# Viscoelastic Properties of Zona Pellucida of Oocytes Characterized by Transient Electrical Impedance Spectroscopy

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## Abstract

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## 1. Introduction

_{S}, resistance R of the zona pellucida at the rim of the micro hole, the capacitance of zona pellucida C and the microhole, and electrode crosstalk capacitance C

_{E}, which occurs in the high frequency range. Fitting was conducted at 30 kHz, the frequency of the highest sensitivity [24]. Aside from the impedance magnitude Z, the resistance R was evaluated. R is the only circuit element that depended on pressure. Changes in pressure at the rim of the microhole squeezed the Z,P which led to an increase in resistance.

_{ZP}is the Poisson ratio of the ZP (υ

_{ZP}= 0.04 [19]); ∆p is the suction pressure; L the corresponding length of the aspirated ZP; r

_{i}is the inner micropipette radius. C is a function of the dimensionless ZP shell thickness h* = h/r

_{i}[26] and can be found as Equation (S1) in the Supplementary Materials.

_{c}assumed to be fixed at the rim of the microhole and thinned due to stretching into the microhole. The thinning at the rim, and therefore the resistance increase, is represented by the circuit element R in the EEC. Depending on the radius r

_{i}of the microhole, the aspiration length L can be correlated with the resistance change ∆R in Equation (2) [24]:

_{0}is the resistance of the open micro hole without oocyte; R

_{2,0}is the resistance of the sealed microhole with trapped oocyte at minimum fixation pressure; R

_{2}is the resistance after recovery of the ZP to equilibrium; r

_{i}and r

_{c}are the radii of the microhole and the oocyte, respectively. By substitution of Equation (2) into Equation (1), the Young’s modulus of the ZP can be calculated [24].

## 2. Materials and Methods

#### 2.1. Materials

#### 2.2. Microfluidic Chip Fabrication

^{®}dry film resist layers were laminated, patterned by standard UV lithography, and in the case of forming the 35–36 µm in diameter microholes, structured by a dry etching process in an inductively coupled plasma reactive ion etching tool (SI 500, SENTECH Instrument GmbH, Berlin, Germany) by applying 60 sccm O

_{2}, 3 sccm SF

_{6}, 0.5 Pa, 100 W power, and −150 V DC-bias voltage. The sidewalls of the exposed microholes showed an inclination angle of 86°. The intermediate electrodes, wires, and connection pads were fabricated by the deposition of thin-film seed layers (titanium and gold), standard UV lithography, and gold electroplating. Each electrode was connected by two wires to enable four-point EIS measurements. On top of the chip, a replica-molded poly(dimethylsiloxane) (PDMS) interposer was bonded to the chip by applying oxygen plasma in combination with the deposition of APTES.

#### 2.3. MAEIS Setup Assembly

#### 2.4. Oocyte Preparation and Handling

_{0}of the open microhole, was used for the calculations. For the measurements, an oocyte with the diameter of around 100 µm was positioned near the microhole with a micropipette. After applying suction pressure to the microchannel, the oocyte was trapped hydrodynamically at the microhole. The trapped cell provided a tight seal of the microhole and stayed in the trapped position when a minimum suction pressure of 1 hPa was applied. In the following, the minimum fixation pressure is defined as 0 hPa as a reference with regard to the applied suction pressure. EIS measurements were carried out while the suction pressure was subsequently increased from 1 reference pressure to 7 hPa in 1 hPa incremental steps.

## 3. Results

_{0}was determined in regard to time. In Figure 3, the corresponding data points for the first, fourth, and seventh pressure steps are shown, whereas in Figure S1 in the Supplementary Materials, the plots for the remaining four steps are depicted. Data points were plotted for a time interval of 100 s after each pressure step.

_{1}is related to the elasticity of the ZP and therefore to the Young’s modulus E, k

_{0}to the initial jump of the impedance signal and η

_{0}to the local friction coefficient, respectively. Typical high values of k

_{0}and low values of η

_{0}(Table S1) represent the rapid response of ZP’s aspiration to the applied suction pressure in our experiments. The dashpot η

_{1}in series with the parallel circuit accounts for the viscous dissipation of the aspirating ZP. The correlation of the circuit elements to the creep curve is illustrated in Figure S2 in the Supplementary Materials. Based on this model, a creep curve can analytically be described by Equation (3) [32]

_{0}values over the whole time period of the pressure step. Then, the L values were fitted with the proposed GM model according to Equation (3). The calculations were carried out using Wolfram Mathematica software. For the fittings, the pressure Δp, radius of microhole r

_{i}, and aspiration length L were set as constants for all fittings. The Young’s modulus E, viscosity η

_{1}, initial jump of the impedance signal k

_{0}, and the local friction coefficient η

_{0}were free parameters obtained from the fitting. Table S1 in the Supplementary Materials summarizes the fitting parameters for the creep curves of each pressure step of oocytes WT1 and DKO3. After extracting parameters E and η

_{1}from the seven creep curves, their mean values were set as constants. A crosscheck was carried out for all curves to find the minimum deviation. Table S2 in the Supplementary Materials contains the mean values of the fitting parameters for all characterized oocytes. Exemplary fitting curves are depicted as colored lines in Figure 3 and Figure S1 in the Supplementary Materials for the WT1 and DKO3 oocytes. In general, all fitted curves corresponded well to the measured data.

_{1}corresponds to viscosity. Following the model of Guevorkian et al. [32], viscosities were determined to be $6\times {10}^{5}\pm 0.8\times {10}^{5}$ Pa∙s for the WT and $3.5\times {10}^{4}\pm 0.45\times {10}^{4}$ Pa∙s for DKO ZPs, respectively.

## 4. Discussion

_{i}, the groups working with the standard micropipette aspiration technique published ratios 0.2 < L/r

_{i}< 1.6. In our measurements, the factor was calculated to be much lower at 0.045 < L/r

_{i}< 0.14. It is most likely that we only aspirated a very small amount at the surface of the hydrogel-like ZP, so we did not measure the bulk properties. Thus, the Young’s modulus obtained with our MAEIS setup was estimated to be lower than the value that would be obtained for a larger amount of ZP sucked into the hole. We therefore developed a surface-sensitive system. Nevertheless, relative values of the Young’s moduli bear more meaningful information than absolute values when the ZP’s modification is measured over time to find the window of highest fertility.

_{1}for mouse zygotes and not for the viscosity [30].

## 5. Conclusions

## Supplementary Materials

_{0}= (R − R

_{0})⁄R

_{0}at 30 kHz in regard to time for selected pressure steps for oocyte WT1 (

**a**) and oocyte DKO3 (

**b**).; Figure S2. Schematic of the overlap of an ideal normalized resistance change ∆R⁄R

_{0}(black thick dashed line) and an ideal creep curve (red) and for a constantly applied suction pressure step.; Table S1. Fitting parameters to Figure 3 and Figure S1 according to the Equation (3) in the main text.; Table S2. Summarized fitting data for the four wild type (WT) and four fetuin-B ovastacin double deficient (DKO) MII oocytes.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**Microfluidic aspiration-assisted electrical impedance spectroscopy system for the characterization of single oocytes. (

**a**) Schematic drawing of the setup. PS represents the pressure sensor. (

**b**) Schematic cross-section of the electrode arrangement at the microhole combined with the equivalent electrical circuit model. CPE: constant phase element, R

_{S}: medium resistance, R: resistance of zona pellucida at the rim of the aperture, C: capacitance of zona pellucida and aperture, C

_{E}: electrode crosstalk capacitance. Drawings in (

**a**) and (

**b**) are not to scale. (

**c**) Photograph of the microfluidic chip. On the left side is the area with 36 contact pads for the wiring of 18 electrodes at nine microholes, in the middle part is the PDMS interposer with the chamber, and on the right side, the area for the tubing connection is shown.

**Figure 2.**Impedance magnitude with regard to time of one measurement with seven suction pressure steps of 1 hPa for oocyte WT1 (

**a**) and DKO3 (

**b**). Impedance measurements were carried out at a frequency of 30 kHz. Z

_{0}shows the blank impedance magnitude value of the open microhole without the trapped oocyte.

**Figure 3.**Calculated normalized resistance change ∆R⁄R

_{0}= (R −R

_{0})⁄R

_{0}at 30 kHz with regard to time for the selected pressure steps for oocyte WT1 (

**a**) and oocyte DKO3 (

**b**). R represents the resistance of the ZP at the rim of the microhole and R

_{0}is the resistance of the open (not sealed with an oocyte) microhole, respectively. R

_{0}was determined to be 27.9 Ω and 26.1 Ω for the WT1 and DKO oocytes, respectively. The curves present the aspiration length L, which was calculated by fitting the proposed GM model to the data points.

**Table 1.**Calculated mean values of the Young’s moduli of ZP of mouse oocytes in the metaphase II (MII) stage. The errors represent standard deviations.

Cell Type (Maturation Stage) | Technique | Young’s Modulus (kPa) | Reference |
---|---|---|---|

Oocyte (wild type, WT) | Micropipette aspiration | 10.9 ± 1.4 | [20] |

Oocyte (wild type, WT) | Micropipette aspiration | 11.8 | [19] |

Oocyte (wild type, WT) | Micropipette aspiration | 14.3 ± 2.1 | [22] |

Oocyte (wild type, WT) | Micropipette aspiration | 8.2 ± 1.2 | [21] |

Oocyte (wild type, WT) | MAEIS | 3.58 ± 0.63 | [24] |

Oocyte (wild type, WT) | MAEIS (creep) | 3.3 ± 0.5 | Current study |

Oocyte (Fetuin-B/ovastacin dd, DKO) | MAEIS | 1.19 ± 0.30 | [24] |

Oocyte (Fetuin-B/ovastacin dd, DKO) | MAEIS (creep) | 1.1 ± 0.2 | Current study |

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**MDPI and ACS Style**

Azarkh, D.; Cao, Y.; Floehr, J.; Schnakenberg, U.
Viscoelastic Properties of Zona Pellucida of Oocytes Characterized by Transient Electrical Impedance Spectroscopy. *Biosensors* **2023**, *13*, 442.
https://doi.org/10.3390/bios13040442

**AMA Style**

Azarkh D, Cao Y, Floehr J, Schnakenberg U.
Viscoelastic Properties of Zona Pellucida of Oocytes Characterized by Transient Electrical Impedance Spectroscopy. *Biosensors*. 2023; 13(4):442.
https://doi.org/10.3390/bios13040442

**Chicago/Turabian Style**

Azarkh, Danyil, Yuan Cao, Julia Floehr, and Uwe Schnakenberg.
2023. "Viscoelastic Properties of Zona Pellucida of Oocytes Characterized by Transient Electrical Impedance Spectroscopy" *Biosensors* 13, no. 4: 442.
https://doi.org/10.3390/bios13040442