# Rheological Characterization of Three-Dimensional Neuronal Cultures Embedded in PEGylated Fibrin Hydrogels

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## Abstract

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## 1. Introduction

## 2. Results and Discussion

#### 2.1. Characterization of Hydrogels’ Viscoelastic Behavior

#### 2.2. Time Evolution of PEGylated Fibrin Hydrogels

#### 2.3. Immunostaining Results

#### 2.4. Discussion

## 3. Conclusions

## 4. Materials and Methods

#### 4.1. Hydrogels Preparation

#### 4.2. Hydrogels Rheological Characterization

#### 4.2.1. Determination of Rheological Properties: Data Analysis

#### 4.2.2. Rheological Tests

**Time sweep**: This rheological test was used to track the evolution of the hydrogel structure along time and procure information such as the degradation, gelation or solvent evaporation. The oscillation frequency, $\omega $, and the strain amplitude, $\gamma $, were kept constant in this test. In the present study, they took values of $2\pi $ rad/s (1 Hz) and $5\%$, respectively (see Table 1).**Strain sweep**: The amplitude of the strain oscillation, $\gamma $, is changed periodically while the frequency, ${\omega}_{0}$, remains constant (see Figure 1b). This test is performed to obtain information about the linear viscoelastic region (LVR). As a consequence of the linear response and the small deformations, the test can be carried out without damaging the microscopic structure of the sample, which is crucial to keep the scaffold and the inner neural network intact. For these experiments, $\omega $ was fixed to ${\omega}_{0}=2\pi $ rad/s (1 Hz) and $\gamma $ was progressively increased from a $0.1$ to $100\%$ strain.**Frequency sweep**: The oscillation frequency, $\omega $, is progressively increased at a constant strain amplitude ${\gamma}_{0}$ (see Figure 1b). This test provides information about the rheological response of the hydrogel at different timescales and reveals whether the sample softens or thickens at faster deformations. The tests are performed at a selected ${\gamma}_{0}$, ensuring that the sample remains in the LVR. For the present work, ${\gamma}_{0}$ was fixed at 5%, and $\omega $ increased from $0.1$ to 100 rad/s.

#### 4.3. Immunochemistry

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Abbreviations

2D | Two dimensional |

3D | Three dimensional |

ECM | Extracellular matrix |

AAV | Adeno-associated virus |

DIV | Day in vitro |

MEM | Modified Eagle Medium |

E16 | Embryonic day 16 |

PEG | Polyethylene glycol |

PEG-NHS | Mono-Methyl polyethylene glycol succinate N-succinimidyl ester |

PDMS | Polydimethylsiloxane |

SAOS | Small Amplitude Oscillatory Shearing |

LVR | Linear viscoelastic regime |

${G}^{\prime}$ | Storage modulus |

${G}^{\u2033}$ | Loss modulus |

${G}^{*}$ | Complex shear modulus |

$\delta $ | Phase shift |

E | Young’s modulus |

$\nu $ | Poisson’s ratio |

$\omega $ | Oscillation frequency |

$\gamma $ | Strain amplitude |

PBS | Phosphate-buffered saline |

RPM | Revolutions per minute |

## References

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**Figure 1.**Overview of neuronal cultures preparation and rheological protocols. (

**a**) Sketch of the preparation of PEGylated fibrin hydrogel, with and without cells. Final appearance of the PEGylated fibrin hydrogel prepared in Soriano’s Lab (left). (

**b**) Established preset protocol for the mechanical characterization of hydrogel samples: strain sweep test with constant ${\omega}_{0}$ (blue) and varying $\gamma $ (green) and frequency sweep test with varying $\omega $ (blue) and constant ${\gamma}_{0}$ (green). Red line represents the controlled shear deformation that oscillates sinusoidally.

**Figure 2.**Time sweep results for (

**a**) PEGylated fibrin hydrogels and (

**b**) PEGylated fibrin hydrogels with neurons. Parameters ${\omega}_{0}$ and ${\gamma}_{0}$ were fixed to $2\pi $ rad/s and 5%, respectively. Results show that samples reached equilibrium few minutes after the oscillatory effort was applied (arrowheads). Data are the average over 3 sample repetitions, and shadings are the corresponding standard error.

**Figure 3.**Viscoelastic behavior characterization of hydrogel samples with and without cells at DIV 1. The plots show the storage (${G}^{\prime}$) and loss modules (${G}^{\u2033}$), averaged over 3 repetitions with the corresponding standard errors. (

**a**) Strain sweep test for PEGylated fibrin gels (left) and PEGylated fibrin gel with neurons (right), with ${\omega}_{0}=2\pi $ rad/s and $\gamma \in [1,100]$%. (

**b**) Frequency sweep test for PEGylated fibrin gels without neurons (left) and with neurons (right), with ${\gamma}_{0}=5$% and $\omega \in [0.1,80]$ rad/s.

**Figure 4.**Evolution of PEGylated fibrin hydrogels with and without cells from DIV 1 to DIV 20. (

**a**) Strain sweep test, with ${\omega}_{0}=2\pi $ rad/s and $\gamma \in [1,100]$%. (

**b**) Frequency sweep test, with ${\gamma}_{0}=5$% and $\omega \in [0.1,100]$ rad/s. In all panels, ${G}^{\prime}$ values were averaged over 3 repetitions with the corresponding standard error shown as colored shadings. Data corresponding to PEGylated fibrin hydrogels without cells are shown on the left, and data with the inclusion of cells on the right.

**Figure 5.**Evolution of the Young’s modulus E with time for PEGylated fibrin hydrogels with and without neurons. Data are plotted as boxplot distributions of E values in representative stages of evolution, namely early (DIV 1–3), young (DIV 4–8) and mature (DIV 13–20). Each dot in the boxplots is an experimental repetition. The black lines mark the mean of the distribution and the color boxes mark the standard deviation. * p < 0.05, ** p < 0.01 (Student’s t-test).

**Figure 6.**Immunostaining images of neurons within the 3D PEGylated fibrin hydrogel scaffolds showing actin in red (left) and nucleus in blue (center); the panels on the right are the merged images of both channels, showing concurrently the actin filaments and cell nuclei in the 3D culture. In the merged image, pink represents the overlapping of red (actin) and blue (nucleus). (

**a**) Sample 1 of PEGylated fibrin hydrogel with neurons at DIV 7, (

**b**) Sample 2 of PEGylated fibrin hydrogel with neurons at DIV 7.

**Table 1.**Summary of the parameter values used to perform the three different oscillation tests. Hydrogels with and without cells are measured at different DIV along three weeks. All test were performed at 37 °C with a $500\phantom{\rule{3.33333pt}{0ex}}\mathsf{\mu}$m gap.

Parameter | Time Sweep | Strain Test | Frequency Sweep |
---|---|---|---|

Frequency $\omega $ (rad/s) | $2\pi $ | $2\pi $ | 0.1–100 |

Strain $\gamma $ (%) | 5 | 0.1–100 | 5 |

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**MDPI and ACS Style**

López-León, C.F.; Soriano, J.; Planet, R.
Rheological Characterization of Three-Dimensional Neuronal Cultures Embedded in PEGylated Fibrin Hydrogels. *Gels* **2023**, *9*, 642.
https://doi.org/10.3390/gels9080642

**AMA Style**

López-León CF, Soriano J, Planet R.
Rheological Characterization of Three-Dimensional Neuronal Cultures Embedded in PEGylated Fibrin Hydrogels. *Gels*. 2023; 9(8):642.
https://doi.org/10.3390/gels9080642

**Chicago/Turabian Style**

López-León, Clara F., Jordi Soriano, and Ramon Planet.
2023. "Rheological Characterization of Three-Dimensional Neuronal Cultures Embedded in PEGylated Fibrin Hydrogels" *Gels* 9, no. 8: 642.
https://doi.org/10.3390/gels9080642