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These authors contributed equally to this work.

Reproduction is permitted for noncommercial purposes.

Non-invasive single cell analyses are increasingly required for the medical diagnostics of test substances or the development of drugs and therapies on the single cell level. For the non-invasive characterisation of cells, impedance spectroscopy which provides the frequency dependent electrical properties has been used. Recently, microfludic systems have been investigated to manipulate the single cells and to characterise the electrical properties of embedded cells. In this article, the impedance of partially embedded single cells dependent on the cellular behaviour was investigated by using the microcapillary. An analytical equation was derived to relate the impedance of embedded cells with respect to the morphological and physiological change of extracellular interface. The capillary system with impedance measurement showed a feasibility to monitor the impedance change of embedded single cells caused by morphological and physiological change of cell during the addition of DMSO. By fitting the derived equation to the measured impedance of cell embedded at different negative pressure levels, it was able to extrapolate the equivalent gap and gap conductivity between the cell and capillary wall representing the cellular behaviour.

In biological cell-based biotechnology, single cell analyses are increasingly required to understand the response and behaviour of individual cells to test substances (e.g. DNA, molecule, protein) or to develop the strategic therapies and drugs against disease on the single cell level [

The goal of this article is to investigate the impedance of single cells considering the interfacial behaviour of cell by using a microcapillary with aspiration. During the aspiration, the elastic single cells are captured at the tip of capillary, which has a hole with smaller diameter than one of cell, and embedded in the capillary in dependence on the pressure, surface tension, and viscoelasticity of cell [

To derive an analytical solution for the interfacial impedance of single cell trapped at the capillary tip, it was assumed that the cell membrane and capillary wall are ideally insulated and that the low frequency current flows only through the extracellular area isotropically and homogenously. In case of no cell in a tubular capillary with length

_{m}

_{o}. The part of cell attracted into the capillary is set as a cylinder with length _{i}, and the end of cell in the capillary is a semi-eccentric with polar radius _{i}. Due to the presence of adhesive proteins, transport organelles, and cellular receptors in the cell membrane, cells contact onto the substratum with the gap of several tens to hundreds of nanometres [_{g}_{cell}) is as follows.

_{1} = cos^{−1} (_{o}), _{2} = cos^{−1} ((_{o}).

In each region 1, 2, 3, and 4 of

From the _{cell} is derived as follows.

Therefore, the difference of resistance for the capillary tip with captured cell and of resistance for the tip without cell, _{diff} (=_{cell} − _{ref}), is defined as a function of the observable parameters, _{i}, _{i}, and _{o}, and the adjustable ones, _{g}_{g}_{diff} was fitted to experimental data (used software: Matlab, The MathWorks Inc., Natick, USA). As shown in _{3}) is determined by the parameters of _{g}_{i} representing the interfacial behaviour of cells. To investigate how much _{diff} is contributed by _{3} with respect to the interfacial parameters _{g}_{i}, _{3}/_{diff} was calculated at different _{i} and _{i} = 2 μm, _{o} = 12 μm, _{m}_{g}_{i} and _{g}_{i} = _{o} = 12 μm, _{m}

For the cells, we prepared cultured L929 murine fibroblasts and removed the medium in the culture dish. The cells were washed once with PBS and then trypsinized with 1 ml of 10% Trypsin/EDTA for 3 minutes in an incubator Heraeus BB 6220 (Heraeus-Christ, Hanau, Germany). The cell suspension was transferred into a 15 ml plastic tube (Greiner BIO-ONE, Frickenhausen, Germany) and the cells were centrifuged at 1000 rpm for 5 minutes. After removing the supernatant, the cells were resuspended in culture medium (RPMI 1640, 10% FCS, 0.5% Penicillin/Streptavidin). For the capillary, we purchased insulated borosilicate glass capillaries (Custom Tip Type II, Eppendorf, Hamburg, Germany). ^{®} Oil, Eppendorf, Hamburg, Germany). After filling culture medium (RPMI 1640, 10% FCS, 0.5% Penicillin/Streptavidin) in the capillary and a dish, the cells were put in the dish. For the impedance measurement, an Ag-wire electrode was installed at the heel of capillary and another Pt electrode in the dish. The electrodes were connected to an electrochemical impedance analyzer (1260, Solartron Analytical, Farnborough, UK). The impedances of capillaries with and without a captured cell at the tip was measured in the frequency range from 100 Hz to 100 kHz. The single cell was captured at the tip of capillary by applying a negative pressure. The peak of input potential used for impedance measurement was 100 mV.

To monitor biological relevant effects, we investigated the influence of DMSO used for the cryopreservation of cells or the increase of membrane permeability on a single cell. It is well known that DMSO is polar and easily diffused through the cell membrane where it can replace water molecules associated with cellular constituents [

Under the assumption that the low frequency current flows only through the extracellular region, the derived _{g}_{3} determined by the interfacial parameters _{i}, _{g}_{diff} at different _{i} with _{g}_{m}_{3} contributes more to _{diff} with increase of _{i} or with decrease of _{g}_{3}/_{diff} on _{g}_{i}. As more as _{3} contributes to _{diff}, the impedance measurement of embedded single cell reflects more the cellular behaviour related with the interfacial parameters _{i}, _{g}_{i} or _{o} causes relatively less the change of impedance of embedded cell as _{3}/_{diff} is higher. From this theoretical investigation, it was estimated how much the impedance measurement on embedded cells reflects the interfacial behaviour of embedded single cells.

During the aspiration with negative pressure, a L929 cell was moved to the capillary entrance along the fluid and captured at the tip of capillary. Then, a part of elastic cell was expanded in the capillary in dependency on the pressure level. When a single L929 cell was captured at the capillary tip at a negative pressure of 9 mbar, the measured impedance magnitude in the frequency range of 100 Hz to 100 kHz was shown in

capture of a particle (cell or bead)

application of DMSO (100 μl of culture medium including 5% DMSO)

breakdown of cell membrane

release of a particle (cell or bead)

The difference of impedance magnitude for a capillary tip with captured cell and of the magnitude for a capillary tip without cell (|Z|_{capture} − |Z|_{non-capture}) was a suitable parameter for the change of impedance. For the measured data of

_{o} and _{i} were 11.73 ± 0.17 μm and 1.60 ± 0.22 μm, respectively.However, both _{i} and the difference of impedance magnitude were increased with increase of negative pressure level (_{i}, |Z|_{capture} − |Z|_{non-capture}: 4.3 μm, 2.82 MΩ at 300 s, 7.5 μm, 4.26 MΩ at 500 s, 9.9 μm, 5.83 MΩ at 700 s, 13.0 μm, 8.05 MΩ at 900 s). By fitting the derived equation _{diff} to the difference of impedance magnitude in _{g}_{m}_{g}_{m}_{g}_{g}

The results of this article show that the behaviour of a partially embedded cell can be determined by the described methods and that the biological relevant changes of cell membrane can be reflected in measured impedance. These are important preconditions for the development of single cell-based sensors using impedance spectroscopy with microhole interfacing single cells. One example for the cell based-sensor would be a cell chip with microhole array. The advantage of a planar microhole array is that the surface chemistry and geometry of the interface region to the cell can be adapted to the physiologic requirements of the cells. Further, with an array of microholes, statistically relevant data on the single cell level about the effect of active substances or the state of the cells can be derived. Such cell-based sensors will be useful for example to test on the single cell level the toxicity of substances or the condition of cells after treatment (e.g. drug injection, gene transfection).

As one precondition for the development of sensor based on the impedance measurement at a cell/microhole interface, the impedance measurement on cells embedded in a microcapillary was investigated. An analytical equation was derived to estimate and to interpret the resistance change of capillary tip with partially embedded single cell by using the interfacial parameters i.e. length of embedded cell, equivalent gap, and gap conductivity. The frequency range in which the capturing of a cell is clearly reflected in an increase of impedance magnitude was experimentally determined by impedance measurement with capillary system. From the impedance monitoring of embedded cell during the addition of DMSO, it was shown that the impedance measurement of capillary tip with partially embedded cell at the low frequency is determined by the morphological and physiological changes of cell. As the length of embedded cell increases during the aspiration, the impedance magnitude at the low frequency was increased correspondingly. By fitting the derived equation to measured impedance of embedded cells deformed at different negative pressure levels, it was able to extrapolate the equivalent gap and gap conductivity related with cellular behaviour. The results of this paper reported important preconditions for the development of single cell-based sensors using impedance measurement with microhole interfacing single cells.

Schematic of a single cell with high surface tension of membrane partially embedded in the tip of capillary with length _{i}: length of cylindrically shaped cell body in the capillary, _{i}: polar radius of semi-eccentrically shaped end of cell in the capillary, _{o} : radius of spherically shaped cell external to the capillary entrance,
_{1} = cos^{−1}((_{o}).

Schematic of experimental setup for impedance measurement of a single cell at the tip of a capillary.

Contribution of resistance in the region 3 of _{3}/_{diff}) at different length of embedded cell _{i} with equivalent gap _{i} = 2 μm, _{o} = 12 μm, _{m}_{g}_{g}_{i} = 2 μm, _{o} = 12 μm, _{m}

A: Measured impedance spectra for a L929 cell captured at the tip of capillary and for a capillary without cell, B and C: Change of impedance magnitude (|Z|_{capture} − |Z|_{non-capture}) at 100 Hz in response on the following events: (a) capture, (b) application of DMSO (100 μl of culture medium with 5% DMSO into 1 ml medium in the dish, (c) cell membrane breakdown, and (d) release, In panel B, the impedance for a latex bead captured at the capillary is shown additionally.

Micrographs of an embedded cell when the level of negative pressure is 8.3 mbar at 300 s, 11 mbar at 500 s, 15.5 mbar at 700 s, and 21.1 mbar at 900 s (A), the difference of impedance magnitude at 100 Hz during the aspiration (B), arrow: the time of capture.

Equivalent gap (_{g}_{m}_{diff} to the difference of impedance magnitude at 100 Hz of