity) and instantaneous Young’s modulus (Einstantaneous) measured for hundreds of single cells were not yet reported. In this study, single cells in suspension (adherent cells treated with trypsin) were aspirated through a microfluidic constriction channel at 25 °C, and the entry processes and impedance profiles were recorded and translated to Cspecific membrane, σconductivity and Einstantaneous. Cspecific membrane, σconductivity and Einstantaneous of five cell types were quantified as 2.10±0.38 μF cm−2, 0.91±0.15 S m−1 and 5.52±0.95 kPa for H460 cells (ncell=437); 2.52±0.54 μF cm−2, 0.83±0.12 S m−1 and 5.54±1.04 kPa for H446 cells (ncell=410); 2.45±0.57 μF cm−2, 0.99±0.18 S m−1 and 5.16±1.68 kPa for A549 cells (ncell=442); 1.86±0.31 μF cm−2, 1.07±0.18 S m−1 and 3.86±0.81 kPa for 95D cells (ncell=415); 2.03±0.35 μF cm−2, 0.99±0.16 S m−1 and 3.49±0.70 kPa for 95C cells (ncell=290). The database of Cspecific membrane, σconductivity and Einstantaneous may serve as a reference for future studies of cellular biophysical properties.


Background & Summary
Biophysical properties of single cells include electrical parameters such as specific membrane capacitance (C specific membrane , i.e., capacitance per unit area for the cell membrane modelled as a capacitor) and cytoplasm conductivity (σ conductivity , i.e., the reciprocal of electrical resistivity or specific electrical resistance for the cytoplasm modelled as a resistor) as well as mechanical parameters such as instantaneous Young's modulus (E instantaneous , which describes the initial elastic response of a cell, modelled as an incompressible viscoelastic solid, in response to mechanical forces), which are indicators of the status of cytoskeletons and cellular membranes 1 . Variations in cellular biophysical properties are closely related to physiological and pathological processes, examples including (1) red blood cells infected by malaria; (2) tumour cells during migration and evasion; (3) leukocytes affected by sepsis; and (4) stem cells undergoing differentiation 2,3 . Conventional techniques for characterizing the electrical properties of cells include patch clamping, electrorotation and dielectrophoresis [4][5][6][7] . On the other hand, atomic force microscopy, micropipette aspiration and optical tweezers have been used for characterizing the mechanical properties of cells [8][9][10][11][12] . Although well established, these approaches suffer from limited throughput (~1 cell per minute). In addition, they are not capable of measuring cellular electrical and mechanical properties simultaneously 1 . Therefore, data recording C specific membrane , σ conductivity and E instantaneous for multiple cell types (hundreds of cells for each cell type) are currently not available in the literature.
Microfluidics is an area focusing on processing small amounts of fluids at the nanoliter to picoliter scale using microfabricated channels with dimensions of tens of micrometers [13][14][15] . The micrometer dimension is comparable to biological cells, and thus microfluidics is well suited for single-cell analysis 16,17 . More specifically, advances in microfluidic technology have enabled high-throughput characterization of the biophysical properties of single cells, e.g., through impedance flow cytometry, microfluidic optical stretchers and microfluidic hydrodynamic stretchers 1,8,18 . Although powerful, these previously reported microfluidics-based approaches only reported electrical (e.g., impedance flow cytometry) or mechanical (e.g., microfluidic optical stretchers and hydrodynamic stretchers) properties of single cells separately, without demonstrating simultaneous characterization of cellular electrical and mechanical properties.
Microfluidic approaches that enable simultaneous characterization of electrical and mechanical properties of single cells have also been developed, specifically through (1) microcantilever-based electrodes 19 , (2) electrodeformation 20 , (3) micropipette aspiration with impedance spectroscopy 21 , or (4) constriction channels with impedance spectroscopy 22 . The first three approaches are limited by their low throughput, and thus cannot be used to collect data from hundreds of single cells. In the fourth approach, cells in suspension were aspirated through a constriction channel (with a width and a height that are smaller than the cell diameter) continuously. The deformation and impedance profiles of individual cells as they enter and travel through the constriction channel were recorded as mechanical and electrical signals, respectively, with an estimated throughput of 1 cell per second.
Based on custom-developed electromechanical models, these raw biophysical signals obtained from constriction channels with impedance spectroscopy were then translated to size-independent intrinsic biophysical markers including C specific membrane , σ conductivity and E instantaneous [23][24][25] , enabling the classification of tumour cells with different malignant levels 26 . However, as proof-of-concept demonstrations, only a limited number of cell types were examined with small populations for each cell type 24 .
In this study, based on the aforementioned approach, C specific membrane , σ conductivity and E instantaneous from five types of tumour cells and hundreds of single cells for each cell type were quantified and reported. This study provides a preliminary database for cellular C specific membrane , σ conductivity and E instantaneous , which may serve as a reference for future studies on characterizing and classifying biological cells based on cellular biophysical properties.

Working flowchart
The working flowchart for characterizing C specific membrane , σ conductivity and E instantaneous includes four key steps: device fabrication, cell preparation, device operation and data processing (see Fig. 1). During operation, cells in suspension were aspirated into the microfluidic constriction channels with the deformation and impedance profiles of the cells recorded by a high-speed camera and an impedance analyser, respectively. Raw biophysical data were obtained by processing the images and impedance data captured in experiments, which were then translated to C specific membrane , σ conductivity and E instantaneous , based on a theoretical electrical model for a cell traveling within the constriction channel and a numerical mechanical model capturing the deformation of a cell when it enters the constriction channel, respectively. The key steps were summarized as follows. The detailed procedures have been reported in a previous publication 24 .

Device fabrication
The microfluidic device consists of a constriction channel (a cross sectional area of 10 μm × 10 μm) in polydimethylsiloxane (PDMS) elastomer (Dow Corning Corp., Midland, MI, USA) which was replicated from a SU-8 (MicroChem Corp., Newton, MA, USA) mould master (see Fig. 1a). Briefly, SU-8 5 was spun coated, prebaked and exposed without development and post exposure bake to form the layer of the constriction channel (10 μm in height). Then SU-8 25 was spin coated on top of the first SU-8 layer, exposed with alignment and developed, forming the cell loading channel with a height of 25 μm. PDMS precursor and curing agents (10:1 in weight) were mixed, poured on channel masters and baked for crosslinking. PDMS channels were then peeled away from the SU-8 masters, punched to form through holes as inlets and outlets, and bonded to glass slides after plasma treatment.

Device operation
During operation the device was first filled with culture medium and and a pipette was used to transfer the cell suspension solution to the entrance of the cell loading channel. A pressure calibrator (DPI-610 pressure calibrator, Druck, Billerica, MA, USA) was used to generate a negative pressure (0.5-1.2 kPa), aspirating cells continuously through the constriction channel with silver wires inserted into the inlet and the outlet of the device for impedance profile recording (see Fig. 1c).
An inverted microscope (IX71, Olympus Inc., Tokyo, Japan) in connection with a high-speed camera (M320S, Phantom Inc., Bublin, OH, USA) was used to capture the process of cellular entry and travelling in the constriction channel at 200 frames per second. Impedance data at both 1 and 100 kHz was measured by a lock-in amplifier (7270, Signal Recovery, Oak Ridge, TN, USA) with a sampling rate of and data processing (d) leveraging developed electrical (e) and mechanical (f) models. During device operation, suspended cells were aspirated into the microfluidic constriction channels with the cell deformation and impedance profiles recorded by a high-speed camera and an impedance analyser, respectively. Preliminary biophysical markers including A 1 kHz , A 100 kHz , L instantaneous , L transitional and L elongation were obtained based on processing of image and impedance data, which were then translated to C specific membrane , σ conductivity and E instantaneous , based on a theoretical electrical model for cells traveling within the constriction channel and a numerical mechanical model capturing cell deformation during the entry process, respectively.

Data processing
At the stage when a cell enters the constriction channel, two preliminary parameters were quantified based on image processing: L instantaneous as the aspiration length when a cell instantaneously jumps into the channel and L transitional as the aspiration length at the point where the creep deformation of the cell ends (see Fig. 1d) 25 . During the stage when the cell is travelling within the constriction channel, the impedance profiles and images of the elongated cell were analysed which produced three preliminary parameters: A 1 kHz and A 100 kHz , i.e., the ratios between the impedance amplitudes with and without a travelling cell at 1 and 100 kHz, respectively, as well as L elongation , i.e., aspiration length of the cell when travelling within the constriction channel (see Fig. 1d) 23 .
A theoretical model 23 was previously developed to model the electrical response of a cell as it is traveling within the constriction channel, thereby enabling the conversion of the measured A 1 kHz , A 100 kHz and L elongation to C specific membrane and σ conductivity as size-independent intrinsic electrical markers for single cells. Briefly, the electrical response of a cell was represented by R cytoplasm and C membrane in series where R leak indicated sealing properties during the cellular travelling process in the constriction channel. R leak was derived from impedance data at 1 kHz (A 1 kHz ) and C membrane and R cytoplasm were derived from impedance at 100 kHz (A 100 kHz ), respectively, which, were further translated to C specific membrane and σ cytoplasm based on geometrical information of the constriction channel (see Fig. 1e). Note that in this study, the lumped electrical model was used for data interpretation where the membrane portion was represented by C membrane and the cytoplasm portion was represented by R cytoplasm , which, to an extent, neglects the potential effects of ion channels in the cell membrane and the membranes of cytosolic organelles in cytoplasm. Future studies may develop more accurate cellular electrical models.
On the other hand, a numerical mechanical model 25 was developed to model the cell deformation as it enters the constriction channel, where the channel walls were modelled as rigid surfaces and the cell was modelled as an incompressible viscoelastic solid. The key mechanical parameter to be extracted was E instantaneous . Based on numerical simulations, the relationships between L instantaneous , L transitional and E instantaneous were obtained as follows: where D channel represents channel geometrical information, ƒ c represents the friction on cell-wall interfaces and P aspiration represents pressure applied to aspirate cells into the constriction channel (see Fig. 1f). The two unknown parameters, i.e., E instantaneous and ƒ c , were solved from these two equations since all the other parameters can be measured from experiments.

Data Records
Raw impedance and image data of five cell types are available at Dryad repository (Data Citation 1, Raw Impedance and Image Data of Single Tumour Cells). The file is an Excel composed of five sheets named after five cell lines of H460, H446, A549, 95D and 95C, respectively. In each sheet of a specific cell type, the first row is the cell number and within each cell number, there are seven columns which are time (collected from impedance analyser), amplitude at 1 kHz, phase at 1 kHz, amplitude at 100 kHz, phase at 100 kHz, time (collected from high-speed camera) and aspiration length. C specific membrane , σ conductivity and E instantaneous of five cell types are available at Dryad repository (Data Citation 1, Biophysical Properties of Single Tumour Cells). The file is an Excel composed of five sheets named after five cell lines of H460, H446, A549, 95D and 95C, respectively. In each sheet of a specific cell type, there are nine columns which are cell number (column A), A 1 kHz (column B), A 100 kHz (column C), L instantaneous (column D), L transitional (column E), L elongation (column F), C specific membrane (column G), σ conductivity (column H) and E instantaneous (column I). In this file, each row represents the biophysical parameters of a specific cell, including A 1 kHz , A 100 kHz , L instantaneous , L transitional , L elongation , C specific membrane , σ conductivity and E instantaneous . Based on the processing of impedance profiles and image processing, five preliminary biophysical markers of A 1 kHz , A 100 kHz , L instantaneous , L transitional , and L elongation were obtained. When the cell entered the constriction channel, an instantaneous jump into the constriction channel was initially observed (see Fig. 2a), enabling the quantification of L instantaneous in Fig. 2e. Then, a gradual increase in aspiration length (see Fig. 2b,e) was observed due to viscoelastic creep. The creep deformation ended when L transitional was reached (see Fig. 2c,e). Figure 2d shows an image of the cell travelling within the constriction channel where L elongation was quantified. Furthermore, impedance ratios at A 1 kHz and A 100 kHz were also quantified during the cellular travelling process in the constriction channel (see Fig. 2e). The averages and standard deviations of five preliminary biophysical markers (A 1 kHz , A 100 kHz , L instantaneous , L transitional and L elongation ) for five types of tumour cells were summarized in Table 1 parameters (e.g., A 1 kHz , A 100 kHz , L instantaneous , L transitional and L elongation ) and three size-independent intrinsic biophysical parameters (e.g., C specific membrane , σ cytoplasm and E instantaneous ) were included. Figure 3a-e show the distributions of C specific membrane , σ conductivity and E instantaneous for five types of tumour cells, respectively. For each type of tumour cells, the scatter plots of (i) C specific membrane versus D cell , (ii) σ conductivity versus D cell , (iii) E instantaneous versus D cell and (iv) C specific membrane versus σ conductivity versus E instantaneous were included. Note that D cell represents the diameter of the cell under measurement, which was calculated from L elongation based on the assumption of volume conservation when the cell deforms. As shown in Table 1, C specific membrane , σ conductivity and E instantaneous of five cell types were found to be 2.10 ± 0.38 μF cm − 2 , 0.91 ± 0.15 S m − 1 and 5.52 ± 0.95 kPa for H460 cells (n cell = 437); 2.52 ± 0.54 μF cm − 2 , 0.83 ± 0.12 S m − 1 and 5.54 ± 1.04 kPa for H446 cells (n cell = 410); 2.45 ± 0.57 μF cm − 2 , 0.99 ± 0.18 S m − 1 and 5.16 ± 1.68 kPa for A549 cells (n cell = 442); 1.86 ± 0.31 μF cm − 2 , 1.07± 0.18 S m − 1 and 3.86 ± 0.81 kPa for 95D cells (n cell = 415); 2.03 ± 0.35 μF cm − 2 , 0.99 ± 0.16 S m − 1 and 3.49 ± 0.70 kPa for 95C cells (n cell = 290). The detailed data of C specific membrane , σ conductivity and E instantaneous for individual cells are included in (Data Citation 1, Biophysical Properties of Single Tumour Cells).