# Water Pores in Planar Lipid Bilayers at Fast and Slow Rise of Transmembrane Voltage

^{1}

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Chemicals

#### 2.2. Experimental Setups

#### 2.3. Measurement Protocols

#### 2.4. Experimental Data Analysis

#### 2.5. The Rate of the Planar Lipid Bilayer Capacitance Change at ${t}_{br}$

#### 2.6. Calculation of a Fraction of the Planar Lipid Bilayer That Is Occupied By Pores

## 3. Results

#### 3.1. Experimental Results

#### 3.2. Modeling Results

## 4. Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Abbreviations

POPC | 1-pamitoyl 2-oleoyl phosphatidylcholine |

POPS | 1-pamitoyl 2-oleoyl phosphatidylserine |

MD | Molecular dynamics simulation |

GUV | Giant unilamellar vesicles |

## References

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**Figure 1.**The measurement protocol consisted of formation of the planar lipid bilayer (

**A**), capacitance measurement (

**B**or

**C**), and measurement of the breakdown voltage ${U}_{br}$ of the planar lipid bilayer (

**D**or

**E**).

**Figure 2.**Breakdown voltages of specific lipid compositions measured during voltage-controlled (

**left**side) and current-controlled (

**right**side) experiments. The gray lines show different slopes (${k}_{u}$—

**left**side, ${k}_{i}$—

**right**side) of linearly rising signal. Colored curves (

**left**side) represent two-parameter strength-duration curves (Equation (2)) fitted to the data obtained by voltage-controlled measurements on POPS, POPC, and POPC:POPS mixture, respectively. Colored lines (

**right**side) represent the average values of measured ${U}_{brI}$ for POPC, POPS, and POPC:POPS mixture, respectively.

**Figure 3.**

**Left**side of the figure presents the rate of the planar lipid bilayer capacitance change at ${t}_{br}$ as a function of breakdown voltage ${U}_{br}$. Results regarding fast rise of transmembrane voltage are enlarged on the

**right**side. Slope m of the linear relation between $ln\left(\frac{dC}{dt}\right)$ and ${U}_{br}$ is related to pore radius. See text for details.(A) The rate of the planar lipid bilayer capacitance change at ${t}_{br}$ as a function of breakdown voltage ${U}_{br}$. Results regarding fast rise of transmembrane voltage are enlarged in (B). Slope m of the linear relation between $ln\left(\frac{dC}{dt}\right)$ and ${U}_{br}$ is related to pore radius. See text for details.

**Figure 4.**The fraction of the planar lipid bilayer area that is occupied by water pores as a function of ${U}_{br}$.

**Table 1.**Specific capacitance of planar lipid bilayers (${c}_{BLM}$) measured by discharge and capacitance to a period converting method. The values are given as mean ± standard deviation (number of measurements).

Lipid Mixtures | Discharge Method [25] ${\mathit{c}}_{\mathbf{BLM}}$ [F/cm ${}^{2}$] | Capacitance to Period Converting Method [26] ${\mathit{c}}_{\mathbf{BLM}}$ [F/cm ${}^{2}$] |
---|---|---|

POPC | 0.51 ± 0.17 (80) | 0.51 ± 0.16 (58) * |

POPS | 0.41 ± 0.14 (76) | 0.41 ± 0.13 (34) * |

POPC:POPS 1:1 | 0.31 ± 0.07 (60) | 0.34 ± 0.17 (25) * |

**Table 2.**Results for planar lipid bilayers composed of POPC. In the upper part of the table, the results of voltage-controlled measurements with seven different slopes ${k}_{u}$ are gathered while the results of current-controlled measurements with five different slopes ${k}_{i}$ are presented in the lower part of the table. For each slope of linearly rising signal, the planar lipid breakdown voltage ${U}_{br}$ and lifetime ${t}_{br}$ are presented. Values are given as means ± standard deviations. $\frac{{A}_{wat}}{A}$ is a calculated fraction of the planar lipid bilayer that is occupied by pores. N is the number of experiments in each experimental group.

POPC | |||||
---|---|---|---|---|---|

${\mathbf{k}}_{\mathbf{u}}$(kV/s) | $\mathbf{N}$ | ${\mathbf{U}}_{\mathbf{br}}$(V) | ${\mathbf{t}}_{\mathbf{br}}$(s) | $\frac{{\mathbf{A}}_{\mathbf{wat}}}{\mathbf{A}}$(%) | |

voltage-cont. | 48.1 | 16 | 0.76 ± 0.05 | 16.76 ± 1.14 | 1.72 |

21.6 | 17 | 0.67 ± 0.05 | 30.50 ± 2.60 | 0.95 | |

16.7 | 12 | 0.65 ± 0.06 | 39.38 ± 3.87 | 0.73 | |

11.5 | 12 | 0.59 ± 0.05 | 52.25 ± 4.65 | 0.55 | |

7.8 | 16 | 0.54 ± 0.04 | 70.74 ± 5.07 | 0.41 | |

5.5 | 16 | 0.54 ± 0.05 | 99.24 ± 9.93 | 0.29 | |

4.8 | 17 | 0.54 ± 0.04 | 112.92 ± 8.32 | 0.27 | |

${\mathbf{k}}_{\mathbf{i}}$(A/s) | $\mathbf{N}$ | ${\mathbf{U}}_{\mathbf{br}}$(V) | ${\mathbf{t}}_{\mathbf{br}}$(s) | $\frac{{\mathbf{A}}_{\mathbf{wat}}}{\mathbf{A}}$(%) | |

current-cont. | 10 | 8 | 0.25 ± 0.14 | 0.64 ± 0.55 | 45.20 $\times {10}^{-6}$ |

8 | 9 | 0.12 ± 0.16 | 1.22 ± 1.16 | 23.63 $\times {10}^{-6}$ | |

4 | 7 | 0.32 ± 0.16 | 1.63 ± 1.35 | 17.76 $\times {10}^{-6}$ | |

1 | 11 | 0.11 ± 0.11 | 3.30 ± 0.98 | 8.74 $\times {10}^{-6}$ | |

0.5 | 16 | 0.26 ± 0.13 | 5.97 ± 2.09 | 4.83 $\times {10}^{-6}$ |

**Table 3.**Results for planar lipid bilayers composed of POPS. In the upper part of the table, the results of voltage-controlled measurements with seven different slopes ${k}_{u}$ are gathered while the results of current-controlled measurements with five different slopes ${k}_{i}$ are presented in the lower part of the table. For each slope of linearly rising signal the planar lipid breakdown voltage ${U}_{br}$ and lifetime ${t}_{br}$ are presented. Values are given as means ± standard deviations. $\frac{{A}_{wat}}{A}$ is a calculated fraction of the planar lipid bilayer that is occupied by pores. N is the number of experiments in each experimental group.

POPS | |||||
---|---|---|---|---|---|

${\mathbf{k}}_{\mathbf{u}}$(kV/s) | $\mathbf{N}$ | ${\mathbf{U}}_{\mathbf{br}}$(V) | ${\mathbf{t}}_{\mathbf{br}}$(s) | $\frac{{\mathbf{A}}_{\mathbf{wat}}}{\mathbf{A}}$(%) | |

voltage-cont. | 48.1 | 18 | 0.80 ± 0.04 | 17.59 ± 0.86 | 0.65 |

21.6 | 14 | 0.72 ± 0.06 | 33.15 ± 2.76 | 0.35 | |

16.7 | 13 | 0.67 ± 0.05 | 41.24 ± 3.34 | 0.28 | |

11.5 | 12 | 0.66 ± 0.09 | 58.66 ± 7.71 | 0.20 | |

7.8 | 15 | 0.62 ± 0.08 | 81.05 ± 10.92 | 0.14 | |

5.5 | 13 | 0.59 ± 0.05 | 108.78 ± 8.72 | 0.11 | |

4.8 | 15 | 0.61 ± 0.04 | 129.24 ± 7.86 | 0.09 | |

${\mathbf{k}}_{\mathbf{i}}$(A/s) | $\mathbf{N}$ | ${\mathbf{U}}_{\mathbf{br}}$(V) | ${\mathbf{t}}_{\mathbf{br}}$(s) | $\frac{{\mathbf{A}}_{\mathbf{wat}}}{\mathbf{A}}$(%) | |

current-cont. | 10 | 5 | 0.33 ± 0.04 | 0.61 ± 0.26 | 18.91 $\times {10}^{-6}$ |

8 | 5 | 0.37 ± 0.04 | 0.98 ± 0.08 | 11.72 $\times {10}^{-6}$ | |

4 | 6 | 0.45 ± 0.14 | 2.37 ± 0.71 | 4.84 $\times {10}^{-6}$ | |

1 | 5 | 0.33 ± 0.04 | 6.99 ± 0.91 | 1.64 $\times {10}^{-6}$ | |

0.5 | 6 | 0.43 ± 0.14 | 17.98 ± 5.85 | 0.64 $\times {10}^{-6}$ |

**Table 4.**Results for planar lipid bilayers composed of POPC:POPS. In the upper part of the table, the results of voltage-controlled measurements with seven different slopes ${k}_{u}$ are gathered while the results of current-controlled measurements with five different slopes ${k}_{i}$ are presented in the lower part of the table. For each slope of linearly rising signal, the planar lipid breakdown voltage ${U}_{br}$ and lifetime ${t}_{br}$ are presented. Values are given as means ± standard deviations. $\frac{{A}_{wat}}{A}$ is a calculated fraction of the planar lipid bilayer that is occupied by pores. N is the number of experiments in each experimental group.

POPC:POPS 1:1 | |||||
---|---|---|---|---|---|

${\mathbf{k}}_{\mathbf{u}}$(kV/s) | $\mathbf{N}$ | ${\mathbf{U}}_{\mathbf{br}}$(V) | ${\mathbf{t}}_{\mathbf{br}}$(s) | $\frac{{\mathbf{A}}_{\mathbf{wat}}}{\mathbf{A}}$(%) | |

voltage-cont. | 48.1 | 7 | 0.72 ± 0.03 | 15.73 ± 0.73 | 1.49 |

21.6 | 7 | 0.63 ± 0.05 | 28.90 ± 2.30 | 0.81 | |

16.7 | 6 | 0.59 ± 0.06 | 35.73 ± 3.70 | 0.66 | |

11.5 | 7 | 0.55 ± 0.04 | 48.49 ± 3.55 | 0.48 | |

7.8 | 11 | 0.53 ± 0.04 | 96.66 ± 4.60 | 0.24 | |

5.5 | 9 | 0.53 ± 0.05 | 96.68 ± 9.12 | 0.24 | |

4.8 | 13 | 0.48 ± 0.03 | 101.24 ± 7.39 | 0.23 | |

${\mathbf{k}}_{\mathbf{i}}$(A/s) | $\mathbf{N}$ | ${\mathbf{U}}_{\mathbf{br}}$(V) | ${\mathbf{t}}_{\mathbf{br}}$(s) | $\frac{{\mathbf{A}}_{\mathbf{wat}}}{\mathbf{A}}$(%) | |

current-cont. | 10 | 3 | 0.27 ± 0.08 | 0.61 ± 0.19 | 15.92 $\times {10}^{-6}$ |

8 | 5 | 0.52 ± 0.23 | 1.47 ± 0.51 | 38.47 $\times {10}^{-6}$ | |

4 | 5 | 0.63 ± 0.17 | 3.56 ± 0.94 | 6.59 $\times {10}^{-6}$ | |

1 | 6 | 0.43 ± 0.16 | 9.90 ± 3.70 | 2.37 $\times {10}^{-6}$ | |

0.5 | 5 | 0.47 ± 0.17 | 20.47 ± 8.92 | 1.15 $\times {10}^{-6}$ |

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**MDPI and ACS Style**

Maček Lebar, A.; Miklavčič, D.; Kotulska, M.; Kramar, P.
Water Pores in Planar Lipid Bilayers at Fast and Slow Rise of Transmembrane Voltage. *Membranes* **2021**, *11*, 263.
https://doi.org/10.3390/membranes11040263

**AMA Style**

Maček Lebar A, Miklavčič D, Kotulska M, Kramar P.
Water Pores in Planar Lipid Bilayers at Fast and Slow Rise of Transmembrane Voltage. *Membranes*. 2021; 11(4):263.
https://doi.org/10.3390/membranes11040263

**Chicago/Turabian Style**

Maček Lebar, Alenka, Damijan Miklavčič, Malgorzata Kotulska, and Peter Kramar.
2021. "Water Pores in Planar Lipid Bilayers at Fast and Slow Rise of Transmembrane Voltage" *Membranes* 11, no. 4: 263.
https://doi.org/10.3390/membranes11040263