# Predicting Value of Binding Constants of Organic Ligands to Beta-Cyclodextrin: Application of MARSplines and Descriptors Encoded in SMILES String

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Molecular Descriptors

#### 2.2. Data Pre-Treatment

#### 2.3. Model Development Using MARSplines

_{i}is the regression factor and a

_{i}are the regression parameters:

_{i}). Only such factors are included in the final model for which $\left|{\beta}_{i}\right|>0.09$. Furthermore, the model was refined, internally validated and characterized in terms of fitting criteria using QSARINS software [54,55,56]. As a result of this procedure, the model was simplified by selecting the most important variables using a genetic algorithm (GA).

## 3. Results and Discussion

#### 3.1. Findings

^{2}(determination coefficient), R

_{adj}

^{2}(adjustment determination coefficient), F (Fisher ratio), SD (standard deviation), MAE (mean absolute error), MAPE (mean absolute percentage error), RMSE (root-mean-square error), PRESS (predicted residual error sum of squares) and K

_{xx}(descriptors’ global correlation measure) [58,59], suggest that the model is well fitted to the training set and, most importantly, the external test set examples were well predicted. The results of external validation are presented in Figure 1. As one can see, the proposed model is characterized by high determination coefficients. Interestingly, R

^{2}, MAE and MAPE values are even slightly better for the external test set (0.936, 0.44, 9.3%, respectively) than for the training set (0.907, 0.49, 15.4%, respectively). This suggests that the model complexity is optimal. It is worth mentioning that the over-fitting problem should be taken into account when analyzing the quality of QSPR models, especially those that are non-linear. In the case of overly complex models, the training set data are exceptionally well fitted, but the test set prediction quality is far inferior. It is worth mentioning that the MARSplines protocol implemented in the STATISTICA software prevents overfitting by taking advantage from of the generalized cross validation (GCV) algorithm, which reduces the model to be as simple as possible.

#### 3.2. Comparison to Existing Models

#### 3.3. Exemplary Model Applications

## 4. Conclusions

## Supplementary Materials

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Table 1.**Multivariate adaptive regression splines (MARSplines) model parameters along with the validation results.

Factor | β_{i} | a_{i} | Basis Functions |
---|---|---|---|

F0 | 5.4277 | ||

F1 | −0.3991 | −1.2679 | max(0; 28.1940-Chiv1plusChiv1) |

F2 | 0.5652 | 1.1090 | max(0; XLogP+0.1340) |

F3 | 0.3772 | 1.3356 | max(0; carbonTypes.8) |

F4 | −0.1559 | −1.4658 | max(0; 0.5620-MLFER_A) |

F5 | −0.1613 | −1.3482 | max(0; Wlambda2.unity-1.2400) |

F6 | −0.1391 | −0.3182 | max(0; 1.2400-Wlambda2.unity) |

F7 | −0.2130 | −2.5385 | max(0; XLogP+0.1340)∙max(0;-15.8078-PNSA-3) |

F8 | −0.1372 | −0.0120 | max(0; 66.0412- AATS6m)∙max(0; MLFER_A -0.5620) |

F9 | −0.0977 | −0.0003 | max(0; PEOEVSA9*PEOEVSA9-988.3780)∙max(0; XLogP +0.1340) |

F10 | −0.1258 | −0.0002 | max(0; 988.378- PEOEVSA9*PEOEVSA9)∙max(0; XLogP +0.1340) |

F11 | 0.0910 | 0.0257 | max(0; Wlambda2.unity -1.2400)∙max(0; AATS4i-154.1756) |

F12 | 0.0944 | 0.2092 | max(0; Wlambda2.unity -1.2400)∙max(0; 154.1756- AATS4i) |

_{CV}= 0.51, RMSE

_{CV}= 0.65, Q

^{2}

_{LOO}= 0.90, Q

^{2}

_{LMO}= 0.90, PRESS

_{CV}= 99.00), fitting criteria (N = 187, R

^{2}= 0.91, R

_{adj}

^{2}= 0.91, MAE

_{tr}= 0.61, RMSE

_{tr}= 0.48, F = 189.45, SD = 0.63, K

_{xx}= 0.35) and external validation (training set: MAE = 0.49, MAPE = 15.4%, test set: MAE = 0.44, MAPE = 9.3%).

Model Description | R^{2} | Source | |
---|---|---|---|

Training Set | Test Set | ||

MARSplines | 0.91 | 0.94 | This work |

Molecular docking-based descriptors | 0.83 | 0.83 | [37] |

Monte Carlo optimised topological descriptors | 0.92 | 0.93 | [38] |

**Table 3.**Biopharmaceutical Classification System (BCS) [73] using solubility and permeability as qualitative criterions.

High Solubility | Low Solubility | |
---|---|---|

High permeability | Class I This class comprise compounds characterized by good absorption profiles. | Class II The bioavailability is directly related to the dissolution behavior. |

Low permeability | Class III The active pharmaceutical ingredient (API) is soluble, however absorption profile is dependent on limited permeation behavior. | Class IV The API is characterized by very low bioavailability. |

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**MDPI and ACS Style**

Cysewski, P.; Przybyłek, M.
Predicting Value of Binding Constants of Organic Ligands to Beta-Cyclodextrin: Application of MARSplines and Descriptors Encoded in SMILES String. *Symmetry* **2019**, *11*, 922.
https://doi.org/10.3390/sym11070922

**AMA Style**

Cysewski P, Przybyłek M.
Predicting Value of Binding Constants of Organic Ligands to Beta-Cyclodextrin: Application of MARSplines and Descriptors Encoded in SMILES String. *Symmetry*. 2019; 11(7):922.
https://doi.org/10.3390/sym11070922

**Chicago/Turabian Style**

Cysewski, Piotr, and Maciej Przybyłek.
2019. "Predicting Value of Binding Constants of Organic Ligands to Beta-Cyclodextrin: Application of MARSplines and Descriptors Encoded in SMILES String" *Symmetry* 11, no. 7: 922.
https://doi.org/10.3390/sym11070922