# The Compositional HJ-Biplot—A New Approach to Identifying the Links among Bioactive Compounds of Tomatoes

^{1}

^{2}

^{3}

^{4}

^{5}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Results and Discussion

#### 2.1. General Description of the Tomato Samples

#### 2.2. Differences in Bioactive Compounds by Cultivar and Cultivation System

## 3. Materials and Methods

#### 3.1. Tomato Sampling

_{3}

^{−}, 0.5 mM NH

_{4}

^{+}, 1.6 mM H

_{2}PO

_{4}

^{−}, 7 mM K

^{+}, 4.5 mM Ca

^{2+}, 3.6 mM Mg

^{2+}, 2.0 mM SO

_{4}

^{2−}, 5 µM Fe-EDTA, 2 µM Mn, 1 µM Zn, 50 µM B, 0.25 µM Cu, and 0.1 µM Mo. Its pH was 5.6–6.0. For the soil tomatoes, the nutrient requirements were adjusted to 690 kg/ha N, 460 kg/ha P

_{2}O

_{5}, 1714 kg/ha K

_{2}O, 1135 kg/ha CaO, 231 kg/ha MgO and 1797 kg/ha SO

_{3}, yearly.

#### 3.2. Sample Preparation

#### 3.3. Analytical Methods

#### 3.4. Statistical Methods

_{1}, x

_{2},…, x

_{D}) is a compositional data vector, the xi are the chemical variables all of which must be expressed in the same units, and g

_{m}(x) is the geometric mean of that compositional data vector. Calculations were performed using the CoDaPack 2.01 software package [32].

_{1}, j

_{2}, …, j

_{n}for its rows and h

_{1}, h

_{2}, …, h

_{p}for its columns. The markers are obtained from the usual singular value decomposition (SVD) of the data matrix X = UΣV

^{T}, where U is formed by the eigenvectors of the matrix XX

^{T}, V by the eigenvectors of the matrix X

^{T}X, and Σ is a diagonal matrix containing the singular values (i.e., the square roots of the non-zero eigenvalues of both XX

^{T}and X

^{T}X), taking as rows the marker rows of J = UΣ and as columns the marker rows of H = VΣ, in the appropriate dimensions. Thus, the matrix X is formed by clr-transformed data, and then double-centered through its SVD to ensure that the components are analyzed on a ratio scale [5] in the appropriate dimensions.

- The similarity (Sij) between two samples or individuals is taken to be an inverse function of their distance, in such a way that closer samples are more similar.
- The centroid represents the center-of-gravity formed by the geometric mean of the compositional parts used in the clr-transformation.
- ray provides information on the variance of the corresponding log-ratio with respect to the geometric mean (gm):$$var\left(ln\frac{{X}_{i}}{{g}_{m}\left(X\right)}\right)$$

_{i}, and is represented by the length of the ray. The cosine of the angle (α) between two rays represents the approximate correlation coefficient between the corresponding variables.

_{1}X

_{5}and X

_{4}X

_{5}), while if they are parallel (or the angle is obtuse) then the pairs of parameters may be strongly correlated (in Figure 1, links X

_{1}X

_{5}and X

_{4}X

_{3}). Coincident vertices or short links mean that the two variables are linearly proportional, so that the two parts involved can be assumed to be redundant. If a subset of links is collinear, this might indicate a possible one-dimensional variability.

## 4. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

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**Figure 2.**(

**A**) Standard HJ-biplot; and (

**B**) Compositional HJ-biplot of the chemical composition data. The Mariana tomato cultivar is represented in red; the Dunkan in green. The soil cultivation method is represented with the marker ●; the no-soil with the marker ▲.

**Table 1.**Proximate and mineral elements composition (mean ± standard deviation, data expressed in fresh weight, FW) of tomato samples grouped according to cultivar and cultivation system.

Compound | Cultivar | Cultivation System | p-Value | |
---|---|---|---|---|

Soil | No-Soil | |||

Proximate Composition (% FW) | ||||

Moisture | Dunkan | 93.78 ± 0.55 | 94.11 ± 0.51 | 0.061 ^{1} |

Mariana | 94.28 ± 0.47 | 93.88 ± 0.58 | ||

p-Value | 0.129 ^{2} | |||

Ash | Dunkan | 0.75 ± 0.09 | 0.73 ± 0.04 | 0.159 |

Mariana | 0.69 ± 0.07 | 0.74 ± 0.07 | ||

p-Value | 0.952 | |||

Protein | Dunkan | 0.68 ± 0.05 | 0.75 ± 0.13 | 0.049 |

Mariana | 0.70 ± 0.07 | 0.77 ± 0.07 | ||

p-Value | 0.015 | |||

Fructose | Dunkan | 1.41 ± 0.09 | 1.38 ± 0.24 | 0.765 |

Mariana | 1.24 ± 0.22 | 1.39 ± 0.17 | ||

p-Value | 0.145 | |||

Glucose | Dunkan | 1.40 ± 0.09 | 1.37 ± 0.24 | 0.798 |

Mariana | 1.23 ± 0.22 | 1.38 ± 0.17 | ||

p-Value | 0.137 | |||

Mineral Elements (mg/kg FW) | ||||

P | Dunkan | 255 ± 26.0 | 280 ± 36.3 | 0.455 |

Mariana | 242 ± 20.8 | 276 ± 32.3 | ||

p-Value | 0.014 | |||

Na | Dunkan | 42.29 ± 5.31 | 46.23 ± 2.67 | 0.405 |

Mariana | 40.66 ± 9.63 | 53.00 ± 12.7 | ||

p-Value | 0.001 | |||

K | Dunkan | 2654 ± 340 | 2844 ± 332 | 0.165 |

Mariana | 2570 ± 275 | 2859 ± 214 | ||

p-Value | 0.093 | |||

Ca | Dunkan | 88.76 ± 8.53 | 83.00 ± 5.74 | 0.295 |

Mariana | 85.65 ± 14.4 | 82.00 ± 7.67 | ||

p-Value | 0.046 | |||

Mg | Dunkan | 159 ± 13 | 167 ± 18 | 3.05 × 10^{−4} |

Mariana | 115 ± 16 | 133 ± 13 | ||

p-Value | 0.009 | |||

Fe | Dunkan | 3.36 ± 0.65 | 3.14 ± 0.48 | 0.109 |

Mariana | 2.66 ± 0.32 | 2.98 ± 0.48 | ||

p-Value | 0.176 | |||

Cu | Dunkan | 0.35 ± 0.18 | 0.47 ± 0.20 | 0.623 |

Mariana | 0.32 ± 0.08 | 0.33 ± 0.04 | ||

p-Value | 0.260 | |||

Zn | Dunkan | 0.80 ± 0.18 | 0.99 ± 0.29 | 0.146 |

Mariana | 0.98 ± 0.31 | 0.96 ± 0.12 | ||

p-Value | 0.718 | |||

Mn | Dunkan | 1.04 ± 0.12 | 0.99 ± 0.12 | 0.053 |

Mariana | 1.04 ± 0.11 | 1.02 ± 0.13 | ||

p-Value | 0.009 |

^{1}p-Value by tomato cultivar;

^{2}p-Value by cultivation system. p-Values in bold mean significant differences after clr-transformation according to Mann–Whitney U test.

**Table 2.**Organic acids and antioxidant compounds composition (mean ± standard deviation, data expressed in fresh weight, FW) of tomato samples grouped according to cultivar and cultivation system.

Compound | Cultivar | Cultivation System | p-Value | |
---|---|---|---|---|

Soil | No-Soil | |||

Organic Acids (mg 100 g^{−1} FW) | ||||

Citric acid | Dunkan | 422 ± 64.7 | 443 ± 93.4 | 0.001 ^{1} |

Mariana | 541 ± 138 | 561 ± 131 | ||

p-Value | 0.999 ^{2} | |||

Malic acid | Dunkan | 25.7 ± 9.87 | 22.1 ± 4.16 | 0.732 |

Mariana | 25.5 ± 9.14 | 19.9 ± 5.95 | ||

p-Value | 0.001 | |||

Ascorbic acid | Dunkan | 14.8 ± 0.61 | 14.4 ± 1.38 | 0.009 |

Mariana | 15.2 ± 2.04 | 15.0 ± 1.67 | ||

p-Value | 0.087 | |||

Oxalic acid | Dunkan | 16.9 ± 6.13 | 17.3 ± 4.06 | 0.104 |

Mariana | 13.2 ± 2.93 | 14.1 ± 4.43 | ||

p-Value | 0.798 | |||

Fumaric acid | Dunkan | 5.69 ± 1.437 | 5.62 ± 1.37 | 0.026 |

Mariana | 4.33 ± 1.37 | 4.08 ± 1.09 | ||

p-Value | 0.499 | |||

Pyruvic acid | Dunkan | 1.40 ± 0.44 | 1.87 ± 0.71 | 0.608 |

Mariana | 1.80 ± 0.89 | 1.40 ± 0.74 | ||

p-Value | 0.079 | |||

Antioxidant Compounds (mg 100 g^{−1} FW) | ||||

Total phenols | Dunkan | 24.3 ± 3.00 | 23.5 ± 1.07 | 0.091 |

Mariana | 26.3 ± 6.77 | 23.6 ± 6.81 | ||

p-Value | 0.016 | |||

Lycopene | Dunkan | 2.34 ± 0.12 | 2.63 ± 0.36 | 0.001 |

Mariana | 1.73 ± 0.36 | 1.76 ± 0.40 | ||

p-Value | 0.741 | |||

Chlorogenic acid | Dunkan | 1.08 ± 0.24 | 1.09 ± 0.13 | 0.814 |

Mariana | 0.996 ± 0.26 | 1.15 ± 0.42 | ||

p-Value | 0.344 | |||

Ferulic acid | Dunkan | 0.124 ± 0.03 | 0.125 ± 0.02 | 0.685 |

Mariana | 0.121 ± 0.03 | 0.130 ± 0.02 | ||

p-Value | 0.548 | |||

Caffeic acid | Dunkan | 0.115 ± 0.02 | 0.115 ± 0.05 | 0.010 |

Mariana | 0.083 ± 0.03 | 0.093 ± 0.02 | ||

p-Value | 0.674 |

^{1}p-Value by tomato cultivar;

^{2}p-Value by cultivation system. p-Values in bold mean significant differences after clr-transformation according to Mann–Whitney U test.

**Table 3.**Variation array of functional compounds (The upper triangle contains the log-ratio variances and the lower diagonal contains the log-ratio means).

Xi/Xj | Variance ln(Xi/Xj) | clr-Variances | |||||||
---|---|---|---|---|---|---|---|---|---|

K | Mg | Ascorbic | Lycopene | Phenols | Chlorogenic | Caffeic | Ferulic | ||

K | 0.026 | 0.018 | 0.063 | 0.057 | 0.061 | 0.121 | 0.047 | 0.012 | |

Mg | −30.59 | 0.045 | 0.043 | 0.104 | 0.087 | 0.111 | 0.081 | 0.025 | |

Ascorbic | −28.77 | 0.182 | 0.084 | 0.051 | 0.080 | 0.138 | 0.057 | 0.022 | |

Lycopene | −50.01 | −19.42 | −21.24 | 0.126 | 0.105 | 0.129 | 0.099 | 0.044 | |

Phenols | −23.87 | 0.672 | 0.490 | 26.14 | 0.112 | 0.164 | 0.092 | 0.052 | |

Chlorogenic | −55.68 | −25.09 | −26.90 | −0.567 | −31.81 | 0.089 | 0.038 | 0.035 | |

Caffeic | −80.43 | −49.84 | −51.66 | −30.42 | −56.56 | −24.76 | 0.130 | 0.073 | |

Ferulic | −77.02 | −46.43 | −48.25 | −27.01 | −53.15 | −21.34 | 0.341 | 0.031 | |

Mean ln(Xi/Xj) | 0.294 |

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**MDPI and ACS Style**

Hernández Suárez, M.; Molina Pérez, D.; Rodríguez-Rodríguez, E.M.; Díaz Romero, C.; Espinosa Borreguero, F.; Galindo-Villardón, P.
The Compositional HJ-Biplot—A New Approach to Identifying the Links among Bioactive Compounds of Tomatoes. *Int. J. Mol. Sci.* **2016**, *17*, 1828.
https://doi.org/10.3390/ijms17111828

**AMA Style**

Hernández Suárez M, Molina Pérez D, Rodríguez-Rodríguez EM, Díaz Romero C, Espinosa Borreguero F, Galindo-Villardón P.
The Compositional HJ-Biplot—A New Approach to Identifying the Links among Bioactive Compounds of Tomatoes. *International Journal of Molecular Sciences*. 2016; 17(11):1828.
https://doi.org/10.3390/ijms17111828

**Chicago/Turabian Style**

Hernández Suárez, Marcos, Daniel Molina Pérez, Elena M. Rodríguez-Rodríguez, Carlos Díaz Romero, Francisco Espinosa Borreguero, and Purificación Galindo-Villardón.
2016. "The Compositional HJ-Biplot—A New Approach to Identifying the Links among Bioactive Compounds of Tomatoes" *International Journal of Molecular Sciences* 17, no. 11: 1828.
https://doi.org/10.3390/ijms17111828