# Is Stress Relaxation in Sea Cucumber Dermis Chemoelastic?

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## Abstract

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## 1. Introduction

#### 1.1. Structure and Mechanics

#### 1.2. Modeling the Time-Dependent Behavior

## 2. Materials and Methods

## 3. Results

## 4. Chemoelastic Parameters in Terms of Kinetic Reactions

#### 4.1. Fibril Chemoelasticity

#### 4.2. Matrix Chemoelasticity

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Abbreviations

MCT | Mutable collagenous tissue |

ECM | Extracellular matrix |

JLC | Juxtaligamental cell |

ASW | Artificial seawater |

KASW | Potassium-enriched artificial seawater |

CaFASW | Calcium ions-deprived artificial seawater |

## Appendix A. Stiffness Matrices for Fibrillar MCT Matrix with Visco- and Chemoelasticity

#### Appendix A.1. Finite Element Model

#### Appendix A.2. Staggered Shear-Lag Model

## Appendix B. Approximate Analytical Solution for the Case Chemoelastic Matrix and Chemoelastic Fibril

## Appendix C. Elastically Active Chains after Chain Scission and Recombination

## Appendix D. Elastically Active Chains after Chain Scission, Cross-Links Splitting, and Chain Recombination

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**Figure 1.**Finite element model of staggered fibrils of length ${L}_{F}$, connected by an interfibrillar matrix. (

**a**) Tissue specimen of length ${L}_{T}$, with an applied constant strain ${\u03f5}_{T}$ and fibrillar microstructure; (

**b**) fibril elements (cylinders), shear elements (blue lines) and node numbering (circled numbers); (

**c**) The matrix cannot carry tensile loads, only shear stresses, ${\tau}_{ij}$.

**Figure 2.**Chemoelastic relaxation for tissue stress; the continuous lines are the numerical results, the dots are the mean of the experimental measures, and the error bar plots are the corresponding standard deviations.

**Figure 3.**Chemoelastic relaxation for the fibril strain; the continuous lines are the numerical results, the dots are the mean of the experimental measures, and the error bar plots are the corresponding standard deviations.

**Figure 6.**Elastic fibrils made by collagen macromolecules: hypothesized reversible reaction of chain scission and recombination; A are macro-chains before scission and B are those after scission.

**Figure 7.**Interfibrillar matrix composed of crosslinked macro-chains (species

**A**); the hypothesized reactions of chain scission, crosslink splitting, and recombination. Species

**B**represents chains after chain scission and

**C**is chains after chain scission and cross-link splitting.

**Figure 8.**The surfaces in Equation (A47). The intersection of the surfaces (red lines) is all the possible reaction rates.

**Figure 9.**Interfibrillar matrix reaction times for ASW, KASW, and CaFASW: in all three conditions, the fastest times are due to chain recombination, with crosslink splitting being around 10 times slower and chain scission being extremely slow.

**Table 1.**Chemoelastical parameters for the interfibrillar matrix shear modulus and fibril Young modulus for the three seawater solutions.

Seawater | ${\mathit{G}}_{\mathit{\infty}}$ (MPa) | ${\mathit{G}}_{1}$ (MPa) | ${\mathit{G}}_{2}$ (MPa) | ${\mathit{E}}_{\mathit{\infty}}$ (MPa) | ${\mathit{E}}_{1}$ (MPa) | ${\mathit{t}}_{{\mathit{M}}_{1}}$ (s) [8] | ${\mathit{t}}_{{\mathit{M}}_{2}}$ (s) [8] |
---|---|---|---|---|---|---|---|

ASW | 6.6974$\xb7{10}^{-8}$ | 6.1561$\xb7{10}^{-8}$ | 9.8484$\xb7{10}^{-8}$ | 27.59 | 0.1314 | 13.35 | 216 |

KASW | 3.8535$\xb7{10}^{-7}$ | 2.2968$\xb7{10}^{-7}$ | 2.7412$\xb7{10}^{-7}$ | 34.6294 | 19.5533 | 20.37 | 229.4 |

CaFASW | 3.6746$\xb7{10}^{-9}$ | 3.4478$\xb7{10}^{-8}$ | 1.1543$\xb7{10}^{-8}$ | 26.2296 | 0.0839 | 11.71 | 171.7 |

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**MDPI and ACS Style**

Barbieri, E.; Gupta, H.S.
Is Stress Relaxation in Sea Cucumber Dermis Chemoelastic? *Mar. Drugs* **2023**, *21*, 610.
https://doi.org/10.3390/md21120610

**AMA Style**

Barbieri E, Gupta HS.
Is Stress Relaxation in Sea Cucumber Dermis Chemoelastic? *Marine Drugs*. 2023; 21(12):610.
https://doi.org/10.3390/md21120610

**Chicago/Turabian Style**

Barbieri, Ettore, and Himadri Shikhar Gupta.
2023. "Is Stress Relaxation in Sea Cucumber Dermis Chemoelastic?" *Marine Drugs* 21, no. 12: 610.
https://doi.org/10.3390/md21120610