# Modelling and Differential Quantification of Electric Cell-Substrate Impedance Sensing Growth Curves

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Cell Culture, Information and Growing Conditions of the Used Cell Lines

_{2}, 37 °C and 95% air humidity, and all sterile work was performed using a lamiar flow bench (ENVAIR eco, Emmendingen). The cells were cultured with DMEM/F12 (Gibco, Thermo Fisher Scientific, without HEPES, with glutamine, phenol red, Schwerte), 5% FCS (Sigma, Hamburg), 100 U/mL penicillin/streptomycin (Sigma, Hamburg, Germany), tested negative in PCR and DAPI staining for Mycoplasma spp. (PCR: AppliChem, PanReac, PCR Mycoplasma Test Kit, Darmstadt; DAPI: Pierce DAPI, Thermo Fisher Scientific, Karlsruhe, Germany) and only used in one of the passages 1–4 after thawing.

#### 2.2. Impedance Measurement and General Experimental Settings

_{2}and 95% humidity and the ECIS system was started. In all the experiments except for the cell dilution experiments, on each 8-well plate, two wells were used purely as the medium control group (mCG) without cells, and two wells were used as the cell control group (control group, CG), where only cells with the medium but without treatment were added. For the dilution experiments, no mCG were performed.

#### 2.3. IPEC-J2 Dilution Experiments and Cell Counting on ECIS Dishes

#### 2.4. IPEC-J2 Ethanol Treatment

#### 2.5. ECIS Data Analysis with the Developed ECIS R Scripts

#### 2.6. Growth Curve Models, Area under the Curve (AUC) and Further Statistics

_{i}at each timepoint t

_{i}. It is feasible to use the AUC in situations where reduction in growth behavior over time is suspected but cannot be interpreted by specific timepoints like the maximum of the first derivative. The AUC can be evaluated with the intECIS function based on the sintegral function of the Bolstad2 package [44]. It takes a vector of x and a corresponding set of positive y = f(x) values and evaluates the AUC according to Simpson’s rule [50]:

_{1}) to f(x

_{n−1}) values.

## 3. Results

#### 3.1. Curve Fitting and Further Statistics

#### 3.2. IPEC-J2 Dilution Experiments and Cell Counting on ECIS Dishes

#### 3.3. Ethanol Treatment of IPEC-J2 Cells

## 4. Discussion

_{50}is to be determined on the basis of the AUC [53].

## 5. Conclusions

## Supplementary Materials

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Compilation of nine ECIS curves with different features and trajectories. The curves were obtained from seven experiments involving IPEC-J2 (

**A**), CACO2 (

**B**,

**C**), C2BBe1 (

**D**,

**E**), HUVEC (

**F**,

**G**), MDCK cell lines (

**H**) and an unknown cell line (

**I**) under different treatment regimes. Note that the curves vary substantially with respect to baseline length (

**A**,

**B**,

**E**), curve smoothness (

**A**,

**E**,

**F**), slope (

**C**,

**E**,

**F**) and plateau length and linearity (

**D**,

**E**,

**G**–

**I**). hrs = hours, Imp = impedance.

**Figure 2.**Essential curve features extracted from the fitting procedure for the smoothing cubic spline fit (

**A**), logistic regression (

**B**) and segmented regression (

**C**). Shown are those parameters that pertain to abscissa values (time) at certain curve locations (FDM, SDM, 0.1/0.2/0.5× range, segmentation knots), where the complete fit parameter output for the three methods is depicted in (

**D**). hrs = hours, Imp = impedance.

**Figure 3.**Nonlinear correlation between the seeded cell counts and the time estimated from the 0.1 quantile value of a spline (

**A**,

**D**), four-parameter logistic (

**B**,

**E**) and the 0.2 quantile value of segmented regression (

**C**,

**F**) of time vs. impedance (compare Figure 2 and Supplemental Data 2) for a 6 h (upper panel) and a plateau phase (lower panel) experiment, see insets. An exponential decay model y = (y

_{0}− y

_{b}) × exp(−kx) + y

_{b}was fitted to the data and displayed as fitted values (bold line), 95% confidence interval (thin line) and 95% prediction interval (dashed line). For both datasets, the area under the curve (AUC) was calculated for the complete time scale ((

**G**); 0–46.9 h) and for a subset ((

**H**); 0–20 h) and fitted with exponential growth model y = y

_{max}/(1 + exp(a + bx)). The corresponding fitted parameters and goodness-of-fit measures for both models are given in Table 2.

**Figure 4.**ECIS growth curve in relation to the IPEC-J2 density on the gold electrodes. The growth curve (

**A**) was microscopically investigated at three different timepoints, 2.5 h (

**B**), 6 h (

**C**) and 22 h (

**D**), with regard to cell density and interaction. Note that although (

**C**,

**D**) are in the plateau phase, the micrographs indicate significantly different cell density without impacting the impedance. hrs = hours, Imp = impedance.

**Figure 5.**Reference points for the ethanol treatment experiment on IPEC-J2 cells. The cells were untreated (control) or treated with 1% or 5% ethanol (EtOH) (typical data shown in (

**A**)) in an experimental setup of five independent experiments of four replicates each. Using the three location indices “Time at 10% spline” (x01.spline; (

**B**)), “Time at 10% logistic fit” (x01.log; (

**C**)) and “Time at 20% segmented regression” (p02.seg; (

**D**)) on (0, 1)-normalized data (inset), a clear right shift of the impedance curve at 5% ethanol is evident. (

**E**) The area under the curve (AUC) estimates of the complete time scale for all 20 replicates. A Welch (unequal variance) t-test, Bonferroni-corrected for multiple testing, was used to obtain p-values for the two group comparisons, control/1% EtOH and control/5% EtOH.

**Table 1.**Analysis functions implemented as R scripts for the manipulation and quantitation of ECIS curves.

Function Name | Brief Description |
---|---|

getECIS | Import of raw ECIS .xlsx files into the R data frame |

plotECIS | Plotting of ECIS datasets in a variety of ways |

cutECIS | Cutting of time ranges from ECIS datasets |

delECIS | Deletion of specific wells from ECIS datasets |

selECIS | Selection of ECIS wells to form a new dataset |

addECIS | Combination of two or more different ECIS datasets |

baseECIS | Subtraction of the baseline value of each specific well |

normECIS | Normalization of ECIS datasets to (0, 1) |

intECIS | Numerical integration of the area under the curve [44] |

fitECIS | Calculation of different curve models and features from ECIS datasets as described in Section 2.6 |

parECIS | Getting all the parameters acquired by fitECIS |

extECIS | Removal and extension of the leading region of ECIS data |

anoECIS | Identification and deletion of outliers of an ECIS dataset |

setECIS | Setting of a start point of an experiment to zero |

**Table 2.**Parameters and goodness-of-fit measures derived from fitting the exponential decay model (spl, log, seg) and the growth model (AUC) to the data in Figure 3.

Cut, 6 h | Cut, Plateau | |||||||
---|---|---|---|---|---|---|---|---|

Spl | Log | Seg | AUC | Spl | Log | Seg | AUC | |

Y_{0} | 42.86 | 43.71 | 42.87 | 21.26 | 18.38 | 19.28 | ||

Y_{b} | 39.65 | 40.93 | 40.98 | 14.64 | 15.8 | 16.15 | ||

k | 0.000063 | 0.000035 | 0.000031 | 0.000083 | 0.000033 | 0.000052 | ||

Y_{max} | 3.89 | 2.04 | ||||||

a | 0.471 | 2.56 | ||||||

b | 0.00008 | 0.00014 | ||||||

RMSE | 0.089 | 0.11 | 0.075 | 0.1 | 0.096 | 0.097 | 0.099 | 0.056 |

RV | 0.0097 | 0.015 | 0.0068 | 0.013 | 0.011 | 0.012 | 0.012 | 0.0037 |

R^{2} | 0.967 | 0.964 | 0.966 | 0.96 | 0.984 | 0.969 | 0.967 | 0.99 |

AIC | −24.11 | −17.26 | −29.71 | −20.07 | −21.5 | −21.33 | −20.74 | −39.18 |

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**MDPI and ACS Style**

Binder, A.R.D.; Spiess, A.-N.; Pfaffl, M.W.
Modelling and Differential Quantification of Electric Cell-Substrate Impedance Sensing Growth Curves. *Sensors* **2021**, *21*, 5286.
https://doi.org/10.3390/s21165286

**AMA Style**

Binder ARD, Spiess A-N, Pfaffl MW.
Modelling and Differential Quantification of Electric Cell-Substrate Impedance Sensing Growth Curves. *Sensors*. 2021; 21(16):5286.
https://doi.org/10.3390/s21165286

**Chicago/Turabian Style**

Binder, Anna Ronja Dorothea, Andrej-Nikolai Spiess, and Michael W. Pfaffl.
2021. "Modelling and Differential Quantification of Electric Cell-Substrate Impedance Sensing Growth Curves" *Sensors* 21, no. 16: 5286.
https://doi.org/10.3390/s21165286