Feasibility of Tracking Multiple Single-Cell Properties with Impedance

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On the Feasibility of Tracking Multiple SingleCell Properties with Impedance Spectroscopy Dingkun Ren, and Chi On Chui ACS Sens., Just Accepted Manuscript • DOI: 10.1021/acssensors.8b00152 • Publication Date (Web): 08 May 2018 Downloaded from http://pubs.acs.org on May 13, 2018

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On the Feasibility of Tracking Multiple Single-Cell Properties with Impedance Spectroscopy Dingkun Ren*†, Chi On Chui*†‡# †

Department of Electrical Engineering, University of California, Los Angeles, Los Angeles 90095, California, USA ‡ Department of Bioengineering, University of California, Los Angeles, Los Angeles 90095, California, USA # California NanoSystems Institute, University of California, Los Angeles, Los Angeles 90095, California, USA

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Abstract

Electric cell-substrate impedance sensing (ECIS) has been instrumental in tracking collective behavior of confluent cell layers for decades. Toward probing cellular heterogeneity in a population, the single-cell version of ECIS has also been explored, yet its intrinsic capability and limitation remain unclear. In this work, we argue for the fundamental feasibility of impedance spectroscopy to track changes of multiple cellular properties using a noninvasive single-cell approach. While changing individual properties is experimentally prohibitive, we take a simulation approach instead and mimic the corresponding changes using a 3D computational model. From the resultant impedance spectra, we identify the spectroscopic signature characteristic to each property considered herein. Since multiple properties change concurrently in practice, the respective signatures often overlap spectroscopically and become hidden. We further attempt to deconvolve such spectra and reveal the underlying property changes. This work provides the theoretical foundation to inspire experimental validation and adoption of ECIS for multi-property single-cell measurements.

Keywords ECIS, single-cell, impedance, spectroscopy, cellular property


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Cellular assays measure biochemical and/or physical properties that reflect changes in vital cell physiology in response to chemical, therapeutic, and nanomaterial stimuli.1 Apart from those that measure the averaged response across a population of treated cells, single-cell assays offer valuable insight into heterogeneity in the population. Many of the current single-cell assays are imaging-based. For example, automated fluorescence microscopy yields superior spatial resolution and phenotypic profiling at the single-cell level, but it has limitations due to its cost, bulky equipment, procedural complexity, limited throughput, and data-processing.2-4 Alternatively, electrical impedance tomography performs noninvasive imaging of single cells and measures no other properties.5 In addition, single-cell electric impedance topography maps the spatial distribution of membrane capacitance, but it reveals little intracellular information.6 There are also nonimaging assays that measure other cellular properties of crucial importance. For instance, electric cell-substrate impedance sensing (ECIS) is a real-time, noninvasive technique for monitoring adherent cell proliferation, morphology, and kinetics in confluent cell layers and tissues that incorporate ~104 cells.7-20 Single-cell ECIS has also been attempted, yet it generates only ensemble impedance values,16,21-25 whose variation in response to single or multiple stimuli cannot be easily untangled to reveal specific cellular property change(s). Nevertheless, we believe that the rich electrical information underlying single-cell impedance spectroscopy can be harnessed to concurrently track several cellular properties and reflect vital physiological changes non-invasively. The first part of this paper concerns the existence of a spectroscopic signature characteristic to each of the several cellular properties examined. Without losing generality, we consider four important single-cell properties, namely, cell diameter (Dcell), membrane capacitance (Cm), cell-electrode distance (d) and cytoplasm resistivity (ρcyto), changes in which are integral to differentiation, apoptosis, necrosis, adhesion, proliferation, or other physiological conditions.20,26-38 Since changing only one of these properties is experimentally impractical as of today, we have developed a three-dimensional (3D) numerical model of a single-cell ECIS setup to implement single and multiple property changes. To date,


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most of efforts on single-cell ECIS modeling rely on analytical solutions,11,23,24,39-43 which are originally derived to explore cell behaviors of confluent cell layers.7-10 In a typical single-cell ECIS, however, electrical current is easily diverted due to complex cell morphology and properties, and therefore analytical solutions cannot be simply found for such comprehensive system. Instead, our technique is more computational, aiming to reconstruct a spatial ECIS measurement environment entirely in 3D by taking account single-cell morphology. In the second part, we discuss a strategy to distinguish the change of one property from other concurrent property changes, whose respective spectroscopic signatures often overlap. This is particularly important in determining whether single-cell ECIS can ever be used to track concurrent changes of multiple properties encountered in reality. Again using our 3D model, we have validated such a strategy based on a hypothetical time-course single-cell evolution scenario. Note that our modeling approach is far from perfect and that it is impossible to cover the numerous other single-cell properties and physiological conditions. Nevertheless, the purpose of this work is to trigger further experimental work to uncover the real strength of single-cell ECIS. MODEL AND SIMULATION SECTION The simulation structure for a typical single-cell ECIS measurement is composed of a working electrode, a counter electrode, a single cell, and a solution, as shown in Figure 1. The working electrode size is 30 μm × 30 μm, which is close to the area of a single cell when it spreads out. The counter electrode is placed above the simulation structure to simplify the boundary conditions, and the single-cell morphology is assumed to be hemispherical resting on the working electrode surface. A similar structure has been reported before.21 A common way to model the impedance-based ECIS setup is to use passive equivalent

circuit

lumped

elements—resistors

(R)

and

capacitors

(C)—to

describe

cells,

electrode/solution interfaces, and solution. We used several pioneering works as our references, including analytical models of confluent cell layers and other electrical components,11,23,24,39-41 a single-cell ECIS model solvable with the finite-element method,21 and a single-cell EIS model for a circuit simulator.42,43


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In our single-cell ECIS model, the entire virtual measurement system shown in Figure 1 is finely meshed to form a spatial resistance (R) and capacitance (C) network, and impedance spectra Z(ω) are calculated at frequencies (ω) between 100 Hz and 10 MHz. More details of the modeling process and software are given in the accompanying the Supporting Information. 3D spatial mesh. In order to efficiently achieve convergence while generating mesh in 3D, we chose tensor mesh based on rectangular hexahedra as elementary units, the same as the mesh implemented in a finite-difference time-domain (FDTD) numerical simulation for electromagnetics. Such tensor mesh is flexible, allowing progression of grid density depending on the desired resolution in each local region. A similar meshing algorithm called “Cartesian transport lattices” has been used for the study of cellular transmembrane potential for individual floating cells, yet the size of the mesh is unchanged throughout the structure,42,43 which was not suitable for our study. In our model, we applied a mesh size of 0.5 μm × 0.5 μm × 0.5 μm to finely discretize the simulation region with a single cell, and we decreased the mesh density of the region without a cell to reduce the total simulation time. Another significant aspect of our meshing approach is that the morphology of single cells could be customized with corresponding adjustments of mesh size or density. Note that this strategy is not possible in the most commonly used analytical model of confluent cell layers. More description of the 3D mesh is given in the Supporting Information. Equivalent electrical lumped elements and the 3D impedance circuit network. The cellular impedance components composed of electrical lumped elements derived by analytical models were incorporated into the spatial mesh to form a 3D impedance network, as shown in Figure 2A. Overall, five fundamental impedance components of a single-cell ECIS setup were considered: (1) the double layer at the interface of the working electrode and solution, (2) the interface of the bottom cell membrane and solution, (3) the interface of the side or top cell membrane and the solution interface, (4) the intercellular cytoplasm, and (5) the solution, as illustrated in Figure 2B. Implemented through those electrical components, four specific cellular properties were set as variables: cell diameter (Dcell), membrane


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capacitance (Cm), cell-electrode distance (d), and cytoplasm resistivity (ρcyto), as discussed above. To investigate the characteristics of spectroscopic signatures, we set the values of each cellular property as follows: (1) Dcell – from 20 μm to 30 μm (20 μm, 25 μm, 30 μm); (2) Cm – from 1 μF/cm2 to 5 μF/cm2 (1 μF/cm2, 2 μF/cm2, 3 μF/cm2, 4 μF/cm2, 5 μF/cm2); (3) d – from 10 nm to 200 nm (10 nm, 50 nm, 100 nm, 150 nm, 200 nm); and (4) ρcyto – from 50 Ω-cm to 250 Ω-cm (50 Ω-cm, 100 Ω-cm, 150 Ω-cm, 200 Ω-cm, 250 Ω-cm). In addition, we assumed that the volume of a single cell was constant in all cases. Another two crucial parameters were Ln and An (as shown in Figure 2B), to represent the length and the common area, respectively, between two neighboring mesh nodes. As for boundary conditions, an input voltage (Vin) of 1 V and a common ground (GND) of 0 V were applied to the working electrode and counter electrode, respectively. The total impedance Z(ω) was then computed at multiple frequencies between 100 Hz and 10 MHz and, finally, plotted as a function of frequency ω as single-cell impedance spectra. More description of equivalent electrical lumped elements is given in the Supporting Information. Impedance Spectra of Individual Cell States. In ECIS measurement, the overall impedance spectrum without any cell is normally used as the reference, i.e., Zref(ω) for spectra without attached cells. Therefore, to describe our simulation results, we use normalized overall impedance, instead of absolute overall impedance, to track changes of impedance corresponding to changes of single or multiple cell properties. We further define a cell state as a specific combination of values of cell properties, i.e., (Dcell, Cm, d, ρcyto), giving its impedance as Z(ω, Dcell, Cm, d, ρcyto). Then, the normalized overall impedance Z'(ω, Dcell, Cm, d, ρcyto) is defined as

Z ' (, Dcell , C m , d ,  cyto ) =

Z (, Dcell , C m , d ,  cyto ) − Z ref ( ) Z ref ( )

(1)

The total number of cell states is thus 375, according to the values of each property given in the previous section. We first validated our single-cell ECIS model by replicating the impedance spectra simulated in Ref. 21 (details are given in the Supporting Information). Next, we simulated the overall impedance of the


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aforementioned single-cell ECIS setup at frequencies between 100 Hz and 10 MHz, with only one of the four cell properties changed at a time. For easy identification of any spectroscopic difference between two cell states, we further calculated for a given frequency the ratio of normalized impedance of two cell states, i and j, which can be written as

nij ( ) =

Z 'j ( , Dcell , C m , d ,  cyto ) Z i' ( , Dcell , C m , d ,  cyto )

(2)

where Zi'(ω, Dcell, Cm, d, ρcyto) and Zj'(ω, Dcell, Cm, d, ρcyto) are the normalized impedance of two respective cell states. Note that such a ratio is frequency dependent. Modeling of a biological process for single-cell spreading and adhesion. To further show the spectroscopic signatures of cell properties and the potential application of our model in single-cell biosensing, we simulated impedance spectra by mimicking a time-course scenario of single-cell spreading and adhesion on a working electrode. This biological process is commonly recognized as a cell culture that takes about 24 hours before impedance measurement is performed. In the simulation, the cell volume, Cm (1 μF/cm2), and ρcyto (100 Ω-cm) were kept fixed, while the cell diameter Dcell and cell-electrode distance d were varied: Dcell was from 20 µm to 30 µm with an increment of 0.5 µm, and d was from 200 nm to 10 nm with a step of 9.5 nm. The total number of time points was 21, and the overall impedance at each time point was written as Zcell,i(ω, Dcell, Cm = 1 μF/cm2, d, ρcyto = 100 Ω-cm, i = 1, 2, 3 . . . 21). Deconvolution of impedance spectra with concurrent changes of cellular properties. Multiple cell properties may concurrently change upon transitioning from one cell state to another. The individual property changes are, however, not often distinguishable from the overall impedance change, as their respective spectroscopic signatures often overlap. In other words, more than one property change may induce the overall impedance change at a given frequency such that resultant spectroscopic ratio nij(ω) change (or lack thereof) cannot be tied to one single source. Thus, the key challenge of the deconvolution of multi-property impedance spectra is to link nij(ω) to two distinct cell states. Here, we suggest that it is fundamentally possible to do so because nij(ω) of any two different cell states would be unique in


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frequency domain. Our strategy is to match nij(ω) corresponding to a pair of single-cell measurements from the impedance database, which contains simulated values of all Z'(ω, Dcell, Cm, d, ρcyto) based on various combinations of Dcell, Cm, d, and ρcyto. Once the match is made, both cell states i and j can be determined, along with the value of each cellular property. Normally, a series of normalized impedance would be obtained from time-course measurement, which gives a series of ratios, and therefore, a common cell state must exist between two neighboring spectroscopic ratios. For instance, there must be the same set of cell properties solved from nij(ω) and njk(ω), where i, j, and k are three successive states. To demonstrate the strategy of deconvolution, we keep cytoplasm resistivity constant at 100 Ωcm, while the other three cell properties are concurrently changing. The allowed values of each property are: (1) Dcell – 20 μm, 22.5 μm, 25 μm, 27.5 μm, and 30 μm; (2) Cm – 1 μF/cm2, 2 μF/cm2, 3 μF/cm2, 4 μF/cm2, and 5 μF/cm2; and (3) d – 10 nm, 50 nm, 100 nm, 150 nm, and 200 nm. Therefore, the database would consist of 125 cell states in total. Next, we have the computer randomly pick five cell states to mimic a time-course impedance sampling at times T1, T2, T3, T4, and T5. Moreover, we define the accuracy of fitting, δ(ω), to describe the deviation between measured and simulated spectroscopic ratios, which can be written as

 ( ) =

nij ( ) − ni ' j ' ( ) nij ( )

(3)

where nij(ω) is obtained from measurement, while ni’j’(ω) represents the ratio of any two cell states in the database. RESULTS AND DISCUSSION Simulation results. We first simulate the overall impedance spectra of single-cell ECIS setup with only one cellular property changed at a time. The volume of a single cell is assumed to be constant, always. Figures 3A-C show the normalized impedance spectra for independently changed membrane capacitance, cell-substrate distance, and cytoplasm resistivity, respectively. Each figure includes spectra for three


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different cell diameters. To further illustrate the spectroscopic signature of each property, we calculate nij(ω)

of two cell states with only one cellular property changed at a time, as shown in the contour plots in

Figure 4. The cell states used as dominators in Eq. 2 for each case are Zi'(ω, Dcell, Cm = 5 μF/cm2, d, ρcyto), Zi'(ω, Dcell, Cm, d = 200 nm, ρcyto), and Zi'(ω, Dcell, Cm, d, ρcyto = 50 Ω-cm), respectively. The spectroscopic signatures for all four properties are mapped in the frequency band from 100 Hz to 10 MHz, as given in Figure 5. Then, we simulate the cell culture, a cell behavior, to investigate the spectroscopic signatures while concurrently changing multiple cell properties, i.e., cell dimeter Dcell and cell-electrode distance d. Figure 6A illustrates the biological process of single-cell spreading and adhesion with varied Dcell from 20 µm to 30 µm and d from 200 nm to 10 nm. The total number of time points is 21, labelled as Tcell,i (i = 1, 2, 3 . . . 21). A contour plot of normalized impedance, i.e., Zcell,i'(ω, Dcell, Cm = 1 μF/cm2, d, ρcyto = 100 Ωcm, i = 1, 2, 3 . . . 21), as a function of time is depicted in Figure 6B. To display the spectroscopic characteristics, we calculate the ratio of normalized impedance ncell,ij(ω) (i = 1, j = 2, 3, 4 . . . 21) by setting Zcell,1' as the reference normalized impedance, as shown in Figure 6C. In addition, to further validate the rationality and generality of our single-cell model, we look at reported studies on monitoring the spreading and adhesion of single cells, multiple cells, and confluent cell layers and then compare the frequency regime that offers the maximized ncell,ij(ω) in the simulations with the ones used in those experiments. The second part of the study is to demonstrate the strategy of deconvolution for overlapping spectra. The five randomly chosen cell states are listed in Table 1. The normalized impedance spectra of the five states are shown in Figure 7A, labeled as Z1', Z2', Z3', Z4', and Z5', respectively, while four spectroscopic ratios between the first state Z1' and other post states are illustrated in Figure 7B, labeled as n1'2', n1'3', n1'4', and n1'5', respectively. The extracted Dcell and d values are respectively shown in Figures 7C and D with δ of 0.05 or 0.10 of which the solutions from respectively higher and lower accuracies are identical. The extracted Cm values with δ tolerance 0.10 and 0.05 are shown in Figure 7E.


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Spectroscopic signatures of individual cellular properties. We first examine the single-cell ECIS impedance as a function of frequency for each cellular property considered. We divide the frequency spectrum examined into three bands: (1) low-frequency band (LF) 100 Hz – 10 kHz, (2) intermediatefrequency band (IF) 10 kHz – 1 MHz, and (3) high-frequency band (HF) 1 MHz – 10 MHz. The effect of changing Cm, d, and ρcyto on the overall impedance spectra depends on the varying amount of AC current passing through the cell membrane, seal space between the working electrode surface and the bottom cell membrane, and cytoplasm resistivity, respectively. Before delving into analyzing the simulated impedance spectra, we can build some intuition about the expected impedance change in each frequency band. At low frequency, the cell membrane (Cm) is rather insulating, as apparent from its impedance expression Z = 1/jωCm, forcing the current to flow around and underneath the cell. The seal resistance, which is the resistance between the bottom cell membrane and the working electrode surface, thus dominates the overall impedance. In other words, the low-frequency impedances are more sensitive to the change in cell adhesion (d). At intermediate frequency, cell membrane impedance starts to decrease, diverting the current to flow through the membrane as well as underneath the cell. As a result, Cm and d contribute equally to the overall impedance. In the high-frequency band, the cell membrane impedance becomes very small, while seal resistance remains constant. Most current flows through the membrane and in and out of the cell such that the cytoplasm resistivity (ρcyto) dominates the overall impedance. Unlike Cm, d, and ρcyto, the change of cell diameter exhibits less subtle spectroscopic dependency. The change of Dcell should affect the whole impedance spectra because Dcell scales geometrically with the seal resistance, membrane impedance, and cytoplasm resistance. The larger the cell diameter, the larger the working electrode area covered by the single cell, resulting in larger change in the respective current flow. The foregoing intuition is validated by the simulated impedance spectra shown in Figures 3A-C. As illustrated in Figure 3A for changing Cm, the impedance change is maximized at intermediate frequency with almost no change at low frequency. As opposed to the case of Cm, the maximum impedance change as a function of d (Figure 3B) occurs at low and intermediate frequencies, while no


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noticeable difference is found at high frequency. In particular, the impedance decreases more when d is increased from 10 nm to 50 nm versus from 50 nm to 100 nm. Additionally, the impedance is not sensitive to ρcyto variation except at high frequency (Figure 3C) because the membrane impedance becomes small in this frequency band (Figure 3A). The contour plots of spectroscopic ratio nij (ω) reveal a more direct intuition of the spectroscopic signature of each cellular property, as shown in Figure 4. It is clearly observed that changing d leads to a much more significant change of nij (ω) than do changes to the other three properties in low-frequency band. Thus, the signature of d could be distinguished from overlapping time-course impedance spectra earlier in the latter deconvolution process. In addition, the distribution of nij (ω) for changing Cm is more symmetric and peaked around 1 MHz, and further extends to 100 kHz and 1 MHz. Fortunately, nij(ω) for changing ρcyto is maximized at the highest frequency 10 MHz, and rapidly decays from 10 MHz to 1 MHz. In other words, though simultaneous changes of Cm and ρcyto would contribute to overlapping change of spectra in high-frequency band, it is still possible to distinguish one from the other because the nij (ω) for each case occurs at a different frequency. The frequency band where major impedance change occurred for each cellular property is illustrated in Figure 5. Spectroscopic signatures of single-cell spreading and adhesion. Turning now to recognize the spectroscopic signatures of concurrently changed cell properties, we start to investigate a more complex single-cell behavior, namely, cell culture, which is associated with spreading and adhesion, shown in Figure 6A. Typically, an expansion of Dcell and a decrease of d can be observed during this process. Thus, using the spectroscopic characteristics of Dcell and d given earlier, we can intuitively suggest that the overall impedance Zcell,i(ω), or the normalized impedance Zcell,i'(ω), will become larger over the time in low and intermediate frequency regimes (100 Hz – 100 kHz). This hypothesis is supported by the change of impedance magnitude shown in the contour plot of Zcell,i'(ω) in Figure 6B. Moreover, we observe that the peak of Zcell,i'(ω) shifts from 100 kHz to 40 kHz (marked by an arrow in Figure 6B); this is because the change of impedance is more sensitive at low frequency with deceasing d. To provide further insight, we


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now look at the ratio of normalized impedance, i.e., ncell,ij(ω). Clearly, the change of ncell,ij(ω) is more remarkable in the low-frequency band, indicating a strong spectroscopic signature of cell-electrode distance d, which agrees with the previous results for individual cell properties shown in Figure 4. In addition, we note that the increase of ncell,ij(ω) becomes more significant in both intermediate- and highfrequency bands from Tcell,1 to Tcell,21; this is because the spectroscopic signature of Dcell covers the entire frequency spectrum, which is very different from the characteristics of any other cell property. Looking back at the published ECIS studies on the spreading and adhesion of single cells, multiple cells, and confluent cell layers, we find that the frequency band of 100 Hz – 10 kHz that gives optimized values of ncell,ij(ω) in our simulations matches the frequency regime of 1 Hz – 32 kHz used in those experiments for real-time monitoring.12,23,25,26,33,36-38,41 Example of such experiments include : (1) studying spreading, adhesion, and resuspension of Spodoptera frugiperda Sf9 multiple cells using 4 kHz;12 (2) investigating adhesion and cell-electrode distance of fibroblast 3T3 single-cells using 1 kHz;23 (3) monitoring cell culture of fibroblast V79 (93-CCL) confluent cell layers using 1 Hz – 10 kHz and performing cell counting of multiple cells using 4 kHz;26 and (4) exploring adhesion (due to apoptosis) of glioblastoma multiforme T98G single-cells using 2 kHz.36 Note that to achieve maximized impedance signals, the frequencies implemented in all those experiments were within the same regime regardless of the geometry or the size of the working electrodes. This fact supports the generality of our single-cell model in impedance spectroscopy to concurrently explore multiple cell properties. Demonstration of the deconvolution strategy. Having obtained the aforementioned insight into spectroscopic characteristics of various cell properties, we propose a possible approach to qualitatively deconvolute time-course impedance spectra and extract the changes of cell properties as well. Our whole argument is based on the fact that nij(ω) of any two different cell states would be spectroscopically unique. Since concurrently changing multiple properties is experimentally practical, we focus on some major cellular parameters—Dcell, Cm, and d—without losing much generality. As a prerequisite, assume that we are not aware of any information about those five randomly


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generated cell states (Table 1) and consider the impedance spectra in Figure 7A as raw experimental data from time-course single-cell impedance spectroscopy. To process the data, we first calculate nij(ω) of those states, as shown in Figure 7B. Note that we normalize the spectra of all post states to the initial state. It is observed that each nij(ω) has a very different response in frequency spectrum, where n15 shows the most significant change in the low-frequency band. Looking at the contour plots in Figure 4 for comparison, we can easily conclude that d has been dramatically changed. As for n12 and n13, the former keeps almost constant at low frequency and becomes maximized at 1 MHz, while the latter is flat over 100 kHz, and its maximum appears at about 3 kHz. Thus, it is possible that while the cell state is changed from 1 to 2, Dcell or Cm is changed accordingly without the change of d. In contrast, the cell state changing from 1 to 3 might be caused by the change of d. Last but not least, n14 shows the smallest and most constant ratio (smaller than 1) across the whole spectrum. As an initial guess, we suspect that the single cell shrinks in size, resulting in the decrease of the overall impedance. Then, those five spectroscopic ratios are fitted to the values in the database with accuracy δ of 0.10 and 0.05, respectively. Theoretically, smaller δ would further eliminate more incorrect solutions. Clearly, the solutions for Dcell and d are unique, as shown in Figure 7C and Figure 7D. Even though multiple solutions for Cm are obtained, as marked with error bars in Figure 7E, the trend of Cm from cell state 1 to 5 perfectly matches the values in Table 1. Therefore, our model is valid if only those three cell properties are changing in real-time single-cell impedance spectroscopy. Indeed, impedance spectra from experiments would be much more complicated, associated with the change of other cell properties as well as noise from the experimental setup. However, we believe Dcell, Cm, and d are the most fundamental properties used to describe cell behaviors in general, and those could be extracted by our deconvolution strategy. As for further investigation, ρcyto will first be considered in the scheme. Second, more cell states will be included in the database for higher resolution. Third, cell morphology can be modified to a more complicated structure instead of a hemispherical cap.


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CONCLUSIONS In summary, we successfully reconstructed a 3D spatial single-cell ECIS system and studied the spectroscopic signatures of four cell properties—cell diameter Dcell, membrane capacitance Cm, cellelectrode distance d, and cytoplasm resistivity ρcyto. Then we made a case study of cell behavior, i.e., cell culture, to explore the spectroscopic characteristics for concurrently changed cell properties. Finally, we demonstrated the deconvolution of multiple time-course impedance spectra by fitting the normalized impedance nij(ω) to the cell states in the database. Certainly, in order to obtain more intercellular and intracellular information by impedance spectroscopy, it is necessary to include more cell properties in the simulation to form a more complete database. We believe that this study establishes a theoretical foundation, paving the way to accomplish multi-property single-cell measurements by ECIS with a simple platform.


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ASSOCIATED CONTENT Supporting Information The Supporting Information is available free of charge on the ACS Publications website at http://pubs.acs.org. More details of the 3D computational model for ECIS single-cell, including the modeling process, 3D mesh, and equivalent electrical lumped elements. A validation of the 3D single-cell model is discussed as well. AUTHOR INFORMATION Corresponding Author E-mail: [email protected] or [email protected] ORCID Dingkun Ren: 0000-0001-9470-1956 Author Contributions D.R. and C.O.C. designed research; C.O.C. guided research; D.R. performed research; D.R. and C.O.C. analyzed data; and D.R. and C.O.C. wrote the manuscript. Notes The authors claim no competing financial interests. ACKNOWLEDGEMENTS The authors would like to appreciate Dr. Andrew Pan for his suggestions about the Matlab coding. We also gratefully acknowledge the support from the National Science Foundation (grant no. 1449395).


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For Table of Contents Only


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Figure 1. Schematics of ECIS setup for single-cell impedance used in the simulation. The actual size of each component is not to scale.


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Figure 2. (A) A cross-section of the mesh network and the corresponding electrical components. Here, the schematics of ECIS setup includes a single cell and a working electrode. Different electrical components projected onto the mesh are illustrated as rectangles in different colors. The boundary conditions, i.e. Vin and GND, are labelled as well. (B) The analytical model of each ECIS component – electrode/solution interface, bottom cell membrane/solution, side cell membrane/solution, cytoplasm, and solution – described by equivalent electrical lumped elements.


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Figure 3. The simulated normalized impedance spectra with only one cellular property changed at a time. Cell diameters Dcell used in the simulation are 20 μm (in blue), 25 μm (in green), and 30 μm (in red), respectively. (A) Normalized impedance as the function of cell membrane capacitance Cm and frequency. (): Cm = 1 μF/cm2. (): Cm = 2 μF/cm2. (): Cm = 3 μF/cm2. (Δ): Cm = 4 μF/cm2. (☆): Cm = 5 μF/cm2. (B) Normalized impedance as the function of cell-electrode distance d and frequency. (): d = 10 nm. (): d = 50 nm. (): d = 100 nm. (Δ): d = 150 nm. (☆): d = 200 nm. (C) Normalized impedance as the function of cell cytoplasm resistivity ρcyto and frequency. (): ρcyto = 50 Ω-cm. (): ρcyto = 100 Ω-cm. (): ρcyto = 150 Ω-cm. (Δ): ρcyto = 200 Ω-cm. (☆): ρcyto = 250 Ω-cm. The right plot shows a close-up look of high-frequency band.


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Figure 4. The simulated contour plots of spectroscopic ratio nij of normalized impedance between two cell states with only one cellular property changed at a time. The cell diameter Dcell is 20 μm for the first column, 25 μm for the second column, and 30 μm for the third column. The ratio nij for changing Cm, d, and ρcyto correspond to the first row to the third row, respectively. The change of membrane capacitance Cm – from 1 μF/cm2 to 5 μF/cm2. The change of cell-electrode distance d – from 10 nm to 200 nm. The change of cytoplasm resistivity ρcyto – from 50 Ω-cm to 250 Ω-cm.


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Figure 5. Summary of spectroscopic signatures for all of four cellular properties in low-frequency band, intermediate-frequency band, and high-frequency band.


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Figure 6. Simulation of a single-cell culture, i.e., single-cell spreading and adhesion. (A) An illustration of the biological process. (B) Normalized impedance spectra Zcell,i' from the time Tcell,1 to the time Tcell,21. The arrow leads the eye to show the shift of peak frequency in the frequency spectrum over the time. (C) Ratio of normalized impedance spectra ncell,ij(ω) from the time Tcell,1 to the time Tcell,21.


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Figure 7. (A) The impedance spectra of five randomly generated cell states, which present the change of overall impedance in time-course. (B) The spectroscopic ratio nij of two cell states – state 1 and 2, state 1 and 3, state 1 and 4, as well as state 1 and 5. (C) Extracted cell diameter with fitting accuracy δ of 0.10 or 0.05. (D) Extracted cell-electrode distance with fitting accuracy δ of 0.10 or 0.05. (E) Extracted cell membrane capacitance with fitting accuracy δ of 0.10 (left) and 0.05 (right), respectively. The error bars show the variation of extracted values.


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Table 1. Five randomly generated cell states. Cell state

Cell diameter [µm]

Membrane capacitance

Cell-electrode distance

Cytoplasm resistivity

[µF/cm2]

[nm]

[Ω-cm]

1

25

4

200

100

2

30

1

200

100

3

30

4

150

100

4

20

2

150

100

5

20

4

10

100


Feasibility of Tracking Multiple Single-Cell Properties with Impedance

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