# Uncertainty Quantification and Sensitivity Analysis for the Electrical Impedance Spectroscopy of Changes to Intercellular Junctions Induced by Cold Atmospheric Plasma

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## Abstract

**:**

_{0}and α were the most sensitive, while R

_{inf}and τ were the least sensitive. The temporal development of major Cole parameters indicates that CAP induced reversible changes in intercellular junctions, but not significant changes in membrane permeability. Sustained changes of τ suggested that long-lived ROS, such as H

_{2}O

_{2}, might play an important role. The proposed analysis confirms that an inherent advantage of EIS is the real time observation for CAP-induced changes on intercellular junctions, with a label-free and in situ method manner.

## 1. Introduction

## 2. Results and Discussion

#### 2.1. UQ and SA of the Cole-Cole Impedance Model

#### 2.1.1. Propagation of Model Input Uncertainties to Outcomes

#### 2.1.2. Parameter Sensitivity for the Real and Imaginary Part of Cole Impedance Outcomes

_{0}, R

_{inf}, α, τ) on the real and imaginary parts of the cell monolayer impedance. The goal was to quantify the sensitivity of each parameter to the model output. The frequency range is set from 1 Hz to 10 MHz. The y-axis quantifies the first-order Sobol index, which varies from 0 to 1 and represents the contribution percentage of the corresponding parameter to the model output. Figure 2a shows the parameter sensitivity for the real part of the impedance. In the low frequency region (f < 50 kHz), R

_{0}is the dominant factor with a value close to 1. As frequency increases, the impacts of α and R

_{inf}begin to increase while the effect of R

_{0}declines progressively. In comparison to the other characteristics, τ has a negligible effect throughout the entire frequency range. At frequencies beyond about 1 MHz, the influence of α on the model output exceeds that of R

_{0}by rising up to 0.45, while R

_{0}falls to 0.1 for10 MHz. At 10 MHz, the influence of R

_{inf}rises from 0 at 10 kHz to 0.5 at 10 MHz. Figure 2b demonstrates that the parameter sensitivity for the imaginary part of the impedance has significantly different frequency-dependent changes than the real part of the impedance. When the frequency is less than 1 kHz, α is the most important parameter. After 10 kHz, the Sobol index of α eventually falls below 0.5 and exhibits an oscillating pattern as the frequency increases. The impacts of R

_{inf}and τ are less than 0.1 across the whole frequency range (1 Hz–10 MHz).

_{inf}and R

_{0}play dominant roles at high and low frequencies of the real part, respectively. The boundary between low and high frequencies of the bioimpedance spectrum, which is typically ambiguous, can be determined via SA analysis. The Sobol index of R

_{inf}is 0.2 at 2 MHz, while that of R

_{0}is 0.19. As frequency increases, the influence of R

_{inf}increases and the influence of R

_{0}decreases. Hence 2 MHz can be identified as the boundary between low and high frequencies when a single Cole-Cole model is satisfied. Another sensitive parameter is α, denoting the dispersion width [27,28]. The dispersion width is related to the multiple time scales of dielectric relaxation processes in a system [18,27]. The SA demonstrates that the impedance around 1 MHz is relatively more sensitive to various polarization components. At different frequencies, the amplitude of the imaginary part is alternately governed by α and R

_{0}. The low frequency is primarily impacted by α, whilst the high frequency is primarily determined by R

_{0}. Since the imaginary part of the impedance is related to the capacitive properties of the system, i.e., dielectric relaxation, the influence of α will be amplified. Overall, SA can aid in determining the measurement range and simplify the fitting process.

_{inf}, which is a low-sensitivity parameter, can be fixed to accelerate the calculation and improve fitting accuracy.

#### 2.2. Temporal Development of the Cole Parameters Extracted from Cell Monolayer Impedance after CAP Treatment

_{inf}was fixed, as calculated from the control group, in following fitting procedures for all groups.

#### 2.2.1. Normalized Low Frequency Resistance (R_{0}) Related to Intercellular Junctions

_{0}, obtained by fitting the impedance spectra of WB-F344 and WB-ras cell monolayers to the Cole-Cole model, after CAP treatment from 1 min to 24 h, respectively. To facilitate comparison, R

_{0}values of both cells were normalized to that of the untreated control. As shown in Figure 4a, R

_{0}of the WB-F344 cell monolayer decreased observably 1 min after CAP treatment. One hour later, it fell to 65% of the untreated level. Four hours later, measurements revealed a considerable recovery in R

_{0}back up to 0.9, which remained almost constant after 24 h. Figure 4b depicts the temporal development of R

_{0}for the WB-ras cell monolayer, showing a similar profile of change to its normal counterpart. There was no notable decline in R

_{0}at 1 min, but it became higher than that for WB-F344 at 1 h and afterwards; e.g., R

_{0}at 24 h has reached 1.05.

_{0}[17]. Disruption of intercellular junctions, such as adhesion junctions and tight junctions, can significantly decrease R

_{0}. Conversely, cell swelling, caused by the imbalance in osmotic pressure between the interior and the exterior of cells after onset of electroporation, could significantly increases R

_{0}. In this investigation, there was no substantial increase in R

_{0}after CAP treatment, and the plasma jet did not come into direct contact with cell monolayers. Therefore, it is reasonable to rule out the existence of CAP-induced electroporation. The results of this work are in line with previous reports that the electric field in the plasma jet plume is insufficient to induce electroporation [30].

_{0}indicates that intercellular junctions of cell monolayers were changed after CAP treatment. Numerous earlier investigations have reached similar conclusions. Hoentsch et al. discovered that a kINPen plasma treatment for only 30 s significantly altered the adhesion capability of mouse epithelial cells (mHepR1), and led to the degradation of the tight junction protein ZO-1. These findings suggest that CAP can damage cell adhesion junctions and tight junctions [11]. Haertel et al. discovered that calmodulin E (E-cadherin) expression of keratinocytes (HaCat) was dramatically decreased and cell adhesion junctions were significantly disrupted following a 30-s kINPen treatment [12]. In addition, experimental and simulation evidence suggests that CAP can inhibit Cx43 (the primary gap junction protein)-related mRNA and protein expression and disrupt the structure of gap junctions [6,14]. For both cell monolayers, the value of R

_{0}was nearly fully restored after 4 h, indicating that damaged intercellular junctions were repaired. The effect of non-lethal CAP treatment on intercellular junctions is therefore reversible, consistent with a previous report. In that work, J. Choi et al. discovered that CAP led to the downregulation of E-calmodulin expression and prevention of intercellular junction formation, and that these alterations were completely reversed within 3 h [13]. Notably, the EIS method employed in this study offers a distinct benefit over existing research in that it permits quick, label-free, continuous in situ monitoring of CAP-induced changes in cell monolayers.

#### 2.2.2. Normalized Dispersion Width (α) Related to Extracellular Space

_{0}values. In a prior work, the outcomes of 100-ns pulsed electric field treatment of WB-F344 and WB-ras cells were compared using the Cole-Cole model. WB-ras cells demonstrated a smaller α change than WB-F344 cells [31], which partially supports the hypothesis above from another perspective.

#### 2.2.3. Normalized Characteristic Time Constant (τ) Related to Membrane Capacitance

_{0}versus α. In our previous study, it was observed that the change in τ of WB-F344 cell monolayers was larger than that of WB-ras cell monolayers after exposure to 100-ns pulsed electric fields [31]. Nevertheless, the differences in stimulation and interaction mechanisms necessitate more research into the potential effects of CAP on cell monolayers.

#### 2.2.4. Potential Mechanisms of CAP Generated RONS Affecting Intercellular Junctions

_{2}O

_{2}among the typical long-lived species in the culture medium, which could have significant effects on treated cells [35,36,37]. In addition, plasma-generated hydroxyl (OH) radicals can induce lipid peroxidation and disrupt cell membranes, which cannot be ignored. Furthermore, it has been demonstrated that the kINPen generated long-lived reactive nitrogen species (RNS) at lower concentrations compared to hydrogen peroxide (H

_{2}O

_{2}) and had insignificant effects on cells [38,39]. Therefore, the possible effects of H

_{2}O

_{2}and OH are worth further exploration.

_{2}O

_{2}on intercellular junctions. According to a study by Haidari et al., H

_{2}O

_{2}can preferentially disrupt E-calcium mucin and damage adherens junctions [40]. Inumaru and colleagues treated ARPE-19 cells with H

_{2}O

_{2}and, discovered diminished expression of N-cadherin and dissociation of intercellular adhesion [41]. In addition, H

_{2}O

_{2}can inhibit the production of Cx43, the primary gap junction protein, so disrupts the Gap junction [42]. Moreover, OH radicals can chemically react with the N terminus of the gap junction, destroying its structure [14]. On the other hand, CAP-generated ROS, such as H

_{2}O

_{2}and OH radicals, can also damage the phospholipid bilayer structure of cell membrane, resulting in lipid peroxidation [43,44], decrease in membrane potential [45], and fragmentation of the membrane structure [46]. In summary, CAP treatment can undoubtedly change intercellular junctions. The lingering effects of long-lived ROS on membranes might explain why τ for WB-F344 cell monolayers remained unrecovered 24 h after CAP-treatment. However, the experimental results of this study were not sufficient to prove the hypothesis and further studies are needed.

## 3. Materials and Methods

#### 3.1. Cell Culture

#### 3.2. CAP Treatments

#### 3.3. Impedimetric Analysis

_{inf}, R

_{0}, α, and τ). The first term in brackets represents electrode polarization; the term in the second bracket describes the contribution of the cell monolayer. R

_{inf}and R

_{0}represent the resistance at infinite frequency and at very low frequency, respectively. (iωτ)

^{α}is known as a constant phase element (CPE) to describe non-ideal capacitance, Z

_{cpe}, with α a dimensionless dispersion factor (0 < α < 1) and τ the characteristic time constant.

#### 3.4. Uncertainty Quantification and Sensitivity Analysis

## 4. Conclusions

_{0}and α were the most sensitive parameters, while R

_{inf}and τ were the least sensitive. The temporal development of Cole parameters suggests that CAP induced reversible changes in intercellular junctions but did not cause significant changes in membrane permeability. Long-term alterations in the cell monolayer after CAP-treatment suggest that long-lived ROS, such as H

_{2}O

_{2}, might play a nonnegligible role. The results of this study may provide some insight into a better understanding of how CAP interacts with intercellular junctions. The UQ and SA proposed for the analysis of Cole parameters could also guide the evaluation of other methods of exposure. Given the broad utility of the Cole model, continuation of this research on biological tissues will be a topic of our interest.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Sample Availability

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**Figure 1.**UQ quantifies the mean, standard deviation, and 90 percent prediction space of real (

**a**), imaginary (

**b**), magnitude (

**c**), and phase (

**d**) of the Cole impedance taking input uncertainties into account. The solid dark blue line depicts the mean value with frequencies ranging from 1 Hz to 10 MHz. The dark red line and light blue area represent the standard deviation and 90% prediction space, respectively.

**Figure 2.**The parameter sensitivity distributions for the real (

**a**) and imaginary (

**b**) parts of the Cole impedance. The low frequency for the real part is determined by R

_{0}, while α amplifies the influence in the high frequency range. On the contrary, α mainly determines the low frequency for the imaginary part, and R

_{0}primarily determines the high frequency.

**Figure 3.**The first order and total Sobol indices of Cole parameters for the real part (

**a**) and imaginary part (

**b**) of the Cole impedance. Larger total Sobol indices than first order Sobol indices indicate interactions among the Cole parameters.

**Figure 4.**Low-frequency resistance R

_{0}as a function of time after CAP treatment of two cell monolayers, WB-F344 (

**a**) and WB-ras (

**b**).

**Figure 5.**Dispersion width α as a function of time after CAP treatment of two cell monolayers, WB-F344 (

**a**) and WB-ras (

**b**).

**Figure 6.**Trends in Cole parameters, characteristic time constant τ, over time following CAP treatment for two cell monolayers, WB-F344 (

**a**) and WB-ras (

**b**).

Parameters | Mean Values | Sigma ^{1} |
---|---|---|

R_{inf} | 200 Ω | 60 Ω |

R_{0} | 1000 Ω | 300 Ω |

α | 0.7 | 0.21 |

τ | 5 × 10^{−6} s | 1.5 × 10^{−6} s |

^{1}Sigma represents the standard deviation for the Gaussian function.

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## Share and Cite

**MDPI and ACS Style**

Zhuang, J.; Zhu, C.; Han, R.; Steuer, A.; Kolb, J.F.; Shi, F.
Uncertainty Quantification and Sensitivity Analysis for the Electrical Impedance Spectroscopy of Changes to Intercellular Junctions Induced by Cold Atmospheric Plasma. *Molecules* **2022**, *27*, 5861.
https://doi.org/10.3390/molecules27185861

**AMA Style**

Zhuang J, Zhu C, Han R, Steuer A, Kolb JF, Shi F.
Uncertainty Quantification and Sensitivity Analysis for the Electrical Impedance Spectroscopy of Changes to Intercellular Junctions Induced by Cold Atmospheric Plasma. *Molecules*. 2022; 27(18):5861.
https://doi.org/10.3390/molecules27185861

**Chicago/Turabian Style**

Zhuang, Jie, Cheng Zhu, Rui Han, Anna Steuer, Juergen F. Kolb, and Fukun Shi.
2022. "Uncertainty Quantification and Sensitivity Analysis for the Electrical Impedance Spectroscopy of Changes to Intercellular Junctions Induced by Cold Atmospheric Plasma" *Molecules* 27, no. 18: 5861.
https://doi.org/10.3390/molecules27185861