# Self-Repair in Cacti Branches: Comparative Analyses of Their Morphology, Anatomy, and Biomechanics

^{1}

^{2}

*liv*MatS @ FIT—Freiburg Center for Interactive Materials and Bioinspired Technologies, University of Freiburg, Georges-Köhler-Allee 105, D-79110 Freiburg, Germany

^{3}

^{4}

^{*}

^{†}

## Abstract

**:**

## 1. Introduction

## 2. Results

#### 2.1. Macroscopic Observations

#### 2.2. Microscopic Observations

#### 2.3. Biomechanics

#### 2.3.1. Bilinear Behavior

^{2}) for the respective linear regression lines indicated that the selected ranges were suitable for all samples (first linear range: R

^{2}for all samples > 0.97; second linear range: R

^{2}for all samples > 0.95). For both species, the calculated bending stiffness ratios (cf. Equation (2)) were not significantly different between the unwounded, freshly wounded, and healed states. Bending stiffness decreased about 7% from the first to second linear part in O. ficus-indica, resulting in ratios very significantly smaller than one, whereas in C. bigelovii, bending stiffness increased about 14% from the first to the second linear range, resulting in ratios highly significantly larger than one. These trends of bilinear stiffening or softening were observed for the individual states and for the pooled data of all states (Table 1).

#### 2.3.2. Bending Stiffness

#### 2.3.3. Work

#### 2.3.4. Bending Elastic Modulus

^{4}) and 4.0 ± 1.6 MPa for plant B ($I$: 4464 ± 2101 mm

^{4}). Values for C. bigelovii were 0.54 ± 0.14 MPa for plant C ($I$: 24,041 ± 4138 mm

^{4}), 0.60 ± 0.04 MPa for plant D ($I$: 30,662 ± 6688 mm

^{4}) and 0.56 ± 0.16 MPa for plant E ($I$: 31,256 ± 3701 mm

^{4}). No significant differences were found between the two plants of O. ficus-indica (t = 0.80, df = 5.68, p = 0.46; Welch’s two-sample t-test), or between the plants of C. bigelovii (Df = 2, Sum Sq = 0.0095, Mean Sq = 0.0047, F = 0.23, p = 0.80). However, highly significant differences were found between the pooled values of the two species (t = 9.92, df = 14.16, p < 0.001; Welch’s two-sample t-test).

#### 2.3.5. Synopsis of Biomechanical Performance

#### 2.3.6. Relative Water Content

## 3. Discussion

#### 3.1. Morphological and Anatomical Repair-Effects: Restoration of Structural Integrity

#### 3.2. Biomechanical Repair-Effects: Restoration of Mechanical Integrity

## 4. Materials and Methods

#### 4.1. Plant Material and Treatment

^{−2}); night conditions: 8 p.m. to 7 a.m., 20 °C, 50% relative humidity, no illumination; conditions were adjusted during the remaining hours: between 7 p.m. and 8 p.m, and 7 a.m. and 8 p.m, respectively) six months prior to and during all experiments.

#### 4.2. Wounding

#### 4.3. Macroscopic Observations

#### 4.4. Anatomy

^{®}O.C.T.™ Compound, Sakura Finetek Europe B.V., Alphen aan den Rijn, Netherlands) and frozen for at least two hours in a floor-standing ECO cryostat (MEV, SLEE medical GmbH, Mainz, Germany). Samples were cut into tangential sections at a thickness of 75 µm by using the integrated microtome blade of the cryostat and were transferred to a 50% bleach solution (Eau du Javel, Floreal Haagen GmbH, Wadgassen, Germany) for 15 to 20 min to remove mucilage before being transferred into distilled water. For contrast staining, the cuttings were dipped into a safranin O solution (1 g safranin O in 100 mL distilled water) for three to five seconds, rinsed for 15 s with an acidic alcohol solution (0.5 mL of 30% hydrochloric acid with 100 mL of 70% ethanol), stained in an Astra blue solution (0.5 g Astra blue in 100 mL of 2% aqueous Tartaric acid) for 12 s and then washed in distilled water for 20 to 30 s. Images of stained sections were obtained via a stereomicroscope (Olympus BX61, Olympus Corporation, Tokyo, Japan) equipped with a microscope camera (DP71, Olympus Corporation, Tokyo, Japan) and Cell^P imaging software (Version 2.6, Olympus Soft Imaging Solutions GmbH, Münster, Germany).

#### 4.5. Biomechanical Testing

#### 4.6. Wounding Effect and Healing Effect

#### 4.7. Bending Elastic Modulus

#### 4.8. Relative Water Content

#### 4.9. Statistics

^{®}Office EXCEL

^{®}2016. Data are either represented by mean values ± one standard deviation or shown as median values with respective interquartile ranges (IQR). Data processing, data visualization, and statistical analyses were performed with GNU R v.3.6.1 [45], including the packages car [46], coin [47], DescTools [48], ggplot2 [49], multcomp [50], and psych [51]. Descriptive statistics were used to describe morphometric data, bending stiffness ratios, RWC values, and approximated values for the bending elastic modulus. Once the assumptions for normally distributed data (Shapiro-Wilk test; α = 0.05) and homoscedasticity (Levene test; α = 0.05) had been checked, datasets from the different plants of one species were tested for significant differences by using the Welch’s two-sample t-test (for O. ficus-indica, normally distributed data with equal variances), Wilcoxon rank-sum test (for O. ficus-indica, not normally distributed data or data with unequal variances), one-way ANOVA (for C. bigelovii, normally distributed data with equal variances), or Kruskal-Wallis rank-sum test (for C. bigelovii, not normally distributed data or data with unequal variances). Due to the small sample size, the conservative Tukey’s test was applied as a post-hoc test. Data of a parameter were pooled if no significant differences were found between the plants of one species. To test for significant differences between $W{E}_{0}$ and $W{E}_{21}$, we employed tests for paired samples (paired t-test for normally distributed data with equal variances and Wilcoxon signed-rank test for not normally distributed data or data with unequal variances). One-sample t-test was used to test whether the bending stiffness ratios differed significantly from 1, and whether $H{E}_{21}$ differed significantly from 0 (all data were normally distributed). The Welch’s two-sample t-test and one-way ANOVA were used to test for differences of bending elastic modulus (all data were normally distributed). Levels of significance were: p > 0.05: not significant (n.s.); p ≤ 0.05: significant (*); p ≤ 0.01: very significant (**); p ≤ 0.001: highly significant (***).

## 5. Conclusions

## Supplementary Materials

**a**–

**h**) and Cylindropuntia bigelovii (

**i**–

**p**), stained with phloroglucinol to establish the presence of lignin. The sections were microscopically examined directly after wounding (

**a**,

**i**), after a healing period of 1 day (

**b**,

**j**), 3 days (

**c**,

**k**), 7 days (

**d**,

**l**), 10 days (

**e**,

**m**), 14 days (

**f**,

**n**), 21 days (

**g**,

**o**), and 31 days (

**h**,

**p**). Scale bars = 500 µm. Table S1: Raw data of measurements carried out on Opuntia ficus-indica and Cylindropuntia bigelovii.

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Abbreviations

WE | Wounding effect |

HE | Healing effect |

SD | Standard deviation |

IQR | Interquartile range |

E | Bending elastic modulus |

I | Axial second moment of area |

RWC | Relative water content |

STL | Stereolithography |

CAD | Computer-aided design |

COM | Center of mass |

EI | Bending stiffness |

uv | Unwounded value |

wv | Wounded value |

## Appendix A

**Table A1.**Statistics of mechanical parameters comparing the individual plants of the plant species O. ficus-indica and C. bigelovii.

Parameter Comparison | O. ficus-indica Plants A and B n = 14 | C. bigelovii Plants C, D, and E n = 14 |
---|---|---|

BS 1 ^{1} | ||

$W{E}_{0}$—$W{E}_{0}\text{}$^{2} | t = −0.441, df = 9.438, p = 0.669 (1) n.s. | Df = 2, Sum Sq = 293, Mean Sq = 146.5, F = 0.391, p = 0.685 (5) n.s. |

$W{E}_{21}$—$W{E}_{21\text{}}$^{3} | t = −2.647, df = 11.804, p = 0.0216 (1) * | Df = 2, Sum Sq = 350, Mean Sq = 175.2, F = 0.514, p = 0.612 (5) n.s. |

$H{E}_{21}$—$H{E}_{21}$^{4} | t = 1.519, df = 11.616, p = 0.155 (1) n.s. | Df = 2, Sum Sq = 1102, Mean Sq = 551.2, F = 4.36, p = 0.0403 Tukey’s test: all p > 0.055 (5,7) n.s. |

BS 2 ^{5} | ||

$W{E}_{0}$—$W{E}_{0}$ | W = 32, p = 0.345 (3) n.s. | Df = 2, Sum Sq = 32.1, Mean Sq = 16.04, F = 0.162, p = 0.853 (5) n.s. |

$W{E}_{21}$—$W{E}_{21}$ | t = 1.832, df = 9.158, p = 0.0996 (1) n.s. | Df = 2, Sum Sq = 44.7, Mean Sq = 22.35, F = 0.228, p = 0.8 (5) n.s. |

$H{E}_{21}$—$H{E}_{21}$ | t = 3.652, df = 11.084, p = 0.00376 (1) ** | Df = 2, Sum Sq = 5.59, Mean Sq = 2.796, F = 0.124, p = 0.885 (5) n.s. |

Work | ||

$W{E}_{0}$—$W{E}_{0}$ | t = 0.446, df = 10.945, p = 0.665 (1) n.s. | Df = 2, Sum Sq = 46.3, Mean Sq = 23.16, F = 0.085, p = 0.92 (5) n.s. |

$W{E}_{21}$—$W{E}_{21}$ | t = 3.343, df = 9.704, p = 0.00777 (1) ** | χ^{2} = 2.143, df = 2, p = 0.343(6) n.s. |

$H{E}_{21}$—$H{E}_{21}$ | t = 2.113, df = 11.653, p = 0.0569 (1) n.s. | Df = 2, Sum Sq = 306, Mean Sq = 153.0, F = 1.227, p = 0.33 (5) n.s. |

^{1}BS 1 = Bending stiffness (based on first linear range of force-defection curves),

^{2}WE

_{0}= wounding effect immediately after ring incision,

^{3}WE

_{21}= wounding effect after a 21-day healing period,

^{4}HE

_{21}= healing effect after a 21-day healing period

^{5}BS 2 = bending stiffness (based on second linear range of force-defection curves), (1) Welch’s two-sample t-test, (2) paired t-test, (3) Wilcoxon rank-sum test, (4) Wilcoxon signed-rank test, (5) ANOVA, (6) Kruskal-Wallis rank-sum test, (7) Tukey’s post hoc test. n.s. = not significant, * p ≤ 0.05, ** p ≤ 0.01, *** p ≤ 0.001.

**Table A2.**Statistics of mechanical parameters comparing wounding effects at two different stages of the two plant species O. ficus-indica and C. bigelovii.

Plant | BS 1 ^{1}$\mathit{W}{\mathit{E}}_{0}$${\text{}}^{2}\u2014\mathit{W}{\mathit{E}}_{21}{\text{}}^{3}$ | BS 2 ^{4}$\mathit{W}{\mathit{E}}_{0}$$\u2014\mathit{W}{\mathit{E}}_{21}$ | Work $\mathit{W}{\mathit{E}}_{0}$$\u2014\mathit{W}{\mathit{E}}_{21}$ |
---|---|---|---|

O. ficus-indica | |||

Plant A (N = 8) | t = 1.4159, df = 7, p = 0.1997 (2) n.s. | V = 16, p = 0.8438 (4) n.s. | t = −0.6040, df = 7, p = 0.565 (2) n.s. |

Plant B (N = 6) | t = 3.5331, df = 5, p = 0.0167 (2) * | t = 7.2921, df = 5, p = 0.00076 (2) *** | t = −4.528, df = 5, p = 0.0062 (2) ** |

C. bigelovii | |||

Plant C (n = 5) | t = -3.0339, df = 4, p = 0.039 (2) * | t = −3.8951, df = 4, p = 0.0176 (2) * | V = 14, p = 0.125 (4) n.s. |

Plant D (n = 4) | t = 0.58275, df = 3, p = 0.601 (2) n.s. | t = −4.9121, df = 3, p = 0.0162 (2) * | t = −0.1308, df = 3, p = 0.904 (2) n.s. |

Plant E (n = 5) | t = 1.142, df = 4, p = 0.3172 (2) n.s. | t = −4.4061, df = 4, p = 0.0116 (2) * | t = 0.6218, df = 4, p = 0.5677 (2) n.s. |

^{1}BS 1 = Bending stiffness (based on first linear range of force-defection curves),

^{2}WE

_{0}= wounding effect immediately after ring incision,

^{3}WE

_{21}= wounding effect after a 21-day healing period,

^{4}HE

_{21}= healing effect after a 21-day healing period

^{5}BS 2 = bending stiffness (based on second linear range of force-defection curves), (1) Welch’s two-sample t-test, (2) paired t-test, (3) Wilcoxon rank sum test, (4) Wilcoxon signed-rank test, (5) ANOVA, (6) Kruskal-Wallis rank-sum test, (7) Tukey’s post hoc test. n.s. = not significant, * p ≤ 0.05, ** p ≤ 0.01, *** p ≤ 0.001.

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**Figure 1.**Morphological wound analysis of Opuntia ficus-indica (upper images) and Cylindropuntia bigelovii (lower images). The same section of one branch per species is presented in an unwounded condition (

**a**,

**f**), immediately after wounding (

**b**,

**g**), and after a healing phase of 3 days (

**c**,

**h**), 7 days (

**d**,

**i**), and 21 days (

**e**,

**j**). Scale bars = 5 mm.

**Figure 2.**Tangential sections of wound areas after artificial ring incision in Opuntia ficus-indica (

**a**–

**h**) and Cylindropuntia bigelovii (

**i**–

**p**), stained with safranin O and Astra blue. The sections were microscopically examined directly after wounding (

**a**,

**i**), after a healing period of 1 day (

**b**,

**j**), 3 days (

**c**,

**k**), 7 days (

**d**,

**l**), 10 days (

**e**,

**m**), 14 days (

**f**,

**n**), 21 days (

**g**,

**o**), and 31 days (

**h**,

**p**). Cellulose cell walls appear blue, ligno-suberized cell walls appear red. e: epidermal and hypodermal layers, mc: mucilage cell, np: newly formed parenchyma, p: parenchyma, sc: suberized cells, wp: wound periderm. The bold arrows indicate exemplarily the areas where the phellogen has detached from the phelloderm caused by the mechanical stresses during the preparation of the section. Scale bars = 500 µm.

**Figure 3.**Exemplary force-displacement diagrams of two-point bending tests on (unwounded) branches of Opuntia ficus-indica (

**a**) and Cylindropuntia bigelovii (

**b**). The sections (colored background) and linear regression lines (colored dashed lines) of the first (from 3.0 to 4.25 mm, blue) and second (from 6.5 to 9.5 mm, red) linear ranges are highlighted. For O. ficus-indica, a decrease of slope from the first to the second range is visible, whereas for C. bigelovii, the value increases.

**Figure 4.**Wounding effects (cf. Equation (3)) directly after ring incision (gray box-plots; calculated from the respective values in the wounded and unwounded state) and after a healing period of 21 days (white box-plots; calculated from the respective values in the healed and unwounded state) of bending stiffness in the first (

**a**,

**b**) and second (

**c**,

**d**) linear range and work (

**e**,

**f**) determined from repeated bending tests on branches of Opuntia ficus-indica and Cylindropuntia bigelovii. All data points outside the range of 1.5 IQR are considered outliers and are represented by an “o”. The values of the three plants of C. bigelovii are presented as pooled since no significant difference was measured for any of the parameters. * p ≤ 0.05, ** p ≤ 0.01, *** p ≤ 0.001.

**Figure 5.**Experimental plants (left images) with macroscopic transverse sections (middle images) and microscopic tangential sections stained with safranin O and Astra blue (right images); Opuntia ficus-indica: (

**a**–

**c**); Cylindropuntia bigelovii: (

**d–f**). Double arrows mark the measured cortex depth (

**b**,

**e**) and the intended depth of the ring incisions through the cortex down to the vascular bundles (

**c**,

**f**). c: cortex; e: epidermis with hypodermal layers; p: pith; vb: vascular bundle. Scale bars = 10 cm in (

**a**,

**d**), 5 mm in (

**b**,

**e**), and 2 mm in (

**c**,

**f**).

**Figure 6.**Schematic drawing of the two-point bending arrangement, shown for Opuntia ficus-indica. (

**a**): Top view of the bending zone, including the 3D-printed clamps and collars (bright boxes), the pulley (dark gray), the Kevlar thread (orange), and the location of the ring incision (dashed red line). (

**b**): Front view with attached collars and the pulley deflecting a vertical into a horizontal force. The universal testing machine above the pulley, which allows vertical force measurement, is not shown.

**Figure 7.**Technical drawings (

**a**,

**c**) including scanned branch models, artificial incision interface (gray dashed line), plane of bending (blue line), center of mass (quartered circle), and dimensions of clamping jaws (left rectangles) and collars (right rectangles). Images of the branches together with clamping jaws (for O. ficus-indica just one of the two halves) and collars (

**b**,

**d**). (

**a**,

**b**) Opuntia ficus-indica; (

**c**,

**d**) Cylindropuntia bigelovii. All length specifications are given in millimeters.

**Table 1.**Mean values ± standard deviation (SD) of bending stiffness ratios in various states for Opuntia ficus-indica and Cylindropuntia bigelovii. These values quantify the stiffening (ratio > 1) or softening (ratio < 1) of the tissues between the first and second linear range.

Bending Stiffness Ratio | ||||
---|---|---|---|---|

States | Unwounded | Wounded | Healed | All States ^{1} |

Sample size (N) | 14 | 14 | 14 | 42 |

O. ficus-indica | 0.88 ± 0.14 | 0.95 ± 0.21 | 0.95 ± 0.13 | 0.93 ± 0.17 |

C. bigelovii | 1.16 ± 0.13 | 1.07 ± 0.17 | 1.18 ± 0.18 | 1.14 ± 0.17 |

^{1}The pooled data of all states significantly differ from one for O. ficus-indica (one-sample t-test, t = −2.92, df = 41, p = 0.005) and C. bigelovii (one-sample t-test, t = 5.19, df = 41, p < 0.001).

**Table 2.**Median values with respective interquartile ranges (IQR) of the mechanical parameters presented for the individual plants A and B of O. ficus-indica and plants C–E of C. bigelovii.

O. ficus-indica | C. bigelovii | ||||
---|---|---|---|---|---|

Plant A | Plant B | Plant C | Plant D | Plant E | |

Sample size (N) | 8 | 6 | 5 | 4 | 5 |

Bending stiffness first linear range (Nmm^{2}) | |||||

unwounded | 13,048 (7589) | 17,978 (3541) | 12,759 (1530) | 16,588 (4637) | 15,534 (3383) |

wounded | 9274 (6221) | 13,470 (5669) | 8873 (343) | 11,619 (1036) | 12,355 (502) |

healed | 8598 (2206) | 9001 (4307) | 10,423 (938) | 12,303 (1384) | 11,334 (690) |

Bending stiffness second linear range (Nmm^{2}) | |||||

unwounded | 10,548 (7755) | 16,746 (7017) | 16,715 (3664) | 19,016 (1995) | 18,804 (1685) |

wounded | 7863 (5932) | 13,650 (6718) | 9447 (2109) | 11,963 (1308) | 12,020 (506) |

healed | 7766 (2829) | 7777 (4434) | 11,356 (987) | 13,509 (1577) | 12,941 (942) |

Work (Nmm) | |||||

unwounded | 7.4 (3.2) | 11.6 (1.8) | 8.6 (0.6) | 10.6 (3.3) | 10.0 (1.0) |

wounded | 5.9 (4.0) | 8.5 (4.2) | 6.1 (0.4) | 7.5 (0.5) | 7.8 (0.6) |

healed | 5.8 (1.5) | 5.6 (1.5) | 6.6 (0.6) | 7.9 (1.4) | 7.2 (0.6) |

**Table 3.**Median values with respective interquartile ranges (IQR) of the healing effect $H{E}_{21}$ presented for the individual plants A and B of O. ficus-indica and C–E of C. bigelovii. Pooled data are given if values between the individual plants did not differ significantly. Significant differences from zero are marked by asterisks (one-sample t-test). * p ≤ 0.05, ** p ≤ 0.01, *** p ≤ 0.001.

O. ficus-indica | C. bigelovii | ||||||
---|---|---|---|---|---|---|---|

Plant A | Plant B | Pooled Data | Plant C | Plant D | Plant E | Pooled Data | |

Sample size (N) | 8 | 6 | 14 | 5 | 4 | 5 | 14 |

$\mathit{H}{\mathit{E}}_{\mathbf{21}}$ of bending stiffness first linear range (%) | |||||||

−15.22 (30.52) | −22.03 * (28.49) | −17.80 ** (21.06) | 14.88 * (2.45) | −1.93 (20.83) | −6.70 (0.75) | 2.44 (20.44) | |

$\mathit{H}{\mathit{E}}_{\mathbf{21}}$ of bending stiffness second linear range (%) | |||||||

−1.47 (25.88) | −31.21 *** (11.53) | 12.32 * (8.74) | 8.72 * (4.91) | 9.48 * (2.90) | 9.72 *** (7.04) | ||

$\mathit{H}{\mathit{E}}_{\mathbf{21}}$ of work (%) | |||||||

1.59 (26.39) | −19.00 ** (10.68) | −14.96 * (27.16) | 5.92 (2.76) | 6.12 (9.78) | −5.44 (20.43) | 5.30 (12.12) |

© 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

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**MDPI and ACS Style**

Mylo, M.D.; Krüger, F.; Speck, T.; Speck, O.
Self-Repair in Cacti Branches: Comparative Analyses of Their Morphology, Anatomy, and Biomechanics. *Int. J. Mol. Sci.* **2020**, *21*, 4630.
https://doi.org/10.3390/ijms21134630

**AMA Style**

Mylo MD, Krüger F, Speck T, Speck O.
Self-Repair in Cacti Branches: Comparative Analyses of Their Morphology, Anatomy, and Biomechanics. *International Journal of Molecular Sciences*. 2020; 21(13):4630.
https://doi.org/10.3390/ijms21134630

**Chicago/Turabian Style**

Mylo, Max D., Friederike Krüger, Thomas Speck, and Olga Speck.
2020. "Self-Repair in Cacti Branches: Comparative Analyses of Their Morphology, Anatomy, and Biomechanics" *International Journal of Molecular Sciences* 21, no. 13: 4630.
https://doi.org/10.3390/ijms21134630